Research ArticlePredicting Shear Capacity of FRP-Reinforced ConcreteBeams without Stirrups by Artificial Neural NetworksGene Expression Programming and Regression Analysis

Ghazi Bahroz Jumaa 12 and Ali Ramadhan Yousif3

1PhD Student Department of Civil Engineering Salahaddin University-Erbil Erbil Iraq2Ass Lecturer University of Garmian Kalar Iraq3Professor Department of Civil Engineering Salahaddin University-Erbil Erbil Iraq

Correspondence should be addressed to Ghazi Bahroz Jumaa ghazijumaagarmianedukrd

Received 29 July 2018 Accepted 18 October 2018 Published 15 November 2018

Guest Editor Tayfun Dede

Copyright copy 2018 Ghazi Bahroz Jumaa and Ali Ramadhan Yousif -is is an open access article distributed under the CreativeCommons Attribution License which permits unrestricted use distribution and reproduction in any medium provided theoriginal work is properly cited

-e shear strength prediction of fiber-reinforced polymer- (FRP-) reinforced concrete beams is one of the most complicated issues instructural engineering applications Developing accurate and reliable prediction models is necessary and cost saving -is paperproposes three new prediction models utilizing artificial neural networks (ANNs) and gene expression programming (GEP) asa recently developed artificial intelligent techniques and nonlinear regression analysis (NLR) as a conventional technique For thispurpose a large database including 269 shear test results of FRP-reinforced concrete members was collected from the literature -eperformance of the proposed models is compared with a large number of available codes and previously proposed equations -ecomparative statistical analysis confirmed that the ANNs GEP and NLR models in sequence showed excellent performance greatefficiency and high level of accuracy over all other existingmodels-eANNsmodel and to a lower level the GEPmodel showed thesuperiority in accuracy and efficiency while the NLR model showed that it is simple rational and yet accurate Additionally theparametric study indicated that the ANNsmodel defines accurately the interaction of all parameters on shear capacity prediction andhave a great ability to predict the actual response of each parameter in spite of its complexity and fluctuation nature

1 Introduction

Although the behavior of steel-reinforced concrete (RC)members in shear has been extensively studied for more thanone hundred years and after numerous research challengeson shear behavior and on identification of the complex shearresistance mechanism of RC members still there is an ab-sence of comprehension and agreement on the mechanismsand behavior of shear resistance While the behavior of steel-RC members in shear is an area of concern the behavior offiber-reinforced polymer-reinforced concrete (FRP-RC)members has additional complications due to their differentmechanical properties [1] Many important issues relatedto shear problems of FRP-RC members still remain with-out in-depth investigations and become open to discussionMoreover past investigations [2ndash4] inferred that the presentshear design equations are exceptionally conservative in

predicting the shear capacity of FRP-RC beams Conse-quently the extra amount of FRP used to resist shear couldbe both costly and likely to create reinforcement congestionproblems and therefore this study was motivated

-e shear strength of RC beams without web re-inforcement was observed to be influenced by several var-iables such as concrete strength (fcprime) shear span-to-depthratio (ad) beam depth (d) longitudinal reinforcement ratio(ρf ) and beam width (bw) [5 6] Additionally for FRP-RCmembers the type of FRP rebar and their variable me-chanical properties like low elastic modulus (Ef ) hightensile strength and low transverse shear strength are otherfactors that should be taken into account

Albeit many theoretical and empirical studies have beenconducted to predict the shear strength of FRP-RC membersand to investigate the interaction between influencing pa-rameters on shear strength mechanisms up to date there is no

HindawiAdvances in Civil EngineeringVolume 2018 Article ID 5157824 16 pageshttpsdoiorg10115520185157824

general agreement on a specific model -e vast majorities ofthe existing shear design equations have different forms and donot give a reliable factor of safety against shear failure addi-tionally there is no general agreement between the existingcodes and equations on the parameters affecting the shearcapacity -is controversy in predicting models may be at-tributed to twomain reasons firstly there is no comprehensiontheory on shear failure due to its complicated behavior andfailure typewhich is sudden and catastrophic and secondly theexistence wide variability in mechanical properties of FRP bars-erefore some existing predicting models were developedbased on modifying the different theories which is originallyproposed for steel-RC members and others are empirical orsemiempirical models which were proposed based on a limiteddata for instance the ACI 440 algorithm was calibrated basedon the test results from 326 steel-RC specimens and 44 FRP-RCspecimens and the latter having a maximum effective depth of360mm An alternative to classical and conventional methodsfor the prediction of complicated problems in various disci-plines such as the shear strength of FRP-RC members is theutilization of artificial intelligence techniques like artificialneural networks (ANNs) fuzzy inference system (FIS) andgenetic programming (GP) -roughout the most recent twodecades these methodologies have been prominent and ef-fectively utilized as a part in an extensive variety of scientificapplications particularly in civil engineering disciplines

Recently several studies have been performed on usingdifferent artificial intelligence techniques for predicting theshear capacity of FRP-RC members without stirrups Kara [7]utilized gene expression programming (GEP) to obtaina simple model based on a set of 104 databases Bashir andAshour [8] suggested a model based on ANN using a set of 128databases Nasrollahzadeh and Basiri [9] developed an FIS topredict a model depending on a 128 database Lee and Lee [10]used a database of 110 samples to propose a theoretical modelutilizingANNGolafshani andAshour [11] introduced amodelusing a new technique of biogeography-based programmingbased on an experimental database of 138 test specimens Mostof these studies proposed good models with a high level ofaccuracy however they used relatively a small size of a data-base -e size of the database used for training and testing themodels plays a great role in the success of proposed models

-e present research aims to propose three new models topredict the shear strength Vc of FRP-RC slender beamswithout stirrups based on utilizing ANNs and GEP as artificialintelligence techniques and nonlinear regression analysis(NLR) as a conventional technique -ese techniques werechosen due to the fact that the ANNs and GEP are powerfulaccurate and highly efficient tools in the model prediction ofcomplicated problems while the NLR is a classical tool whichcan be used to derive a simple rational and yet accuratemodel -e main affected parameters on shear strength areconsidered in modeling process which are fcprime d bw ad ρf and Ef -e three models are derived using the largest col-lected database from the literature of (269) test specimens-eresults of obtained models are compared to a large number ofcodes and proposed equations from the literature to examinetheir accuracy validity and efficiency Additionally a para-metric study was conducted to indicate and compare the effect

of all parameters on shear capacity predicted by the proposedmodels and different well-known codes

2 Reviews of Available Shear Design Equations

-e last two decades witnessed development and rapid in-crease of using FRP-reinforcement for concrete structurestherefore there are universal endeavors to create predictionmodels -ese endeavors have brought about distributinga few codes and outline rules However there is no agreementin regards to shear configuration models among all availablecodes and guidelines Table 1 provides a summary of the sheardesign equations for FRP-RC members without stirrups

Most of the available shear design equations of FRP-RCmembers have been developed by modifying the existingequations adopted by design codes for steel-RCmembers-emethods of modification tried to cover the major changes inmaterial properties by taking into account the effect of thelower elastic modulus higher tensile strength lower trans-verse shear strength and no yielding criteria in the FRP rebarNevertheless the relatively large variations in mechanicalproperties such as tensile strength elastic modulus bondproperties and transverse shear strength between the dif-ferent FRP types have made it hard to precisely predict theshear capacity Furthermore the procedure that adopted byvarious codes manuals and guidelines to predict the shearstrength are significantly different and most of them areempirical and based on a limited set of test results Conse-quently some of the design models are quite conservativewhereas others sometimes yield unconservative results [3 22]as well as these equations are differing from each other inconsidered parameters On the contrary the design modelthat does not consider the effect of known parameters wouldlack generality and its applicability to general design situa-tions would be dubious [23] -erefore there is a need todevelop shear design equations which will consider the effectof all parameters as well as it will be accurate consistent andsimple to use for the general application

3 Collected Databases

For the purpose of this study an extensive survey of theopen literature was conducted and a large database con-taining the test results of a large number of 269 FRP-RCbeams and one-way slabs were assembled -e database ofthe specimens were collected from 42 different referencesreinforced with FRP rebars without transverse re-inforcement and only those that failed in the shear modewas compiled [1ndash3 20 22 24ndash60] Only slender beams andone way slabs with ad ge 25 were considered in this study-e specimens included 230 beams and 39 one way slabs allwere simply supported and were tested either under threepoints or four bending points -e details of the specimensthat were used as a database are shown in Table 2

4 Artificial Neural Networks (ANNs)

41 General Background In its most broad frame a neuralnetwork is a machine that is intended to demonstrate the

2 Advances in Civil Engineering

manner by which the brain plays out a specific errand orfunction the system is generally executed by utilizingelectronic parts or is mimicked in programming on anadvanced PC -e ANNs perform helpful calculations andsimulate complex modeling through a procedure of learningsimilar to that of the human brain ANNs do not representthe sophistication complication and multifaceted nature ofthe brain as the simulated neurons are substantially morestraightforward than natural neurons in the area of recog-nition efficiency control and learning Nonetheless ANNsare similar to the brain in two main points first the buildingsquares of the two systems are straightforward computa-tional tools which are exceedingly interconnected secondthe connections between neurons decide the task of thenetworks [61 62]

ANNs are made out of numerous interconnected pro-cessing units operating in parallel Each processing unitkeeps some data locally can play out some basic calculationscan have numerous input data and however can send justa single output-e ANNs have the ability to react and createthe relating response and to adjust to the changing conditionby learning from experience [63]

Generally ANNs are trained with the goal that specificinput data prompt a particular target output -e network isbalanced in view of an examination of the output and thetarget until the networks yield the objective Graduallytraining the network modifies the weights and biases re-quired after the introduction of every individual inputvector ANNs have been prepared to perform complexfunctions in different fields of application including bi-ological engineering business financial manufacturingmedical andmilitary Today ANNs can be prepared to tackleissues that are troublesome for regular PCs or human beings[64] -e drawback of the ANNs modeling is that it is not assimple as ordinary design provision where it is consist ofregularly numerous small units therefore simple calcula-tions of the ANNs models are excessively monotonous andusually computers are needed for calculations

42 Back Propagation ANNs -e multilayer perceptrontrained through the back-propagation algorithm is nowa-days the most broadly utilized neural networks -e termback propagation neural networks (BPNNs) alludes to

Table 1 Shear design equations for FRP-RC beams without stirrups

Reference Provisions

[12] Vc (25)

fcprime1113969

bwc c kd k

2ρfnf + (ρfnf )2

1113969

minus ρfnf ρf Af (bwd)

[13] Vc βdβpβnfvcdbwdcb fvcd 02(fcprime)13 le 072 Nmm2 βd (1000d)14 le 15 βp ((100ρflEfl)Es)

13 le 15 βn 10 forsections without the axial force cb member safety factor cb 13

[14] Vc 079(100ρw(EfEs))13(400d)14(fcu25)13bwd (100ρw(EfEs)) should not be taken greater than 3 and (400d)14

should not be taken if less than 1 for members with shear reinforcement

[15]Vc 25βφcfcrbwdv β (04(1 + 1500εx))(1300(1000 + Sze)) εx (Mfdv+Vf+05Nf

)(2(EfAf)) le 0003Sze ((35Sz)(15 + ag))ge 085Sz where fcr 04

fc

1113968fc le 69 Nmm2

[16]

Vc 02λφc

fcprime1113969

bwdEflEs

1113969

For sections with an effective depth greater than 300mm the concrete shear resistance Vc is taken as

Vc (260(1000 + d))λφc

fcprime1113969

bwd(EflEs)

1113969ge 01λφc

fcprime1113969

bwd(EflEs)

1113969

(EflEs)

1113969le 10

Where λ modification factor for density of concrete and φc resistance factor for concrete

[17]

VRdct 13(EfEs)12τRdk(12 + 40ρ1)bwd

Satisfying the limitation 13(EfEs)12 le 1 VRdmax 05vfcbw09dv 07minusfc200ge 05

Where τRd design shear stress MPa defined as 025fct fct characteristic tensile strength of concrete (5 fractile)MPafct 033

fcprime1113969

cc is the strength safety factor f concrete cc 16 k factor taken equal to |1| in members where morethan 50 of the bottom reinforcement is interrupted if not it will be k |(16minusd)ge 1| d depth

in meters ρ1 (Afbwd) which cannot be taken less than 001 and greater than 002

[18]

Vc 005λφckmkr(fcprime)13bwdv km

((Vfd)Mf)

1113969le 10 kr 1 + (Efρfw)13 Such that

011λφc

fcprime1113969

bwdv leVc le 022λφc

fcprime1113969

bwdv for fcprime le 60MPaIn members with effective depth greater than 300mm and with transverse reinforcement less than the minimum Vc should

be multiplied by ks (750(450 + d))le 10[4] Vc 21(((fcprimeρfd)a)(EfEs))

03bwd

[7] Vc c0c2(da3

radic100ρf(EfEs)fc

prime(c21c0))13bwd c0 7696 c1 7254 c2 7718

[19]

Vc 0045kmkrkaks(fcprime)13bwd km ((Vd)M)12 kr 1 + (Efρf )

13 ka 1 for (M(Vd))ge 25

25(M(Vd)) for (M(Vd))lt 251113896

ks 1 for dle 300

750(450 + d) for dgt 3001113896

[1] Vc ((02λ)(ad)23)((ρfEf )d)13

fcprime1113969

bwd

[20] Vc 276(ρfl(EflEs)(da)fcprime)13bwd dle 300 mm Vc 276(ρfl(EflEs)(da)fcprime)

13(300d)025bwd dgt 300 mm

[21] Vc vcbwd ((0134

fcprime1113969

)(1 + (d(12dc))

1113968))bwd dc (ρwE(da + 16))(100(ad)

fcprime1113969

)

Advances in Civil Engineering 3

the way in which the gradient is processed for nonlinearmultilayer networks [64] -e BPNNs algorithm followsa technique to minimize the errors through the calibration ofthe weights in each cycle by a small amount for a specifictraining scheme

BPNNs is one of the straightforward and most ap-propriate networks being utilized in the prediction of civilengineering problems [63 65 66] principally because ofthat it can modify the weights of each layer in view of theerrors introduced at the output A common structure ofBPNNs display comprises of an input layer at least onehidden layer and an output layer and each layer comprises

of many neurons Every neuron is a processing unit thatgets at least one source of input and produces an outputresponse through the transfer function Related to everyconnection is a weighting that communicates the impacton the present procedure component of an informationset or another procedure component in the past layer asshown in Figure 1 -e connection weighting and biasvalues are at first picked as arbitrary numbers and af-terward settled by the consequences of the training pro-cedure [67]

-e calculations that carried out inside the BPNNs in-clude summation process of weighted input values with the

Table 2 Details of database

Reference Number of members d (mm) ad b (mm) ρf () fcprime (MPa) Ef (GPa) FRP type Vexp (kN)[24] 4 250 3 150 055ndash22 275ndash35 94 C 383ndash591[27] 2 250ndash500 25 150ndash300 104 295ndash34 100 C 384ndash1428[26] 2 150 4 300 134ndash18 227ndash28 294 G 337ndash37[25] 3 250 3 150 151ndash30 343 105 C 412ndash476[28] 1 260 269 200 136 347 130 C 629[29] 2 210 365 150 136 329ndash381 45 G 228ndash273[30] 1 222 315 154 136 39 34 G 39[31] 2 104ndash154 844ndash125 1000 049ndash076 66 413 G 421ndash852[32] 5 1575 45ndash58 305 073 27ndash308 40 G 28ndash309[33] 3 279ndash287 261ndash269 178 077ndash23 241 40 G 367ndash54[2] 18 225 406 178ndash254 111ndash227 363 403 G 281ndash511[34] 2 258 25 150 091 538ndash685 48 G 385ndash414[35] 6 360 339 457 096ndash192 399ndash426 376ndash471 A G 948ndash177[36] 12 225 406 152ndash203 125ndash256 796 403 G 304ndash483[37] 11 310ndash346 275ndash371 130ndash160 072ndash154 341ndash432 42ndash120 G C 427ndash523[38] 11 143 636 89ndash159 033ndash076 603ndash814 139 C 88ndash231[3] 6 225 267ndash45 200 025ndash088 405 145 C 361ndash472[39] 1 970 314 450 046 40 40 G 136[40] 2 190 796 121 11ndash165 40ndash743 40 G 139ndash169[41] 8 159ndash165 606ndash649 1000 039ndash263 40 40ndash114 G C 118ndash195[42] 11 78ndash83 361ndash641 420 061ndash261 61ndash93 42 G 221ndash556[22] 6 326 307 250 087ndash172 436ndash50 39ndash134 G C 63ndash1275[43] 4 326 307 250 171ndash22 63 42ndash135 G C 90ndash177[44] 6 163ndash263 254ndash409 150 045ndash139 289ndash502 32 G 131ndash309[45] 1 150 335 224 128 43 45 G 279[46] 9 75 6ndash616 420 068ndash116 48ndash92 42 G 246ndash343[47] 3 404ndash441 302ndash371 300 325ndash398 43 44ndash63 G 1184ndash1543[48] 2 262 668 600 077ndash153 68 48 G 912ndash1182[49] 4 170 412 150 092ndash154 20ndash266 46 G 127ndash154[50] 4 170 588 150 133ndash222 20ndash266 113 C 193ndash277[51] 6 194ndash937 326ndash393 450 051ndash254 35ndash46 37 G 74ndash232[52] 6 200ndash500 35ndash65 300 028ndash035 523 114 C 541ndash712[53] 6 291ndash594 25 250ndash300 042ndash137 653ndash742 463ndash144 G C 716ndash1552[54] 13 146ndash883 313 114ndash457 06ndash117 295ndash597 41ndash432 G 179ndash2648[1] 8 305ndash744 25 250ndash300 042ndash091 345ndash447 47ndash144 G C 61ndash1385[55] 9 140 62 1000 052ndash125 413ndash862 140ndash144 C 1185ndash192[56] 34 216 25ndash45 150ndash200 033ndash079 30 48ndash148 G C 169ndash354[57] 3 150 4ndash45 245ndash270 039ndash085 60 70 B 209ndash292[20] 6 170ndash370 27ndash59 200 012ndash052 221ndash287 1414 C 176ndash361[58] 6 170 565ndash7 300 08ndash41 359 48ndash53 B 293ndash515[59] 8 206ndash220 25ndash33 152 031ndash152 49 50 B 17ndash30[60] 12 234ndash635 26 200 071ndash269 422ndash734 58 B 54ndash1695Mean 2588 413 2904 1123 462 738 588Standard deviation 1572 151 2205 07290 1819 4293 4844Minimum 73 25 89 012 20 294 88Maximum 970 125 1000 4121 93 1479 232

4 Advances in Civil Engineering

bias of the input layer as in Equation (1) and then the resultspassed into the hidden layer neurons Inside neurons theprocess of sigmoid transformed function was performed byusing one of the transformed functions such as that inEquation (2) Another linear process using the purelinfunction was carried out by summing the weighted outputfrom the hidden layer neurons with the bias of the hiddenlayer as in Equation (3)

netj sumn

i1wijxi + biasj (1)

yj f netj( ) 1

1 + expminus netj( )( ) (2)

yk purelin summ

j1wjkyj + biask (3)

where netj is the weighted sum generated at the jthhidden neuron xi is the input value from the ith inputneuron wij and wjk are the weights added to the hiddenlayer and the output layer neurons respectively biasjand biask are the biases added to the hidden layer and theoutput layer neurons respectively yj is the processedoutput from the jth hidden neuron yk is the processedoutput from the kth output neuron and n is the numberof input neurons and m is the number of neurons in thehidden layer

43 BPNNs Model Used for the Prediction of Shear CapacityIn this study the BPNNs were utilized to produce a pre-dictive model for shear strength of FRP-reinforced concretemembers without stirrups e key parameters aectingthe shear strength which considered in this study are fcprime dbw ad ρf and Ef e most important issue in BPNNsmodeling is selecting the number of hidden layers and thenumber of neurons in each hidden layer which depend onseveral factors like type of problem of interest the associ-ation of input parameters with the output pattern size ofinstances number of input parameters and number ofoutputs However there is no basic acknowledged criteriato pick the number of hidden layers and the number of

neurons therefore a trial and error method was achievedbased on training and testing up to obtain a reasonable tConsequently a BPNNs training algorithm was utilized ina feed-forward network trained using nonlinear hyperboliclog-sigmoid transfer function in the hidden layer anda linear purelin transfer function in the output layer as inEquations (1)ndash(3)

e trial and error procedure resulted in that the besttting model was that obtained using thirteen neurons ina single hidden layer (6-13-1) as demonstrated in Figure 2e predictive model was trained through numerous iter-ations to nd the best epoch value momentum rate andlearning rate which give the optimum model for shearstrength prediction e data were divided arbitrarily intoldquotrainingrdquo 70 ldquovalidatingrdquo 15 and ldquotestingrdquo 15 and thepartitioning of data was chosen based on the results of modelperformance after numerous trials

It is recommended by many authors [11 63 68 69]to normalize the input and output data before using them topredict the model In this study the data of input and targetwere scaled by the linear normalization function in the rangeof (0 to 1) as shown in the following equation

xn 06xminus xmin

xmin minus xmax+ 02 (4)

where x is the data sample xn is the normalized data samplexmin and xmax is the minimum and maximum values of thedata for the interested parameter

e input layer weights (ILWs) the input layer biases(ILBs) the hidden layer weights (HLWs) and the hiddenlayer bias (HLB) of the (6-13-1) predictive BPNNsmodel areshown below

sum

sum

sumXi

Input layer Hidden layer Output layer

W11ij

W11jk

y1j

W12jk

W12ij

netj1

net2j

biasj1

bias2j

biask

netk yk

y2j

yj = logsig(WijXi + biasj) yk = purlin(Wjkyj + biask)

Figure 1 Typical architecture and log-sigmoid function of (1-2-1)BPNNs

1

2

3

4

5

6

1

2

3

4

5

6

7

8

9

10

11

12

13

fcprime

d

b

ad

ρf

Ef

1Vpred

[HLW][ILW] [ILB] [HLB]

Output layer

Input layer

Hidden layer

Figure 2 Architecture of BPNNs used for the prediction of theshear strength

Advances in Civil Engineering 5

ILW

minus23567 027166 14696 minus14038 099307 22234

23842 minus22831 083159 22855 14806 minus083455

28211 075441 minus4086 14427 17982 minus10877

059955 minus074937 20882 minus26609 18418 minus15433

14527 minus17869 minus10477 16872 minus081981 minus25634

35416 minus19591 minus034353 10741 minus15276 22139

15643 minus28231 26211 minus16244 10879 17129

22825 minus040079 048425 minus2312 007062 015858

minus1749 minus025004 minus045657 minus22347 minus10796 minus10232

minus078404 266 minus28673 minus10803 minus086988 minus16247

minus025678 minus32562 22726 16206 minus12616 26619

minus12662 minus078168 minus052983 minus25791 10124 23284

minus23043 055942 minus12328 minus28413 minus13658 26415

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

⎫⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎬

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎭

ILB

51888

minus14396

minus21773

minus24823

minus16444

minus008813

012198

22041

minus2362

minus19906

minus052466

minus37706

minus26641

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

⎫⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎬

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎭

HLW ⎧⎨

⎩ minus07663 12834 minus09729 minus066761 minus03835 minus087847 12312 13464 minus13058 1206 1169 minus09465 minus06511⎫⎬

⎭

HLB minus044036

(5)

5 Genetic Programming

51 General Background Genetic programming (GP) isa naturally inspired machine learning (evolutionary) tech-nique utilized for randomly reproducing a population ofcomputer programs in light of Darwinrsquos advancement hy-pothesis GP which was developed by Koza [70] can beregarded as a developed form of the genetic algorithm (GA)which is an evolutionary optimization tool that depends onthe principles of genetics and normal determination -esystems of GA incorporate altering and changing the extentof chromosomes by genetic operators to solve functionoptimization problems -e fundamental contrast amongst

GA and GP is that the solution of GA is a binary string offixed length utilized for parameters optimization of a specificarrangement of model parameters while the solution of GPis a development program represented as a subset of parsetrees which use input variables and corresponding outputsfor generating optimized models [71ndash73]

-e GP techniques for modeling incorporate productionof an initial population of chromosomes (models) whichinclude an arrangement of functions and an arrangement ofterminals that selected and arranged randomly in the form ofthe parse tree (computer model) -e models composed ofa root node functional nodes and terminals as shown inFigure 3

6 Advances in Civil Engineering

At that point the produced population models areassessed and the tness of the models is evaluated using theprovided data of the particular problem After that othergenerations of models are produced by primary genetic op-erators reproduction crossover and mutation as shown inFigure 4e evolutionary procedure of assessing the tness ofthe present population and producing new population iscontinued until the point when an end termination criterion isapproached which can be either a particular acceptable erroror a specied maximum number of generations e modelwith the best solution which developed after each generationassigns the outcome of the GP program [76]

52 Gene Expression Programming e most widely usedGP in civil engineering problems is gene expressionprogramming (GEP) which was developed by Ferreira[71] GEP utilizes development of numerical conditionsthat is encoded linearly in chromosomes of a consistentlength and considered nonlinearly as expression trees(ETs) with various shapes and sizes e chromosomes arecomposed of several genes each gene contains a smallersubprogram or subexpression trees (Sub-ETs) Every genehas a consistent length and comprises a head and a tail eschematic of the GEP centowchart is shown in Figure 5 eimplementation of GEP predictive modeling incorporatesve main components including function set terminal settness function control parameters and terminationcondition [7 75]

e preferred quality of GEP is that the genetic operatorswork at the chromosome level and the production of geneticdiversity is to a great degree simplied Another favorableposition is credited to the remarkable multigenetic nature ofGEP which permits the advancement of all the more capablemodels made out of a few subprograms [71]

53 GEPModel for Predicting Shear Capacity For predictingthe shear strength of FRP-reinforced concrete beamswithout stirrups by GEP-based formulation six incentuencingparameters were consideredfcprime d b adEf and ρf throughtraining and testing the experimental results e data areevaluated on the GeneXproTools 5 [78] to develop theempirical model which is the most widely used software for

GEP model prediction Similar to the ANNs model the dataare partitioned randomly to 70 for training and remaining30 for testing such that both portions of data have balancedstatistical parameters like mean standard deviation andmax and min values

To obtain the best GEP prediction model many modelswith a dierent number of genes were evolved throughouta set of genetic operators (mutation transposition andcrossover) Initially a model composed of two genes withmultiplication linking functions and head sizes of three wasselected and evolved many times en the model param-eters were changed step by step through increasing thenumber of genes head size number of chromosomes andweights of function sets e program was evolved nu-merous times for various models and the outcome modelswere monitored and compared to evaluate their perfor-mance Other parameters like mutation rate inversion andpoints of recombination were chosen based on previousworks [7 79ndash82] and then evaluated to get their optimumeects After many trials the nal mathematical model waschosen for which the utilized parameters tness functionand function sets are given in Table 3 e nal model wasselected based on criteria of the best tness and less com-plicity of mathematical formulation the expression trees areshown in Figure 6 and themathematical formulation is givenin the following equation

sqrt

x1 x2 x34

ndash +

Functional nodes

Terminal nodes

Root node

Figure 3 Typical example of a GP tree representation model((4minusx1)(x2 + x3))

12 [74]

radicradic

+

+

+

1 3

+

+

+

times

times

2

2

Log

Crossover

Mutation

Log

Log Log

a

a

c

c d

d d

d

bb

Figure 4 Typical operations of crossover and mutation in GP [75]

Advances in Civil Engineering 7

Vc absc3 + d5 lowastd3( ) d2 + d0( )2

4( )

13

lowast tanhd2d1( )

15 minus tanh d2 lowast d3( )4( )

5

lowast d2 +d153

max d1 c6( )c8 + d4( )( )

2

lowast tanhd2d1( )

15 minus

d1d0

radic

3

5

(6)

where d0 d1 d2 d3 d4 and d5 refer to d ad bρf fcprime and Ef respectively c2 656723946184092 c3 minus241413053630399 c4 minus121479701959083 c6 307014791103389 and c8 220241396443835

6 Nonlinear Regression Model (NLR)

Regression analysis is considered as an important toolthat can be used in the modeling process for solvingcomplicated problems of various engineering disciplines

However the proposed models based on nonlinear re-gression (NLR) are less accurate than the ANN and GEPhowever it is characterized by that it is simple and easy forapplication without the need of computers for calculationsA nonlinear regression model based on the experimentaldatabase collected from the literature was suggested eproposed equation was derived based on developinga model similar to that proposed by Zsutty [83] which is themost accurate and simple empirical equation that wasproposed for shear prediction of steel-RC members Inorder to predict the shear strength of FRP-RC beams moreaccurately considering the eect of all incentuencing pa-rameters the experimental shear strength was analyzedwith most common incentuencing parameters fcprime d b adEf and ρf Based on data tting analysis and after somesimplication the following equation was proposed

Vc 0321d( )

13 Efρfad( )

25fcprime( )15bwd (7)

It can be observed that the equation is simple rationaland more generalized than most codes and proposedequations from the literature as it considers the eect of allthe incentuencing parameters on the shear strength of FRP-RCmembers without stirrups

7 Results and Discussion

e shear strength results of FRP-reinforced concretemembers for the three proposed models the ANNs GEPand NLR are evaluated and compared with the commondesign provisions (ACI 440-15 JSCE-97 CSA 806-12) andseven proposed equations [1 4 7 10 19ndash21] e com-parison was examined based on statistical terms such as

Start

Initial population creation

Chromosome expression as ET

ET execution

Fitness evaluation

Stop

Chromosome selection

Reproduction

Terminate

New generation creation

Yes

No

Figure 5 Flowchart of GEP [77]

Table 3 Parameters used in the GEP Model

Parameters ValuesNumber of chromosomes 30ndash500Head size 3 5 8Number of genes 2 3 4Linking function Multiplication

Function set + minus lowast abs tanh x2 x12 x13 x15

Generation withoutchanges 2000

Number of tries 12Maximum complexity 10Fitness function RMSEMutation 0044Inversion 01One-pointrecombination 03

Two-pointrecombination 03

Gene recombination 01Gene transposition 01IS transposition 01RIS transposition 01Data type Floating pointConstants per gene 10

8 Advances in Civil Engineering

mean standard deviation (SD) and coelaquocient of variation(COV) in addition to error values such as mean absoluteerror (MAE) root mean square error (RMSE) and R2 asshown below

RMSE

sumN

i0 ei minuspi( )2

N

radic

MAE 1NsumN

i0ei minuspi∣∣∣∣

∣∣∣∣

R2 1minussumN

i0 ei minuspi( )2

sumN

i0 ei minus e( )2

(8)

where ei and pi are the experimental and predicted shearforce in kN respectively e is the average of the experimentalvalues andN is the total number of the considered samplese model that minimized the error values (MAE andRMSE) and maximized R2 is selected as the optimummodel

Figure 7 presents the scatter of the experimental shearforce Vexp versus the predicted shear strength Vpred for theproposed models codes and proposed equations from theliterature It is clear that the best models for predicting theshear strength are those suggested in this study which ina sequence are ANNs GEP and NLR as these modelspredict the shear strength very accurately with the optimumstatistical performance of R2 RMSE and MAE High cor-relation coelaquocients with low error rates indicate that theproposed three models are excellent models and exhibitgeneralization performance in predicting shear strength ofFRP-reinforced concrete beams without stirrups In con-trast the code design provisions and other proposedequations from the literature yielded dispersion results with

lower R2 and larger error rates as given in the scatterrelationships

Table 4 presents the statistical parameters (meanstandard deviation (SD) coelaquocient of variation (COV)minimum maximum range RMSE MAE and R2) of theratio of experimental shear strength to the predicted shearstrength VexpVpred for the proposed models in thisstudy seven well-known codes and seven proposedequations from literature based on the (269) collecteddatabase It is clear that the proposed equations yieldedsuperior accuracy between all the codes and proposedequation from the literature because their optimumstatistical parameters such as the mean SD range RMSEand R2 are 0998 0113 072 53 and 09877 respectivelyfor ANNs 1007 0162 088 82 and 0970 respectivelyfor GEP and 1003 0174 099 107 and 095 re-spectively for NLR

e ANNs and GEP models are articial intelligentmodels derived based on soft computing as veried abovethese models are accurate superior and highly elaquocient inpredicting the complicated problem such as shear strengthHowever the drawback of articial intelligent models is thatit cannot be calculated manually and it needs computers forcalculation Besides it is considered as a powerful and ef-cient tool which can be used in soft programs specializedfor analysis and design of reinforced concrete structures Onthe contrary the NLR model is simply accurate and rationalwhich can be used manually with sulaquocient accuracy morethan the design codes and previously proposed equationsNevertheless the regression equations cannot properlydene with the same level of elaquociency of articial intelligenttechniques the interactions between the input and outputparameters due to that the regression models usually areproduced based only on a few predened equations [79]

3Rt

c3 lowast

lowast

d0

d3d5

lowast Avg2 c2

c2 d0

Avg2

+

(a)

x5

lowast

ndash

5Rt

Tanh

x4

c4d3d2d1

Tanh

(b)

+

d2x2

+

d1d3

Max2d4

c6

c8

5Rt

lowast

(c)

x5

ndash

5Rt

x3

d0d1d2d1

Tanh

Sqrt

(d)

Figure 6 Expression trees ETs for the GEP model (a) Sub-ET 1 (b) Sub-ET 2 (c) Sub-ET 3 (d) Sub-ET 4

Advances in Civil Engineering 9

Finally it can be said that all the three proposed equationscan be considered as accurate efficient and useful modelswhich were trained on a largest collected database forpredicting the shear strength of FRP-reinforced concretemembers

8 Parametric Analyses

For further verification of the proposed ANNs GEP andNLR prediction models a parametric analysis was per-formed in this study -e main goal was to find the

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

ANNsR2 = 09877RMSE = 53MAE = 39

GEPR2 = 09709

RMSE = 82kNMAE = 59kN

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

ACI 440-06R2 = 0575

RMSE = 315MAE = 242

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

CSA 806-12R2 = 0783

RMSE = 225MAE = 117

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

R2 = 0805RMSE = 213MAE = 121

Nehdi et al (2007)

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

R2 = 0772RMSE = 231MAE = 144

Razaqpur and Spadea (2011)

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

R2 = 08347RMSE = 196MAE = 110

Kara (2011)

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

R2 = 0865RMSE = 177MAE = 109

Alam and Husein (2013)

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

R2 = 0885RMSE = 164MAE = 102

Ashour and Kara (2014)

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

R2 = 0902RMSE = 151MAE = 96

Lee (2014)

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

JSCE97R2 = 0792

RMSE = 220MAE = 149

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

NLR

Vexp (kN)

R2 = 0950RMSE = 107MAE = 73

Figure 7 Scatter of Vexp versus Vpred for ANN GEP NLR and different models from the literature

10 Advances in Civil Engineering

response of the three proposed models to predict the shearstrength for a set of input parameters which are selectedtaking into account the average value of each parame-ter in the collected database For further showing theperformance of the proposed models and for comparisonpurpose the response of three well-known codes (ACI1R440-15 JSCE-97 and CSA S806-12) was also considered-e approach depends on keeping all input parameters attheir selected values except that in each time a singleparameter value was changed incrementally within theexpected practical values Consequently an arrangementof manufactured data for the single considered parameteris produced this procedure was repeated for all parametersso that all models are examined for the entire input pa-rameters -e selected input parameters are fcprime 46MPabw 200mm d 400mm ad 4 ρf 0011 and Ef

74 GPa It is worthy to note that the ANNs model cannotproperly predict the shear strength for input parametersoutside the range of training data therefore it is only validfor prediction within the range of input parameters of thetraining data [8]

Figure 8 indicates the tendency of the predicted shearstrength by differentmodels to the varieties of themain designparameters (d fcprime ρf Ef ad and bw) Generally it can beobserved that the proposed models particularly the ANNsmodel yielded larger shear capacities for all parameters whileACI 440-15 yielded the lowest shear capacities which indicatethat the ACI 440-15 is very conservative

-e relationship of beam depth with the predicted shearstrength showed that all the proposed models and codesincreased with the increase in the beam depth throughoutthe range of 100ndash1000mm -e ACI 440-15 considers theeffect of beam depth linearly while all other models rep-resent the effect of depth nonlinearly the ANNs GEP andNLR models consider the depth raised to a power of 083067 and 066 respectively Also it can be observed that theGEP and NLR yield almost the same results All the pro-posed models and codes showed an increase in shearstrength with the increase in the concrete compressive

strength but in different rates It was found that fcprime is raisedto a power of 066 030 and 02 for ANNs GEP and NLRrespectively

-e effect of the flexure reinforcement ratio on shearstrength indicates a similar trend of the NLR model and thedesign codes but the ANNs and GEP models showeda slightly decreased trend for reinforcement ratios greaterthan 003 this is not in agreement with codes and previousstudies because of that only few data were available with ρflarger than 003 and these data actually showed decreasingshear capacity Additionally these models were derivedbased only on the artificial technology of data trainingwithout manually choosing the general mathematical shapeof the model in contrary to the NLRmodel and design codeswhich was derived based on the theoretical or semiempiricalcriteria

-e shear strength also increased with the increase inthe elastic modulus of the flexure reinforcement ratio Itcan be observed that all models showed a similar trend linefor the entire range of data while the ANNs model showedan increased rate up to about 110 GPa and then the in-crease rate reduced significantly similar results also ob-tained by Bashir and Ashour [8] On the contrary thetrend lines of the shear span to depth ratio are decreasedfor GEP and NLR models for the entire range of datameanwhile for ANNs model it decreases up to ad of 5and then it started to increase slightly -is behavior is inagreement with the few available experimental results[32 52 56] which were studied as ad greater than 5However other codes do not consider the effect of ad asthe trend lines for ACI 440-15 and JSCE-97 are constantwhile the CSA S806 trend line remains constant beyondthe ad value of 5 Finally the effect of beam width on shearstrength is linear as indicated by trend lines for all modelsexcept the ANNs model which showed a lower increaserate beyond 700mm width

To investigate how the proposed models consider thesize effect on shear capacity the same parametric data usedfor studying the beam depth are used Figure 9 presents

Table 4 Statistical parameters of (VexpVpred) for the proposed models and different design equations

Design equations Mean (VexpVpred) SD COV Minimum Maximum Range RMSE MAE R2

[12] 1813 0416 2306 113 374 261 315 242 0575[13] 1302 0282 2163 046 251 205 220 149 0792[18] 1091 0227 2085 047 185 137 225 117 0783[16] 1193 0386 3249 044 248 203 2633 1758 0703[17] 0948 0265 2799 039 174 134 2257 1403 0782[14] 1072 0247 231 054 192 138 1470 980 0908[15] 1393 0254 1835 070 248 178 2456 1661 0742[4] 1113 0219 1967 055 192 136 213 121 0805[19] 1305 0235 1801 084 214 129 231 184 0772[7] 1025 0205 2003 054 191 136 196 110 0835[1] 1148 0227 1981 059 172 113 177 109 0865[20] 0965 0174 1806 063 168 105 164 102 0885[10] 1015 0229 2251 053 196 143 151 96 0905[21] 1096 0283 2587 056 212 156 1915 1180 0843NLR 1003 0174 1732 062 161 099 107 73 0950GEP 1007 0162 1608 066 155 088 82 59 09709ANNs 0998 0113 1131 071 144 072 53 39 09877

Advances in Civil Engineering 11

0

30

60

90

120

150

180

0 150 300 450 600 750 900 1050

V pre

d (k

N)

d (mm)

ANNGEPJSCE 97

NLRACI 440CSA S806

0

20

40

60

80

100

120

0 10 20 30 40 50 60 70 80 90 100 110

V pre

d (k

N)

fcprime (MPa)

ANNGEPJSCE 97

NLRACI 440SCA S806

0

20

40

60

80

100

120

0 001 002 003 004 005

V pre

d (k

N)

ρf

ANNGEPJSCE 97

NLRACI 440CSA S806

0

20

40

60

80

100

120

0 25 50 75 100 125 150 175

V pre

d (k

N)

Ef (MPa)

ANNGEPJSCE 97

NLRACI 440CSA S806

0

20

40

60

80

100

120

0 2 4 6 8 10

V pre

d (k

N)

ad

ANNGEPJSCE 97

NLRACI 440CSA S806

0

60

120

180

240

300

360

0 200 400 600 800 1000 1200

V pre

d (k

N)

b (mm)

ANNGEPJSCE 97

NLRACI 440CSA S806

Figure 8 Eect of the parameters (d fcprime ρf Ef ad and bw) on shear capacity predicted by ANNs GEP NLR and three design codes(ACI1R 440-06 JSCE-97 and CSA S806-12)

12 Advances in Civil Engineering

the relationship between normalized shear strength as(Vpredbwd

fcprime1113969

) and beam depth It is clear that the nor-malized shear strength is decreased with the increase in thebeam depth for ANNs GEP and NLR showing that the sizeeffect is efficiently presented in these models -e trends ofGEP and NLR are very close and compatible and decreasedfrom a depth of 100mm to 1000mm while the ANNsmodelseems to be more accurate as it shows an increase in thetrend up to the depth of 200mm and then it decreasedsimilarly to that of GEP and NLR after that the trend startsto increase slightly

It can be summed up to that the artificial intelligentmodels due to their efficiency and powerful ability in rec-ognizing the parameters interaction demonstrate variousrates of change and fluctuation for the entire scope of inputparameters -e ANNs and GEP models define accurately theinteraction of each parameter on shear strength predictionand have a great ability to represent the actual response ofeach parameter in spite of its complexity and fluctuationnature Furthermore these models are evolved by trainingnumerous preliminary linear and nonlinear models withoutany prior assumption regarding the shape and structure of themathematical model

9 Conclusions

An experimental database including 269 shear test results ofFRP-reinforced concrete members without stirrups availablein the literature was established to propose three predictionmodels to estimate the shear capacity of FRP-RC membersusing three powerful tools which are ANNs GEP and NLR-e following conclusions can be drawn from this study

(i) -e proposed models for predicting the shear ca-pacity of FRP-RC members based on ANNs andGEP techniques showed excellent performancegreat efficiency and high level of accuracy andyielded consistent results throughout a wide rangeof influencing parameters moreover the ANNsmodel is more superior than the GEP as the SD andR2 for ANNs are 0113 and 09877 and for GEP are0162 and 097 respectively

(ii) A simple rational and yet accurate empiricalequation was proposed for predicting shearstrength of FRP-RC members by NLR -e equa-tion considers all the important influencing pa-rameters and simplified to be easy for use Inaddition it gives consistent and accurate resultswith SD and R2 of 0173 and 095 respectively

(iii) -rough a comparative statistical analysis for theproposed models with seven shear design codes andsix proposed equations from the literature it hasbeen found that the most accurate and efficientmodels are ANNs and GEP and to a lower dgreeNLR Among the codes and available proposals theCSA S806-12 and Ashour and Kara [20] equationswere appearing to be more accurate than the others

(iv) From a parametric study considering all the influ-encing parameters on shear capacity it was found thatthe ANNs model and to a lower level GEP modeldefines accurately the interaction of each parameteron shear capacity prediction and has a great ability torepresent the actual response of each parameter inspite of its complexity and fluctuation nature

(v) -e ANNs and GEP models demonstrate that theeffect of flexure reinforcement ratio on shear ca-pacity decreased beyond 003 as a real response tothe available few data in this range therefore morestudies are needed to confirm this case

(vi) -e ANNs model demonstrated that the effect ofad does not absolutely reduce the shear capacitywhile beyond the ad value of 5 its effect couldbecome reverse and contribute to increase in theshear capacity as confirmed by few previous studies

(vii) -e size effect is considered properly by the pro-posed models particularly the ANNs model whichyields more accurate shear capacity prediction tothe experimental results

Data Availability

-e (database of shear strength of beams without stirrups)data used to support the findings of this study are includedwithin the article

Conflicts of Interest

-e authors declare that they have no conflicts of interest

0

004

008

012

016

02

024

0 200 400 600 800 1000 1200

ANNNLRGEP

d (mm)

V pre

db wd

fc

Figure 9 Normalized shear strength (Vpredbwd

fcprime1113969

) versus beamdepth

Advances in Civil Engineering 13

References

[1] M S Alam and A Hussein ldquoSize effect on shear strength ofFRP reinforced concrete beams without stirrupsrdquo Journal ofComposites for Construction vol 17 no 4 pp 507ndash516 2013

[2] J R Yost S P Gross and D W Dinehart ldquoShear strength ofnormal strength concrete beams reinforced with deformedGFRP barsrdquo Journal of Composites for Construction vol 5no 4 pp 268ndash275 2001

[3] A G Razaqpur B O Isgor S Greenaway and A SelleyldquoConcrete contribution to the shear resistance of fiber rein-forced polymer reinforced concrete membersrdquo Journal ofComposites for Construction vol 8 no 5 pp 452ndash460 2004

[4] M Nehdi H El Chabib and A A Saıd ldquoProposed sheardesign equations for FRP-reinforced concrete beams based ongenetic algorithms approachrdquo Journal of Materials in CivilEngineering vol 19 no 12 pp 1033ndash1042 2007

[5] ASCE-ACI445 ldquoRecent approaches to shear design ofstructural concreterdquo Journal of Structural Engineeringvol 124 no 12 pp 1375ndash1417 1998

[6] R Park and T Paulay Reinforced Concrete Structures JohnWiley amp Sons Hoboken NJ USA 1975

[7] I F Kara ldquoPrediction of shear strength of FRP-reinforcedconcrete beams without stirrups based on genetic pro-grammingrdquo Advances in Engineering Software vol 42 no 6pp 295ndash304 2011

[8] R Bashir and A Ashour ldquoNeural networkmodelling for shearstrength of concrete members reinforced with FRP barsrdquoComposites Part B Engineering vol 43 no 8 pp 3198ndash32072012

[9] K Nasrollahzadeh and M M Basiri ldquoPrediction of shearstrength of FRP reinforced concrete beams using fuzzy in-ference systemrdquo Expert Systems with Applications vol 41no 4 pp 1006ndash1020 2014

[10] S Lee and C Lee ldquoPrediction of shear strength of FRP-reinforced concrete flexural members without stirrups usingartificial neural networksrdquo Engineering Structures vol 61pp 99ndash112 2014

[11] E M Golafshani and A Ashour ldquoA feasibility study of BBPfor predicting shear capacity of FRP reinforced concretebeams without stirrupsrdquo Advances in Engineering Softwarevol 97 pp 29ndash39 2016

[12] ACI-440 Guide for the Design and Construction of StructuralConcrete Reinforced with Fiber-Reinforced Polymer (FRP)ACI 440 1R-15 American Concrete Institute FarmingtonsHills MI USA 2015

[13] JSCE ldquoRecommendation for design and construction ofconcrete structures using continuous fiber reinforcing ma-terialsrdquo in Concrete Engineering Series 23 A Machida EdJapan Society of Civil Engineers Tokyo Japan 1997

[14] BISE Interim Guidance on the Design of Reinforced ConcreteStructures Using Fiber Composite Reinforcement British In-stitution of Structural Engineers Seto Ltd London UK1999

[15] CSA Canadian Highway Bridge Design Code SupplementNo 1 to CANCSA S6-06 (S61S1-10) Canadian StandardsAssociation (CSA) Mississauga ON Canada 2010

[16] ISIS Reinforced Concrete Structures with Fibre ReinforcedPolymersmdashDesign Manual No 3 University of Manitoba ISISCanada Corporation Winnipeg MB Canada 2007

[17] CNR-DT203 ldquoGuide for the design and construction ofconcrete structures reinforced with fiber-reinforced polymerbarsrdquo inAdvisory Committee on Technical Recommendations

for Construction CNR-DT 2032006 CNR Rome Italy2007

[18] CSA ldquoCode for the design and construction of buildingstructures with fibre-reinforced polymersrdquo in CANCSAS806-12 p 198 Canadian Standard Association TorontoON Canada 2012

[19] A Razaqpur and S Spadea ldquoResistenza a taglio di elementi dicalcestruzzzo reinforzatti e staffe di FRPrdquo in Proceedings ofAIAS Maratea Italy September 2010

[20] A F Ashour and I F Kara ldquoSize effect on shear strength ofFRP reinforced concrete beamsrdquo Composites Part B Engi-neering vol 60 pp 612ndash620 2014

[21] A R Yousif ldquoShear strength of large FRP-reinforced concretebeams without shear reinforcementrdquo Journal of Pure andApplied Sciences vol 27 pp 9ndash28 2015

[22] A K El-Sayed E F El-Salakawy and B Benmokrane ldquoShearcapacity of high-strength concrete beams reinforced with FRPbarsrdquo ACI Structural Journal vol 103 p 383 2006

[23] A G Razaqpur and O B Isgor ldquoProposed shear designmethod for FRP-reinforced concrete members without stir-rupsrdquo ACI Structural Journal vol 103 p 93 2006

[24] K Maruyama andW Zhao ldquoFlexural and shear behaviour ofconcrete beams reinforced with FRP rodsrdquo in Proceedings ofthe International Conference on Corrosion and CorrosionProtection of Steel in Concrete pp 24ndash28 Sheffield UK1994

[25] W Zhao K Maruyama and H Suzuki ldquoShear behavior ofconcrete beams reinforced by FRP rods as longitudinal andshear reinforcementrdquo in Proceedings of the Second In-ternational RILEM Symposium on Non-Metallic (FRP) Re-inforcement for Concrete Structures p 352 Ghent BelgiumAugust 1995

[26] H Nakamura and T Higai ldquoEvaluation of shear strength ofthe concrete beams reinforced with FRPrdquo in Proceedings ofJapan Society of Civil Engineers p 89 Ghent Belgium 1995

[27] K Maruyama and W Zhao ldquoSize effect in shear behavior ofFRP reinforced concrete beamrdquo in Advanced CompositeMaterials in Bridges and Structures pp 227ndash234 CanadianSociety for Civil Engineering Montreal QC Canada 1996

[28] Y Mizukawa Y Sato T Ueda and Y Kakuta ldquoA studyon shear fatigue behavior of concrete beams with FRP rodsrdquoin Proceedings of the Cird International Symposium onNon-Metallic (FRP) Reinforcement for Concrete Structures(FRPRCS-3) pp 309ndash316 Japan Concrete Institute SapporoJapan 1997

[29] N Duranovic K Pilakoutas and P Waldron ldquoTests onconcrete beams reinforced with glass fibre reinforced plasticbarsrdquo in Proceedings of the Cird International Symposium onNon-Metallic (FRP) Reinforcement for Concrete Structures(FRPRCS-3) pp 479ndash486 Sapporo Japan 1997

[30] N Swamy and M Aburawi ldquoStructural implications of usingGFRP bars as concrete reinforcementrdquo in Proceedings of 3rdInternational Symposium FRPRCS pp 503ndash510 SapporoJapan 1997

[31] C R Michaluk S H Rizkalla G Tadros and B BenmokraneldquoFlexural behavior of one-way concrete slabs reinforced byfiber reinforced plastic reinforcementsrdquo ACI StructuralJournal vol 95 pp 353ndash365 1998

[32] D Deitz I Harik and H Gesund ldquoOne-way slabs reinforcedwith glass fiber reinforced polymer reinforcing barsrdquo SpecialPublication vol 188 pp 279ndash286 1999

[33] T Alkhrdaji M Wideman A Belarbi and A Nanni ldquoShearstrength of GFRP RC beams and slabsrdquo in Proceedings of the

14 Advances in Civil Engineering

International Conference Composites in Construction-CCCpp 409ndash414 Porto Portugal 2001

[34] G S Melo and J A Rayol ldquoShear resistance of GFRPreinforced concrete beamsrdquo in Proceedings of the Rehabil-itating and Repairing the Buildings and Bridges of AmericasHemispheric Workshop on Future Directions Mayaguumlez PRUSA pp 47ndash64 2002

[35] A K Tureyen and R J Frosch ldquoShear tests of FRP-reinforcedconcrete beams without stirrupsrdquo ACI Structural Journalvol 99 pp 427ndash434 2002

[36] S P Gross J R Yost D W Dinehart E Svensen and N LiuldquoShear strength of normal and high strength concrete beamsreinforced with GFRP barsrdquo in Proceedings of InternationalConference on High Performance Materials in Bridgespp 426ndash437 ASCE Reston VA USA 2003

[37] M Tariq and J Newhook ldquoShear testing of FRP reinforcedconcrete without transverse reinforcementrdquo in Proceedings ofAnnual Conference of the Canadian Society for Civil Engi-neering pp 1330ndash1339 Moncton NB Canada June 2003

[38] S Gross D Dinehart J Yost and P -eisz ldquoExperimentaltests of high-strength concrete beams reinforced with CFRPbarsrdquo in Proceedings of the 4th International Conference onAdvanced Composite Materials in Bridges and Structures(ACMBS-4) Calgary AB Canada 2004

[39] A Lubell T Sherwood E Bentz and M P Collins ldquoSafe sheardesign of large wide beams adding shear reinforcement isrecommendedrdquoConcrete International vol 26 pp 66ndash78 2004

[40] J Yost S Gross G Masone and P Hamelin ldquoSustained loadeffects on deflection and ultimate strength of concrete beamsreinforced with GFRPrdquo in Proceedings of the InternationalConference Composites in Construction (CCC2005) LyonFrance July 2005

[41] A El-Sayed E El-Salakawy and B Benmokrane ldquoShearstrength of one-way concrete slabs reinforced with fiber-reinforced polymer composite barsrdquo Journal of Compositesfor Construction vol 9 no 2 pp 147ndash157 2005

[42] A E Kilpatrick and L Easden ldquoShear capacity of GFRPreinforced high strength concrete slabsrdquo in Proceedings of the18th Australasian Conference on the Mechanics of Structuresand Materials Perth Australia vol 1 pp 119ndash124 Taylor ampFrancis London UK 2005

[43] A K El-Sayed E F El-Salakawy and B BenmokraneldquoShear strength of FRP-reinforced concrete beams withouttransverse reinforcementrdquo ACI Structural Journal vol 103p 235 2006

[44] A Ashour ldquoFlexural and shear capacities of concrete beamsreinforced with GFRP barsrdquo Construction and BuildingMaterials vol 20 no 10 pp 1005ndash1015 2006

[45] M Guadagnini K Pilakoutas and P Waldron ldquoShear re-sistance of FRP RC beams experimental studyrdquo Journal ofComposites for Construction vol 10 no 6 pp 464ndash473 2006

[46] R Dawborn and A Kilpatrick Flexural Shear Capacity ofHigh Strength Concrete Slabs Reinforced with LongitudinalGFRP Bars 2006

[47] J Niewels ldquoZum Tragverhalten von Betonbauteilen mitFaserverbundkunststoffbewehrungrdquo Rheinisch-WestfalischeTechnische Hochschule Aachen Lehrstuhl und Institut furMassivbau Dissertation 2008

[48] A El-Sayed K Soudki and E Kling ldquoFlexural behaviour ofself-consolidating concrete slabs reinforced with GFRP barsrdquoin Proceedings of the 9th International Symposium on FiberReinforced Polymer Reinforcement for Reinforced ConcreteStructures pp 13ndash15 Sydney NSW Australia 2009

[49] A Caporale and R Luciano ldquoIndagine sperimentale enumerica sulla resistenza a taglio di travi di calcestruzzoarmate con barre di GFRPrdquo in Proceedings of XXXVIIIConvegno Nazionale AIAS Turin Italy September 2009

[50] R Olivito and F Zuccarello ldquoOn the shear behaviour ofconcrete beams reinforced by carbon fibre-reinforced poly-mer bars an experimental investigation by means of acousticemission techniquerdquo Strain vol 46 no 5 pp 470ndash481 2010

[51] E C Bentz L Massam and M P Collins ldquoShear strength oflarge concrete members with FRP reinforcementrdquo Journal ofComposites for Construction vol 14 no 6 pp 637ndash646 2010

[52] A G Razaqpur M Shedid and B Isgor ldquoShear strength offiber-reinforced polymer reinforced concrete beams subject tounsymmetric loadingrdquo Journal of Composites for Construc-tion vol 15 no 4 pp 500ndash512 2011

[53] M Alam and A Hussein ldquoEffect of member depth on shearstrength of high-strength fiber-reinforced polymerndashreinforced concrete beamsrdquo Journal of Composites for Con-struction vol 16 no 2 pp 119ndash126 2012

[54] F Matta A K El-Sayed A Nanni and B Benmokrane ldquoSizeeffect on concrete shear strength in beams reinforced withfiber-reinforced polymer barsrdquo ACI Structural Journalvol 110-S50 pp 617ndash628 2013

[55] B Abdul-Salam A Farghaly and B Benmokrane ldquoEvalua-tion of shear behavior for one-way concrete slabs reinforcedwith carbon-FRP barsrdquo GEN vol 243 p 1 2013

[56] C H Kim and H S Jang ldquoConcrete shear strength of normaland lightweight concrete beams reinforced with FRP barsrdquoJournal of Composites for Construction vol 18 no 2 article04013038 2014

[57] D Tomlinson and A Fam ldquoPerformance of concrete beamsreinforced with basalt FRP for flexure and shearrdquo Journal ofComposites for Construction vol 19 no 2 article 040140362014

[58] M A Issa T Ovitigala and M Ibrahim ldquoShear behavior ofbasalt fiber reinforced concrete beams with and without basaltFRP stirrupsrdquo Journal of Composites for Construction vol 20no 4 article 04015083 2015

[59] A El Refai and F Abed ldquoConcrete contribution to shearstrength of beams reinforced with basalt fiber-reinforcedbarsrdquo Journal of Composites for Construction vol 20 no 4article 04015082 2015

[60] G B Jumaa and A R Yuosif ldquoSize effect in shear failure ofhigh strength concrete beams without stirrups reinforcedwith basalt FRP barsrdquo KSCE Journal of Civil Engineering2018 In press

[61] M T Hagan H B Demuth and M H BealeNeural NetworkDesign (Electrical Engineering) -omson Learning BostonMA USA 1995

[62] S S Haykin S S Haykin S S Haykin and S S HaykinNeural Networks and Learning Machines Pearson Vol 3Pearson Upper Saddle River NJ USA 2009

[63] M Y Mansour M Dicleli J-Y Lee and J Zhang ldquoPredictingthe shear strength of reinforced concrete beams using artificialneural networksrdquo Engineering Structures vol 26 no 6pp 781ndash799 2004

[64] H Demuth M Beale and M Hagan Neural NetworkToolboxtrade 6 Userrsquos Guide -e MathWorks Inc vol 10 p 11Natick MA USA 2008

[65] A W Oreta and K Kawashima ldquoNeural network modeling ofconfined compressive strength and strain of circular concretecolumnsrdquo Journal of Structural Engineering vol 129 no 4pp 554ndash561 2003

Advances in Civil Engineering 15

[66] S Jung and K S Kim ldquoKnowledge-based predictionof shear strength of concrete beams without shear re-inforcementrdquo Engineering Structures vol 30 no 6pp 1515ndash1525 2008

[67] Z-H Duan S-C Kou and C-S Poon ldquoPrediction ofcompressive strength of recycled aggregate concrete usingartificial neural networksrdquo Construction and Building Mate-rials vol 40 pp 1200ndash1206 2013

[68] H El-Chabib M Nehdi and A Said ldquoPredicting shear ca-pacity of NSC and HSC slender beams without stirrups usingartificial intelligencerdquo Computers and Concrete vol 2 no 1pp 79ndash96 2005

[69] F Altun O Kisi and K Aydin ldquoPredicting the compressivestrength of steel fiber added lightweight concrete using neuralnetworkrdquo Computational Materials Science vol 42 no 2pp 259ndash265 2008

[70] J R Koza ldquoGenetic programming as a means for pro-gramming computers by natural selectionrdquo Statistics andComputing vol 4 no 2 pp 87ndash112 1994

[71] C Ferreira ldquoGene expression programming in problemsolvingrdquo in Soft Computing and Industry pp 635ndash653Springer Berlin Germany 2002

[72] C Kayadelen ldquoSoil liquefaction modeling by genetic ex-pression programming and neuro-fuzzyrdquo Expert Systems withApplications vol 38 no 4 pp 4080ndash4087 2011

[73] A H Gandomi A H Alavi and G J Yun ldquoFormulation ofuplift capacity of suction caissons using multi expressionprogrammingrdquo KSCE Journal of Civil Engineering vol 15no 2 pp 363ndash373 2011

[74] A H Gandomi A H Alavi and C RyanHandbook of GeneticProgramming Applications Springer Berlin Germany 2015

[75] A H Gandomi and A H Alavi ldquoA new multi-gene geneticprogramming approach to non-linear system modeling PartII geotechnical and earthquake engineering problemsrdquoNeural Computing and Applications vol 21 no 1 pp 189ndash201 2012

[76] A H Alavi and A H Gandomi ldquoEnergy-based numericalmodels for assessment of soil liquefactionrdquo GeoscienceFrontiers vol 3 no 4 pp 541ndash555 2012

[77] L Teodorescu and D Sherwood ldquoHigh energy physics eventselection with gene expression programmingrdquo ComputerPhysics Communications vol 178 no 6 pp 409ndash419 2008

[78] GEPSOFT GeneXproTools Version 50 GEPSOFT BristolUK 2013 httpwwwgepsoftcom

[79] S M Mousavi P Aminian A H Gandomi A H Alavi andH Bolandi ldquoA new predictive model for compressive strengthof HPC using gene expression programmingrdquo Advances inEngineering Software vol 45 no 1 pp 105ndash114 2012

[80] M Sarıdemir ldquoEmpirical modeling of splitting tensilestrength from cylinder compressive strength of concrete bygenetic programmingrdquo Expert Systems with Applicationsvol 38 no 11 pp 14257ndash14268 2011

[81] M Sonebi and A Cevik ldquoGenetic programming based for-mulation for fresh and hardened properties of self-compacting concrete containing pulverised fuel ashrdquo Con-struction and Building Materials vol 23 no 7 pp 2614ndash26222009

[82] A H Alavi P Aminian A H Gandomi and M A EsmaeilildquoGenetic-based modeling of uplift capacity of suction cais-sonsrdquo Expert Systems with Applications vol 38 no 10pp 12608ndash12618 2011

[83] T Zsutty ldquoShear strength prediction for separate catagories ofsimple beam testsrdquo ACI Journal Proceedings vol 68 no 2pp 138ndash143 1971

16 Advances in Civil Engineering

manner by which the brain plays out a specific errand orfunction the system is generally executed by utilizingelectronic parts or is mimicked in programming on anadvanced PC -e ANNs perform helpful calculations andsimulate complex modeling through a procedure of learningsimilar to that of the human brain ANNs do not representthe sophistication complication and multifaceted nature ofthe brain as the simulated neurons are substantially morestraightforward than natural neurons in the area of recog-nition efficiency control and learning Nonetheless ANNsare similar to the brain in two main points first the buildingsquares of the two systems are straightforward computa-tional tools which are exceedingly interconnected secondthe connections between neurons decide the task of thenetworks [61 62]

ANNs are made out of numerous interconnected pro-cessing units operating in parallel Each processing unitkeeps some data locally can play out some basic calculationscan have numerous input data and however can send justa single output-e ANNs have the ability to react and createthe relating response and to adjust to the changing conditionby learning from experience [63]

Generally ANNs are trained with the goal that specificinput data prompt a particular target output -e network isbalanced in view of an examination of the output and thetarget until the networks yield the objective Graduallytraining the network modifies the weights and biases re-quired after the introduction of every individual inputvector ANNs have been prepared to perform complexfunctions in different fields of application including bi-ological engineering business financial manufacturingmedical andmilitary Today ANNs can be prepared to tackleissues that are troublesome for regular PCs or human beings[64] -e drawback of the ANNs modeling is that it is not assimple as ordinary design provision where it is consist ofregularly numerous small units therefore simple calcula-tions of the ANNs models are excessively monotonous andusually computers are needed for calculations

42 Back Propagation ANNs -e multilayer perceptrontrained through the back-propagation algorithm is nowa-days the most broadly utilized neural networks -e termback propagation neural networks (BPNNs) alludes to

Table 1 Shear design equations for FRP-RC beams without stirrups

Reference Provisions

[12] Vc (25)

fcprime1113969

bwc c kd k

2ρfnf + (ρfnf )2

1113969

minus ρfnf ρf Af (bwd)

[13] Vc βdβpβnfvcdbwdcb fvcd 02(fcprime)13 le 072 Nmm2 βd (1000d)14 le 15 βp ((100ρflEfl)Es)

13 le 15 βn 10 forsections without the axial force cb member safety factor cb 13

[14] Vc 079(100ρw(EfEs))13(400d)14(fcu25)13bwd (100ρw(EfEs)) should not be taken greater than 3 and (400d)14

should not be taken if less than 1 for members with shear reinforcement

[15]Vc 25βφcfcrbwdv β (04(1 + 1500εx))(1300(1000 + Sze)) εx (Mfdv+Vf+05Nf

)(2(EfAf)) le 0003Sze ((35Sz)(15 + ag))ge 085Sz where fcr 04

fc

1113968fc le 69 Nmm2

[16]

Vc 02λφc

fcprime1113969

bwdEflEs

1113969

For sections with an effective depth greater than 300mm the concrete shear resistance Vc is taken as

Vc (260(1000 + d))λφc

fcprime1113969

bwd(EflEs)

1113969ge 01λφc

fcprime1113969

bwd(EflEs)

1113969

(EflEs)

1113969le 10

Where λ modification factor for density of concrete and φc resistance factor for concrete

[17]

VRdct 13(EfEs)12τRdk(12 + 40ρ1)bwd

Satisfying the limitation 13(EfEs)12 le 1 VRdmax 05vfcbw09dv 07minusfc200ge 05

Where τRd design shear stress MPa defined as 025fct fct characteristic tensile strength of concrete (5 fractile)MPafct 033

fcprime1113969

cc is the strength safety factor f concrete cc 16 k factor taken equal to |1| in members where morethan 50 of the bottom reinforcement is interrupted if not it will be k |(16minusd)ge 1| d depth

in meters ρ1 (Afbwd) which cannot be taken less than 001 and greater than 002

[18]

Vc 005λφckmkr(fcprime)13bwdv km

((Vfd)Mf)

1113969le 10 kr 1 + (Efρfw)13 Such that

011λφc

fcprime1113969

bwdv leVc le 022λφc

fcprime1113969

bwdv for fcprime le 60MPaIn members with effective depth greater than 300mm and with transverse reinforcement less than the minimum Vc should

be multiplied by ks (750(450 + d))le 10[4] Vc 21(((fcprimeρfd)a)(EfEs))

03bwd

[7] Vc c0c2(da3

radic100ρf(EfEs)fc

prime(c21c0))13bwd c0 7696 c1 7254 c2 7718

[19]

Vc 0045kmkrkaks(fcprime)13bwd km ((Vd)M)12 kr 1 + (Efρf )

13 ka 1 for (M(Vd))ge 25

25(M(Vd)) for (M(Vd))lt 251113896

ks 1 for dle 300

750(450 + d) for dgt 3001113896

[1] Vc ((02λ)(ad)23)((ρfEf )d)13

fcprime1113969

bwd

[20] Vc 276(ρfl(EflEs)(da)fcprime)13bwd dle 300 mm Vc 276(ρfl(EflEs)(da)fcprime)

13(300d)025bwd dgt 300 mm

[21] Vc vcbwd ((0134

fcprime1113969

)(1 + (d(12dc))

1113968))bwd dc (ρwE(da + 16))(100(ad)

fcprime1113969

)

Advances in Civil Engineering 3

the way in which the gradient is processed for nonlinearmultilayer networks [64] -e BPNNs algorithm followsa technique to minimize the errors through the calibration ofthe weights in each cycle by a small amount for a specifictraining scheme

BPNNs is one of the straightforward and most ap-propriate networks being utilized in the prediction of civilengineering problems [63 65 66] principally because ofthat it can modify the weights of each layer in view of theerrors introduced at the output A common structure ofBPNNs display comprises of an input layer at least onehidden layer and an output layer and each layer comprises

of many neurons Every neuron is a processing unit thatgets at least one source of input and produces an outputresponse through the transfer function Related to everyconnection is a weighting that communicates the impacton the present procedure component of an informationset or another procedure component in the past layer asshown in Figure 1 -e connection weighting and biasvalues are at first picked as arbitrary numbers and af-terward settled by the consequences of the training pro-cedure [67]

-e calculations that carried out inside the BPNNs in-clude summation process of weighted input values with the

Table 2 Details of database

Reference Number of members d (mm) ad b (mm) ρf () fcprime (MPa) Ef (GPa) FRP type Vexp (kN)[24] 4 250 3 150 055ndash22 275ndash35 94 C 383ndash591[27] 2 250ndash500 25 150ndash300 104 295ndash34 100 C 384ndash1428[26] 2 150 4 300 134ndash18 227ndash28 294 G 337ndash37[25] 3 250 3 150 151ndash30 343 105 C 412ndash476[28] 1 260 269 200 136 347 130 C 629[29] 2 210 365 150 136 329ndash381 45 G 228ndash273[30] 1 222 315 154 136 39 34 G 39[31] 2 104ndash154 844ndash125 1000 049ndash076 66 413 G 421ndash852[32] 5 1575 45ndash58 305 073 27ndash308 40 G 28ndash309[33] 3 279ndash287 261ndash269 178 077ndash23 241 40 G 367ndash54[2] 18 225 406 178ndash254 111ndash227 363 403 G 281ndash511[34] 2 258 25 150 091 538ndash685 48 G 385ndash414[35] 6 360 339 457 096ndash192 399ndash426 376ndash471 A G 948ndash177[36] 12 225 406 152ndash203 125ndash256 796 403 G 304ndash483[37] 11 310ndash346 275ndash371 130ndash160 072ndash154 341ndash432 42ndash120 G C 427ndash523[38] 11 143 636 89ndash159 033ndash076 603ndash814 139 C 88ndash231[3] 6 225 267ndash45 200 025ndash088 405 145 C 361ndash472[39] 1 970 314 450 046 40 40 G 136[40] 2 190 796 121 11ndash165 40ndash743 40 G 139ndash169[41] 8 159ndash165 606ndash649 1000 039ndash263 40 40ndash114 G C 118ndash195[42] 11 78ndash83 361ndash641 420 061ndash261 61ndash93 42 G 221ndash556[22] 6 326 307 250 087ndash172 436ndash50 39ndash134 G C 63ndash1275[43] 4 326 307 250 171ndash22 63 42ndash135 G C 90ndash177[44] 6 163ndash263 254ndash409 150 045ndash139 289ndash502 32 G 131ndash309[45] 1 150 335 224 128 43 45 G 279[46] 9 75 6ndash616 420 068ndash116 48ndash92 42 G 246ndash343[47] 3 404ndash441 302ndash371 300 325ndash398 43 44ndash63 G 1184ndash1543[48] 2 262 668 600 077ndash153 68 48 G 912ndash1182[49] 4 170 412 150 092ndash154 20ndash266 46 G 127ndash154[50] 4 170 588 150 133ndash222 20ndash266 113 C 193ndash277[51] 6 194ndash937 326ndash393 450 051ndash254 35ndash46 37 G 74ndash232[52] 6 200ndash500 35ndash65 300 028ndash035 523 114 C 541ndash712[53] 6 291ndash594 25 250ndash300 042ndash137 653ndash742 463ndash144 G C 716ndash1552[54] 13 146ndash883 313 114ndash457 06ndash117 295ndash597 41ndash432 G 179ndash2648[1] 8 305ndash744 25 250ndash300 042ndash091 345ndash447 47ndash144 G C 61ndash1385[55] 9 140 62 1000 052ndash125 413ndash862 140ndash144 C 1185ndash192[56] 34 216 25ndash45 150ndash200 033ndash079 30 48ndash148 G C 169ndash354[57] 3 150 4ndash45 245ndash270 039ndash085 60 70 B 209ndash292[20] 6 170ndash370 27ndash59 200 012ndash052 221ndash287 1414 C 176ndash361[58] 6 170 565ndash7 300 08ndash41 359 48ndash53 B 293ndash515[59] 8 206ndash220 25ndash33 152 031ndash152 49 50 B 17ndash30[60] 12 234ndash635 26 200 071ndash269 422ndash734 58 B 54ndash1695Mean 2588 413 2904 1123 462 738 588Standard deviation 1572 151 2205 07290 1819 4293 4844Minimum 73 25 89 012 20 294 88Maximum 970 125 1000 4121 93 1479 232

4 Advances in Civil Engineering

bias of the input layer as in Equation (1) and then the resultspassed into the hidden layer neurons Inside neurons theprocess of sigmoid transformed function was performed byusing one of the transformed functions such as that inEquation (2) Another linear process using the purelinfunction was carried out by summing the weighted outputfrom the hidden layer neurons with the bias of the hiddenlayer as in Equation (3)

netj sumn

i1wijxi + biasj (1)

yj f netj( ) 1

1 + expminus netj( )( ) (2)

yk purelin summ

j1wjkyj + biask (3)

where netj is the weighted sum generated at the jthhidden neuron xi is the input value from the ith inputneuron wij and wjk are the weights added to the hiddenlayer and the output layer neurons respectively biasjand biask are the biases added to the hidden layer and theoutput layer neurons respectively yj is the processedoutput from the jth hidden neuron yk is the processedoutput from the kth output neuron and n is the numberof input neurons and m is the number of neurons in thehidden layer

43 BPNNs Model Used for the Prediction of Shear CapacityIn this study the BPNNs were utilized to produce a pre-dictive model for shear strength of FRP-reinforced concretemembers without stirrups e key parameters aectingthe shear strength which considered in this study are fcprime dbw ad ρf and Ef e most important issue in BPNNsmodeling is selecting the number of hidden layers and thenumber of neurons in each hidden layer which depend onseveral factors like type of problem of interest the associ-ation of input parameters with the output pattern size ofinstances number of input parameters and number ofoutputs However there is no basic acknowledged criteriato pick the number of hidden layers and the number of

neurons therefore a trial and error method was achievedbased on training and testing up to obtain a reasonable tConsequently a BPNNs training algorithm was utilized ina feed-forward network trained using nonlinear hyperboliclog-sigmoid transfer function in the hidden layer anda linear purelin transfer function in the output layer as inEquations (1)ndash(3)

e trial and error procedure resulted in that the besttting model was that obtained using thirteen neurons ina single hidden layer (6-13-1) as demonstrated in Figure 2e predictive model was trained through numerous iter-ations to nd the best epoch value momentum rate andlearning rate which give the optimum model for shearstrength prediction e data were divided arbitrarily intoldquotrainingrdquo 70 ldquovalidatingrdquo 15 and ldquotestingrdquo 15 and thepartitioning of data was chosen based on the results of modelperformance after numerous trials

It is recommended by many authors [11 63 68 69]to normalize the input and output data before using them topredict the model In this study the data of input and targetwere scaled by the linear normalization function in the rangeof (0 to 1) as shown in the following equation

xn 06xminus xmin

xmin minus xmax+ 02 (4)

where x is the data sample xn is the normalized data samplexmin and xmax is the minimum and maximum values of thedata for the interested parameter

e input layer weights (ILWs) the input layer biases(ILBs) the hidden layer weights (HLWs) and the hiddenlayer bias (HLB) of the (6-13-1) predictive BPNNsmodel areshown below

sum

sum

sumXi

Input layer Hidden layer Output layer

W11ij

W11jk

y1j

W12jk

W12ij

netj1

net2j

biasj1

bias2j

biask

netk yk

y2j

yj = logsig(WijXi + biasj) yk = purlin(Wjkyj + biask)

Figure 1 Typical architecture and log-sigmoid function of (1-2-1)BPNNs

1

2

3

4

5

6

1

2

3

4

5

6

7

8

9

10

11

12

13

fcprime

d

b

ad

ρf

Ef

1Vpred

[HLW][ILW] [ILB] [HLB]

Output layer

Input layer

Hidden layer

Figure 2 Architecture of BPNNs used for the prediction of theshear strength

Advances in Civil Engineering 5

ILW

minus23567 027166 14696 minus14038 099307 22234

23842 minus22831 083159 22855 14806 minus083455

28211 075441 minus4086 14427 17982 minus10877

059955 minus074937 20882 minus26609 18418 minus15433

14527 minus17869 minus10477 16872 minus081981 minus25634

35416 minus19591 minus034353 10741 minus15276 22139

15643 minus28231 26211 minus16244 10879 17129

22825 minus040079 048425 minus2312 007062 015858

minus1749 minus025004 minus045657 minus22347 minus10796 minus10232

minus078404 266 minus28673 minus10803 minus086988 minus16247

minus025678 minus32562 22726 16206 minus12616 26619

minus12662 minus078168 minus052983 minus25791 10124 23284

minus23043 055942 minus12328 minus28413 minus13658 26415

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

⎫⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎬

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎭

ILB

51888

minus14396

minus21773

minus24823

minus16444

minus008813

012198

22041

minus2362

minus19906

minus052466

minus37706

minus26641

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

⎫⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎬

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎭

HLW ⎧⎨

⎩ minus07663 12834 minus09729 minus066761 minus03835 minus087847 12312 13464 minus13058 1206 1169 minus09465 minus06511⎫⎬

⎭

HLB minus044036

(5)

5 Genetic Programming

51 General Background Genetic programming (GP) isa naturally inspired machine learning (evolutionary) tech-nique utilized for randomly reproducing a population ofcomputer programs in light of Darwinrsquos advancement hy-pothesis GP which was developed by Koza [70] can beregarded as a developed form of the genetic algorithm (GA)which is an evolutionary optimization tool that depends onthe principles of genetics and normal determination -esystems of GA incorporate altering and changing the extentof chromosomes by genetic operators to solve functionoptimization problems -e fundamental contrast amongst

GA and GP is that the solution of GA is a binary string offixed length utilized for parameters optimization of a specificarrangement of model parameters while the solution of GPis a development program represented as a subset of parsetrees which use input variables and corresponding outputsfor generating optimized models [71ndash73]

-e GP techniques for modeling incorporate productionof an initial population of chromosomes (models) whichinclude an arrangement of functions and an arrangement ofterminals that selected and arranged randomly in the form ofthe parse tree (computer model) -e models composed ofa root node functional nodes and terminals as shown inFigure 3

6 Advances in Civil Engineering

At that point the produced population models areassessed and the tness of the models is evaluated using theprovided data of the particular problem After that othergenerations of models are produced by primary genetic op-erators reproduction crossover and mutation as shown inFigure 4e evolutionary procedure of assessing the tness ofthe present population and producing new population iscontinued until the point when an end termination criterion isapproached which can be either a particular acceptable erroror a specied maximum number of generations e modelwith the best solution which developed after each generationassigns the outcome of the GP program [76]

52 Gene Expression Programming e most widely usedGP in civil engineering problems is gene expressionprogramming (GEP) which was developed by Ferreira[71] GEP utilizes development of numerical conditionsthat is encoded linearly in chromosomes of a consistentlength and considered nonlinearly as expression trees(ETs) with various shapes and sizes e chromosomes arecomposed of several genes each gene contains a smallersubprogram or subexpression trees (Sub-ETs) Every genehas a consistent length and comprises a head and a tail eschematic of the GEP centowchart is shown in Figure 5 eimplementation of GEP predictive modeling incorporatesve main components including function set terminal settness function control parameters and terminationcondition [7 75]

e preferred quality of GEP is that the genetic operatorswork at the chromosome level and the production of geneticdiversity is to a great degree simplied Another favorableposition is credited to the remarkable multigenetic nature ofGEP which permits the advancement of all the more capablemodels made out of a few subprograms [71]

53 GEPModel for Predicting Shear Capacity For predictingthe shear strength of FRP-reinforced concrete beamswithout stirrups by GEP-based formulation six incentuencingparameters were consideredfcprime d b adEf and ρf throughtraining and testing the experimental results e data areevaluated on the GeneXproTools 5 [78] to develop theempirical model which is the most widely used software for

GEP model prediction Similar to the ANNs model the dataare partitioned randomly to 70 for training and remaining30 for testing such that both portions of data have balancedstatistical parameters like mean standard deviation andmax and min values

To obtain the best GEP prediction model many modelswith a dierent number of genes were evolved throughouta set of genetic operators (mutation transposition andcrossover) Initially a model composed of two genes withmultiplication linking functions and head sizes of three wasselected and evolved many times en the model param-eters were changed step by step through increasing thenumber of genes head size number of chromosomes andweights of function sets e program was evolved nu-merous times for various models and the outcome modelswere monitored and compared to evaluate their perfor-mance Other parameters like mutation rate inversion andpoints of recombination were chosen based on previousworks [7 79ndash82] and then evaluated to get their optimumeects After many trials the nal mathematical model waschosen for which the utilized parameters tness functionand function sets are given in Table 3 e nal model wasselected based on criteria of the best tness and less com-plicity of mathematical formulation the expression trees areshown in Figure 6 and themathematical formulation is givenin the following equation

sqrt

x1 x2 x34

ndash +

Functional nodes

Terminal nodes

Root node

Figure 3 Typical example of a GP tree representation model((4minusx1)(x2 + x3))

12 [74]

radicradic

+

+

+

1 3

+

+

+

times

times

2

2

Log

Crossover

Mutation

Log

Log Log

a

a

c

c d

d d

d

bb

Figure 4 Typical operations of crossover and mutation in GP [75]

Advances in Civil Engineering 7

Vc absc3 + d5 lowastd3( ) d2 + d0( )2

4( )

13

lowast tanhd2d1( )

15 minus tanh d2 lowast d3( )4( )

5

lowast d2 +d153

max d1 c6( )c8 + d4( )( )

2

lowast tanhd2d1( )

15 minus

d1d0

radic

3

5

(6)

where d0 d1 d2 d3 d4 and d5 refer to d ad bρf fcprime and Ef respectively c2 656723946184092 c3 minus241413053630399 c4 minus121479701959083 c6 307014791103389 and c8 220241396443835

6 Nonlinear Regression Model (NLR)

Regression analysis is considered as an important toolthat can be used in the modeling process for solvingcomplicated problems of various engineering disciplines

However the proposed models based on nonlinear re-gression (NLR) are less accurate than the ANN and GEPhowever it is characterized by that it is simple and easy forapplication without the need of computers for calculationsA nonlinear regression model based on the experimentaldatabase collected from the literature was suggested eproposed equation was derived based on developinga model similar to that proposed by Zsutty [83] which is themost accurate and simple empirical equation that wasproposed for shear prediction of steel-RC members Inorder to predict the shear strength of FRP-RC beams moreaccurately considering the eect of all incentuencing pa-rameters the experimental shear strength was analyzedwith most common incentuencing parameters fcprime d b adEf and ρf Based on data tting analysis and after somesimplication the following equation was proposed

Vc 0321d( )

13 Efρfad( )

25fcprime( )15bwd (7)

It can be observed that the equation is simple rationaland more generalized than most codes and proposedequations from the literature as it considers the eect of allthe incentuencing parameters on the shear strength of FRP-RCmembers without stirrups

7 Results and Discussion

e shear strength results of FRP-reinforced concretemembers for the three proposed models the ANNs GEPand NLR are evaluated and compared with the commondesign provisions (ACI 440-15 JSCE-97 CSA 806-12) andseven proposed equations [1 4 7 10 19ndash21] e com-parison was examined based on statistical terms such as

Start

Initial population creation

Chromosome expression as ET

ET execution

Fitness evaluation

Stop

Chromosome selection

Reproduction

Terminate

New generation creation

Yes

No

Figure 5 Flowchart of GEP [77]

Table 3 Parameters used in the GEP Model

Parameters ValuesNumber of chromosomes 30ndash500Head size 3 5 8Number of genes 2 3 4Linking function Multiplication

Function set + minus lowast abs tanh x2 x12 x13 x15

Generation withoutchanges 2000

Number of tries 12Maximum complexity 10Fitness function RMSEMutation 0044Inversion 01One-pointrecombination 03

Two-pointrecombination 03

Gene recombination 01Gene transposition 01IS transposition 01RIS transposition 01Data type Floating pointConstants per gene 10

8 Advances in Civil Engineering

mean standard deviation (SD) and coelaquocient of variation(COV) in addition to error values such as mean absoluteerror (MAE) root mean square error (RMSE) and R2 asshown below

RMSE

sumN

i0 ei minuspi( )2

N

radic

MAE 1NsumN

i0ei minuspi∣∣∣∣

∣∣∣∣

R2 1minussumN

i0 ei minuspi( )2

sumN

i0 ei minus e( )2

(8)

where ei and pi are the experimental and predicted shearforce in kN respectively e is the average of the experimentalvalues andN is the total number of the considered samplese model that minimized the error values (MAE andRMSE) and maximized R2 is selected as the optimummodel

Figure 7 presents the scatter of the experimental shearforce Vexp versus the predicted shear strength Vpred for theproposed models codes and proposed equations from theliterature It is clear that the best models for predicting theshear strength are those suggested in this study which ina sequence are ANNs GEP and NLR as these modelspredict the shear strength very accurately with the optimumstatistical performance of R2 RMSE and MAE High cor-relation coelaquocients with low error rates indicate that theproposed three models are excellent models and exhibitgeneralization performance in predicting shear strength ofFRP-reinforced concrete beams without stirrups In con-trast the code design provisions and other proposedequations from the literature yielded dispersion results with

lower R2 and larger error rates as given in the scatterrelationships

Table 4 presents the statistical parameters (meanstandard deviation (SD) coelaquocient of variation (COV)minimum maximum range RMSE MAE and R2) of theratio of experimental shear strength to the predicted shearstrength VexpVpred for the proposed models in thisstudy seven well-known codes and seven proposedequations from literature based on the (269) collecteddatabase It is clear that the proposed equations yieldedsuperior accuracy between all the codes and proposedequation from the literature because their optimumstatistical parameters such as the mean SD range RMSEand R2 are 0998 0113 072 53 and 09877 respectivelyfor ANNs 1007 0162 088 82 and 0970 respectivelyfor GEP and 1003 0174 099 107 and 095 re-spectively for NLR

e ANNs and GEP models are articial intelligentmodels derived based on soft computing as veried abovethese models are accurate superior and highly elaquocient inpredicting the complicated problem such as shear strengthHowever the drawback of articial intelligent models is thatit cannot be calculated manually and it needs computers forcalculation Besides it is considered as a powerful and ef-cient tool which can be used in soft programs specializedfor analysis and design of reinforced concrete structures Onthe contrary the NLR model is simply accurate and rationalwhich can be used manually with sulaquocient accuracy morethan the design codes and previously proposed equationsNevertheless the regression equations cannot properlydene with the same level of elaquociency of articial intelligenttechniques the interactions between the input and outputparameters due to that the regression models usually areproduced based only on a few predened equations [79]

3Rt

c3 lowast

lowast

d0

d3d5

lowast Avg2 c2

c2 d0

Avg2

+

(a)

x5

lowast

ndash

5Rt

Tanh

x4

c4d3d2d1

Tanh

(b)

+

d2x2

+

d1d3

Max2d4

c6

c8

5Rt

lowast

(c)

x5

ndash

5Rt

x3

d0d1d2d1

Tanh

Sqrt

(d)

Figure 6 Expression trees ETs for the GEP model (a) Sub-ET 1 (b) Sub-ET 2 (c) Sub-ET 3 (d) Sub-ET 4

Advances in Civil Engineering 9

Finally it can be said that all the three proposed equationscan be considered as accurate efficient and useful modelswhich were trained on a largest collected database forpredicting the shear strength of FRP-reinforced concretemembers

8 Parametric Analyses

For further verification of the proposed ANNs GEP andNLR prediction models a parametric analysis was per-formed in this study -e main goal was to find the

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

ANNsR2 = 09877RMSE = 53MAE = 39

GEPR2 = 09709

RMSE = 82kNMAE = 59kN

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

ACI 440-06R2 = 0575

RMSE = 315MAE = 242

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

CSA 806-12R2 = 0783

RMSE = 225MAE = 117

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

R2 = 0805RMSE = 213MAE = 121

Nehdi et al (2007)

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

R2 = 0772RMSE = 231MAE = 144

Razaqpur and Spadea (2011)

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

R2 = 08347RMSE = 196MAE = 110

Kara (2011)

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

R2 = 0865RMSE = 177MAE = 109

Alam and Husein (2013)

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

R2 = 0885RMSE = 164MAE = 102

Ashour and Kara (2014)

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

R2 = 0902RMSE = 151MAE = 96

Lee (2014)

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

JSCE97R2 = 0792

RMSE = 220MAE = 149

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

NLR

Vexp (kN)

R2 = 0950RMSE = 107MAE = 73

Figure 7 Scatter of Vexp versus Vpred for ANN GEP NLR and different models from the literature

10 Advances in Civil Engineering

response of the three proposed models to predict the shearstrength for a set of input parameters which are selectedtaking into account the average value of each parame-ter in the collected database For further showing theperformance of the proposed models and for comparisonpurpose the response of three well-known codes (ACI1R440-15 JSCE-97 and CSA S806-12) was also considered-e approach depends on keeping all input parameters attheir selected values except that in each time a singleparameter value was changed incrementally within theexpected practical values Consequently an arrangementof manufactured data for the single considered parameteris produced this procedure was repeated for all parametersso that all models are examined for the entire input pa-rameters -e selected input parameters are fcprime 46MPabw 200mm d 400mm ad 4 ρf 0011 and Ef

74 GPa It is worthy to note that the ANNs model cannotproperly predict the shear strength for input parametersoutside the range of training data therefore it is only validfor prediction within the range of input parameters of thetraining data [8]

Figure 8 indicates the tendency of the predicted shearstrength by differentmodels to the varieties of themain designparameters (d fcprime ρf Ef ad and bw) Generally it can beobserved that the proposed models particularly the ANNsmodel yielded larger shear capacities for all parameters whileACI 440-15 yielded the lowest shear capacities which indicatethat the ACI 440-15 is very conservative

-e relationship of beam depth with the predicted shearstrength showed that all the proposed models and codesincreased with the increase in the beam depth throughoutthe range of 100ndash1000mm -e ACI 440-15 considers theeffect of beam depth linearly while all other models rep-resent the effect of depth nonlinearly the ANNs GEP andNLR models consider the depth raised to a power of 083067 and 066 respectively Also it can be observed that theGEP and NLR yield almost the same results All the pro-posed models and codes showed an increase in shearstrength with the increase in the concrete compressive

strength but in different rates It was found that fcprime is raisedto a power of 066 030 and 02 for ANNs GEP and NLRrespectively

-e effect of the flexure reinforcement ratio on shearstrength indicates a similar trend of the NLR model and thedesign codes but the ANNs and GEP models showeda slightly decreased trend for reinforcement ratios greaterthan 003 this is not in agreement with codes and previousstudies because of that only few data were available with ρflarger than 003 and these data actually showed decreasingshear capacity Additionally these models were derivedbased only on the artificial technology of data trainingwithout manually choosing the general mathematical shapeof the model in contrary to the NLRmodel and design codeswhich was derived based on the theoretical or semiempiricalcriteria

-e shear strength also increased with the increase inthe elastic modulus of the flexure reinforcement ratio Itcan be observed that all models showed a similar trend linefor the entire range of data while the ANNs model showedan increased rate up to about 110 GPa and then the in-crease rate reduced significantly similar results also ob-tained by Bashir and Ashour [8] On the contrary thetrend lines of the shear span to depth ratio are decreasedfor GEP and NLR models for the entire range of datameanwhile for ANNs model it decreases up to ad of 5and then it started to increase slightly -is behavior is inagreement with the few available experimental results[32 52 56] which were studied as ad greater than 5However other codes do not consider the effect of ad asthe trend lines for ACI 440-15 and JSCE-97 are constantwhile the CSA S806 trend line remains constant beyondthe ad value of 5 Finally the effect of beam width on shearstrength is linear as indicated by trend lines for all modelsexcept the ANNs model which showed a lower increaserate beyond 700mm width

To investigate how the proposed models consider thesize effect on shear capacity the same parametric data usedfor studying the beam depth are used Figure 9 presents

Table 4 Statistical parameters of (VexpVpred) for the proposed models and different design equations

Design equations Mean (VexpVpred) SD COV Minimum Maximum Range RMSE MAE R2

[12] 1813 0416 2306 113 374 261 315 242 0575[13] 1302 0282 2163 046 251 205 220 149 0792[18] 1091 0227 2085 047 185 137 225 117 0783[16] 1193 0386 3249 044 248 203 2633 1758 0703[17] 0948 0265 2799 039 174 134 2257 1403 0782[14] 1072 0247 231 054 192 138 1470 980 0908[15] 1393 0254 1835 070 248 178 2456 1661 0742[4] 1113 0219 1967 055 192 136 213 121 0805[19] 1305 0235 1801 084 214 129 231 184 0772[7] 1025 0205 2003 054 191 136 196 110 0835[1] 1148 0227 1981 059 172 113 177 109 0865[20] 0965 0174 1806 063 168 105 164 102 0885[10] 1015 0229 2251 053 196 143 151 96 0905[21] 1096 0283 2587 056 212 156 1915 1180 0843NLR 1003 0174 1732 062 161 099 107 73 0950GEP 1007 0162 1608 066 155 088 82 59 09709ANNs 0998 0113 1131 071 144 072 53 39 09877

Advances in Civil Engineering 11

0

30

60

90

120

150

180

0 150 300 450 600 750 900 1050

V pre

d (k

N)

d (mm)

ANNGEPJSCE 97

NLRACI 440CSA S806

0

20

40

60

80

100

120

0 10 20 30 40 50 60 70 80 90 100 110

V pre

d (k

N)

fcprime (MPa)

ANNGEPJSCE 97

NLRACI 440SCA S806

0

20

40

60

80

100

120

0 001 002 003 004 005

V pre

d (k

N)

ρf

ANNGEPJSCE 97

NLRACI 440CSA S806

0

20

40

60

80

100

120

0 25 50 75 100 125 150 175

V pre

d (k

N)

Ef (MPa)

ANNGEPJSCE 97

NLRACI 440CSA S806

0

20

40

60

80

100

120

0 2 4 6 8 10

V pre

d (k

N)

ad

ANNGEPJSCE 97

NLRACI 440CSA S806

0

60

120

180

240

300

360

0 200 400 600 800 1000 1200

V pre

d (k

N)

b (mm)

ANNGEPJSCE 97

NLRACI 440CSA S806

Figure 8 Eect of the parameters (d fcprime ρf Ef ad and bw) on shear capacity predicted by ANNs GEP NLR and three design codes(ACI1R 440-06 JSCE-97 and CSA S806-12)

12 Advances in Civil Engineering

the relationship between normalized shear strength as(Vpredbwd

fcprime1113969

) and beam depth It is clear that the nor-malized shear strength is decreased with the increase in thebeam depth for ANNs GEP and NLR showing that the sizeeffect is efficiently presented in these models -e trends ofGEP and NLR are very close and compatible and decreasedfrom a depth of 100mm to 1000mm while the ANNsmodelseems to be more accurate as it shows an increase in thetrend up to the depth of 200mm and then it decreasedsimilarly to that of GEP and NLR after that the trend startsto increase slightly

It can be summed up to that the artificial intelligentmodels due to their efficiency and powerful ability in rec-ognizing the parameters interaction demonstrate variousrates of change and fluctuation for the entire scope of inputparameters -e ANNs and GEP models define accurately theinteraction of each parameter on shear strength predictionand have a great ability to represent the actual response ofeach parameter in spite of its complexity and fluctuationnature Furthermore these models are evolved by trainingnumerous preliminary linear and nonlinear models withoutany prior assumption regarding the shape and structure of themathematical model

9 Conclusions

An experimental database including 269 shear test results ofFRP-reinforced concrete members without stirrups availablein the literature was established to propose three predictionmodels to estimate the shear capacity of FRP-RC membersusing three powerful tools which are ANNs GEP and NLR-e following conclusions can be drawn from this study

(i) -e proposed models for predicting the shear ca-pacity of FRP-RC members based on ANNs andGEP techniques showed excellent performancegreat efficiency and high level of accuracy andyielded consistent results throughout a wide rangeof influencing parameters moreover the ANNsmodel is more superior than the GEP as the SD andR2 for ANNs are 0113 and 09877 and for GEP are0162 and 097 respectively

(ii) A simple rational and yet accurate empiricalequation was proposed for predicting shearstrength of FRP-RC members by NLR -e equa-tion considers all the important influencing pa-rameters and simplified to be easy for use Inaddition it gives consistent and accurate resultswith SD and R2 of 0173 and 095 respectively

(iii) -rough a comparative statistical analysis for theproposed models with seven shear design codes andsix proposed equations from the literature it hasbeen found that the most accurate and efficientmodels are ANNs and GEP and to a lower dgreeNLR Among the codes and available proposals theCSA S806-12 and Ashour and Kara [20] equationswere appearing to be more accurate than the others

(iv) From a parametric study considering all the influ-encing parameters on shear capacity it was found thatthe ANNs model and to a lower level GEP modeldefines accurately the interaction of each parameteron shear capacity prediction and has a great ability torepresent the actual response of each parameter inspite of its complexity and fluctuation nature

(v) -e ANNs and GEP models demonstrate that theeffect of flexure reinforcement ratio on shear ca-pacity decreased beyond 003 as a real response tothe available few data in this range therefore morestudies are needed to confirm this case

(vi) -e ANNs model demonstrated that the effect ofad does not absolutely reduce the shear capacitywhile beyond the ad value of 5 its effect couldbecome reverse and contribute to increase in theshear capacity as confirmed by few previous studies

(vii) -e size effect is considered properly by the pro-posed models particularly the ANNs model whichyields more accurate shear capacity prediction tothe experimental results

Data Availability

-e (database of shear strength of beams without stirrups)data used to support the findings of this study are includedwithin the article

Conflicts of Interest

-e authors declare that they have no conflicts of interest

0

004

008

012

016

02

024

0 200 400 600 800 1000 1200

ANNNLRGEP

d (mm)

V pre

db wd

fc

Figure 9 Normalized shear strength (Vpredbwd

fcprime1113969

) versus beamdepth

Advances in Civil Engineering 13

References

[1] M S Alam and A Hussein ldquoSize effect on shear strength ofFRP reinforced concrete beams without stirrupsrdquo Journal ofComposites for Construction vol 17 no 4 pp 507ndash516 2013

[2] J R Yost S P Gross and D W Dinehart ldquoShear strength ofnormal strength concrete beams reinforced with deformedGFRP barsrdquo Journal of Composites for Construction vol 5no 4 pp 268ndash275 2001

[3] A G Razaqpur B O Isgor S Greenaway and A SelleyldquoConcrete contribution to the shear resistance of fiber rein-forced polymer reinforced concrete membersrdquo Journal ofComposites for Construction vol 8 no 5 pp 452ndash460 2004

[4] M Nehdi H El Chabib and A A Saıd ldquoProposed sheardesign equations for FRP-reinforced concrete beams based ongenetic algorithms approachrdquo Journal of Materials in CivilEngineering vol 19 no 12 pp 1033ndash1042 2007

[5] ASCE-ACI445 ldquoRecent approaches to shear design ofstructural concreterdquo Journal of Structural Engineeringvol 124 no 12 pp 1375ndash1417 1998

[6] R Park and T Paulay Reinforced Concrete Structures JohnWiley amp Sons Hoboken NJ USA 1975

[7] I F Kara ldquoPrediction of shear strength of FRP-reinforcedconcrete beams without stirrups based on genetic pro-grammingrdquo Advances in Engineering Software vol 42 no 6pp 295ndash304 2011

[8] R Bashir and A Ashour ldquoNeural networkmodelling for shearstrength of concrete members reinforced with FRP barsrdquoComposites Part B Engineering vol 43 no 8 pp 3198ndash32072012

[9] K Nasrollahzadeh and M M Basiri ldquoPrediction of shearstrength of FRP reinforced concrete beams using fuzzy in-ference systemrdquo Expert Systems with Applications vol 41no 4 pp 1006ndash1020 2014

[10] S Lee and C Lee ldquoPrediction of shear strength of FRP-reinforced concrete flexural members without stirrups usingartificial neural networksrdquo Engineering Structures vol 61pp 99ndash112 2014

[11] E M Golafshani and A Ashour ldquoA feasibility study of BBPfor predicting shear capacity of FRP reinforced concretebeams without stirrupsrdquo Advances in Engineering Softwarevol 97 pp 29ndash39 2016

[12] ACI-440 Guide for the Design and Construction of StructuralConcrete Reinforced with Fiber-Reinforced Polymer (FRP)ACI 440 1R-15 American Concrete Institute FarmingtonsHills MI USA 2015

[13] JSCE ldquoRecommendation for design and construction ofconcrete structures using continuous fiber reinforcing ma-terialsrdquo in Concrete Engineering Series 23 A Machida EdJapan Society of Civil Engineers Tokyo Japan 1997

[14] BISE Interim Guidance on the Design of Reinforced ConcreteStructures Using Fiber Composite Reinforcement British In-stitution of Structural Engineers Seto Ltd London UK1999

[15] CSA Canadian Highway Bridge Design Code SupplementNo 1 to CANCSA S6-06 (S61S1-10) Canadian StandardsAssociation (CSA) Mississauga ON Canada 2010

[16] ISIS Reinforced Concrete Structures with Fibre ReinforcedPolymersmdashDesign Manual No 3 University of Manitoba ISISCanada Corporation Winnipeg MB Canada 2007

[17] CNR-DT203 ldquoGuide for the design and construction ofconcrete structures reinforced with fiber-reinforced polymerbarsrdquo inAdvisory Committee on Technical Recommendations

for Construction CNR-DT 2032006 CNR Rome Italy2007

[18] CSA ldquoCode for the design and construction of buildingstructures with fibre-reinforced polymersrdquo in CANCSAS806-12 p 198 Canadian Standard Association TorontoON Canada 2012

[19] A Razaqpur and S Spadea ldquoResistenza a taglio di elementi dicalcestruzzzo reinforzatti e staffe di FRPrdquo in Proceedings ofAIAS Maratea Italy September 2010

[20] A F Ashour and I F Kara ldquoSize effect on shear strength ofFRP reinforced concrete beamsrdquo Composites Part B Engi-neering vol 60 pp 612ndash620 2014

[21] A R Yousif ldquoShear strength of large FRP-reinforced concretebeams without shear reinforcementrdquo Journal of Pure andApplied Sciences vol 27 pp 9ndash28 2015

[22] A K El-Sayed E F El-Salakawy and B Benmokrane ldquoShearcapacity of high-strength concrete beams reinforced with FRPbarsrdquo ACI Structural Journal vol 103 p 383 2006

[23] A G Razaqpur and O B Isgor ldquoProposed shear designmethod for FRP-reinforced concrete members without stir-rupsrdquo ACI Structural Journal vol 103 p 93 2006

[24] K Maruyama andW Zhao ldquoFlexural and shear behaviour ofconcrete beams reinforced with FRP rodsrdquo in Proceedings ofthe International Conference on Corrosion and CorrosionProtection of Steel in Concrete pp 24ndash28 Sheffield UK1994

[25] W Zhao K Maruyama and H Suzuki ldquoShear behavior ofconcrete beams reinforced by FRP rods as longitudinal andshear reinforcementrdquo in Proceedings of the Second In-ternational RILEM Symposium on Non-Metallic (FRP) Re-inforcement for Concrete Structures p 352 Ghent BelgiumAugust 1995

[26] H Nakamura and T Higai ldquoEvaluation of shear strength ofthe concrete beams reinforced with FRPrdquo in Proceedings ofJapan Society of Civil Engineers p 89 Ghent Belgium 1995

[27] K Maruyama and W Zhao ldquoSize effect in shear behavior ofFRP reinforced concrete beamrdquo in Advanced CompositeMaterials in Bridges and Structures pp 227ndash234 CanadianSociety for Civil Engineering Montreal QC Canada 1996

[28] Y Mizukawa Y Sato T Ueda and Y Kakuta ldquoA studyon shear fatigue behavior of concrete beams with FRP rodsrdquoin Proceedings of the Cird International Symposium onNon-Metallic (FRP) Reinforcement for Concrete Structures(FRPRCS-3) pp 309ndash316 Japan Concrete Institute SapporoJapan 1997

[29] N Duranovic K Pilakoutas and P Waldron ldquoTests onconcrete beams reinforced with glass fibre reinforced plasticbarsrdquo in Proceedings of the Cird International Symposium onNon-Metallic (FRP) Reinforcement for Concrete Structures(FRPRCS-3) pp 479ndash486 Sapporo Japan 1997

[30] N Swamy and M Aburawi ldquoStructural implications of usingGFRP bars as concrete reinforcementrdquo in Proceedings of 3rdInternational Symposium FRPRCS pp 503ndash510 SapporoJapan 1997

[31] C R Michaluk S H Rizkalla G Tadros and B BenmokraneldquoFlexural behavior of one-way concrete slabs reinforced byfiber reinforced plastic reinforcementsrdquo ACI StructuralJournal vol 95 pp 353ndash365 1998

[32] D Deitz I Harik and H Gesund ldquoOne-way slabs reinforcedwith glass fiber reinforced polymer reinforcing barsrdquo SpecialPublication vol 188 pp 279ndash286 1999

[33] T Alkhrdaji M Wideman A Belarbi and A Nanni ldquoShearstrength of GFRP RC beams and slabsrdquo in Proceedings of the

14 Advances in Civil Engineering

International Conference Composites in Construction-CCCpp 409ndash414 Porto Portugal 2001

[34] G S Melo and J A Rayol ldquoShear resistance of GFRPreinforced concrete beamsrdquo in Proceedings of the Rehabil-itating and Repairing the Buildings and Bridges of AmericasHemispheric Workshop on Future Directions Mayaguumlez PRUSA pp 47ndash64 2002

[35] A K Tureyen and R J Frosch ldquoShear tests of FRP-reinforcedconcrete beams without stirrupsrdquo ACI Structural Journalvol 99 pp 427ndash434 2002

[36] S P Gross J R Yost D W Dinehart E Svensen and N LiuldquoShear strength of normal and high strength concrete beamsreinforced with GFRP barsrdquo in Proceedings of InternationalConference on High Performance Materials in Bridgespp 426ndash437 ASCE Reston VA USA 2003

[37] M Tariq and J Newhook ldquoShear testing of FRP reinforcedconcrete without transverse reinforcementrdquo in Proceedings ofAnnual Conference of the Canadian Society for Civil Engi-neering pp 1330ndash1339 Moncton NB Canada June 2003

[38] S Gross D Dinehart J Yost and P -eisz ldquoExperimentaltests of high-strength concrete beams reinforced with CFRPbarsrdquo in Proceedings of the 4th International Conference onAdvanced Composite Materials in Bridges and Structures(ACMBS-4) Calgary AB Canada 2004

[39] A Lubell T Sherwood E Bentz and M P Collins ldquoSafe sheardesign of large wide beams adding shear reinforcement isrecommendedrdquoConcrete International vol 26 pp 66ndash78 2004

[40] J Yost S Gross G Masone and P Hamelin ldquoSustained loadeffects on deflection and ultimate strength of concrete beamsreinforced with GFRPrdquo in Proceedings of the InternationalConference Composites in Construction (CCC2005) LyonFrance July 2005

[41] A El-Sayed E El-Salakawy and B Benmokrane ldquoShearstrength of one-way concrete slabs reinforced with fiber-reinforced polymer composite barsrdquo Journal of Compositesfor Construction vol 9 no 2 pp 147ndash157 2005

[42] A E Kilpatrick and L Easden ldquoShear capacity of GFRPreinforced high strength concrete slabsrdquo in Proceedings of the18th Australasian Conference on the Mechanics of Structuresand Materials Perth Australia vol 1 pp 119ndash124 Taylor ampFrancis London UK 2005

[43] A K El-Sayed E F El-Salakawy and B BenmokraneldquoShear strength of FRP-reinforced concrete beams withouttransverse reinforcementrdquo ACI Structural Journal vol 103p 235 2006

[44] A Ashour ldquoFlexural and shear capacities of concrete beamsreinforced with GFRP barsrdquo Construction and BuildingMaterials vol 20 no 10 pp 1005ndash1015 2006

[45] M Guadagnini K Pilakoutas and P Waldron ldquoShear re-sistance of FRP RC beams experimental studyrdquo Journal ofComposites for Construction vol 10 no 6 pp 464ndash473 2006

[46] R Dawborn and A Kilpatrick Flexural Shear Capacity ofHigh Strength Concrete Slabs Reinforced with LongitudinalGFRP Bars 2006

[47] J Niewels ldquoZum Tragverhalten von Betonbauteilen mitFaserverbundkunststoffbewehrungrdquo Rheinisch-WestfalischeTechnische Hochschule Aachen Lehrstuhl und Institut furMassivbau Dissertation 2008

[48] A El-Sayed K Soudki and E Kling ldquoFlexural behaviour ofself-consolidating concrete slabs reinforced with GFRP barsrdquoin Proceedings of the 9th International Symposium on FiberReinforced Polymer Reinforcement for Reinforced ConcreteStructures pp 13ndash15 Sydney NSW Australia 2009

[49] A Caporale and R Luciano ldquoIndagine sperimentale enumerica sulla resistenza a taglio di travi di calcestruzzoarmate con barre di GFRPrdquo in Proceedings of XXXVIIIConvegno Nazionale AIAS Turin Italy September 2009

[50] R Olivito and F Zuccarello ldquoOn the shear behaviour ofconcrete beams reinforced by carbon fibre-reinforced poly-mer bars an experimental investigation by means of acousticemission techniquerdquo Strain vol 46 no 5 pp 470ndash481 2010

[51] E C Bentz L Massam and M P Collins ldquoShear strength oflarge concrete members with FRP reinforcementrdquo Journal ofComposites for Construction vol 14 no 6 pp 637ndash646 2010

[52] A G Razaqpur M Shedid and B Isgor ldquoShear strength offiber-reinforced polymer reinforced concrete beams subject tounsymmetric loadingrdquo Journal of Composites for Construc-tion vol 15 no 4 pp 500ndash512 2011

[53] M Alam and A Hussein ldquoEffect of member depth on shearstrength of high-strength fiber-reinforced polymerndashreinforced concrete beamsrdquo Journal of Composites for Con-struction vol 16 no 2 pp 119ndash126 2012

[54] F Matta A K El-Sayed A Nanni and B Benmokrane ldquoSizeeffect on concrete shear strength in beams reinforced withfiber-reinforced polymer barsrdquo ACI Structural Journalvol 110-S50 pp 617ndash628 2013

[55] B Abdul-Salam A Farghaly and B Benmokrane ldquoEvalua-tion of shear behavior for one-way concrete slabs reinforcedwith carbon-FRP barsrdquo GEN vol 243 p 1 2013

[56] C H Kim and H S Jang ldquoConcrete shear strength of normaland lightweight concrete beams reinforced with FRP barsrdquoJournal of Composites for Construction vol 18 no 2 article04013038 2014

[57] D Tomlinson and A Fam ldquoPerformance of concrete beamsreinforced with basalt FRP for flexure and shearrdquo Journal ofComposites for Construction vol 19 no 2 article 040140362014

[58] M A Issa T Ovitigala and M Ibrahim ldquoShear behavior ofbasalt fiber reinforced concrete beams with and without basaltFRP stirrupsrdquo Journal of Composites for Construction vol 20no 4 article 04015083 2015

[59] A El Refai and F Abed ldquoConcrete contribution to shearstrength of beams reinforced with basalt fiber-reinforcedbarsrdquo Journal of Composites for Construction vol 20 no 4article 04015082 2015

[60] G B Jumaa and A R Yuosif ldquoSize effect in shear failure ofhigh strength concrete beams without stirrups reinforcedwith basalt FRP barsrdquo KSCE Journal of Civil Engineering2018 In press

[61] M T Hagan H B Demuth and M H BealeNeural NetworkDesign (Electrical Engineering) -omson Learning BostonMA USA 1995

[62] S S Haykin S S Haykin S S Haykin and S S HaykinNeural Networks and Learning Machines Pearson Vol 3Pearson Upper Saddle River NJ USA 2009

[63] M Y Mansour M Dicleli J-Y Lee and J Zhang ldquoPredictingthe shear strength of reinforced concrete beams using artificialneural networksrdquo Engineering Structures vol 26 no 6pp 781ndash799 2004

[64] H Demuth M Beale and M Hagan Neural NetworkToolboxtrade 6 Userrsquos Guide -e MathWorks Inc vol 10 p 11Natick MA USA 2008

[65] A W Oreta and K Kawashima ldquoNeural network modeling ofconfined compressive strength and strain of circular concretecolumnsrdquo Journal of Structural Engineering vol 129 no 4pp 554ndash561 2003

Advances in Civil Engineering 15

[66] S Jung and K S Kim ldquoKnowledge-based predictionof shear strength of concrete beams without shear re-inforcementrdquo Engineering Structures vol 30 no 6pp 1515ndash1525 2008

[67] Z-H Duan S-C Kou and C-S Poon ldquoPrediction ofcompressive strength of recycled aggregate concrete usingartificial neural networksrdquo Construction and Building Mate-rials vol 40 pp 1200ndash1206 2013

[68] H El-Chabib M Nehdi and A Said ldquoPredicting shear ca-pacity of NSC and HSC slender beams without stirrups usingartificial intelligencerdquo Computers and Concrete vol 2 no 1pp 79ndash96 2005

[69] F Altun O Kisi and K Aydin ldquoPredicting the compressivestrength of steel fiber added lightweight concrete using neuralnetworkrdquo Computational Materials Science vol 42 no 2pp 259ndash265 2008

[70] J R Koza ldquoGenetic programming as a means for pro-gramming computers by natural selectionrdquo Statistics andComputing vol 4 no 2 pp 87ndash112 1994

[71] C Ferreira ldquoGene expression programming in problemsolvingrdquo in Soft Computing and Industry pp 635ndash653Springer Berlin Germany 2002

[72] C Kayadelen ldquoSoil liquefaction modeling by genetic ex-pression programming and neuro-fuzzyrdquo Expert Systems withApplications vol 38 no 4 pp 4080ndash4087 2011

[73] A H Gandomi A H Alavi and G J Yun ldquoFormulation ofuplift capacity of suction caissons using multi expressionprogrammingrdquo KSCE Journal of Civil Engineering vol 15no 2 pp 363ndash373 2011

[74] A H Gandomi A H Alavi and C RyanHandbook of GeneticProgramming Applications Springer Berlin Germany 2015

[75] A H Gandomi and A H Alavi ldquoA new multi-gene geneticprogramming approach to non-linear system modeling PartII geotechnical and earthquake engineering problemsrdquoNeural Computing and Applications vol 21 no 1 pp 189ndash201 2012

[76] A H Alavi and A H Gandomi ldquoEnergy-based numericalmodels for assessment of soil liquefactionrdquo GeoscienceFrontiers vol 3 no 4 pp 541ndash555 2012

[77] L Teodorescu and D Sherwood ldquoHigh energy physics eventselection with gene expression programmingrdquo ComputerPhysics Communications vol 178 no 6 pp 409ndash419 2008

[78] GEPSOFT GeneXproTools Version 50 GEPSOFT BristolUK 2013 httpwwwgepsoftcom

[79] S M Mousavi P Aminian A H Gandomi A H Alavi andH Bolandi ldquoA new predictive model for compressive strengthof HPC using gene expression programmingrdquo Advances inEngineering Software vol 45 no 1 pp 105ndash114 2012

[80] M Sarıdemir ldquoEmpirical modeling of splitting tensilestrength from cylinder compressive strength of concrete bygenetic programmingrdquo Expert Systems with Applicationsvol 38 no 11 pp 14257ndash14268 2011

[81] M Sonebi and A Cevik ldquoGenetic programming based for-mulation for fresh and hardened properties of self-compacting concrete containing pulverised fuel ashrdquo Con-struction and Building Materials vol 23 no 7 pp 2614ndash26222009

[82] A H Alavi P Aminian A H Gandomi and M A EsmaeilildquoGenetic-based modeling of uplift capacity of suction cais-sonsrdquo Expert Systems with Applications vol 38 no 10pp 12608ndash12618 2011

[83] T Zsutty ldquoShear strength prediction for separate catagories ofsimple beam testsrdquo ACI Journal Proceedings vol 68 no 2pp 138ndash143 1971

16 Advances in Civil Engineering

the way in which the gradient is processed for nonlinearmultilayer networks [64] -e BPNNs algorithm followsa technique to minimize the errors through the calibration ofthe weights in each cycle by a small amount for a specifictraining scheme

BPNNs is one of the straightforward and most ap-propriate networks being utilized in the prediction of civilengineering problems [63 65 66] principally because ofthat it can modify the weights of each layer in view of theerrors introduced at the output A common structure ofBPNNs display comprises of an input layer at least onehidden layer and an output layer and each layer comprises

of many neurons Every neuron is a processing unit thatgets at least one source of input and produces an outputresponse through the transfer function Related to everyconnection is a weighting that communicates the impacton the present procedure component of an informationset or another procedure component in the past layer asshown in Figure 1 -e connection weighting and biasvalues are at first picked as arbitrary numbers and af-terward settled by the consequences of the training pro-cedure [67]

-e calculations that carried out inside the BPNNs in-clude summation process of weighted input values with the

Table 2 Details of database

Reference Number of members d (mm) ad b (mm) ρf () fcprime (MPa) Ef (GPa) FRP type Vexp (kN)[24] 4 250 3 150 055ndash22 275ndash35 94 C 383ndash591[27] 2 250ndash500 25 150ndash300 104 295ndash34 100 C 384ndash1428[26] 2 150 4 300 134ndash18 227ndash28 294 G 337ndash37[25] 3 250 3 150 151ndash30 343 105 C 412ndash476[28] 1 260 269 200 136 347 130 C 629[29] 2 210 365 150 136 329ndash381 45 G 228ndash273[30] 1 222 315 154 136 39 34 G 39[31] 2 104ndash154 844ndash125 1000 049ndash076 66 413 G 421ndash852[32] 5 1575 45ndash58 305 073 27ndash308 40 G 28ndash309[33] 3 279ndash287 261ndash269 178 077ndash23 241 40 G 367ndash54[2] 18 225 406 178ndash254 111ndash227 363 403 G 281ndash511[34] 2 258 25 150 091 538ndash685 48 G 385ndash414[35] 6 360 339 457 096ndash192 399ndash426 376ndash471 A G 948ndash177[36] 12 225 406 152ndash203 125ndash256 796 403 G 304ndash483[37] 11 310ndash346 275ndash371 130ndash160 072ndash154 341ndash432 42ndash120 G C 427ndash523[38] 11 143 636 89ndash159 033ndash076 603ndash814 139 C 88ndash231[3] 6 225 267ndash45 200 025ndash088 405 145 C 361ndash472[39] 1 970 314 450 046 40 40 G 136[40] 2 190 796 121 11ndash165 40ndash743 40 G 139ndash169[41] 8 159ndash165 606ndash649 1000 039ndash263 40 40ndash114 G C 118ndash195[42] 11 78ndash83 361ndash641 420 061ndash261 61ndash93 42 G 221ndash556[22] 6 326 307 250 087ndash172 436ndash50 39ndash134 G C 63ndash1275[43] 4 326 307 250 171ndash22 63 42ndash135 G C 90ndash177[44] 6 163ndash263 254ndash409 150 045ndash139 289ndash502 32 G 131ndash309[45] 1 150 335 224 128 43 45 G 279[46] 9 75 6ndash616 420 068ndash116 48ndash92 42 G 246ndash343[47] 3 404ndash441 302ndash371 300 325ndash398 43 44ndash63 G 1184ndash1543[48] 2 262 668 600 077ndash153 68 48 G 912ndash1182[49] 4 170 412 150 092ndash154 20ndash266 46 G 127ndash154[50] 4 170 588 150 133ndash222 20ndash266 113 C 193ndash277[51] 6 194ndash937 326ndash393 450 051ndash254 35ndash46 37 G 74ndash232[52] 6 200ndash500 35ndash65 300 028ndash035 523 114 C 541ndash712[53] 6 291ndash594 25 250ndash300 042ndash137 653ndash742 463ndash144 G C 716ndash1552[54] 13 146ndash883 313 114ndash457 06ndash117 295ndash597 41ndash432 G 179ndash2648[1] 8 305ndash744 25 250ndash300 042ndash091 345ndash447 47ndash144 G C 61ndash1385[55] 9 140 62 1000 052ndash125 413ndash862 140ndash144 C 1185ndash192[56] 34 216 25ndash45 150ndash200 033ndash079 30 48ndash148 G C 169ndash354[57] 3 150 4ndash45 245ndash270 039ndash085 60 70 B 209ndash292[20] 6 170ndash370 27ndash59 200 012ndash052 221ndash287 1414 C 176ndash361[58] 6 170 565ndash7 300 08ndash41 359 48ndash53 B 293ndash515[59] 8 206ndash220 25ndash33 152 031ndash152 49 50 B 17ndash30[60] 12 234ndash635 26 200 071ndash269 422ndash734 58 B 54ndash1695Mean 2588 413 2904 1123 462 738 588Standard deviation 1572 151 2205 07290 1819 4293 4844Minimum 73 25 89 012 20 294 88Maximum 970 125 1000 4121 93 1479 232

4 Advances in Civil Engineering

bias of the input layer as in Equation (1) and then the resultspassed into the hidden layer neurons Inside neurons theprocess of sigmoid transformed function was performed byusing one of the transformed functions such as that inEquation (2) Another linear process using the purelinfunction was carried out by summing the weighted outputfrom the hidden layer neurons with the bias of the hiddenlayer as in Equation (3)

netj sumn

i1wijxi + biasj (1)

yj f netj( ) 1

1 + expminus netj( )( ) (2)

yk purelin summ

j1wjkyj + biask (3)

where netj is the weighted sum generated at the jthhidden neuron xi is the input value from the ith inputneuron wij and wjk are the weights added to the hiddenlayer and the output layer neurons respectively biasjand biask are the biases added to the hidden layer and theoutput layer neurons respectively yj is the processedoutput from the jth hidden neuron yk is the processedoutput from the kth output neuron and n is the numberof input neurons and m is the number of neurons in thehidden layer

43 BPNNs Model Used for the Prediction of Shear CapacityIn this study the BPNNs were utilized to produce a pre-dictive model for shear strength of FRP-reinforced concretemembers without stirrups e key parameters aectingthe shear strength which considered in this study are fcprime dbw ad ρf and Ef e most important issue in BPNNsmodeling is selecting the number of hidden layers and thenumber of neurons in each hidden layer which depend onseveral factors like type of problem of interest the associ-ation of input parameters with the output pattern size ofinstances number of input parameters and number ofoutputs However there is no basic acknowledged criteriato pick the number of hidden layers and the number of

neurons therefore a trial and error method was achievedbased on training and testing up to obtain a reasonable tConsequently a BPNNs training algorithm was utilized ina feed-forward network trained using nonlinear hyperboliclog-sigmoid transfer function in the hidden layer anda linear purelin transfer function in the output layer as inEquations (1)ndash(3)

e trial and error procedure resulted in that the besttting model was that obtained using thirteen neurons ina single hidden layer (6-13-1) as demonstrated in Figure 2e predictive model was trained through numerous iter-ations to nd the best epoch value momentum rate andlearning rate which give the optimum model for shearstrength prediction e data were divided arbitrarily intoldquotrainingrdquo 70 ldquovalidatingrdquo 15 and ldquotestingrdquo 15 and thepartitioning of data was chosen based on the results of modelperformance after numerous trials

It is recommended by many authors [11 63 68 69]to normalize the input and output data before using them topredict the model In this study the data of input and targetwere scaled by the linear normalization function in the rangeof (0 to 1) as shown in the following equation

xn 06xminus xmin

xmin minus xmax+ 02 (4)

where x is the data sample xn is the normalized data samplexmin and xmax is the minimum and maximum values of thedata for the interested parameter

e input layer weights (ILWs) the input layer biases(ILBs) the hidden layer weights (HLWs) and the hiddenlayer bias (HLB) of the (6-13-1) predictive BPNNsmodel areshown below

sum

sum

sumXi

Input layer Hidden layer Output layer

W11ij

W11jk

y1j

W12jk

W12ij

netj1

net2j

biasj1

bias2j

biask

netk yk

y2j

yj = logsig(WijXi + biasj) yk = purlin(Wjkyj + biask)

Figure 1 Typical architecture and log-sigmoid function of (1-2-1)BPNNs

1

2

3

4

5

6

1

2

3

4

5

6

7

8

9

10

11

12

13

fcprime

d

b

ad

ρf

Ef

1Vpred

[HLW][ILW] [ILB] [HLB]

Output layer

Input layer

Hidden layer

Figure 2 Architecture of BPNNs used for the prediction of theshear strength

Advances in Civil Engineering 5

ILW

minus23567 027166 14696 minus14038 099307 22234

23842 minus22831 083159 22855 14806 minus083455

28211 075441 minus4086 14427 17982 minus10877

059955 minus074937 20882 minus26609 18418 minus15433

14527 minus17869 minus10477 16872 minus081981 minus25634

35416 minus19591 minus034353 10741 minus15276 22139

15643 minus28231 26211 minus16244 10879 17129

22825 minus040079 048425 minus2312 007062 015858

minus1749 minus025004 minus045657 minus22347 minus10796 minus10232

minus078404 266 minus28673 minus10803 minus086988 minus16247

minus025678 minus32562 22726 16206 minus12616 26619

minus12662 minus078168 minus052983 minus25791 10124 23284

minus23043 055942 minus12328 minus28413 minus13658 26415

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

⎫⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎬

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎭

ILB

51888

minus14396

minus21773

minus24823

minus16444

minus008813

012198

22041

minus2362

minus19906

minus052466

minus37706

minus26641

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

⎫⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎬

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎭

HLW ⎧⎨

⎩ minus07663 12834 minus09729 minus066761 minus03835 minus087847 12312 13464 minus13058 1206 1169 minus09465 minus06511⎫⎬

⎭

HLB minus044036

(5)

5 Genetic Programming

51 General Background Genetic programming (GP) isa naturally inspired machine learning (evolutionary) tech-nique utilized for randomly reproducing a population ofcomputer programs in light of Darwinrsquos advancement hy-pothesis GP which was developed by Koza [70] can beregarded as a developed form of the genetic algorithm (GA)which is an evolutionary optimization tool that depends onthe principles of genetics and normal determination -esystems of GA incorporate altering and changing the extentof chromosomes by genetic operators to solve functionoptimization problems -e fundamental contrast amongst

GA and GP is that the solution of GA is a binary string offixed length utilized for parameters optimization of a specificarrangement of model parameters while the solution of GPis a development program represented as a subset of parsetrees which use input variables and corresponding outputsfor generating optimized models [71ndash73]

-e GP techniques for modeling incorporate productionof an initial population of chromosomes (models) whichinclude an arrangement of functions and an arrangement ofterminals that selected and arranged randomly in the form ofthe parse tree (computer model) -e models composed ofa root node functional nodes and terminals as shown inFigure 3

6 Advances in Civil Engineering

At that point the produced population models areassessed and the tness of the models is evaluated using theprovided data of the particular problem After that othergenerations of models are produced by primary genetic op-erators reproduction crossover and mutation as shown inFigure 4e evolutionary procedure of assessing the tness ofthe present population and producing new population iscontinued until the point when an end termination criterion isapproached which can be either a particular acceptable erroror a specied maximum number of generations e modelwith the best solution which developed after each generationassigns the outcome of the GP program [76]

52 Gene Expression Programming e most widely usedGP in civil engineering problems is gene expressionprogramming (GEP) which was developed by Ferreira[71] GEP utilizes development of numerical conditionsthat is encoded linearly in chromosomes of a consistentlength and considered nonlinearly as expression trees(ETs) with various shapes and sizes e chromosomes arecomposed of several genes each gene contains a smallersubprogram or subexpression trees (Sub-ETs) Every genehas a consistent length and comprises a head and a tail eschematic of the GEP centowchart is shown in Figure 5 eimplementation of GEP predictive modeling incorporatesve main components including function set terminal settness function control parameters and terminationcondition [7 75]

e preferred quality of GEP is that the genetic operatorswork at the chromosome level and the production of geneticdiversity is to a great degree simplied Another favorableposition is credited to the remarkable multigenetic nature ofGEP which permits the advancement of all the more capablemodels made out of a few subprograms [71]

53 GEPModel for Predicting Shear Capacity For predictingthe shear strength of FRP-reinforced concrete beamswithout stirrups by GEP-based formulation six incentuencingparameters were consideredfcprime d b adEf and ρf throughtraining and testing the experimental results e data areevaluated on the GeneXproTools 5 [78] to develop theempirical model which is the most widely used software for

GEP model prediction Similar to the ANNs model the dataare partitioned randomly to 70 for training and remaining30 for testing such that both portions of data have balancedstatistical parameters like mean standard deviation andmax and min values

To obtain the best GEP prediction model many modelswith a dierent number of genes were evolved throughouta set of genetic operators (mutation transposition andcrossover) Initially a model composed of two genes withmultiplication linking functions and head sizes of three wasselected and evolved many times en the model param-eters were changed step by step through increasing thenumber of genes head size number of chromosomes andweights of function sets e program was evolved nu-merous times for various models and the outcome modelswere monitored and compared to evaluate their perfor-mance Other parameters like mutation rate inversion andpoints of recombination were chosen based on previousworks [7 79ndash82] and then evaluated to get their optimumeects After many trials the nal mathematical model waschosen for which the utilized parameters tness functionand function sets are given in Table 3 e nal model wasselected based on criteria of the best tness and less com-plicity of mathematical formulation the expression trees areshown in Figure 6 and themathematical formulation is givenin the following equation

sqrt

x1 x2 x34

ndash +

Functional nodes

Terminal nodes

Root node

Figure 3 Typical example of a GP tree representation model((4minusx1)(x2 + x3))

12 [74]

radicradic

+

+

+

1 3

+

+

+

times

times

2

2

Log

Crossover

Mutation

Log

Log Log

a

a

c

c d

d d

d

bb

Figure 4 Typical operations of crossover and mutation in GP [75]

Advances in Civil Engineering 7

Vc absc3 + d5 lowastd3( ) d2 + d0( )2

4( )

13

lowast tanhd2d1( )

15 minus tanh d2 lowast d3( )4( )

5

lowast d2 +d153

max d1 c6( )c8 + d4( )( )

2

lowast tanhd2d1( )

15 minus

d1d0

radic

3

5

(6)

where d0 d1 d2 d3 d4 and d5 refer to d ad bρf fcprime and Ef respectively c2 656723946184092 c3 minus241413053630399 c4 minus121479701959083 c6 307014791103389 and c8 220241396443835

6 Nonlinear Regression Model (NLR)

Regression analysis is considered as an important toolthat can be used in the modeling process for solvingcomplicated problems of various engineering disciplines

However the proposed models based on nonlinear re-gression (NLR) are less accurate than the ANN and GEPhowever it is characterized by that it is simple and easy forapplication without the need of computers for calculationsA nonlinear regression model based on the experimentaldatabase collected from the literature was suggested eproposed equation was derived based on developinga model similar to that proposed by Zsutty [83] which is themost accurate and simple empirical equation that wasproposed for shear prediction of steel-RC members Inorder to predict the shear strength of FRP-RC beams moreaccurately considering the eect of all incentuencing pa-rameters the experimental shear strength was analyzedwith most common incentuencing parameters fcprime d b adEf and ρf Based on data tting analysis and after somesimplication the following equation was proposed

Vc 0321d( )

13 Efρfad( )

25fcprime( )15bwd (7)

It can be observed that the equation is simple rationaland more generalized than most codes and proposedequations from the literature as it considers the eect of allthe incentuencing parameters on the shear strength of FRP-RCmembers without stirrups

7 Results and Discussion

e shear strength results of FRP-reinforced concretemembers for the three proposed models the ANNs GEPand NLR are evaluated and compared with the commondesign provisions (ACI 440-15 JSCE-97 CSA 806-12) andseven proposed equations [1 4 7 10 19ndash21] e com-parison was examined based on statistical terms such as

Start

Initial population creation

Chromosome expression as ET

ET execution

Fitness evaluation

Stop

Chromosome selection

Reproduction

Terminate

New generation creation

Yes

No

Figure 5 Flowchart of GEP [77]

Table 3 Parameters used in the GEP Model

Parameters ValuesNumber of chromosomes 30ndash500Head size 3 5 8Number of genes 2 3 4Linking function Multiplication

Function set + minus lowast abs tanh x2 x12 x13 x15

Generation withoutchanges 2000

Number of tries 12Maximum complexity 10Fitness function RMSEMutation 0044Inversion 01One-pointrecombination 03

Two-pointrecombination 03

Gene recombination 01Gene transposition 01IS transposition 01RIS transposition 01Data type Floating pointConstants per gene 10

8 Advances in Civil Engineering

mean standard deviation (SD) and coelaquocient of variation(COV) in addition to error values such as mean absoluteerror (MAE) root mean square error (RMSE) and R2 asshown below

RMSE

sumN

i0 ei minuspi( )2

N

radic

MAE 1NsumN

i0ei minuspi∣∣∣∣

∣∣∣∣

R2 1minussumN

i0 ei minuspi( )2

sumN

i0 ei minus e( )2

(8)

where ei and pi are the experimental and predicted shearforce in kN respectively e is the average of the experimentalvalues andN is the total number of the considered samplese model that minimized the error values (MAE andRMSE) and maximized R2 is selected as the optimummodel

Figure 7 presents the scatter of the experimental shearforce Vexp versus the predicted shear strength Vpred for theproposed models codes and proposed equations from theliterature It is clear that the best models for predicting theshear strength are those suggested in this study which ina sequence are ANNs GEP and NLR as these modelspredict the shear strength very accurately with the optimumstatistical performance of R2 RMSE and MAE High cor-relation coelaquocients with low error rates indicate that theproposed three models are excellent models and exhibitgeneralization performance in predicting shear strength ofFRP-reinforced concrete beams without stirrups In con-trast the code design provisions and other proposedequations from the literature yielded dispersion results with

lower R2 and larger error rates as given in the scatterrelationships

Table 4 presents the statistical parameters (meanstandard deviation (SD) coelaquocient of variation (COV)minimum maximum range RMSE MAE and R2) of theratio of experimental shear strength to the predicted shearstrength VexpVpred for the proposed models in thisstudy seven well-known codes and seven proposedequations from literature based on the (269) collecteddatabase It is clear that the proposed equations yieldedsuperior accuracy between all the codes and proposedequation from the literature because their optimumstatistical parameters such as the mean SD range RMSEand R2 are 0998 0113 072 53 and 09877 respectivelyfor ANNs 1007 0162 088 82 and 0970 respectivelyfor GEP and 1003 0174 099 107 and 095 re-spectively for NLR

e ANNs and GEP models are articial intelligentmodels derived based on soft computing as veried abovethese models are accurate superior and highly elaquocient inpredicting the complicated problem such as shear strengthHowever the drawback of articial intelligent models is thatit cannot be calculated manually and it needs computers forcalculation Besides it is considered as a powerful and ef-cient tool which can be used in soft programs specializedfor analysis and design of reinforced concrete structures Onthe contrary the NLR model is simply accurate and rationalwhich can be used manually with sulaquocient accuracy morethan the design codes and previously proposed equationsNevertheless the regression equations cannot properlydene with the same level of elaquociency of articial intelligenttechniques the interactions between the input and outputparameters due to that the regression models usually areproduced based only on a few predened equations [79]

3Rt

c3 lowast

lowast

d0

d3d5

lowast Avg2 c2

c2 d0

Avg2

+

(a)

x5

lowast

ndash

5Rt

Tanh

x4

c4d3d2d1

Tanh

(b)

+

d2x2

+

d1d3

Max2d4

c6

c8

5Rt

lowast

(c)

x5

ndash

5Rt

x3

d0d1d2d1

Tanh

Sqrt

(d)

Figure 6 Expression trees ETs for the GEP model (a) Sub-ET 1 (b) Sub-ET 2 (c) Sub-ET 3 (d) Sub-ET 4

Advances in Civil Engineering 9

Finally it can be said that all the three proposed equationscan be considered as accurate efficient and useful modelswhich were trained on a largest collected database forpredicting the shear strength of FRP-reinforced concretemembers

8 Parametric Analyses

For further verification of the proposed ANNs GEP andNLR prediction models a parametric analysis was per-formed in this study -e main goal was to find the

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

ANNsR2 = 09877RMSE = 53MAE = 39

GEPR2 = 09709

RMSE = 82kNMAE = 59kN

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

ACI 440-06R2 = 0575

RMSE = 315MAE = 242

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

CSA 806-12R2 = 0783

RMSE = 225MAE = 117

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

R2 = 0805RMSE = 213MAE = 121

Nehdi et al (2007)

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

R2 = 0772RMSE = 231MAE = 144

Razaqpur and Spadea (2011)

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

R2 = 08347RMSE = 196MAE = 110

Kara (2011)

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

R2 = 0865RMSE = 177MAE = 109

Alam and Husein (2013)

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

R2 = 0885RMSE = 164MAE = 102

Ashour and Kara (2014)

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

R2 = 0902RMSE = 151MAE = 96

Lee (2014)

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

JSCE97R2 = 0792

RMSE = 220MAE = 149

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

NLR

Vexp (kN)

R2 = 0950RMSE = 107MAE = 73

Figure 7 Scatter of Vexp versus Vpred for ANN GEP NLR and different models from the literature

10 Advances in Civil Engineering

response of the three proposed models to predict the shearstrength for a set of input parameters which are selectedtaking into account the average value of each parame-ter in the collected database For further showing theperformance of the proposed models and for comparisonpurpose the response of three well-known codes (ACI1R440-15 JSCE-97 and CSA S806-12) was also considered-e approach depends on keeping all input parameters attheir selected values except that in each time a singleparameter value was changed incrementally within theexpected practical values Consequently an arrangementof manufactured data for the single considered parameteris produced this procedure was repeated for all parametersso that all models are examined for the entire input pa-rameters -e selected input parameters are fcprime 46MPabw 200mm d 400mm ad 4 ρf 0011 and Ef

74 GPa It is worthy to note that the ANNs model cannotproperly predict the shear strength for input parametersoutside the range of training data therefore it is only validfor prediction within the range of input parameters of thetraining data [8]

Figure 8 indicates the tendency of the predicted shearstrength by differentmodels to the varieties of themain designparameters (d fcprime ρf Ef ad and bw) Generally it can beobserved that the proposed models particularly the ANNsmodel yielded larger shear capacities for all parameters whileACI 440-15 yielded the lowest shear capacities which indicatethat the ACI 440-15 is very conservative

-e relationship of beam depth with the predicted shearstrength showed that all the proposed models and codesincreased with the increase in the beam depth throughoutthe range of 100ndash1000mm -e ACI 440-15 considers theeffect of beam depth linearly while all other models rep-resent the effect of depth nonlinearly the ANNs GEP andNLR models consider the depth raised to a power of 083067 and 066 respectively Also it can be observed that theGEP and NLR yield almost the same results All the pro-posed models and codes showed an increase in shearstrength with the increase in the concrete compressive

strength but in different rates It was found that fcprime is raisedto a power of 066 030 and 02 for ANNs GEP and NLRrespectively

-e effect of the flexure reinforcement ratio on shearstrength indicates a similar trend of the NLR model and thedesign codes but the ANNs and GEP models showeda slightly decreased trend for reinforcement ratios greaterthan 003 this is not in agreement with codes and previousstudies because of that only few data were available with ρflarger than 003 and these data actually showed decreasingshear capacity Additionally these models were derivedbased only on the artificial technology of data trainingwithout manually choosing the general mathematical shapeof the model in contrary to the NLRmodel and design codeswhich was derived based on the theoretical or semiempiricalcriteria

-e shear strength also increased with the increase inthe elastic modulus of the flexure reinforcement ratio Itcan be observed that all models showed a similar trend linefor the entire range of data while the ANNs model showedan increased rate up to about 110 GPa and then the in-crease rate reduced significantly similar results also ob-tained by Bashir and Ashour [8] On the contrary thetrend lines of the shear span to depth ratio are decreasedfor GEP and NLR models for the entire range of datameanwhile for ANNs model it decreases up to ad of 5and then it started to increase slightly -is behavior is inagreement with the few available experimental results[32 52 56] which were studied as ad greater than 5However other codes do not consider the effect of ad asthe trend lines for ACI 440-15 and JSCE-97 are constantwhile the CSA S806 trend line remains constant beyondthe ad value of 5 Finally the effect of beam width on shearstrength is linear as indicated by trend lines for all modelsexcept the ANNs model which showed a lower increaserate beyond 700mm width

To investigate how the proposed models consider thesize effect on shear capacity the same parametric data usedfor studying the beam depth are used Figure 9 presents

Table 4 Statistical parameters of (VexpVpred) for the proposed models and different design equations

Design equations Mean (VexpVpred) SD COV Minimum Maximum Range RMSE MAE R2

[12] 1813 0416 2306 113 374 261 315 242 0575[13] 1302 0282 2163 046 251 205 220 149 0792[18] 1091 0227 2085 047 185 137 225 117 0783[16] 1193 0386 3249 044 248 203 2633 1758 0703[17] 0948 0265 2799 039 174 134 2257 1403 0782[14] 1072 0247 231 054 192 138 1470 980 0908[15] 1393 0254 1835 070 248 178 2456 1661 0742[4] 1113 0219 1967 055 192 136 213 121 0805[19] 1305 0235 1801 084 214 129 231 184 0772[7] 1025 0205 2003 054 191 136 196 110 0835[1] 1148 0227 1981 059 172 113 177 109 0865[20] 0965 0174 1806 063 168 105 164 102 0885[10] 1015 0229 2251 053 196 143 151 96 0905[21] 1096 0283 2587 056 212 156 1915 1180 0843NLR 1003 0174 1732 062 161 099 107 73 0950GEP 1007 0162 1608 066 155 088 82 59 09709ANNs 0998 0113 1131 071 144 072 53 39 09877

Advances in Civil Engineering 11

0

30

60

90

120

150

180

0 150 300 450 600 750 900 1050

V pre

d (k

N)

d (mm)

ANNGEPJSCE 97

NLRACI 440CSA S806

0

20

40

60

80

100

120

0 10 20 30 40 50 60 70 80 90 100 110

V pre

d (k

N)

fcprime (MPa)

ANNGEPJSCE 97

NLRACI 440SCA S806

0

20

40

60

80

100

120

0 001 002 003 004 005

V pre

d (k

N)

ρf

ANNGEPJSCE 97

NLRACI 440CSA S806

0

20

40

60

80

100

120

0 25 50 75 100 125 150 175

V pre

d (k

N)

Ef (MPa)

ANNGEPJSCE 97

NLRACI 440CSA S806

0

20

40

60

80

100

120

0 2 4 6 8 10

V pre

d (k

N)

ad

ANNGEPJSCE 97

NLRACI 440CSA S806

0

60

120

180

240

300

360

0 200 400 600 800 1000 1200

V pre

d (k

N)

b (mm)

ANNGEPJSCE 97

NLRACI 440CSA S806

Figure 8 Eect of the parameters (d fcprime ρf Ef ad and bw) on shear capacity predicted by ANNs GEP NLR and three design codes(ACI1R 440-06 JSCE-97 and CSA S806-12)

12 Advances in Civil Engineering

the relationship between normalized shear strength as(Vpredbwd

fcprime1113969

) and beam depth It is clear that the nor-malized shear strength is decreased with the increase in thebeam depth for ANNs GEP and NLR showing that the sizeeffect is efficiently presented in these models -e trends ofGEP and NLR are very close and compatible and decreasedfrom a depth of 100mm to 1000mm while the ANNsmodelseems to be more accurate as it shows an increase in thetrend up to the depth of 200mm and then it decreasedsimilarly to that of GEP and NLR after that the trend startsto increase slightly

It can be summed up to that the artificial intelligentmodels due to their efficiency and powerful ability in rec-ognizing the parameters interaction demonstrate variousrates of change and fluctuation for the entire scope of inputparameters -e ANNs and GEP models define accurately theinteraction of each parameter on shear strength predictionand have a great ability to represent the actual response ofeach parameter in spite of its complexity and fluctuationnature Furthermore these models are evolved by trainingnumerous preliminary linear and nonlinear models withoutany prior assumption regarding the shape and structure of themathematical model

9 Conclusions

An experimental database including 269 shear test results ofFRP-reinforced concrete members without stirrups availablein the literature was established to propose three predictionmodels to estimate the shear capacity of FRP-RC membersusing three powerful tools which are ANNs GEP and NLR-e following conclusions can be drawn from this study

(i) -e proposed models for predicting the shear ca-pacity of FRP-RC members based on ANNs andGEP techniques showed excellent performancegreat efficiency and high level of accuracy andyielded consistent results throughout a wide rangeof influencing parameters moreover the ANNsmodel is more superior than the GEP as the SD andR2 for ANNs are 0113 and 09877 and for GEP are0162 and 097 respectively

(ii) A simple rational and yet accurate empiricalequation was proposed for predicting shearstrength of FRP-RC members by NLR -e equa-tion considers all the important influencing pa-rameters and simplified to be easy for use Inaddition it gives consistent and accurate resultswith SD and R2 of 0173 and 095 respectively

(iii) -rough a comparative statistical analysis for theproposed models with seven shear design codes andsix proposed equations from the literature it hasbeen found that the most accurate and efficientmodels are ANNs and GEP and to a lower dgreeNLR Among the codes and available proposals theCSA S806-12 and Ashour and Kara [20] equationswere appearing to be more accurate than the others

(iv) From a parametric study considering all the influ-encing parameters on shear capacity it was found thatthe ANNs model and to a lower level GEP modeldefines accurately the interaction of each parameteron shear capacity prediction and has a great ability torepresent the actual response of each parameter inspite of its complexity and fluctuation nature

(v) -e ANNs and GEP models demonstrate that theeffect of flexure reinforcement ratio on shear ca-pacity decreased beyond 003 as a real response tothe available few data in this range therefore morestudies are needed to confirm this case

(vi) -e ANNs model demonstrated that the effect ofad does not absolutely reduce the shear capacitywhile beyond the ad value of 5 its effect couldbecome reverse and contribute to increase in theshear capacity as confirmed by few previous studies

(vii) -e size effect is considered properly by the pro-posed models particularly the ANNs model whichyields more accurate shear capacity prediction tothe experimental results

Data Availability

-e (database of shear strength of beams without stirrups)data used to support the findings of this study are includedwithin the article

Conflicts of Interest

-e authors declare that they have no conflicts of interest

0

004

008

012

016

02

024

0 200 400 600 800 1000 1200

ANNNLRGEP

d (mm)

V pre

db wd

fc

Figure 9 Normalized shear strength (Vpredbwd

fcprime1113969

) versus beamdepth

Advances in Civil Engineering 13

References

[1] M S Alam and A Hussein ldquoSize effect on shear strength ofFRP reinforced concrete beams without stirrupsrdquo Journal ofComposites for Construction vol 17 no 4 pp 507ndash516 2013

[2] J R Yost S P Gross and D W Dinehart ldquoShear strength ofnormal strength concrete beams reinforced with deformedGFRP barsrdquo Journal of Composites for Construction vol 5no 4 pp 268ndash275 2001

[3] A G Razaqpur B O Isgor S Greenaway and A SelleyldquoConcrete contribution to the shear resistance of fiber rein-forced polymer reinforced concrete membersrdquo Journal ofComposites for Construction vol 8 no 5 pp 452ndash460 2004

[4] M Nehdi H El Chabib and A A Saıd ldquoProposed sheardesign equations for FRP-reinforced concrete beams based ongenetic algorithms approachrdquo Journal of Materials in CivilEngineering vol 19 no 12 pp 1033ndash1042 2007

[5] ASCE-ACI445 ldquoRecent approaches to shear design ofstructural concreterdquo Journal of Structural Engineeringvol 124 no 12 pp 1375ndash1417 1998

[6] R Park and T Paulay Reinforced Concrete Structures JohnWiley amp Sons Hoboken NJ USA 1975

[7] I F Kara ldquoPrediction of shear strength of FRP-reinforcedconcrete beams without stirrups based on genetic pro-grammingrdquo Advances in Engineering Software vol 42 no 6pp 295ndash304 2011

[8] R Bashir and A Ashour ldquoNeural networkmodelling for shearstrength of concrete members reinforced with FRP barsrdquoComposites Part B Engineering vol 43 no 8 pp 3198ndash32072012

[9] K Nasrollahzadeh and M M Basiri ldquoPrediction of shearstrength of FRP reinforced concrete beams using fuzzy in-ference systemrdquo Expert Systems with Applications vol 41no 4 pp 1006ndash1020 2014

[10] S Lee and C Lee ldquoPrediction of shear strength of FRP-reinforced concrete flexural members without stirrups usingartificial neural networksrdquo Engineering Structures vol 61pp 99ndash112 2014

[11] E M Golafshani and A Ashour ldquoA feasibility study of BBPfor predicting shear capacity of FRP reinforced concretebeams without stirrupsrdquo Advances in Engineering Softwarevol 97 pp 29ndash39 2016

[12] ACI-440 Guide for the Design and Construction of StructuralConcrete Reinforced with Fiber-Reinforced Polymer (FRP)ACI 440 1R-15 American Concrete Institute FarmingtonsHills MI USA 2015

[13] JSCE ldquoRecommendation for design and construction ofconcrete structures using continuous fiber reinforcing ma-terialsrdquo in Concrete Engineering Series 23 A Machida EdJapan Society of Civil Engineers Tokyo Japan 1997

[14] BISE Interim Guidance on the Design of Reinforced ConcreteStructures Using Fiber Composite Reinforcement British In-stitution of Structural Engineers Seto Ltd London UK1999

[15] CSA Canadian Highway Bridge Design Code SupplementNo 1 to CANCSA S6-06 (S61S1-10) Canadian StandardsAssociation (CSA) Mississauga ON Canada 2010

[16] ISIS Reinforced Concrete Structures with Fibre ReinforcedPolymersmdashDesign Manual No 3 University of Manitoba ISISCanada Corporation Winnipeg MB Canada 2007

[17] CNR-DT203 ldquoGuide for the design and construction ofconcrete structures reinforced with fiber-reinforced polymerbarsrdquo inAdvisory Committee on Technical Recommendations

for Construction CNR-DT 2032006 CNR Rome Italy2007

[18] CSA ldquoCode for the design and construction of buildingstructures with fibre-reinforced polymersrdquo in CANCSAS806-12 p 198 Canadian Standard Association TorontoON Canada 2012

[19] A Razaqpur and S Spadea ldquoResistenza a taglio di elementi dicalcestruzzzo reinforzatti e staffe di FRPrdquo in Proceedings ofAIAS Maratea Italy September 2010

[20] A F Ashour and I F Kara ldquoSize effect on shear strength ofFRP reinforced concrete beamsrdquo Composites Part B Engi-neering vol 60 pp 612ndash620 2014

[21] A R Yousif ldquoShear strength of large FRP-reinforced concretebeams without shear reinforcementrdquo Journal of Pure andApplied Sciences vol 27 pp 9ndash28 2015

[22] A K El-Sayed E F El-Salakawy and B Benmokrane ldquoShearcapacity of high-strength concrete beams reinforced with FRPbarsrdquo ACI Structural Journal vol 103 p 383 2006

[23] A G Razaqpur and O B Isgor ldquoProposed shear designmethod for FRP-reinforced concrete members without stir-rupsrdquo ACI Structural Journal vol 103 p 93 2006

[24] K Maruyama andW Zhao ldquoFlexural and shear behaviour ofconcrete beams reinforced with FRP rodsrdquo in Proceedings ofthe International Conference on Corrosion and CorrosionProtection of Steel in Concrete pp 24ndash28 Sheffield UK1994

[25] W Zhao K Maruyama and H Suzuki ldquoShear behavior ofconcrete beams reinforced by FRP rods as longitudinal andshear reinforcementrdquo in Proceedings of the Second In-ternational RILEM Symposium on Non-Metallic (FRP) Re-inforcement for Concrete Structures p 352 Ghent BelgiumAugust 1995

[26] H Nakamura and T Higai ldquoEvaluation of shear strength ofthe concrete beams reinforced with FRPrdquo in Proceedings ofJapan Society of Civil Engineers p 89 Ghent Belgium 1995

[27] K Maruyama and W Zhao ldquoSize effect in shear behavior ofFRP reinforced concrete beamrdquo in Advanced CompositeMaterials in Bridges and Structures pp 227ndash234 CanadianSociety for Civil Engineering Montreal QC Canada 1996

[28] Y Mizukawa Y Sato T Ueda and Y Kakuta ldquoA studyon shear fatigue behavior of concrete beams with FRP rodsrdquoin Proceedings of the Cird International Symposium onNon-Metallic (FRP) Reinforcement for Concrete Structures(FRPRCS-3) pp 309ndash316 Japan Concrete Institute SapporoJapan 1997

[29] N Duranovic K Pilakoutas and P Waldron ldquoTests onconcrete beams reinforced with glass fibre reinforced plasticbarsrdquo in Proceedings of the Cird International Symposium onNon-Metallic (FRP) Reinforcement for Concrete Structures(FRPRCS-3) pp 479ndash486 Sapporo Japan 1997

[30] N Swamy and M Aburawi ldquoStructural implications of usingGFRP bars as concrete reinforcementrdquo in Proceedings of 3rdInternational Symposium FRPRCS pp 503ndash510 SapporoJapan 1997

[31] C R Michaluk S H Rizkalla G Tadros and B BenmokraneldquoFlexural behavior of one-way concrete slabs reinforced byfiber reinforced plastic reinforcementsrdquo ACI StructuralJournal vol 95 pp 353ndash365 1998

[32] D Deitz I Harik and H Gesund ldquoOne-way slabs reinforcedwith glass fiber reinforced polymer reinforcing barsrdquo SpecialPublication vol 188 pp 279ndash286 1999

[33] T Alkhrdaji M Wideman A Belarbi and A Nanni ldquoShearstrength of GFRP RC beams and slabsrdquo in Proceedings of the

14 Advances in Civil Engineering

International Conference Composites in Construction-CCCpp 409ndash414 Porto Portugal 2001

[34] G S Melo and J A Rayol ldquoShear resistance of GFRPreinforced concrete beamsrdquo in Proceedings of the Rehabil-itating and Repairing the Buildings and Bridges of AmericasHemispheric Workshop on Future Directions Mayaguumlez PRUSA pp 47ndash64 2002

[35] A K Tureyen and R J Frosch ldquoShear tests of FRP-reinforcedconcrete beams without stirrupsrdquo ACI Structural Journalvol 99 pp 427ndash434 2002

[36] S P Gross J R Yost D W Dinehart E Svensen and N LiuldquoShear strength of normal and high strength concrete beamsreinforced with GFRP barsrdquo in Proceedings of InternationalConference on High Performance Materials in Bridgespp 426ndash437 ASCE Reston VA USA 2003

[37] M Tariq and J Newhook ldquoShear testing of FRP reinforcedconcrete without transverse reinforcementrdquo in Proceedings ofAnnual Conference of the Canadian Society for Civil Engi-neering pp 1330ndash1339 Moncton NB Canada June 2003

[38] S Gross D Dinehart J Yost and P -eisz ldquoExperimentaltests of high-strength concrete beams reinforced with CFRPbarsrdquo in Proceedings of the 4th International Conference onAdvanced Composite Materials in Bridges and Structures(ACMBS-4) Calgary AB Canada 2004

[39] A Lubell T Sherwood E Bentz and M P Collins ldquoSafe sheardesign of large wide beams adding shear reinforcement isrecommendedrdquoConcrete International vol 26 pp 66ndash78 2004

[40] J Yost S Gross G Masone and P Hamelin ldquoSustained loadeffects on deflection and ultimate strength of concrete beamsreinforced with GFRPrdquo in Proceedings of the InternationalConference Composites in Construction (CCC2005) LyonFrance July 2005

[41] A El-Sayed E El-Salakawy and B Benmokrane ldquoShearstrength of one-way concrete slabs reinforced with fiber-reinforced polymer composite barsrdquo Journal of Compositesfor Construction vol 9 no 2 pp 147ndash157 2005

[42] A E Kilpatrick and L Easden ldquoShear capacity of GFRPreinforced high strength concrete slabsrdquo in Proceedings of the18th Australasian Conference on the Mechanics of Structuresand Materials Perth Australia vol 1 pp 119ndash124 Taylor ampFrancis London UK 2005

[43] A K El-Sayed E F El-Salakawy and B BenmokraneldquoShear strength of FRP-reinforced concrete beams withouttransverse reinforcementrdquo ACI Structural Journal vol 103p 235 2006

[44] A Ashour ldquoFlexural and shear capacities of concrete beamsreinforced with GFRP barsrdquo Construction and BuildingMaterials vol 20 no 10 pp 1005ndash1015 2006

[45] M Guadagnini K Pilakoutas and P Waldron ldquoShear re-sistance of FRP RC beams experimental studyrdquo Journal ofComposites for Construction vol 10 no 6 pp 464ndash473 2006

[46] R Dawborn and A Kilpatrick Flexural Shear Capacity ofHigh Strength Concrete Slabs Reinforced with LongitudinalGFRP Bars 2006

[47] J Niewels ldquoZum Tragverhalten von Betonbauteilen mitFaserverbundkunststoffbewehrungrdquo Rheinisch-WestfalischeTechnische Hochschule Aachen Lehrstuhl und Institut furMassivbau Dissertation 2008

[48] A El-Sayed K Soudki and E Kling ldquoFlexural behaviour ofself-consolidating concrete slabs reinforced with GFRP barsrdquoin Proceedings of the 9th International Symposium on FiberReinforced Polymer Reinforcement for Reinforced ConcreteStructures pp 13ndash15 Sydney NSW Australia 2009

[49] A Caporale and R Luciano ldquoIndagine sperimentale enumerica sulla resistenza a taglio di travi di calcestruzzoarmate con barre di GFRPrdquo in Proceedings of XXXVIIIConvegno Nazionale AIAS Turin Italy September 2009

[50] R Olivito and F Zuccarello ldquoOn the shear behaviour ofconcrete beams reinforced by carbon fibre-reinforced poly-mer bars an experimental investigation by means of acousticemission techniquerdquo Strain vol 46 no 5 pp 470ndash481 2010

[51] E C Bentz L Massam and M P Collins ldquoShear strength oflarge concrete members with FRP reinforcementrdquo Journal ofComposites for Construction vol 14 no 6 pp 637ndash646 2010

[52] A G Razaqpur M Shedid and B Isgor ldquoShear strength offiber-reinforced polymer reinforced concrete beams subject tounsymmetric loadingrdquo Journal of Composites for Construc-tion vol 15 no 4 pp 500ndash512 2011

[53] M Alam and A Hussein ldquoEffect of member depth on shearstrength of high-strength fiber-reinforced polymerndashreinforced concrete beamsrdquo Journal of Composites for Con-struction vol 16 no 2 pp 119ndash126 2012

[54] F Matta A K El-Sayed A Nanni and B Benmokrane ldquoSizeeffect on concrete shear strength in beams reinforced withfiber-reinforced polymer barsrdquo ACI Structural Journalvol 110-S50 pp 617ndash628 2013

[55] B Abdul-Salam A Farghaly and B Benmokrane ldquoEvalua-tion of shear behavior for one-way concrete slabs reinforcedwith carbon-FRP barsrdquo GEN vol 243 p 1 2013

[56] C H Kim and H S Jang ldquoConcrete shear strength of normaland lightweight concrete beams reinforced with FRP barsrdquoJournal of Composites for Construction vol 18 no 2 article04013038 2014

[57] D Tomlinson and A Fam ldquoPerformance of concrete beamsreinforced with basalt FRP for flexure and shearrdquo Journal ofComposites for Construction vol 19 no 2 article 040140362014

[58] M A Issa T Ovitigala and M Ibrahim ldquoShear behavior ofbasalt fiber reinforced concrete beams with and without basaltFRP stirrupsrdquo Journal of Composites for Construction vol 20no 4 article 04015083 2015

[59] A El Refai and F Abed ldquoConcrete contribution to shearstrength of beams reinforced with basalt fiber-reinforcedbarsrdquo Journal of Composites for Construction vol 20 no 4article 04015082 2015

[60] G B Jumaa and A R Yuosif ldquoSize effect in shear failure ofhigh strength concrete beams without stirrups reinforcedwith basalt FRP barsrdquo KSCE Journal of Civil Engineering2018 In press

[61] M T Hagan H B Demuth and M H BealeNeural NetworkDesign (Electrical Engineering) -omson Learning BostonMA USA 1995

[62] S S Haykin S S Haykin S S Haykin and S S HaykinNeural Networks and Learning Machines Pearson Vol 3Pearson Upper Saddle River NJ USA 2009

[63] M Y Mansour M Dicleli J-Y Lee and J Zhang ldquoPredictingthe shear strength of reinforced concrete beams using artificialneural networksrdquo Engineering Structures vol 26 no 6pp 781ndash799 2004

[64] H Demuth M Beale and M Hagan Neural NetworkToolboxtrade 6 Userrsquos Guide -e MathWorks Inc vol 10 p 11Natick MA USA 2008

[65] A W Oreta and K Kawashima ldquoNeural network modeling ofconfined compressive strength and strain of circular concretecolumnsrdquo Journal of Structural Engineering vol 129 no 4pp 554ndash561 2003

Advances in Civil Engineering 15

[66] S Jung and K S Kim ldquoKnowledge-based predictionof shear strength of concrete beams without shear re-inforcementrdquo Engineering Structures vol 30 no 6pp 1515ndash1525 2008

[67] Z-H Duan S-C Kou and C-S Poon ldquoPrediction ofcompressive strength of recycled aggregate concrete usingartificial neural networksrdquo Construction and Building Mate-rials vol 40 pp 1200ndash1206 2013

[68] H El-Chabib M Nehdi and A Said ldquoPredicting shear ca-pacity of NSC and HSC slender beams without stirrups usingartificial intelligencerdquo Computers and Concrete vol 2 no 1pp 79ndash96 2005

[69] F Altun O Kisi and K Aydin ldquoPredicting the compressivestrength of steel fiber added lightweight concrete using neuralnetworkrdquo Computational Materials Science vol 42 no 2pp 259ndash265 2008

[70] J R Koza ldquoGenetic programming as a means for pro-gramming computers by natural selectionrdquo Statistics andComputing vol 4 no 2 pp 87ndash112 1994

[71] C Ferreira ldquoGene expression programming in problemsolvingrdquo in Soft Computing and Industry pp 635ndash653Springer Berlin Germany 2002

[72] C Kayadelen ldquoSoil liquefaction modeling by genetic ex-pression programming and neuro-fuzzyrdquo Expert Systems withApplications vol 38 no 4 pp 4080ndash4087 2011

[73] A H Gandomi A H Alavi and G J Yun ldquoFormulation ofuplift capacity of suction caissons using multi expressionprogrammingrdquo KSCE Journal of Civil Engineering vol 15no 2 pp 363ndash373 2011

[74] A H Gandomi A H Alavi and C RyanHandbook of GeneticProgramming Applications Springer Berlin Germany 2015

[75] A H Gandomi and A H Alavi ldquoA new multi-gene geneticprogramming approach to non-linear system modeling PartII geotechnical and earthquake engineering problemsrdquoNeural Computing and Applications vol 21 no 1 pp 189ndash201 2012

[76] A H Alavi and A H Gandomi ldquoEnergy-based numericalmodels for assessment of soil liquefactionrdquo GeoscienceFrontiers vol 3 no 4 pp 541ndash555 2012

[77] L Teodorescu and D Sherwood ldquoHigh energy physics eventselection with gene expression programmingrdquo ComputerPhysics Communications vol 178 no 6 pp 409ndash419 2008

[78] GEPSOFT GeneXproTools Version 50 GEPSOFT BristolUK 2013 httpwwwgepsoftcom

[79] S M Mousavi P Aminian A H Gandomi A H Alavi andH Bolandi ldquoA new predictive model for compressive strengthof HPC using gene expression programmingrdquo Advances inEngineering Software vol 45 no 1 pp 105ndash114 2012

[80] M Sarıdemir ldquoEmpirical modeling of splitting tensilestrength from cylinder compressive strength of concrete bygenetic programmingrdquo Expert Systems with Applicationsvol 38 no 11 pp 14257ndash14268 2011

[81] M Sonebi and A Cevik ldquoGenetic programming based for-mulation for fresh and hardened properties of self-compacting concrete containing pulverised fuel ashrdquo Con-struction and Building Materials vol 23 no 7 pp 2614ndash26222009

[82] A H Alavi P Aminian A H Gandomi and M A EsmaeilildquoGenetic-based modeling of uplift capacity of suction cais-sonsrdquo Expert Systems with Applications vol 38 no 10pp 12608ndash12618 2011

[83] T Zsutty ldquoShear strength prediction for separate catagories ofsimple beam testsrdquo ACI Journal Proceedings vol 68 no 2pp 138ndash143 1971

16 Advances in Civil Engineering

bias of the input layer as in Equation (1) and then the resultspassed into the hidden layer neurons Inside neurons theprocess of sigmoid transformed function was performed byusing one of the transformed functions such as that inEquation (2) Another linear process using the purelinfunction was carried out by summing the weighted outputfrom the hidden layer neurons with the bias of the hiddenlayer as in Equation (3)

netj sumn

i1wijxi + biasj (1)

yj f netj( ) 1

1 + expminus netj( )( ) (2)

yk purelin summ

j1wjkyj + biask (3)

where netj is the weighted sum generated at the jthhidden neuron xi is the input value from the ith inputneuron wij and wjk are the weights added to the hiddenlayer and the output layer neurons respectively biasjand biask are the biases added to the hidden layer and theoutput layer neurons respectively yj is the processedoutput from the jth hidden neuron yk is the processedoutput from the kth output neuron and n is the numberof input neurons and m is the number of neurons in thehidden layer

43 BPNNs Model Used for the Prediction of Shear CapacityIn this study the BPNNs were utilized to produce a pre-dictive model for shear strength of FRP-reinforced concretemembers without stirrups e key parameters aectingthe shear strength which considered in this study are fcprime dbw ad ρf and Ef e most important issue in BPNNsmodeling is selecting the number of hidden layers and thenumber of neurons in each hidden layer which depend onseveral factors like type of problem of interest the associ-ation of input parameters with the output pattern size ofinstances number of input parameters and number ofoutputs However there is no basic acknowledged criteriato pick the number of hidden layers and the number of

neurons therefore a trial and error method was achievedbased on training and testing up to obtain a reasonable tConsequently a BPNNs training algorithm was utilized ina feed-forward network trained using nonlinear hyperboliclog-sigmoid transfer function in the hidden layer anda linear purelin transfer function in the output layer as inEquations (1)ndash(3)

e trial and error procedure resulted in that the besttting model was that obtained using thirteen neurons ina single hidden layer (6-13-1) as demonstrated in Figure 2e predictive model was trained through numerous iter-ations to nd the best epoch value momentum rate andlearning rate which give the optimum model for shearstrength prediction e data were divided arbitrarily intoldquotrainingrdquo 70 ldquovalidatingrdquo 15 and ldquotestingrdquo 15 and thepartitioning of data was chosen based on the results of modelperformance after numerous trials

It is recommended by many authors [11 63 68 69]to normalize the input and output data before using them topredict the model In this study the data of input and targetwere scaled by the linear normalization function in the rangeof (0 to 1) as shown in the following equation

xn 06xminus xmin

xmin minus xmax+ 02 (4)

where x is the data sample xn is the normalized data samplexmin and xmax is the minimum and maximum values of thedata for the interested parameter

e input layer weights (ILWs) the input layer biases(ILBs) the hidden layer weights (HLWs) and the hiddenlayer bias (HLB) of the (6-13-1) predictive BPNNsmodel areshown below

sum

sum

sumXi

Input layer Hidden layer Output layer

W11ij

W11jk

y1j

W12jk

W12ij

netj1

net2j

biasj1

bias2j

biask

netk yk

y2j

yj = logsig(WijXi + biasj) yk = purlin(Wjkyj + biask)

Figure 1 Typical architecture and log-sigmoid function of (1-2-1)BPNNs

1

2

3

4

5

6

1

2

3

4

5

6

7

8

9

10

11

12

13

fcprime

d

b

ad

ρf

Ef

1Vpred

[HLW][ILW] [ILB] [HLB]

Output layer

Input layer

Hidden layer

Figure 2 Architecture of BPNNs used for the prediction of theshear strength

Advances in Civil Engineering 5

ILW

minus23567 027166 14696 minus14038 099307 22234

23842 minus22831 083159 22855 14806 minus083455

28211 075441 minus4086 14427 17982 minus10877

059955 minus074937 20882 minus26609 18418 minus15433

14527 minus17869 minus10477 16872 minus081981 minus25634

35416 minus19591 minus034353 10741 minus15276 22139

15643 minus28231 26211 minus16244 10879 17129

22825 minus040079 048425 minus2312 007062 015858

minus1749 minus025004 minus045657 minus22347 minus10796 minus10232

minus078404 266 minus28673 minus10803 minus086988 minus16247

minus025678 minus32562 22726 16206 minus12616 26619

minus12662 minus078168 minus052983 minus25791 10124 23284

minus23043 055942 minus12328 minus28413 minus13658 26415

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

⎫⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎬

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎭

ILB

51888

minus14396

minus21773

minus24823

minus16444

minus008813

012198

22041

minus2362

minus19906

minus052466

minus37706

minus26641

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

⎫⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎬

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎭

HLW ⎧⎨

⎩ minus07663 12834 minus09729 minus066761 minus03835 minus087847 12312 13464 minus13058 1206 1169 minus09465 minus06511⎫⎬

⎭

HLB minus044036

(5)

5 Genetic Programming

51 General Background Genetic programming (GP) isa naturally inspired machine learning (evolutionary) tech-nique utilized for randomly reproducing a population ofcomputer programs in light of Darwinrsquos advancement hy-pothesis GP which was developed by Koza [70] can beregarded as a developed form of the genetic algorithm (GA)which is an evolutionary optimization tool that depends onthe principles of genetics and normal determination -esystems of GA incorporate altering and changing the extentof chromosomes by genetic operators to solve functionoptimization problems -e fundamental contrast amongst

GA and GP is that the solution of GA is a binary string offixed length utilized for parameters optimization of a specificarrangement of model parameters while the solution of GPis a development program represented as a subset of parsetrees which use input variables and corresponding outputsfor generating optimized models [71ndash73]

-e GP techniques for modeling incorporate productionof an initial population of chromosomes (models) whichinclude an arrangement of functions and an arrangement ofterminals that selected and arranged randomly in the form ofthe parse tree (computer model) -e models composed ofa root node functional nodes and terminals as shown inFigure 3

6 Advances in Civil Engineering

At that point the produced population models areassessed and the tness of the models is evaluated using theprovided data of the particular problem After that othergenerations of models are produced by primary genetic op-erators reproduction crossover and mutation as shown inFigure 4e evolutionary procedure of assessing the tness ofthe present population and producing new population iscontinued until the point when an end termination criterion isapproached which can be either a particular acceptable erroror a specied maximum number of generations e modelwith the best solution which developed after each generationassigns the outcome of the GP program [76]

52 Gene Expression Programming e most widely usedGP in civil engineering problems is gene expressionprogramming (GEP) which was developed by Ferreira[71] GEP utilizes development of numerical conditionsthat is encoded linearly in chromosomes of a consistentlength and considered nonlinearly as expression trees(ETs) with various shapes and sizes e chromosomes arecomposed of several genes each gene contains a smallersubprogram or subexpression trees (Sub-ETs) Every genehas a consistent length and comprises a head and a tail eschematic of the GEP centowchart is shown in Figure 5 eimplementation of GEP predictive modeling incorporatesve main components including function set terminal settness function control parameters and terminationcondition [7 75]

e preferred quality of GEP is that the genetic operatorswork at the chromosome level and the production of geneticdiversity is to a great degree simplied Another favorableposition is credited to the remarkable multigenetic nature ofGEP which permits the advancement of all the more capablemodels made out of a few subprograms [71]

53 GEPModel for Predicting Shear Capacity For predictingthe shear strength of FRP-reinforced concrete beamswithout stirrups by GEP-based formulation six incentuencingparameters were consideredfcprime d b adEf and ρf throughtraining and testing the experimental results e data areevaluated on the GeneXproTools 5 [78] to develop theempirical model which is the most widely used software for

GEP model prediction Similar to the ANNs model the dataare partitioned randomly to 70 for training and remaining30 for testing such that both portions of data have balancedstatistical parameters like mean standard deviation andmax and min values

To obtain the best GEP prediction model many modelswith a dierent number of genes were evolved throughouta set of genetic operators (mutation transposition andcrossover) Initially a model composed of two genes withmultiplication linking functions and head sizes of three wasselected and evolved many times en the model param-eters were changed step by step through increasing thenumber of genes head size number of chromosomes andweights of function sets e program was evolved nu-merous times for various models and the outcome modelswere monitored and compared to evaluate their perfor-mance Other parameters like mutation rate inversion andpoints of recombination were chosen based on previousworks [7 79ndash82] and then evaluated to get their optimumeects After many trials the nal mathematical model waschosen for which the utilized parameters tness functionand function sets are given in Table 3 e nal model wasselected based on criteria of the best tness and less com-plicity of mathematical formulation the expression trees areshown in Figure 6 and themathematical formulation is givenin the following equation

sqrt

x1 x2 x34

ndash +

Functional nodes

Terminal nodes

Root node

Figure 3 Typical example of a GP tree representation model((4minusx1)(x2 + x3))

12 [74]

radicradic

+

+

+

1 3

+

+

+

times

times

2

2

Log

Crossover

Mutation

Log

Log Log

a

a

c

c d

d d

d

bb

Figure 4 Typical operations of crossover and mutation in GP [75]

Advances in Civil Engineering 7

Vc absc3 + d5 lowastd3( ) d2 + d0( )2

4( )

13

lowast tanhd2d1( )

15 minus tanh d2 lowast d3( )4( )

5

lowast d2 +d153

max d1 c6( )c8 + d4( )( )

2

lowast tanhd2d1( )

15 minus

d1d0

radic

3

5

(6)

where d0 d1 d2 d3 d4 and d5 refer to d ad bρf fcprime and Ef respectively c2 656723946184092 c3 minus241413053630399 c4 minus121479701959083 c6 307014791103389 and c8 220241396443835

6 Nonlinear Regression Model (NLR)

Regression analysis is considered as an important toolthat can be used in the modeling process for solvingcomplicated problems of various engineering disciplines

However the proposed models based on nonlinear re-gression (NLR) are less accurate than the ANN and GEPhowever it is characterized by that it is simple and easy forapplication without the need of computers for calculationsA nonlinear regression model based on the experimentaldatabase collected from the literature was suggested eproposed equation was derived based on developinga model similar to that proposed by Zsutty [83] which is themost accurate and simple empirical equation that wasproposed for shear prediction of steel-RC members Inorder to predict the shear strength of FRP-RC beams moreaccurately considering the eect of all incentuencing pa-rameters the experimental shear strength was analyzedwith most common incentuencing parameters fcprime d b adEf and ρf Based on data tting analysis and after somesimplication the following equation was proposed

Vc 0321d( )

13 Efρfad( )

25fcprime( )15bwd (7)

It can be observed that the equation is simple rationaland more generalized than most codes and proposedequations from the literature as it considers the eect of allthe incentuencing parameters on the shear strength of FRP-RCmembers without stirrups

7 Results and Discussion

e shear strength results of FRP-reinforced concretemembers for the three proposed models the ANNs GEPand NLR are evaluated and compared with the commondesign provisions (ACI 440-15 JSCE-97 CSA 806-12) andseven proposed equations [1 4 7 10 19ndash21] e com-parison was examined based on statistical terms such as

Start

Initial population creation

Chromosome expression as ET

ET execution

Fitness evaluation

Stop

Chromosome selection

Reproduction

Terminate

New generation creation

Yes

No

Figure 5 Flowchart of GEP [77]

Table 3 Parameters used in the GEP Model

Parameters ValuesNumber of chromosomes 30ndash500Head size 3 5 8Number of genes 2 3 4Linking function Multiplication

Function set + minus lowast abs tanh x2 x12 x13 x15

Generation withoutchanges 2000

Number of tries 12Maximum complexity 10Fitness function RMSEMutation 0044Inversion 01One-pointrecombination 03

Two-pointrecombination 03

Gene recombination 01Gene transposition 01IS transposition 01RIS transposition 01Data type Floating pointConstants per gene 10

8 Advances in Civil Engineering

mean standard deviation (SD) and coelaquocient of variation(COV) in addition to error values such as mean absoluteerror (MAE) root mean square error (RMSE) and R2 asshown below

RMSE

sumN

i0 ei minuspi( )2

N

radic

MAE 1NsumN

i0ei minuspi∣∣∣∣

∣∣∣∣

R2 1minussumN

i0 ei minuspi( )2

sumN

i0 ei minus e( )2

(8)

where ei and pi are the experimental and predicted shearforce in kN respectively e is the average of the experimentalvalues andN is the total number of the considered samplese model that minimized the error values (MAE andRMSE) and maximized R2 is selected as the optimummodel

Figure 7 presents the scatter of the experimental shearforce Vexp versus the predicted shear strength Vpred for theproposed models codes and proposed equations from theliterature It is clear that the best models for predicting theshear strength are those suggested in this study which ina sequence are ANNs GEP and NLR as these modelspredict the shear strength very accurately with the optimumstatistical performance of R2 RMSE and MAE High cor-relation coelaquocients with low error rates indicate that theproposed three models are excellent models and exhibitgeneralization performance in predicting shear strength ofFRP-reinforced concrete beams without stirrups In con-trast the code design provisions and other proposedequations from the literature yielded dispersion results with

lower R2 and larger error rates as given in the scatterrelationships

Table 4 presents the statistical parameters (meanstandard deviation (SD) coelaquocient of variation (COV)minimum maximum range RMSE MAE and R2) of theratio of experimental shear strength to the predicted shearstrength VexpVpred for the proposed models in thisstudy seven well-known codes and seven proposedequations from literature based on the (269) collecteddatabase It is clear that the proposed equations yieldedsuperior accuracy between all the codes and proposedequation from the literature because their optimumstatistical parameters such as the mean SD range RMSEand R2 are 0998 0113 072 53 and 09877 respectivelyfor ANNs 1007 0162 088 82 and 0970 respectivelyfor GEP and 1003 0174 099 107 and 095 re-spectively for NLR

e ANNs and GEP models are articial intelligentmodels derived based on soft computing as veried abovethese models are accurate superior and highly elaquocient inpredicting the complicated problem such as shear strengthHowever the drawback of articial intelligent models is thatit cannot be calculated manually and it needs computers forcalculation Besides it is considered as a powerful and ef-cient tool which can be used in soft programs specializedfor analysis and design of reinforced concrete structures Onthe contrary the NLR model is simply accurate and rationalwhich can be used manually with sulaquocient accuracy morethan the design codes and previously proposed equationsNevertheless the regression equations cannot properlydene with the same level of elaquociency of articial intelligenttechniques the interactions between the input and outputparameters due to that the regression models usually areproduced based only on a few predened equations [79]

3Rt

c3 lowast

lowast

d0

d3d5

lowast Avg2 c2

c2 d0

Avg2

+

(a)

x5

lowast

ndash

5Rt

Tanh

x4

c4d3d2d1

Tanh

(b)

+

d2x2

+

d1d3

Max2d4

c6

c8

5Rt

lowast

(c)

x5

ndash

5Rt

x3

d0d1d2d1

Tanh

Sqrt

(d)

Figure 6 Expression trees ETs for the GEP model (a) Sub-ET 1 (b) Sub-ET 2 (c) Sub-ET 3 (d) Sub-ET 4

Advances in Civil Engineering 9

Finally it can be said that all the three proposed equationscan be considered as accurate efficient and useful modelswhich were trained on a largest collected database forpredicting the shear strength of FRP-reinforced concretemembers

8 Parametric Analyses

For further verification of the proposed ANNs GEP andNLR prediction models a parametric analysis was per-formed in this study -e main goal was to find the

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

ANNsR2 = 09877RMSE = 53MAE = 39

GEPR2 = 09709

RMSE = 82kNMAE = 59kN

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

ACI 440-06R2 = 0575

RMSE = 315MAE = 242

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

CSA 806-12R2 = 0783

RMSE = 225MAE = 117

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

R2 = 0805RMSE = 213MAE = 121

Nehdi et al (2007)

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

R2 = 0772RMSE = 231MAE = 144

Razaqpur and Spadea (2011)

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

R2 = 08347RMSE = 196MAE = 110

Kara (2011)

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

R2 = 0865RMSE = 177MAE = 109

Alam and Husein (2013)

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

R2 = 0885RMSE = 164MAE = 102

Ashour and Kara (2014)

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

R2 = 0902RMSE = 151MAE = 96

Lee (2014)

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

JSCE97R2 = 0792

RMSE = 220MAE = 149

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

NLR

Vexp (kN)

R2 = 0950RMSE = 107MAE = 73

Figure 7 Scatter of Vexp versus Vpred for ANN GEP NLR and different models from the literature

10 Advances in Civil Engineering

response of the three proposed models to predict the shearstrength for a set of input parameters which are selectedtaking into account the average value of each parame-ter in the collected database For further showing theperformance of the proposed models and for comparisonpurpose the response of three well-known codes (ACI1R440-15 JSCE-97 and CSA S806-12) was also considered-e approach depends on keeping all input parameters attheir selected values except that in each time a singleparameter value was changed incrementally within theexpected practical values Consequently an arrangementof manufactured data for the single considered parameteris produced this procedure was repeated for all parametersso that all models are examined for the entire input pa-rameters -e selected input parameters are fcprime 46MPabw 200mm d 400mm ad 4 ρf 0011 and Ef

74 GPa It is worthy to note that the ANNs model cannotproperly predict the shear strength for input parametersoutside the range of training data therefore it is only validfor prediction within the range of input parameters of thetraining data [8]

Figure 8 indicates the tendency of the predicted shearstrength by differentmodels to the varieties of themain designparameters (d fcprime ρf Ef ad and bw) Generally it can beobserved that the proposed models particularly the ANNsmodel yielded larger shear capacities for all parameters whileACI 440-15 yielded the lowest shear capacities which indicatethat the ACI 440-15 is very conservative

-e relationship of beam depth with the predicted shearstrength showed that all the proposed models and codesincreased with the increase in the beam depth throughoutthe range of 100ndash1000mm -e ACI 440-15 considers theeffect of beam depth linearly while all other models rep-resent the effect of depth nonlinearly the ANNs GEP andNLR models consider the depth raised to a power of 083067 and 066 respectively Also it can be observed that theGEP and NLR yield almost the same results All the pro-posed models and codes showed an increase in shearstrength with the increase in the concrete compressive

strength but in different rates It was found that fcprime is raisedto a power of 066 030 and 02 for ANNs GEP and NLRrespectively

-e effect of the flexure reinforcement ratio on shearstrength indicates a similar trend of the NLR model and thedesign codes but the ANNs and GEP models showeda slightly decreased trend for reinforcement ratios greaterthan 003 this is not in agreement with codes and previousstudies because of that only few data were available with ρflarger than 003 and these data actually showed decreasingshear capacity Additionally these models were derivedbased only on the artificial technology of data trainingwithout manually choosing the general mathematical shapeof the model in contrary to the NLRmodel and design codeswhich was derived based on the theoretical or semiempiricalcriteria

-e shear strength also increased with the increase inthe elastic modulus of the flexure reinforcement ratio Itcan be observed that all models showed a similar trend linefor the entire range of data while the ANNs model showedan increased rate up to about 110 GPa and then the in-crease rate reduced significantly similar results also ob-tained by Bashir and Ashour [8] On the contrary thetrend lines of the shear span to depth ratio are decreasedfor GEP and NLR models for the entire range of datameanwhile for ANNs model it decreases up to ad of 5and then it started to increase slightly -is behavior is inagreement with the few available experimental results[32 52 56] which were studied as ad greater than 5However other codes do not consider the effect of ad asthe trend lines for ACI 440-15 and JSCE-97 are constantwhile the CSA S806 trend line remains constant beyondthe ad value of 5 Finally the effect of beam width on shearstrength is linear as indicated by trend lines for all modelsexcept the ANNs model which showed a lower increaserate beyond 700mm width

To investigate how the proposed models consider thesize effect on shear capacity the same parametric data usedfor studying the beam depth are used Figure 9 presents

Table 4 Statistical parameters of (VexpVpred) for the proposed models and different design equations

Design equations Mean (VexpVpred) SD COV Minimum Maximum Range RMSE MAE R2

[12] 1813 0416 2306 113 374 261 315 242 0575[13] 1302 0282 2163 046 251 205 220 149 0792[18] 1091 0227 2085 047 185 137 225 117 0783[16] 1193 0386 3249 044 248 203 2633 1758 0703[17] 0948 0265 2799 039 174 134 2257 1403 0782[14] 1072 0247 231 054 192 138 1470 980 0908[15] 1393 0254 1835 070 248 178 2456 1661 0742[4] 1113 0219 1967 055 192 136 213 121 0805[19] 1305 0235 1801 084 214 129 231 184 0772[7] 1025 0205 2003 054 191 136 196 110 0835[1] 1148 0227 1981 059 172 113 177 109 0865[20] 0965 0174 1806 063 168 105 164 102 0885[10] 1015 0229 2251 053 196 143 151 96 0905[21] 1096 0283 2587 056 212 156 1915 1180 0843NLR 1003 0174 1732 062 161 099 107 73 0950GEP 1007 0162 1608 066 155 088 82 59 09709ANNs 0998 0113 1131 071 144 072 53 39 09877

Advances in Civil Engineering 11

0

30

60

90

120

150

180

0 150 300 450 600 750 900 1050

V pre

d (k

N)

d (mm)

ANNGEPJSCE 97

NLRACI 440CSA S806

0

20

40

60

80

100

120

0 10 20 30 40 50 60 70 80 90 100 110

V pre

d (k

N)

fcprime (MPa)

ANNGEPJSCE 97

NLRACI 440SCA S806

0

20

40

60

80

100

120

0 001 002 003 004 005

V pre

d (k

N)

ρf

ANNGEPJSCE 97

NLRACI 440CSA S806

0

20

40

60

80

100

120

0 25 50 75 100 125 150 175

V pre

d (k

N)

Ef (MPa)

ANNGEPJSCE 97

NLRACI 440CSA S806

0

20

40

60

80

100

120

0 2 4 6 8 10

V pre

d (k

N)

ad

ANNGEPJSCE 97

NLRACI 440CSA S806

0

60

120

180

240

300

360

0 200 400 600 800 1000 1200

V pre

d (k

N)

b (mm)

ANNGEPJSCE 97

NLRACI 440CSA S806

Figure 8 Eect of the parameters (d fcprime ρf Ef ad and bw) on shear capacity predicted by ANNs GEP NLR and three design codes(ACI1R 440-06 JSCE-97 and CSA S806-12)

12 Advances in Civil Engineering

the relationship between normalized shear strength as(Vpredbwd

fcprime1113969

) and beam depth It is clear that the nor-malized shear strength is decreased with the increase in thebeam depth for ANNs GEP and NLR showing that the sizeeffect is efficiently presented in these models -e trends ofGEP and NLR are very close and compatible and decreasedfrom a depth of 100mm to 1000mm while the ANNsmodelseems to be more accurate as it shows an increase in thetrend up to the depth of 200mm and then it decreasedsimilarly to that of GEP and NLR after that the trend startsto increase slightly

It can be summed up to that the artificial intelligentmodels due to their efficiency and powerful ability in rec-ognizing the parameters interaction demonstrate variousrates of change and fluctuation for the entire scope of inputparameters -e ANNs and GEP models define accurately theinteraction of each parameter on shear strength predictionand have a great ability to represent the actual response ofeach parameter in spite of its complexity and fluctuationnature Furthermore these models are evolved by trainingnumerous preliminary linear and nonlinear models withoutany prior assumption regarding the shape and structure of themathematical model

9 Conclusions

An experimental database including 269 shear test results ofFRP-reinforced concrete members without stirrups availablein the literature was established to propose three predictionmodels to estimate the shear capacity of FRP-RC membersusing three powerful tools which are ANNs GEP and NLR-e following conclusions can be drawn from this study

(i) -e proposed models for predicting the shear ca-pacity of FRP-RC members based on ANNs andGEP techniques showed excellent performancegreat efficiency and high level of accuracy andyielded consistent results throughout a wide rangeof influencing parameters moreover the ANNsmodel is more superior than the GEP as the SD andR2 for ANNs are 0113 and 09877 and for GEP are0162 and 097 respectively

(ii) A simple rational and yet accurate empiricalequation was proposed for predicting shearstrength of FRP-RC members by NLR -e equa-tion considers all the important influencing pa-rameters and simplified to be easy for use Inaddition it gives consistent and accurate resultswith SD and R2 of 0173 and 095 respectively

(iii) -rough a comparative statistical analysis for theproposed models with seven shear design codes andsix proposed equations from the literature it hasbeen found that the most accurate and efficientmodels are ANNs and GEP and to a lower dgreeNLR Among the codes and available proposals theCSA S806-12 and Ashour and Kara [20] equationswere appearing to be more accurate than the others

(iv) From a parametric study considering all the influ-encing parameters on shear capacity it was found thatthe ANNs model and to a lower level GEP modeldefines accurately the interaction of each parameteron shear capacity prediction and has a great ability torepresent the actual response of each parameter inspite of its complexity and fluctuation nature

(v) -e ANNs and GEP models demonstrate that theeffect of flexure reinforcement ratio on shear ca-pacity decreased beyond 003 as a real response tothe available few data in this range therefore morestudies are needed to confirm this case

(vi) -e ANNs model demonstrated that the effect ofad does not absolutely reduce the shear capacitywhile beyond the ad value of 5 its effect couldbecome reverse and contribute to increase in theshear capacity as confirmed by few previous studies

(vii) -e size effect is considered properly by the pro-posed models particularly the ANNs model whichyields more accurate shear capacity prediction tothe experimental results

Data Availability

-e (database of shear strength of beams without stirrups)data used to support the findings of this study are includedwithin the article

Conflicts of Interest

-e authors declare that they have no conflicts of interest

0

004

008

012

016

02

024

0 200 400 600 800 1000 1200

ANNNLRGEP

d (mm)

V pre

db wd

fc

Figure 9 Normalized shear strength (Vpredbwd

fcprime1113969

) versus beamdepth

Advances in Civil Engineering 13

References

[1] M S Alam and A Hussein ldquoSize effect on shear strength ofFRP reinforced concrete beams without stirrupsrdquo Journal ofComposites for Construction vol 17 no 4 pp 507ndash516 2013

[2] J R Yost S P Gross and D W Dinehart ldquoShear strength ofnormal strength concrete beams reinforced with deformedGFRP barsrdquo Journal of Composites for Construction vol 5no 4 pp 268ndash275 2001

[3] A G Razaqpur B O Isgor S Greenaway and A SelleyldquoConcrete contribution to the shear resistance of fiber rein-forced polymer reinforced concrete membersrdquo Journal ofComposites for Construction vol 8 no 5 pp 452ndash460 2004

[4] M Nehdi H El Chabib and A A Saıd ldquoProposed sheardesign equations for FRP-reinforced concrete beams based ongenetic algorithms approachrdquo Journal of Materials in CivilEngineering vol 19 no 12 pp 1033ndash1042 2007

[5] ASCE-ACI445 ldquoRecent approaches to shear design ofstructural concreterdquo Journal of Structural Engineeringvol 124 no 12 pp 1375ndash1417 1998

[6] R Park and T Paulay Reinforced Concrete Structures JohnWiley amp Sons Hoboken NJ USA 1975

[7] I F Kara ldquoPrediction of shear strength of FRP-reinforcedconcrete beams without stirrups based on genetic pro-grammingrdquo Advances in Engineering Software vol 42 no 6pp 295ndash304 2011

[8] R Bashir and A Ashour ldquoNeural networkmodelling for shearstrength of concrete members reinforced with FRP barsrdquoComposites Part B Engineering vol 43 no 8 pp 3198ndash32072012

[9] K Nasrollahzadeh and M M Basiri ldquoPrediction of shearstrength of FRP reinforced concrete beams using fuzzy in-ference systemrdquo Expert Systems with Applications vol 41no 4 pp 1006ndash1020 2014

[10] S Lee and C Lee ldquoPrediction of shear strength of FRP-reinforced concrete flexural members without stirrups usingartificial neural networksrdquo Engineering Structures vol 61pp 99ndash112 2014

[11] E M Golafshani and A Ashour ldquoA feasibility study of BBPfor predicting shear capacity of FRP reinforced concretebeams without stirrupsrdquo Advances in Engineering Softwarevol 97 pp 29ndash39 2016

[12] ACI-440 Guide for the Design and Construction of StructuralConcrete Reinforced with Fiber-Reinforced Polymer (FRP)ACI 440 1R-15 American Concrete Institute FarmingtonsHills MI USA 2015

[13] JSCE ldquoRecommendation for design and construction ofconcrete structures using continuous fiber reinforcing ma-terialsrdquo in Concrete Engineering Series 23 A Machida EdJapan Society of Civil Engineers Tokyo Japan 1997

[14] BISE Interim Guidance on the Design of Reinforced ConcreteStructures Using Fiber Composite Reinforcement British In-stitution of Structural Engineers Seto Ltd London UK1999

[15] CSA Canadian Highway Bridge Design Code SupplementNo 1 to CANCSA S6-06 (S61S1-10) Canadian StandardsAssociation (CSA) Mississauga ON Canada 2010

[16] ISIS Reinforced Concrete Structures with Fibre ReinforcedPolymersmdashDesign Manual No 3 University of Manitoba ISISCanada Corporation Winnipeg MB Canada 2007

[17] CNR-DT203 ldquoGuide for the design and construction ofconcrete structures reinforced with fiber-reinforced polymerbarsrdquo inAdvisory Committee on Technical Recommendations

for Construction CNR-DT 2032006 CNR Rome Italy2007

[18] CSA ldquoCode for the design and construction of buildingstructures with fibre-reinforced polymersrdquo in CANCSAS806-12 p 198 Canadian Standard Association TorontoON Canada 2012

[19] A Razaqpur and S Spadea ldquoResistenza a taglio di elementi dicalcestruzzzo reinforzatti e staffe di FRPrdquo in Proceedings ofAIAS Maratea Italy September 2010

[20] A F Ashour and I F Kara ldquoSize effect on shear strength ofFRP reinforced concrete beamsrdquo Composites Part B Engi-neering vol 60 pp 612ndash620 2014

[21] A R Yousif ldquoShear strength of large FRP-reinforced concretebeams without shear reinforcementrdquo Journal of Pure andApplied Sciences vol 27 pp 9ndash28 2015

[22] A K El-Sayed E F El-Salakawy and B Benmokrane ldquoShearcapacity of high-strength concrete beams reinforced with FRPbarsrdquo ACI Structural Journal vol 103 p 383 2006

[23] A G Razaqpur and O B Isgor ldquoProposed shear designmethod for FRP-reinforced concrete members without stir-rupsrdquo ACI Structural Journal vol 103 p 93 2006

[24] K Maruyama andW Zhao ldquoFlexural and shear behaviour ofconcrete beams reinforced with FRP rodsrdquo in Proceedings ofthe International Conference on Corrosion and CorrosionProtection of Steel in Concrete pp 24ndash28 Sheffield UK1994

[25] W Zhao K Maruyama and H Suzuki ldquoShear behavior ofconcrete beams reinforced by FRP rods as longitudinal andshear reinforcementrdquo in Proceedings of the Second In-ternational RILEM Symposium on Non-Metallic (FRP) Re-inforcement for Concrete Structures p 352 Ghent BelgiumAugust 1995

[26] H Nakamura and T Higai ldquoEvaluation of shear strength ofthe concrete beams reinforced with FRPrdquo in Proceedings ofJapan Society of Civil Engineers p 89 Ghent Belgium 1995

[27] K Maruyama and W Zhao ldquoSize effect in shear behavior ofFRP reinforced concrete beamrdquo in Advanced CompositeMaterials in Bridges and Structures pp 227ndash234 CanadianSociety for Civil Engineering Montreal QC Canada 1996

[28] Y Mizukawa Y Sato T Ueda and Y Kakuta ldquoA studyon shear fatigue behavior of concrete beams with FRP rodsrdquoin Proceedings of the Cird International Symposium onNon-Metallic (FRP) Reinforcement for Concrete Structures(FRPRCS-3) pp 309ndash316 Japan Concrete Institute SapporoJapan 1997

[29] N Duranovic K Pilakoutas and P Waldron ldquoTests onconcrete beams reinforced with glass fibre reinforced plasticbarsrdquo in Proceedings of the Cird International Symposium onNon-Metallic (FRP) Reinforcement for Concrete Structures(FRPRCS-3) pp 479ndash486 Sapporo Japan 1997

[30] N Swamy and M Aburawi ldquoStructural implications of usingGFRP bars as concrete reinforcementrdquo in Proceedings of 3rdInternational Symposium FRPRCS pp 503ndash510 SapporoJapan 1997

[31] C R Michaluk S H Rizkalla G Tadros and B BenmokraneldquoFlexural behavior of one-way concrete slabs reinforced byfiber reinforced plastic reinforcementsrdquo ACI StructuralJournal vol 95 pp 353ndash365 1998

[32] D Deitz I Harik and H Gesund ldquoOne-way slabs reinforcedwith glass fiber reinforced polymer reinforcing barsrdquo SpecialPublication vol 188 pp 279ndash286 1999

[33] T Alkhrdaji M Wideman A Belarbi and A Nanni ldquoShearstrength of GFRP RC beams and slabsrdquo in Proceedings of the

14 Advances in Civil Engineering

International Conference Composites in Construction-CCCpp 409ndash414 Porto Portugal 2001

[34] G S Melo and J A Rayol ldquoShear resistance of GFRPreinforced concrete beamsrdquo in Proceedings of the Rehabil-itating and Repairing the Buildings and Bridges of AmericasHemispheric Workshop on Future Directions Mayaguumlez PRUSA pp 47ndash64 2002

[35] A K Tureyen and R J Frosch ldquoShear tests of FRP-reinforcedconcrete beams without stirrupsrdquo ACI Structural Journalvol 99 pp 427ndash434 2002

[36] S P Gross J R Yost D W Dinehart E Svensen and N LiuldquoShear strength of normal and high strength concrete beamsreinforced with GFRP barsrdquo in Proceedings of InternationalConference on High Performance Materials in Bridgespp 426ndash437 ASCE Reston VA USA 2003

[37] M Tariq and J Newhook ldquoShear testing of FRP reinforcedconcrete without transverse reinforcementrdquo in Proceedings ofAnnual Conference of the Canadian Society for Civil Engi-neering pp 1330ndash1339 Moncton NB Canada June 2003

[38] S Gross D Dinehart J Yost and P -eisz ldquoExperimentaltests of high-strength concrete beams reinforced with CFRPbarsrdquo in Proceedings of the 4th International Conference onAdvanced Composite Materials in Bridges and Structures(ACMBS-4) Calgary AB Canada 2004

[39] A Lubell T Sherwood E Bentz and M P Collins ldquoSafe sheardesign of large wide beams adding shear reinforcement isrecommendedrdquoConcrete International vol 26 pp 66ndash78 2004

[40] J Yost S Gross G Masone and P Hamelin ldquoSustained loadeffects on deflection and ultimate strength of concrete beamsreinforced with GFRPrdquo in Proceedings of the InternationalConference Composites in Construction (CCC2005) LyonFrance July 2005

[41] A El-Sayed E El-Salakawy and B Benmokrane ldquoShearstrength of one-way concrete slabs reinforced with fiber-reinforced polymer composite barsrdquo Journal of Compositesfor Construction vol 9 no 2 pp 147ndash157 2005

[42] A E Kilpatrick and L Easden ldquoShear capacity of GFRPreinforced high strength concrete slabsrdquo in Proceedings of the18th Australasian Conference on the Mechanics of Structuresand Materials Perth Australia vol 1 pp 119ndash124 Taylor ampFrancis London UK 2005

[43] A K El-Sayed E F El-Salakawy and B BenmokraneldquoShear strength of FRP-reinforced concrete beams withouttransverse reinforcementrdquo ACI Structural Journal vol 103p 235 2006

[44] A Ashour ldquoFlexural and shear capacities of concrete beamsreinforced with GFRP barsrdquo Construction and BuildingMaterials vol 20 no 10 pp 1005ndash1015 2006

[45] M Guadagnini K Pilakoutas and P Waldron ldquoShear re-sistance of FRP RC beams experimental studyrdquo Journal ofComposites for Construction vol 10 no 6 pp 464ndash473 2006

[46] R Dawborn and A Kilpatrick Flexural Shear Capacity ofHigh Strength Concrete Slabs Reinforced with LongitudinalGFRP Bars 2006

[47] J Niewels ldquoZum Tragverhalten von Betonbauteilen mitFaserverbundkunststoffbewehrungrdquo Rheinisch-WestfalischeTechnische Hochschule Aachen Lehrstuhl und Institut furMassivbau Dissertation 2008

[48] A El-Sayed K Soudki and E Kling ldquoFlexural behaviour ofself-consolidating concrete slabs reinforced with GFRP barsrdquoin Proceedings of the 9th International Symposium on FiberReinforced Polymer Reinforcement for Reinforced ConcreteStructures pp 13ndash15 Sydney NSW Australia 2009

[49] A Caporale and R Luciano ldquoIndagine sperimentale enumerica sulla resistenza a taglio di travi di calcestruzzoarmate con barre di GFRPrdquo in Proceedings of XXXVIIIConvegno Nazionale AIAS Turin Italy September 2009

[50] R Olivito and F Zuccarello ldquoOn the shear behaviour ofconcrete beams reinforced by carbon fibre-reinforced poly-mer bars an experimental investigation by means of acousticemission techniquerdquo Strain vol 46 no 5 pp 470ndash481 2010

[51] E C Bentz L Massam and M P Collins ldquoShear strength oflarge concrete members with FRP reinforcementrdquo Journal ofComposites for Construction vol 14 no 6 pp 637ndash646 2010

[52] A G Razaqpur M Shedid and B Isgor ldquoShear strength offiber-reinforced polymer reinforced concrete beams subject tounsymmetric loadingrdquo Journal of Composites for Construc-tion vol 15 no 4 pp 500ndash512 2011

[53] M Alam and A Hussein ldquoEffect of member depth on shearstrength of high-strength fiber-reinforced polymerndashreinforced concrete beamsrdquo Journal of Composites for Con-struction vol 16 no 2 pp 119ndash126 2012

[54] F Matta A K El-Sayed A Nanni and B Benmokrane ldquoSizeeffect on concrete shear strength in beams reinforced withfiber-reinforced polymer barsrdquo ACI Structural Journalvol 110-S50 pp 617ndash628 2013

[55] B Abdul-Salam A Farghaly and B Benmokrane ldquoEvalua-tion of shear behavior for one-way concrete slabs reinforcedwith carbon-FRP barsrdquo GEN vol 243 p 1 2013

[56] C H Kim and H S Jang ldquoConcrete shear strength of normaland lightweight concrete beams reinforced with FRP barsrdquoJournal of Composites for Construction vol 18 no 2 article04013038 2014

[57] D Tomlinson and A Fam ldquoPerformance of concrete beamsreinforced with basalt FRP for flexure and shearrdquo Journal ofComposites for Construction vol 19 no 2 article 040140362014

[58] M A Issa T Ovitigala and M Ibrahim ldquoShear behavior ofbasalt fiber reinforced concrete beams with and without basaltFRP stirrupsrdquo Journal of Composites for Construction vol 20no 4 article 04015083 2015

[59] A El Refai and F Abed ldquoConcrete contribution to shearstrength of beams reinforced with basalt fiber-reinforcedbarsrdquo Journal of Composites for Construction vol 20 no 4article 04015082 2015

[60] G B Jumaa and A R Yuosif ldquoSize effect in shear failure ofhigh strength concrete beams without stirrups reinforcedwith basalt FRP barsrdquo KSCE Journal of Civil Engineering2018 In press

[61] M T Hagan H B Demuth and M H BealeNeural NetworkDesign (Electrical Engineering) -omson Learning BostonMA USA 1995

[62] S S Haykin S S Haykin S S Haykin and S S HaykinNeural Networks and Learning Machines Pearson Vol 3Pearson Upper Saddle River NJ USA 2009

[63] M Y Mansour M Dicleli J-Y Lee and J Zhang ldquoPredictingthe shear strength of reinforced concrete beams using artificialneural networksrdquo Engineering Structures vol 26 no 6pp 781ndash799 2004

[64] H Demuth M Beale and M Hagan Neural NetworkToolboxtrade 6 Userrsquos Guide -e MathWorks Inc vol 10 p 11Natick MA USA 2008

[65] A W Oreta and K Kawashima ldquoNeural network modeling ofconfined compressive strength and strain of circular concretecolumnsrdquo Journal of Structural Engineering vol 129 no 4pp 554ndash561 2003

Advances in Civil Engineering 15

[66] S Jung and K S Kim ldquoKnowledge-based predictionof shear strength of concrete beams without shear re-inforcementrdquo Engineering Structures vol 30 no 6pp 1515ndash1525 2008

[67] Z-H Duan S-C Kou and C-S Poon ldquoPrediction ofcompressive strength of recycled aggregate concrete usingartificial neural networksrdquo Construction and Building Mate-rials vol 40 pp 1200ndash1206 2013

[68] H El-Chabib M Nehdi and A Said ldquoPredicting shear ca-pacity of NSC and HSC slender beams without stirrups usingartificial intelligencerdquo Computers and Concrete vol 2 no 1pp 79ndash96 2005

[69] F Altun O Kisi and K Aydin ldquoPredicting the compressivestrength of steel fiber added lightweight concrete using neuralnetworkrdquo Computational Materials Science vol 42 no 2pp 259ndash265 2008

[70] J R Koza ldquoGenetic programming as a means for pro-gramming computers by natural selectionrdquo Statistics andComputing vol 4 no 2 pp 87ndash112 1994

[71] C Ferreira ldquoGene expression programming in problemsolvingrdquo in Soft Computing and Industry pp 635ndash653Springer Berlin Germany 2002

[72] C Kayadelen ldquoSoil liquefaction modeling by genetic ex-pression programming and neuro-fuzzyrdquo Expert Systems withApplications vol 38 no 4 pp 4080ndash4087 2011

[73] A H Gandomi A H Alavi and G J Yun ldquoFormulation ofuplift capacity of suction caissons using multi expressionprogrammingrdquo KSCE Journal of Civil Engineering vol 15no 2 pp 363ndash373 2011

[74] A H Gandomi A H Alavi and C RyanHandbook of GeneticProgramming Applications Springer Berlin Germany 2015

[75] A H Gandomi and A H Alavi ldquoA new multi-gene geneticprogramming approach to non-linear system modeling PartII geotechnical and earthquake engineering problemsrdquoNeural Computing and Applications vol 21 no 1 pp 189ndash201 2012

[76] A H Alavi and A H Gandomi ldquoEnergy-based numericalmodels for assessment of soil liquefactionrdquo GeoscienceFrontiers vol 3 no 4 pp 541ndash555 2012

[77] L Teodorescu and D Sherwood ldquoHigh energy physics eventselection with gene expression programmingrdquo ComputerPhysics Communications vol 178 no 6 pp 409ndash419 2008

[78] GEPSOFT GeneXproTools Version 50 GEPSOFT BristolUK 2013 httpwwwgepsoftcom

[79] S M Mousavi P Aminian A H Gandomi A H Alavi andH Bolandi ldquoA new predictive model for compressive strengthof HPC using gene expression programmingrdquo Advances inEngineering Software vol 45 no 1 pp 105ndash114 2012

[80] M Sarıdemir ldquoEmpirical modeling of splitting tensilestrength from cylinder compressive strength of concrete bygenetic programmingrdquo Expert Systems with Applicationsvol 38 no 11 pp 14257ndash14268 2011

[81] M Sonebi and A Cevik ldquoGenetic programming based for-mulation for fresh and hardened properties of self-compacting concrete containing pulverised fuel ashrdquo Con-struction and Building Materials vol 23 no 7 pp 2614ndash26222009

[82] A H Alavi P Aminian A H Gandomi and M A EsmaeilildquoGenetic-based modeling of uplift capacity of suction cais-sonsrdquo Expert Systems with Applications vol 38 no 10pp 12608ndash12618 2011

[83] T Zsutty ldquoShear strength prediction for separate catagories ofsimple beam testsrdquo ACI Journal Proceedings vol 68 no 2pp 138ndash143 1971

16 Advances in Civil Engineering

ILW

minus23567 027166 14696 minus14038 099307 22234

23842 minus22831 083159 22855 14806 minus083455

28211 075441 minus4086 14427 17982 minus10877

059955 minus074937 20882 minus26609 18418 minus15433

14527 minus17869 minus10477 16872 minus081981 minus25634

35416 minus19591 minus034353 10741 minus15276 22139

15643 minus28231 26211 minus16244 10879 17129

22825 minus040079 048425 minus2312 007062 015858

minus1749 minus025004 minus045657 minus22347 minus10796 minus10232

minus078404 266 minus28673 minus10803 minus086988 minus16247

minus025678 minus32562 22726 16206 minus12616 26619

minus12662 minus078168 minus052983 minus25791 10124 23284

minus23043 055942 minus12328 minus28413 minus13658 26415

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

⎫⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎬

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎭

ILB

51888

minus14396

minus21773

minus24823

minus16444

minus008813

012198

22041

minus2362

minus19906

minus052466

minus37706

minus26641

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

⎫⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎬

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎭

HLW ⎧⎨

⎩ minus07663 12834 minus09729 minus066761 minus03835 minus087847 12312 13464 minus13058 1206 1169 minus09465 minus06511⎫⎬

⎭

HLB minus044036

(5)

5 Genetic Programming

51 General Background Genetic programming (GP) isa naturally inspired machine learning (evolutionary) tech-nique utilized for randomly reproducing a population ofcomputer programs in light of Darwinrsquos advancement hy-pothesis GP which was developed by Koza [70] can beregarded as a developed form of the genetic algorithm (GA)which is an evolutionary optimization tool that depends onthe principles of genetics and normal determination -esystems of GA incorporate altering and changing the extentof chromosomes by genetic operators to solve functionoptimization problems -e fundamental contrast amongst

GA and GP is that the solution of GA is a binary string offixed length utilized for parameters optimization of a specificarrangement of model parameters while the solution of GPis a development program represented as a subset of parsetrees which use input variables and corresponding outputsfor generating optimized models [71ndash73]

-e GP techniques for modeling incorporate productionof an initial population of chromosomes (models) whichinclude an arrangement of functions and an arrangement ofterminals that selected and arranged randomly in the form ofthe parse tree (computer model) -e models composed ofa root node functional nodes and terminals as shown inFigure 3

6 Advances in Civil Engineering

At that point the produced population models areassessed and the tness of the models is evaluated using theprovided data of the particular problem After that othergenerations of models are produced by primary genetic op-erators reproduction crossover and mutation as shown inFigure 4e evolutionary procedure of assessing the tness ofthe present population and producing new population iscontinued until the point when an end termination criterion isapproached which can be either a particular acceptable erroror a specied maximum number of generations e modelwith the best solution which developed after each generationassigns the outcome of the GP program [76]

52 Gene Expression Programming e most widely usedGP in civil engineering problems is gene expressionprogramming (GEP) which was developed by Ferreira[71] GEP utilizes development of numerical conditionsthat is encoded linearly in chromosomes of a consistentlength and considered nonlinearly as expression trees(ETs) with various shapes and sizes e chromosomes arecomposed of several genes each gene contains a smallersubprogram or subexpression trees (Sub-ETs) Every genehas a consistent length and comprises a head and a tail eschematic of the GEP centowchart is shown in Figure 5 eimplementation of GEP predictive modeling incorporatesve main components including function set terminal settness function control parameters and terminationcondition [7 75]

e preferred quality of GEP is that the genetic operatorswork at the chromosome level and the production of geneticdiversity is to a great degree simplied Another favorableposition is credited to the remarkable multigenetic nature ofGEP which permits the advancement of all the more capablemodels made out of a few subprograms [71]

53 GEPModel for Predicting Shear Capacity For predictingthe shear strength of FRP-reinforced concrete beamswithout stirrups by GEP-based formulation six incentuencingparameters were consideredfcprime d b adEf and ρf throughtraining and testing the experimental results e data areevaluated on the GeneXproTools 5 [78] to develop theempirical model which is the most widely used software for

GEP model prediction Similar to the ANNs model the dataare partitioned randomly to 70 for training and remaining30 for testing such that both portions of data have balancedstatistical parameters like mean standard deviation andmax and min values

To obtain the best GEP prediction model many modelswith a dierent number of genes were evolved throughouta set of genetic operators (mutation transposition andcrossover) Initially a model composed of two genes withmultiplication linking functions and head sizes of three wasselected and evolved many times en the model param-eters were changed step by step through increasing thenumber of genes head size number of chromosomes andweights of function sets e program was evolved nu-merous times for various models and the outcome modelswere monitored and compared to evaluate their perfor-mance Other parameters like mutation rate inversion andpoints of recombination were chosen based on previousworks [7 79ndash82] and then evaluated to get their optimumeects After many trials the nal mathematical model waschosen for which the utilized parameters tness functionand function sets are given in Table 3 e nal model wasselected based on criteria of the best tness and less com-plicity of mathematical formulation the expression trees areshown in Figure 6 and themathematical formulation is givenin the following equation

sqrt

x1 x2 x34

ndash +

Functional nodes

Terminal nodes

Root node

Figure 3 Typical example of a GP tree representation model((4minusx1)(x2 + x3))

12 [74]

radicradic

+

+

+

1 3

+

+

+

times

times

2

2

Log

Crossover

Mutation

Log

Log Log

a

a

c

c d

d d

d

bb

Figure 4 Typical operations of crossover and mutation in GP [75]

Advances in Civil Engineering 7

Vc absc3 + d5 lowastd3( ) d2 + d0( )2

4( )

13

lowast tanhd2d1( )

15 minus tanh d2 lowast d3( )4( )

5

lowast d2 +d153

max d1 c6( )c8 + d4( )( )

2

lowast tanhd2d1( )

15 minus

d1d0

radic

3

5

(6)

where d0 d1 d2 d3 d4 and d5 refer to d ad bρf fcprime and Ef respectively c2 656723946184092 c3 minus241413053630399 c4 minus121479701959083 c6 307014791103389 and c8 220241396443835

6 Nonlinear Regression Model (NLR)

Regression analysis is considered as an important toolthat can be used in the modeling process for solvingcomplicated problems of various engineering disciplines

However the proposed models based on nonlinear re-gression (NLR) are less accurate than the ANN and GEPhowever it is characterized by that it is simple and easy forapplication without the need of computers for calculationsA nonlinear regression model based on the experimentaldatabase collected from the literature was suggested eproposed equation was derived based on developinga model similar to that proposed by Zsutty [83] which is themost accurate and simple empirical equation that wasproposed for shear prediction of steel-RC members Inorder to predict the shear strength of FRP-RC beams moreaccurately considering the eect of all incentuencing pa-rameters the experimental shear strength was analyzedwith most common incentuencing parameters fcprime d b adEf and ρf Based on data tting analysis and after somesimplication the following equation was proposed

Vc 0321d( )

13 Efρfad( )

25fcprime( )15bwd (7)

It can be observed that the equation is simple rationaland more generalized than most codes and proposedequations from the literature as it considers the eect of allthe incentuencing parameters on the shear strength of FRP-RCmembers without stirrups

7 Results and Discussion

e shear strength results of FRP-reinforced concretemembers for the three proposed models the ANNs GEPand NLR are evaluated and compared with the commondesign provisions (ACI 440-15 JSCE-97 CSA 806-12) andseven proposed equations [1 4 7 10 19ndash21] e com-parison was examined based on statistical terms such as

Start

Initial population creation

Chromosome expression as ET

ET execution

Fitness evaluation

Stop

Chromosome selection

Reproduction

Terminate

New generation creation

Yes

No

Figure 5 Flowchart of GEP [77]

Table 3 Parameters used in the GEP Model

Parameters ValuesNumber of chromosomes 30ndash500Head size 3 5 8Number of genes 2 3 4Linking function Multiplication

Function set + minus lowast abs tanh x2 x12 x13 x15

Generation withoutchanges 2000

Number of tries 12Maximum complexity 10Fitness function RMSEMutation 0044Inversion 01One-pointrecombination 03

Two-pointrecombination 03

Gene recombination 01Gene transposition 01IS transposition 01RIS transposition 01Data type Floating pointConstants per gene 10

8 Advances in Civil Engineering

mean standard deviation (SD) and coelaquocient of variation(COV) in addition to error values such as mean absoluteerror (MAE) root mean square error (RMSE) and R2 asshown below

RMSE

sumN

i0 ei minuspi( )2

N

radic

MAE 1NsumN

i0ei minuspi∣∣∣∣

∣∣∣∣

R2 1minussumN

i0 ei minuspi( )2

sumN

i0 ei minus e( )2

(8)

where ei and pi are the experimental and predicted shearforce in kN respectively e is the average of the experimentalvalues andN is the total number of the considered samplese model that minimized the error values (MAE andRMSE) and maximized R2 is selected as the optimummodel

Figure 7 presents the scatter of the experimental shearforce Vexp versus the predicted shear strength Vpred for theproposed models codes and proposed equations from theliterature It is clear that the best models for predicting theshear strength are those suggested in this study which ina sequence are ANNs GEP and NLR as these modelspredict the shear strength very accurately with the optimumstatistical performance of R2 RMSE and MAE High cor-relation coelaquocients with low error rates indicate that theproposed three models are excellent models and exhibitgeneralization performance in predicting shear strength ofFRP-reinforced concrete beams without stirrups In con-trast the code design provisions and other proposedequations from the literature yielded dispersion results with

lower R2 and larger error rates as given in the scatterrelationships

Table 4 presents the statistical parameters (meanstandard deviation (SD) coelaquocient of variation (COV)minimum maximum range RMSE MAE and R2) of theratio of experimental shear strength to the predicted shearstrength VexpVpred for the proposed models in thisstudy seven well-known codes and seven proposedequations from literature based on the (269) collecteddatabase It is clear that the proposed equations yieldedsuperior accuracy between all the codes and proposedequation from the literature because their optimumstatistical parameters such as the mean SD range RMSEand R2 are 0998 0113 072 53 and 09877 respectivelyfor ANNs 1007 0162 088 82 and 0970 respectivelyfor GEP and 1003 0174 099 107 and 095 re-spectively for NLR

e ANNs and GEP models are articial intelligentmodels derived based on soft computing as veried abovethese models are accurate superior and highly elaquocient inpredicting the complicated problem such as shear strengthHowever the drawback of articial intelligent models is thatit cannot be calculated manually and it needs computers forcalculation Besides it is considered as a powerful and ef-cient tool which can be used in soft programs specializedfor analysis and design of reinforced concrete structures Onthe contrary the NLR model is simply accurate and rationalwhich can be used manually with sulaquocient accuracy morethan the design codes and previously proposed equationsNevertheless the regression equations cannot properlydene with the same level of elaquociency of articial intelligenttechniques the interactions between the input and outputparameters due to that the regression models usually areproduced based only on a few predened equations [79]

3Rt

c3 lowast

lowast

d0

d3d5

lowast Avg2 c2

c2 d0

Avg2

+

(a)

x5

lowast

ndash

5Rt

Tanh

x4

c4d3d2d1

Tanh

(b)

+

d2x2

+

d1d3

Max2d4

c6

c8

5Rt

lowast

(c)

x5

ndash

5Rt

x3

d0d1d2d1

Tanh

Sqrt

(d)

Figure 6 Expression trees ETs for the GEP model (a) Sub-ET 1 (b) Sub-ET 2 (c) Sub-ET 3 (d) Sub-ET 4

Advances in Civil Engineering 9

Finally it can be said that all the three proposed equationscan be considered as accurate efficient and useful modelswhich were trained on a largest collected database forpredicting the shear strength of FRP-reinforced concretemembers

8 Parametric Analyses

For further verification of the proposed ANNs GEP andNLR prediction models a parametric analysis was per-formed in this study -e main goal was to find the

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

ANNsR2 = 09877RMSE = 53MAE = 39

GEPR2 = 09709

RMSE = 82kNMAE = 59kN

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

ACI 440-06R2 = 0575

RMSE = 315MAE = 242

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

CSA 806-12R2 = 0783

RMSE = 225MAE = 117

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

R2 = 0805RMSE = 213MAE = 121

Nehdi et al (2007)

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

R2 = 0772RMSE = 231MAE = 144

Razaqpur and Spadea (2011)

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

R2 = 08347RMSE = 196MAE = 110

Kara (2011)

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

R2 = 0865RMSE = 177MAE = 109

Alam and Husein (2013)

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

R2 = 0885RMSE = 164MAE = 102

Ashour and Kara (2014)

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

R2 = 0902RMSE = 151MAE = 96

Lee (2014)

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

JSCE97R2 = 0792

RMSE = 220MAE = 149

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

NLR

Vexp (kN)

R2 = 0950RMSE = 107MAE = 73

Figure 7 Scatter of Vexp versus Vpred for ANN GEP NLR and different models from the literature

10 Advances in Civil Engineering

response of the three proposed models to predict the shearstrength for a set of input parameters which are selectedtaking into account the average value of each parame-ter in the collected database For further showing theperformance of the proposed models and for comparisonpurpose the response of three well-known codes (ACI1R440-15 JSCE-97 and CSA S806-12) was also considered-e approach depends on keeping all input parameters attheir selected values except that in each time a singleparameter value was changed incrementally within theexpected practical values Consequently an arrangementof manufactured data for the single considered parameteris produced this procedure was repeated for all parametersso that all models are examined for the entire input pa-rameters -e selected input parameters are fcprime 46MPabw 200mm d 400mm ad 4 ρf 0011 and Ef

74 GPa It is worthy to note that the ANNs model cannotproperly predict the shear strength for input parametersoutside the range of training data therefore it is only validfor prediction within the range of input parameters of thetraining data [8]

Figure 8 indicates the tendency of the predicted shearstrength by differentmodels to the varieties of themain designparameters (d fcprime ρf Ef ad and bw) Generally it can beobserved that the proposed models particularly the ANNsmodel yielded larger shear capacities for all parameters whileACI 440-15 yielded the lowest shear capacities which indicatethat the ACI 440-15 is very conservative

-e relationship of beam depth with the predicted shearstrength showed that all the proposed models and codesincreased with the increase in the beam depth throughoutthe range of 100ndash1000mm -e ACI 440-15 considers theeffect of beam depth linearly while all other models rep-resent the effect of depth nonlinearly the ANNs GEP andNLR models consider the depth raised to a power of 083067 and 066 respectively Also it can be observed that theGEP and NLR yield almost the same results All the pro-posed models and codes showed an increase in shearstrength with the increase in the concrete compressive

strength but in different rates It was found that fcprime is raisedto a power of 066 030 and 02 for ANNs GEP and NLRrespectively

-e effect of the flexure reinforcement ratio on shearstrength indicates a similar trend of the NLR model and thedesign codes but the ANNs and GEP models showeda slightly decreased trend for reinforcement ratios greaterthan 003 this is not in agreement with codes and previousstudies because of that only few data were available with ρflarger than 003 and these data actually showed decreasingshear capacity Additionally these models were derivedbased only on the artificial technology of data trainingwithout manually choosing the general mathematical shapeof the model in contrary to the NLRmodel and design codeswhich was derived based on the theoretical or semiempiricalcriteria

-e shear strength also increased with the increase inthe elastic modulus of the flexure reinforcement ratio Itcan be observed that all models showed a similar trend linefor the entire range of data while the ANNs model showedan increased rate up to about 110 GPa and then the in-crease rate reduced significantly similar results also ob-tained by Bashir and Ashour [8] On the contrary thetrend lines of the shear span to depth ratio are decreasedfor GEP and NLR models for the entire range of datameanwhile for ANNs model it decreases up to ad of 5and then it started to increase slightly -is behavior is inagreement with the few available experimental results[32 52 56] which were studied as ad greater than 5However other codes do not consider the effect of ad asthe trend lines for ACI 440-15 and JSCE-97 are constantwhile the CSA S806 trend line remains constant beyondthe ad value of 5 Finally the effect of beam width on shearstrength is linear as indicated by trend lines for all modelsexcept the ANNs model which showed a lower increaserate beyond 700mm width

To investigate how the proposed models consider thesize effect on shear capacity the same parametric data usedfor studying the beam depth are used Figure 9 presents

Table 4 Statistical parameters of (VexpVpred) for the proposed models and different design equations

Design equations Mean (VexpVpred) SD COV Minimum Maximum Range RMSE MAE R2

[12] 1813 0416 2306 113 374 261 315 242 0575[13] 1302 0282 2163 046 251 205 220 149 0792[18] 1091 0227 2085 047 185 137 225 117 0783[16] 1193 0386 3249 044 248 203 2633 1758 0703[17] 0948 0265 2799 039 174 134 2257 1403 0782[14] 1072 0247 231 054 192 138 1470 980 0908[15] 1393 0254 1835 070 248 178 2456 1661 0742[4] 1113 0219 1967 055 192 136 213 121 0805[19] 1305 0235 1801 084 214 129 231 184 0772[7] 1025 0205 2003 054 191 136 196 110 0835[1] 1148 0227 1981 059 172 113 177 109 0865[20] 0965 0174 1806 063 168 105 164 102 0885[10] 1015 0229 2251 053 196 143 151 96 0905[21] 1096 0283 2587 056 212 156 1915 1180 0843NLR 1003 0174 1732 062 161 099 107 73 0950GEP 1007 0162 1608 066 155 088 82 59 09709ANNs 0998 0113 1131 071 144 072 53 39 09877

Advances in Civil Engineering 11

0

30

60

90

120

150

180

0 150 300 450 600 750 900 1050

V pre

d (k

N)

d (mm)

ANNGEPJSCE 97

NLRACI 440CSA S806

0

20

40

60

80

100

120

0 10 20 30 40 50 60 70 80 90 100 110

V pre

d (k

N)

fcprime (MPa)

ANNGEPJSCE 97

NLRACI 440SCA S806

0

20

40

60

80

100

120

0 001 002 003 004 005

V pre

d (k

N)

ρf

ANNGEPJSCE 97

NLRACI 440CSA S806

0

20

40

60

80

100

120

0 25 50 75 100 125 150 175

V pre

d (k

N)

Ef (MPa)

ANNGEPJSCE 97

NLRACI 440CSA S806

0

20

40

60

80

100

120

0 2 4 6 8 10

V pre

d (k

N)

ad

ANNGEPJSCE 97

NLRACI 440CSA S806

0

60

120

180

240

300

360

0 200 400 600 800 1000 1200

V pre

d (k

N)

b (mm)

ANNGEPJSCE 97

NLRACI 440CSA S806

Figure 8 Eect of the parameters (d fcprime ρf Ef ad and bw) on shear capacity predicted by ANNs GEP NLR and three design codes(ACI1R 440-06 JSCE-97 and CSA S806-12)

12 Advances in Civil Engineering

the relationship between normalized shear strength as(Vpredbwd

fcprime1113969

) and beam depth It is clear that the nor-malized shear strength is decreased with the increase in thebeam depth for ANNs GEP and NLR showing that the sizeeffect is efficiently presented in these models -e trends ofGEP and NLR are very close and compatible and decreasedfrom a depth of 100mm to 1000mm while the ANNsmodelseems to be more accurate as it shows an increase in thetrend up to the depth of 200mm and then it decreasedsimilarly to that of GEP and NLR after that the trend startsto increase slightly

It can be summed up to that the artificial intelligentmodels due to their efficiency and powerful ability in rec-ognizing the parameters interaction demonstrate variousrates of change and fluctuation for the entire scope of inputparameters -e ANNs and GEP models define accurately theinteraction of each parameter on shear strength predictionand have a great ability to represent the actual response ofeach parameter in spite of its complexity and fluctuationnature Furthermore these models are evolved by trainingnumerous preliminary linear and nonlinear models withoutany prior assumption regarding the shape and structure of themathematical model

9 Conclusions

An experimental database including 269 shear test results ofFRP-reinforced concrete members without stirrups availablein the literature was established to propose three predictionmodels to estimate the shear capacity of FRP-RC membersusing three powerful tools which are ANNs GEP and NLR-e following conclusions can be drawn from this study

(i) -e proposed models for predicting the shear ca-pacity of FRP-RC members based on ANNs andGEP techniques showed excellent performancegreat efficiency and high level of accuracy andyielded consistent results throughout a wide rangeof influencing parameters moreover the ANNsmodel is more superior than the GEP as the SD andR2 for ANNs are 0113 and 09877 and for GEP are0162 and 097 respectively

(ii) A simple rational and yet accurate empiricalequation was proposed for predicting shearstrength of FRP-RC members by NLR -e equa-tion considers all the important influencing pa-rameters and simplified to be easy for use Inaddition it gives consistent and accurate resultswith SD and R2 of 0173 and 095 respectively

(iii) -rough a comparative statistical analysis for theproposed models with seven shear design codes andsix proposed equations from the literature it hasbeen found that the most accurate and efficientmodels are ANNs and GEP and to a lower dgreeNLR Among the codes and available proposals theCSA S806-12 and Ashour and Kara [20] equationswere appearing to be more accurate than the others

(iv) From a parametric study considering all the influ-encing parameters on shear capacity it was found thatthe ANNs model and to a lower level GEP modeldefines accurately the interaction of each parameteron shear capacity prediction and has a great ability torepresent the actual response of each parameter inspite of its complexity and fluctuation nature

(v) -e ANNs and GEP models demonstrate that theeffect of flexure reinforcement ratio on shear ca-pacity decreased beyond 003 as a real response tothe available few data in this range therefore morestudies are needed to confirm this case

(vi) -e ANNs model demonstrated that the effect ofad does not absolutely reduce the shear capacitywhile beyond the ad value of 5 its effect couldbecome reverse and contribute to increase in theshear capacity as confirmed by few previous studies

(vii) -e size effect is considered properly by the pro-posed models particularly the ANNs model whichyields more accurate shear capacity prediction tothe experimental results

Data Availability

-e (database of shear strength of beams without stirrups)data used to support the findings of this study are includedwithin the article

Conflicts of Interest

-e authors declare that they have no conflicts of interest

0

004

008

012

016

02

024

0 200 400 600 800 1000 1200

ANNNLRGEP

d (mm)

V pre

db wd

fc

Figure 9 Normalized shear strength (Vpredbwd

fcprime1113969

) versus beamdepth

Advances in Civil Engineering 13

References

[1] M S Alam and A Hussein ldquoSize effect on shear strength ofFRP reinforced concrete beams without stirrupsrdquo Journal ofComposites for Construction vol 17 no 4 pp 507ndash516 2013

[2] J R Yost S P Gross and D W Dinehart ldquoShear strength ofnormal strength concrete beams reinforced with deformedGFRP barsrdquo Journal of Composites for Construction vol 5no 4 pp 268ndash275 2001

[3] A G Razaqpur B O Isgor S Greenaway and A SelleyldquoConcrete contribution to the shear resistance of fiber rein-forced polymer reinforced concrete membersrdquo Journal ofComposites for Construction vol 8 no 5 pp 452ndash460 2004

[4] M Nehdi H El Chabib and A A Saıd ldquoProposed sheardesign equations for FRP-reinforced concrete beams based ongenetic algorithms approachrdquo Journal of Materials in CivilEngineering vol 19 no 12 pp 1033ndash1042 2007

[5] ASCE-ACI445 ldquoRecent approaches to shear design ofstructural concreterdquo Journal of Structural Engineeringvol 124 no 12 pp 1375ndash1417 1998

[6] R Park and T Paulay Reinforced Concrete Structures JohnWiley amp Sons Hoboken NJ USA 1975

[7] I F Kara ldquoPrediction of shear strength of FRP-reinforcedconcrete beams without stirrups based on genetic pro-grammingrdquo Advances in Engineering Software vol 42 no 6pp 295ndash304 2011

[8] R Bashir and A Ashour ldquoNeural networkmodelling for shearstrength of concrete members reinforced with FRP barsrdquoComposites Part B Engineering vol 43 no 8 pp 3198ndash32072012

[9] K Nasrollahzadeh and M M Basiri ldquoPrediction of shearstrength of FRP reinforced concrete beams using fuzzy in-ference systemrdquo Expert Systems with Applications vol 41no 4 pp 1006ndash1020 2014

[10] S Lee and C Lee ldquoPrediction of shear strength of FRP-reinforced concrete flexural members without stirrups usingartificial neural networksrdquo Engineering Structures vol 61pp 99ndash112 2014

[11] E M Golafshani and A Ashour ldquoA feasibility study of BBPfor predicting shear capacity of FRP reinforced concretebeams without stirrupsrdquo Advances in Engineering Softwarevol 97 pp 29ndash39 2016

[12] ACI-440 Guide for the Design and Construction of StructuralConcrete Reinforced with Fiber-Reinforced Polymer (FRP)ACI 440 1R-15 American Concrete Institute FarmingtonsHills MI USA 2015

[13] JSCE ldquoRecommendation for design and construction ofconcrete structures using continuous fiber reinforcing ma-terialsrdquo in Concrete Engineering Series 23 A Machida EdJapan Society of Civil Engineers Tokyo Japan 1997

[14] BISE Interim Guidance on the Design of Reinforced ConcreteStructures Using Fiber Composite Reinforcement British In-stitution of Structural Engineers Seto Ltd London UK1999

[15] CSA Canadian Highway Bridge Design Code SupplementNo 1 to CANCSA S6-06 (S61S1-10) Canadian StandardsAssociation (CSA) Mississauga ON Canada 2010

[16] ISIS Reinforced Concrete Structures with Fibre ReinforcedPolymersmdashDesign Manual No 3 University of Manitoba ISISCanada Corporation Winnipeg MB Canada 2007

[17] CNR-DT203 ldquoGuide for the design and construction ofconcrete structures reinforced with fiber-reinforced polymerbarsrdquo inAdvisory Committee on Technical Recommendations

for Construction CNR-DT 2032006 CNR Rome Italy2007

[18] CSA ldquoCode for the design and construction of buildingstructures with fibre-reinforced polymersrdquo in CANCSAS806-12 p 198 Canadian Standard Association TorontoON Canada 2012

[19] A Razaqpur and S Spadea ldquoResistenza a taglio di elementi dicalcestruzzzo reinforzatti e staffe di FRPrdquo in Proceedings ofAIAS Maratea Italy September 2010

[20] A F Ashour and I F Kara ldquoSize effect on shear strength ofFRP reinforced concrete beamsrdquo Composites Part B Engi-neering vol 60 pp 612ndash620 2014

[21] A R Yousif ldquoShear strength of large FRP-reinforced concretebeams without shear reinforcementrdquo Journal of Pure andApplied Sciences vol 27 pp 9ndash28 2015

[22] A K El-Sayed E F El-Salakawy and B Benmokrane ldquoShearcapacity of high-strength concrete beams reinforced with FRPbarsrdquo ACI Structural Journal vol 103 p 383 2006

[23] A G Razaqpur and O B Isgor ldquoProposed shear designmethod for FRP-reinforced concrete members without stir-rupsrdquo ACI Structural Journal vol 103 p 93 2006

[24] K Maruyama andW Zhao ldquoFlexural and shear behaviour ofconcrete beams reinforced with FRP rodsrdquo in Proceedings ofthe International Conference on Corrosion and CorrosionProtection of Steel in Concrete pp 24ndash28 Sheffield UK1994

[25] W Zhao K Maruyama and H Suzuki ldquoShear behavior ofconcrete beams reinforced by FRP rods as longitudinal andshear reinforcementrdquo in Proceedings of the Second In-ternational RILEM Symposium on Non-Metallic (FRP) Re-inforcement for Concrete Structures p 352 Ghent BelgiumAugust 1995

[26] H Nakamura and T Higai ldquoEvaluation of shear strength ofthe concrete beams reinforced with FRPrdquo in Proceedings ofJapan Society of Civil Engineers p 89 Ghent Belgium 1995

[27] K Maruyama and W Zhao ldquoSize effect in shear behavior ofFRP reinforced concrete beamrdquo in Advanced CompositeMaterials in Bridges and Structures pp 227ndash234 CanadianSociety for Civil Engineering Montreal QC Canada 1996

[28] Y Mizukawa Y Sato T Ueda and Y Kakuta ldquoA studyon shear fatigue behavior of concrete beams with FRP rodsrdquoin Proceedings of the Cird International Symposium onNon-Metallic (FRP) Reinforcement for Concrete Structures(FRPRCS-3) pp 309ndash316 Japan Concrete Institute SapporoJapan 1997

[29] N Duranovic K Pilakoutas and P Waldron ldquoTests onconcrete beams reinforced with glass fibre reinforced plasticbarsrdquo in Proceedings of the Cird International Symposium onNon-Metallic (FRP) Reinforcement for Concrete Structures(FRPRCS-3) pp 479ndash486 Sapporo Japan 1997

[30] N Swamy and M Aburawi ldquoStructural implications of usingGFRP bars as concrete reinforcementrdquo in Proceedings of 3rdInternational Symposium FRPRCS pp 503ndash510 SapporoJapan 1997

[31] C R Michaluk S H Rizkalla G Tadros and B BenmokraneldquoFlexural behavior of one-way concrete slabs reinforced byfiber reinforced plastic reinforcementsrdquo ACI StructuralJournal vol 95 pp 353ndash365 1998

[32] D Deitz I Harik and H Gesund ldquoOne-way slabs reinforcedwith glass fiber reinforced polymer reinforcing barsrdquo SpecialPublication vol 188 pp 279ndash286 1999

[33] T Alkhrdaji M Wideman A Belarbi and A Nanni ldquoShearstrength of GFRP RC beams and slabsrdquo in Proceedings of the

14 Advances in Civil Engineering

International Conference Composites in Construction-CCCpp 409ndash414 Porto Portugal 2001

[34] G S Melo and J A Rayol ldquoShear resistance of GFRPreinforced concrete beamsrdquo in Proceedings of the Rehabil-itating and Repairing the Buildings and Bridges of AmericasHemispheric Workshop on Future Directions Mayaguumlez PRUSA pp 47ndash64 2002

[35] A K Tureyen and R J Frosch ldquoShear tests of FRP-reinforcedconcrete beams without stirrupsrdquo ACI Structural Journalvol 99 pp 427ndash434 2002

[36] S P Gross J R Yost D W Dinehart E Svensen and N LiuldquoShear strength of normal and high strength concrete beamsreinforced with GFRP barsrdquo in Proceedings of InternationalConference on High Performance Materials in Bridgespp 426ndash437 ASCE Reston VA USA 2003

[37] M Tariq and J Newhook ldquoShear testing of FRP reinforcedconcrete without transverse reinforcementrdquo in Proceedings ofAnnual Conference of the Canadian Society for Civil Engi-neering pp 1330ndash1339 Moncton NB Canada June 2003

[38] S Gross D Dinehart J Yost and P -eisz ldquoExperimentaltests of high-strength concrete beams reinforced with CFRPbarsrdquo in Proceedings of the 4th International Conference onAdvanced Composite Materials in Bridges and Structures(ACMBS-4) Calgary AB Canada 2004

[39] A Lubell T Sherwood E Bentz and M P Collins ldquoSafe sheardesign of large wide beams adding shear reinforcement isrecommendedrdquoConcrete International vol 26 pp 66ndash78 2004

[40] J Yost S Gross G Masone and P Hamelin ldquoSustained loadeffects on deflection and ultimate strength of concrete beamsreinforced with GFRPrdquo in Proceedings of the InternationalConference Composites in Construction (CCC2005) LyonFrance July 2005

[41] A El-Sayed E El-Salakawy and B Benmokrane ldquoShearstrength of one-way concrete slabs reinforced with fiber-reinforced polymer composite barsrdquo Journal of Compositesfor Construction vol 9 no 2 pp 147ndash157 2005

[42] A E Kilpatrick and L Easden ldquoShear capacity of GFRPreinforced high strength concrete slabsrdquo in Proceedings of the18th Australasian Conference on the Mechanics of Structuresand Materials Perth Australia vol 1 pp 119ndash124 Taylor ampFrancis London UK 2005

[43] A K El-Sayed E F El-Salakawy and B BenmokraneldquoShear strength of FRP-reinforced concrete beams withouttransverse reinforcementrdquo ACI Structural Journal vol 103p 235 2006

[44] A Ashour ldquoFlexural and shear capacities of concrete beamsreinforced with GFRP barsrdquo Construction and BuildingMaterials vol 20 no 10 pp 1005ndash1015 2006

[45] M Guadagnini K Pilakoutas and P Waldron ldquoShear re-sistance of FRP RC beams experimental studyrdquo Journal ofComposites for Construction vol 10 no 6 pp 464ndash473 2006

[46] R Dawborn and A Kilpatrick Flexural Shear Capacity ofHigh Strength Concrete Slabs Reinforced with LongitudinalGFRP Bars 2006

[47] J Niewels ldquoZum Tragverhalten von Betonbauteilen mitFaserverbundkunststoffbewehrungrdquo Rheinisch-WestfalischeTechnische Hochschule Aachen Lehrstuhl und Institut furMassivbau Dissertation 2008

[48] A El-Sayed K Soudki and E Kling ldquoFlexural behaviour ofself-consolidating concrete slabs reinforced with GFRP barsrdquoin Proceedings of the 9th International Symposium on FiberReinforced Polymer Reinforcement for Reinforced ConcreteStructures pp 13ndash15 Sydney NSW Australia 2009

[49] A Caporale and R Luciano ldquoIndagine sperimentale enumerica sulla resistenza a taglio di travi di calcestruzzoarmate con barre di GFRPrdquo in Proceedings of XXXVIIIConvegno Nazionale AIAS Turin Italy September 2009

[50] R Olivito and F Zuccarello ldquoOn the shear behaviour ofconcrete beams reinforced by carbon fibre-reinforced poly-mer bars an experimental investigation by means of acousticemission techniquerdquo Strain vol 46 no 5 pp 470ndash481 2010

[51] E C Bentz L Massam and M P Collins ldquoShear strength oflarge concrete members with FRP reinforcementrdquo Journal ofComposites for Construction vol 14 no 6 pp 637ndash646 2010

[52] A G Razaqpur M Shedid and B Isgor ldquoShear strength offiber-reinforced polymer reinforced concrete beams subject tounsymmetric loadingrdquo Journal of Composites for Construc-tion vol 15 no 4 pp 500ndash512 2011

[53] M Alam and A Hussein ldquoEffect of member depth on shearstrength of high-strength fiber-reinforced polymerndashreinforced concrete beamsrdquo Journal of Composites for Con-struction vol 16 no 2 pp 119ndash126 2012

[54] F Matta A K El-Sayed A Nanni and B Benmokrane ldquoSizeeffect on concrete shear strength in beams reinforced withfiber-reinforced polymer barsrdquo ACI Structural Journalvol 110-S50 pp 617ndash628 2013

[55] B Abdul-Salam A Farghaly and B Benmokrane ldquoEvalua-tion of shear behavior for one-way concrete slabs reinforcedwith carbon-FRP barsrdquo GEN vol 243 p 1 2013

[56] C H Kim and H S Jang ldquoConcrete shear strength of normaland lightweight concrete beams reinforced with FRP barsrdquoJournal of Composites for Construction vol 18 no 2 article04013038 2014

[57] D Tomlinson and A Fam ldquoPerformance of concrete beamsreinforced with basalt FRP for flexure and shearrdquo Journal ofComposites for Construction vol 19 no 2 article 040140362014

[58] M A Issa T Ovitigala and M Ibrahim ldquoShear behavior ofbasalt fiber reinforced concrete beams with and without basaltFRP stirrupsrdquo Journal of Composites for Construction vol 20no 4 article 04015083 2015

[59] A El Refai and F Abed ldquoConcrete contribution to shearstrength of beams reinforced with basalt fiber-reinforcedbarsrdquo Journal of Composites for Construction vol 20 no 4article 04015082 2015

[60] G B Jumaa and A R Yuosif ldquoSize effect in shear failure ofhigh strength concrete beams without stirrups reinforcedwith basalt FRP barsrdquo KSCE Journal of Civil Engineering2018 In press

[61] M T Hagan H B Demuth and M H BealeNeural NetworkDesign (Electrical Engineering) -omson Learning BostonMA USA 1995

[62] S S Haykin S S Haykin S S Haykin and S S HaykinNeural Networks and Learning Machines Pearson Vol 3Pearson Upper Saddle River NJ USA 2009

[63] M Y Mansour M Dicleli J-Y Lee and J Zhang ldquoPredictingthe shear strength of reinforced concrete beams using artificialneural networksrdquo Engineering Structures vol 26 no 6pp 781ndash799 2004

[64] H Demuth M Beale and M Hagan Neural NetworkToolboxtrade 6 Userrsquos Guide -e MathWorks Inc vol 10 p 11Natick MA USA 2008

[65] A W Oreta and K Kawashima ldquoNeural network modeling ofconfined compressive strength and strain of circular concretecolumnsrdquo Journal of Structural Engineering vol 129 no 4pp 554ndash561 2003

Advances in Civil Engineering 15

[66] S Jung and K S Kim ldquoKnowledge-based predictionof shear strength of concrete beams without shear re-inforcementrdquo Engineering Structures vol 30 no 6pp 1515ndash1525 2008

[67] Z-H Duan S-C Kou and C-S Poon ldquoPrediction ofcompressive strength of recycled aggregate concrete usingartificial neural networksrdquo Construction and Building Mate-rials vol 40 pp 1200ndash1206 2013

[68] H El-Chabib M Nehdi and A Said ldquoPredicting shear ca-pacity of NSC and HSC slender beams without stirrups usingartificial intelligencerdquo Computers and Concrete vol 2 no 1pp 79ndash96 2005

[69] F Altun O Kisi and K Aydin ldquoPredicting the compressivestrength of steel fiber added lightweight concrete using neuralnetworkrdquo Computational Materials Science vol 42 no 2pp 259ndash265 2008

[70] J R Koza ldquoGenetic programming as a means for pro-gramming computers by natural selectionrdquo Statistics andComputing vol 4 no 2 pp 87ndash112 1994

[71] C Ferreira ldquoGene expression programming in problemsolvingrdquo in Soft Computing and Industry pp 635ndash653Springer Berlin Germany 2002

[72] C Kayadelen ldquoSoil liquefaction modeling by genetic ex-pression programming and neuro-fuzzyrdquo Expert Systems withApplications vol 38 no 4 pp 4080ndash4087 2011

[73] A H Gandomi A H Alavi and G J Yun ldquoFormulation ofuplift capacity of suction caissons using multi expressionprogrammingrdquo KSCE Journal of Civil Engineering vol 15no 2 pp 363ndash373 2011

[74] A H Gandomi A H Alavi and C RyanHandbook of GeneticProgramming Applications Springer Berlin Germany 2015

[75] A H Gandomi and A H Alavi ldquoA new multi-gene geneticprogramming approach to non-linear system modeling PartII geotechnical and earthquake engineering problemsrdquoNeural Computing and Applications vol 21 no 1 pp 189ndash201 2012

[76] A H Alavi and A H Gandomi ldquoEnergy-based numericalmodels for assessment of soil liquefactionrdquo GeoscienceFrontiers vol 3 no 4 pp 541ndash555 2012

[77] L Teodorescu and D Sherwood ldquoHigh energy physics eventselection with gene expression programmingrdquo ComputerPhysics Communications vol 178 no 6 pp 409ndash419 2008

[78] GEPSOFT GeneXproTools Version 50 GEPSOFT BristolUK 2013 httpwwwgepsoftcom

[79] S M Mousavi P Aminian A H Gandomi A H Alavi andH Bolandi ldquoA new predictive model for compressive strengthof HPC using gene expression programmingrdquo Advances inEngineering Software vol 45 no 1 pp 105ndash114 2012

[80] M Sarıdemir ldquoEmpirical modeling of splitting tensilestrength from cylinder compressive strength of concrete bygenetic programmingrdquo Expert Systems with Applicationsvol 38 no 11 pp 14257ndash14268 2011

[81] M Sonebi and A Cevik ldquoGenetic programming based for-mulation for fresh and hardened properties of self-compacting concrete containing pulverised fuel ashrdquo Con-struction and Building Materials vol 23 no 7 pp 2614ndash26222009

[82] A H Alavi P Aminian A H Gandomi and M A EsmaeilildquoGenetic-based modeling of uplift capacity of suction cais-sonsrdquo Expert Systems with Applications vol 38 no 10pp 12608ndash12618 2011

[83] T Zsutty ldquoShear strength prediction for separate catagories ofsimple beam testsrdquo ACI Journal Proceedings vol 68 no 2pp 138ndash143 1971

16 Advances in Civil Engineering

At that point the produced population models areassessed and the tness of the models is evaluated using theprovided data of the particular problem After that othergenerations of models are produced by primary genetic op-erators reproduction crossover and mutation as shown inFigure 4e evolutionary procedure of assessing the tness ofthe present population and producing new population iscontinued until the point when an end termination criterion isapproached which can be either a particular acceptable erroror a specied maximum number of generations e modelwith the best solution which developed after each generationassigns the outcome of the GP program [76]

52 Gene Expression Programming e most widely usedGP in civil engineering problems is gene expressionprogramming (GEP) which was developed by Ferreira[71] GEP utilizes development of numerical conditionsthat is encoded linearly in chromosomes of a consistentlength and considered nonlinearly as expression trees(ETs) with various shapes and sizes e chromosomes arecomposed of several genes each gene contains a smallersubprogram or subexpression trees (Sub-ETs) Every genehas a consistent length and comprises a head and a tail eschematic of the GEP centowchart is shown in Figure 5 eimplementation of GEP predictive modeling incorporatesve main components including function set terminal settness function control parameters and terminationcondition [7 75]

e preferred quality of GEP is that the genetic operatorswork at the chromosome level and the production of geneticdiversity is to a great degree simplied Another favorableposition is credited to the remarkable multigenetic nature ofGEP which permits the advancement of all the more capablemodels made out of a few subprograms [71]

53 GEPModel for Predicting Shear Capacity For predictingthe shear strength of FRP-reinforced concrete beamswithout stirrups by GEP-based formulation six incentuencingparameters were consideredfcprime d b adEf and ρf throughtraining and testing the experimental results e data areevaluated on the GeneXproTools 5 [78] to develop theempirical model which is the most widely used software for

GEP model prediction Similar to the ANNs model the dataare partitioned randomly to 70 for training and remaining30 for testing such that both portions of data have balancedstatistical parameters like mean standard deviation andmax and min values

To obtain the best GEP prediction model many modelswith a dierent number of genes were evolved throughouta set of genetic operators (mutation transposition andcrossover) Initially a model composed of two genes withmultiplication linking functions and head sizes of three wasselected and evolved many times en the model param-eters were changed step by step through increasing thenumber of genes head size number of chromosomes andweights of function sets e program was evolved nu-merous times for various models and the outcome modelswere monitored and compared to evaluate their perfor-mance Other parameters like mutation rate inversion andpoints of recombination were chosen based on previousworks [7 79ndash82] and then evaluated to get their optimumeects After many trials the nal mathematical model waschosen for which the utilized parameters tness functionand function sets are given in Table 3 e nal model wasselected based on criteria of the best tness and less com-plicity of mathematical formulation the expression trees areshown in Figure 6 and themathematical formulation is givenin the following equation

sqrt

x1 x2 x34

ndash +

Functional nodes

Terminal nodes

Root node

Figure 3 Typical example of a GP tree representation model((4minusx1)(x2 + x3))

12 [74]

radicradic

+

+

+

1 3

+

+

+

times

times

2

2

Log

Crossover

Mutation

Log

Log Log

a

a

c

c d

d d

d

bb

Figure 4 Typical operations of crossover and mutation in GP [75]

Advances in Civil Engineering 7

Vc absc3 + d5 lowastd3( ) d2 + d0( )2

4( )

13

lowast tanhd2d1( )

15 minus tanh d2 lowast d3( )4( )

5

lowast d2 +d153

max d1 c6( )c8 + d4( )( )

2

lowast tanhd2d1( )

15 minus

d1d0

radic

3

5

(6)

where d0 d1 d2 d3 d4 and d5 refer to d ad bρf fcprime and Ef respectively c2 656723946184092 c3 minus241413053630399 c4 minus121479701959083 c6 307014791103389 and c8 220241396443835

6 Nonlinear Regression Model (NLR)

Regression analysis is considered as an important toolthat can be used in the modeling process for solvingcomplicated problems of various engineering disciplines

However the proposed models based on nonlinear re-gression (NLR) are less accurate than the ANN and GEPhowever it is characterized by that it is simple and easy forapplication without the need of computers for calculationsA nonlinear regression model based on the experimentaldatabase collected from the literature was suggested eproposed equation was derived based on developinga model similar to that proposed by Zsutty [83] which is themost accurate and simple empirical equation that wasproposed for shear prediction of steel-RC members Inorder to predict the shear strength of FRP-RC beams moreaccurately considering the eect of all incentuencing pa-rameters the experimental shear strength was analyzedwith most common incentuencing parameters fcprime d b adEf and ρf Based on data tting analysis and after somesimplication the following equation was proposed

Vc 0321d( )

13 Efρfad( )

25fcprime( )15bwd (7)

It can be observed that the equation is simple rationaland more generalized than most codes and proposedequations from the literature as it considers the eect of allthe incentuencing parameters on the shear strength of FRP-RCmembers without stirrups

7 Results and Discussion

e shear strength results of FRP-reinforced concretemembers for the three proposed models the ANNs GEPand NLR are evaluated and compared with the commondesign provisions (ACI 440-15 JSCE-97 CSA 806-12) andseven proposed equations [1 4 7 10 19ndash21] e com-parison was examined based on statistical terms such as

Start

Initial population creation

Chromosome expression as ET

ET execution

Fitness evaluation

Stop

Chromosome selection

Reproduction

Terminate

New generation creation

Yes

No

Figure 5 Flowchart of GEP [77]

Table 3 Parameters used in the GEP Model

Parameters ValuesNumber of chromosomes 30ndash500Head size 3 5 8Number of genes 2 3 4Linking function Multiplication

Function set + minus lowast abs tanh x2 x12 x13 x15

Generation withoutchanges 2000

Number of tries 12Maximum complexity 10Fitness function RMSEMutation 0044Inversion 01One-pointrecombination 03

Two-pointrecombination 03

Gene recombination 01Gene transposition 01IS transposition 01RIS transposition 01Data type Floating pointConstants per gene 10

8 Advances in Civil Engineering

mean standard deviation (SD) and coelaquocient of variation(COV) in addition to error values such as mean absoluteerror (MAE) root mean square error (RMSE) and R2 asshown below

RMSE

sumN

i0 ei minuspi( )2

N

radic

MAE 1NsumN

i0ei minuspi∣∣∣∣

∣∣∣∣

R2 1minussumN

i0 ei minuspi( )2

sumN

i0 ei minus e( )2

(8)

where ei and pi are the experimental and predicted shearforce in kN respectively e is the average of the experimentalvalues andN is the total number of the considered samplese model that minimized the error values (MAE andRMSE) and maximized R2 is selected as the optimummodel

Figure 7 presents the scatter of the experimental shearforce Vexp versus the predicted shear strength Vpred for theproposed models codes and proposed equations from theliterature It is clear that the best models for predicting theshear strength are those suggested in this study which ina sequence are ANNs GEP and NLR as these modelspredict the shear strength very accurately with the optimumstatistical performance of R2 RMSE and MAE High cor-relation coelaquocients with low error rates indicate that theproposed three models are excellent models and exhibitgeneralization performance in predicting shear strength ofFRP-reinforced concrete beams without stirrups In con-trast the code design provisions and other proposedequations from the literature yielded dispersion results with

lower R2 and larger error rates as given in the scatterrelationships

Table 4 presents the statistical parameters (meanstandard deviation (SD) coelaquocient of variation (COV)minimum maximum range RMSE MAE and R2) of theratio of experimental shear strength to the predicted shearstrength VexpVpred for the proposed models in thisstudy seven well-known codes and seven proposedequations from literature based on the (269) collecteddatabase It is clear that the proposed equations yieldedsuperior accuracy between all the codes and proposedequation from the literature because their optimumstatistical parameters such as the mean SD range RMSEand R2 are 0998 0113 072 53 and 09877 respectivelyfor ANNs 1007 0162 088 82 and 0970 respectivelyfor GEP and 1003 0174 099 107 and 095 re-spectively for NLR

e ANNs and GEP models are articial intelligentmodels derived based on soft computing as veried abovethese models are accurate superior and highly elaquocient inpredicting the complicated problem such as shear strengthHowever the drawback of articial intelligent models is thatit cannot be calculated manually and it needs computers forcalculation Besides it is considered as a powerful and ef-cient tool which can be used in soft programs specializedfor analysis and design of reinforced concrete structures Onthe contrary the NLR model is simply accurate and rationalwhich can be used manually with sulaquocient accuracy morethan the design codes and previously proposed equationsNevertheless the regression equations cannot properlydene with the same level of elaquociency of articial intelligenttechniques the interactions between the input and outputparameters due to that the regression models usually areproduced based only on a few predened equations [79]

3Rt

c3 lowast

lowast

d0

d3d5

lowast Avg2 c2

c2 d0

Avg2

+

(a)

x5

lowast

ndash

5Rt

Tanh

x4

c4d3d2d1

Tanh

(b)

+

d2x2

+

d1d3

Max2d4

c6

c8

5Rt

lowast

(c)

x5

ndash

5Rt

x3

d0d1d2d1

Tanh

Sqrt

(d)

Figure 6 Expression trees ETs for the GEP model (a) Sub-ET 1 (b) Sub-ET 2 (c) Sub-ET 3 (d) Sub-ET 4

Advances in Civil Engineering 9

Finally it can be said that all the three proposed equationscan be considered as accurate efficient and useful modelswhich were trained on a largest collected database forpredicting the shear strength of FRP-reinforced concretemembers

8 Parametric Analyses

For further verification of the proposed ANNs GEP andNLR prediction models a parametric analysis was per-formed in this study -e main goal was to find the

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

ANNsR2 = 09877RMSE = 53MAE = 39

GEPR2 = 09709

RMSE = 82kNMAE = 59kN

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

ACI 440-06R2 = 0575

RMSE = 315MAE = 242

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

CSA 806-12R2 = 0783

RMSE = 225MAE = 117

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

R2 = 0805RMSE = 213MAE = 121

Nehdi et al (2007)

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

R2 = 0772RMSE = 231MAE = 144

Razaqpur and Spadea (2011)

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

R2 = 08347RMSE = 196MAE = 110

Kara (2011)

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

R2 = 0865RMSE = 177MAE = 109

Alam and Husein (2013)

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

R2 = 0885RMSE = 164MAE = 102

Ashour and Kara (2014)

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

R2 = 0902RMSE = 151MAE = 96

Lee (2014)

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

JSCE97R2 = 0792

RMSE = 220MAE = 149

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

NLR

Vexp (kN)

R2 = 0950RMSE = 107MAE = 73

Figure 7 Scatter of Vexp versus Vpred for ANN GEP NLR and different models from the literature

10 Advances in Civil Engineering

response of the three proposed models to predict the shearstrength for a set of input parameters which are selectedtaking into account the average value of each parame-ter in the collected database For further showing theperformance of the proposed models and for comparisonpurpose the response of three well-known codes (ACI1R440-15 JSCE-97 and CSA S806-12) was also considered-e approach depends on keeping all input parameters attheir selected values except that in each time a singleparameter value was changed incrementally within theexpected practical values Consequently an arrangementof manufactured data for the single considered parameteris produced this procedure was repeated for all parametersso that all models are examined for the entire input pa-rameters -e selected input parameters are fcprime 46MPabw 200mm d 400mm ad 4 ρf 0011 and Ef

74 GPa It is worthy to note that the ANNs model cannotproperly predict the shear strength for input parametersoutside the range of training data therefore it is only validfor prediction within the range of input parameters of thetraining data [8]

Figure 8 indicates the tendency of the predicted shearstrength by differentmodels to the varieties of themain designparameters (d fcprime ρf Ef ad and bw) Generally it can beobserved that the proposed models particularly the ANNsmodel yielded larger shear capacities for all parameters whileACI 440-15 yielded the lowest shear capacities which indicatethat the ACI 440-15 is very conservative

-e relationship of beam depth with the predicted shearstrength showed that all the proposed models and codesincreased with the increase in the beam depth throughoutthe range of 100ndash1000mm -e ACI 440-15 considers theeffect of beam depth linearly while all other models rep-resent the effect of depth nonlinearly the ANNs GEP andNLR models consider the depth raised to a power of 083067 and 066 respectively Also it can be observed that theGEP and NLR yield almost the same results All the pro-posed models and codes showed an increase in shearstrength with the increase in the concrete compressive

strength but in different rates It was found that fcprime is raisedto a power of 066 030 and 02 for ANNs GEP and NLRrespectively

-e effect of the flexure reinforcement ratio on shearstrength indicates a similar trend of the NLR model and thedesign codes but the ANNs and GEP models showeda slightly decreased trend for reinforcement ratios greaterthan 003 this is not in agreement with codes and previousstudies because of that only few data were available with ρflarger than 003 and these data actually showed decreasingshear capacity Additionally these models were derivedbased only on the artificial technology of data trainingwithout manually choosing the general mathematical shapeof the model in contrary to the NLRmodel and design codeswhich was derived based on the theoretical or semiempiricalcriteria

-e shear strength also increased with the increase inthe elastic modulus of the flexure reinforcement ratio Itcan be observed that all models showed a similar trend linefor the entire range of data while the ANNs model showedan increased rate up to about 110 GPa and then the in-crease rate reduced significantly similar results also ob-tained by Bashir and Ashour [8] On the contrary thetrend lines of the shear span to depth ratio are decreasedfor GEP and NLR models for the entire range of datameanwhile for ANNs model it decreases up to ad of 5and then it started to increase slightly -is behavior is inagreement with the few available experimental results[32 52 56] which were studied as ad greater than 5However other codes do not consider the effect of ad asthe trend lines for ACI 440-15 and JSCE-97 are constantwhile the CSA S806 trend line remains constant beyondthe ad value of 5 Finally the effect of beam width on shearstrength is linear as indicated by trend lines for all modelsexcept the ANNs model which showed a lower increaserate beyond 700mm width

To investigate how the proposed models consider thesize effect on shear capacity the same parametric data usedfor studying the beam depth are used Figure 9 presents

Table 4 Statistical parameters of (VexpVpred) for the proposed models and different design equations

Design equations Mean (VexpVpred) SD COV Minimum Maximum Range RMSE MAE R2

[12] 1813 0416 2306 113 374 261 315 242 0575[13] 1302 0282 2163 046 251 205 220 149 0792[18] 1091 0227 2085 047 185 137 225 117 0783[16] 1193 0386 3249 044 248 203 2633 1758 0703[17] 0948 0265 2799 039 174 134 2257 1403 0782[14] 1072 0247 231 054 192 138 1470 980 0908[15] 1393 0254 1835 070 248 178 2456 1661 0742[4] 1113 0219 1967 055 192 136 213 121 0805[19] 1305 0235 1801 084 214 129 231 184 0772[7] 1025 0205 2003 054 191 136 196 110 0835[1] 1148 0227 1981 059 172 113 177 109 0865[20] 0965 0174 1806 063 168 105 164 102 0885[10] 1015 0229 2251 053 196 143 151 96 0905[21] 1096 0283 2587 056 212 156 1915 1180 0843NLR 1003 0174 1732 062 161 099 107 73 0950GEP 1007 0162 1608 066 155 088 82 59 09709ANNs 0998 0113 1131 071 144 072 53 39 09877

Advances in Civil Engineering 11

0

30

60

90

120

150

180

0 150 300 450 600 750 900 1050

V pre

d (k

N)

d (mm)

ANNGEPJSCE 97

NLRACI 440CSA S806

0

20

40

60

80

100

120

0 10 20 30 40 50 60 70 80 90 100 110

V pre

d (k

N)

fcprime (MPa)

ANNGEPJSCE 97

NLRACI 440SCA S806

0

20

40

60

80

100

120

0 001 002 003 004 005

V pre

d (k

N)

ρf

ANNGEPJSCE 97

NLRACI 440CSA S806

0

20

40

60

80

100

120

0 25 50 75 100 125 150 175

V pre

d (k

N)

Ef (MPa)

ANNGEPJSCE 97

NLRACI 440CSA S806

0

20

40

60

80

100

120

0 2 4 6 8 10

V pre

d (k

N)

ad

ANNGEPJSCE 97

NLRACI 440CSA S806

0

60

120

180

240

300

360

0 200 400 600 800 1000 1200

V pre

d (k

N)

b (mm)

ANNGEPJSCE 97

NLRACI 440CSA S806

Figure 8 Eect of the parameters (d fcprime ρf Ef ad and bw) on shear capacity predicted by ANNs GEP NLR and three design codes(ACI1R 440-06 JSCE-97 and CSA S806-12)

12 Advances in Civil Engineering

the relationship between normalized shear strength as(Vpredbwd

fcprime1113969

) and beam depth It is clear that the nor-malized shear strength is decreased with the increase in thebeam depth for ANNs GEP and NLR showing that the sizeeffect is efficiently presented in these models -e trends ofGEP and NLR are very close and compatible and decreasedfrom a depth of 100mm to 1000mm while the ANNsmodelseems to be more accurate as it shows an increase in thetrend up to the depth of 200mm and then it decreasedsimilarly to that of GEP and NLR after that the trend startsto increase slightly

It can be summed up to that the artificial intelligentmodels due to their efficiency and powerful ability in rec-ognizing the parameters interaction demonstrate variousrates of change and fluctuation for the entire scope of inputparameters -e ANNs and GEP models define accurately theinteraction of each parameter on shear strength predictionand have a great ability to represent the actual response ofeach parameter in spite of its complexity and fluctuationnature Furthermore these models are evolved by trainingnumerous preliminary linear and nonlinear models withoutany prior assumption regarding the shape and structure of themathematical model

9 Conclusions

An experimental database including 269 shear test results ofFRP-reinforced concrete members without stirrups availablein the literature was established to propose three predictionmodels to estimate the shear capacity of FRP-RC membersusing three powerful tools which are ANNs GEP and NLR-e following conclusions can be drawn from this study

(i) -e proposed models for predicting the shear ca-pacity of FRP-RC members based on ANNs andGEP techniques showed excellent performancegreat efficiency and high level of accuracy andyielded consistent results throughout a wide rangeof influencing parameters moreover the ANNsmodel is more superior than the GEP as the SD andR2 for ANNs are 0113 and 09877 and for GEP are0162 and 097 respectively

(ii) A simple rational and yet accurate empiricalequation was proposed for predicting shearstrength of FRP-RC members by NLR -e equa-tion considers all the important influencing pa-rameters and simplified to be easy for use Inaddition it gives consistent and accurate resultswith SD and R2 of 0173 and 095 respectively

(iii) -rough a comparative statistical analysis for theproposed models with seven shear design codes andsix proposed equations from the literature it hasbeen found that the most accurate and efficientmodels are ANNs and GEP and to a lower dgreeNLR Among the codes and available proposals theCSA S806-12 and Ashour and Kara [20] equationswere appearing to be more accurate than the others

(iv) From a parametric study considering all the influ-encing parameters on shear capacity it was found thatthe ANNs model and to a lower level GEP modeldefines accurately the interaction of each parameteron shear capacity prediction and has a great ability torepresent the actual response of each parameter inspite of its complexity and fluctuation nature

(v) -e ANNs and GEP models demonstrate that theeffect of flexure reinforcement ratio on shear ca-pacity decreased beyond 003 as a real response tothe available few data in this range therefore morestudies are needed to confirm this case

(vi) -e ANNs model demonstrated that the effect ofad does not absolutely reduce the shear capacitywhile beyond the ad value of 5 its effect couldbecome reverse and contribute to increase in theshear capacity as confirmed by few previous studies

(vii) -e size effect is considered properly by the pro-posed models particularly the ANNs model whichyields more accurate shear capacity prediction tothe experimental results

Data Availability

-e (database of shear strength of beams without stirrups)data used to support the findings of this study are includedwithin the article

Conflicts of Interest

-e authors declare that they have no conflicts of interest

0

004

008

012

016

02

024

0 200 400 600 800 1000 1200

ANNNLRGEP

d (mm)

V pre

db wd

fc

Figure 9 Normalized shear strength (Vpredbwd

fcprime1113969

) versus beamdepth

Advances in Civil Engineering 13

References

[1] M S Alam and A Hussein ldquoSize effect on shear strength ofFRP reinforced concrete beams without stirrupsrdquo Journal ofComposites for Construction vol 17 no 4 pp 507ndash516 2013

[2] J R Yost S P Gross and D W Dinehart ldquoShear strength ofnormal strength concrete beams reinforced with deformedGFRP barsrdquo Journal of Composites for Construction vol 5no 4 pp 268ndash275 2001

[3] A G Razaqpur B O Isgor S Greenaway and A SelleyldquoConcrete contribution to the shear resistance of fiber rein-forced polymer reinforced concrete membersrdquo Journal ofComposites for Construction vol 8 no 5 pp 452ndash460 2004

[4] M Nehdi H El Chabib and A A Saıd ldquoProposed sheardesign equations for FRP-reinforced concrete beams based ongenetic algorithms approachrdquo Journal of Materials in CivilEngineering vol 19 no 12 pp 1033ndash1042 2007

[5] ASCE-ACI445 ldquoRecent approaches to shear design ofstructural concreterdquo Journal of Structural Engineeringvol 124 no 12 pp 1375ndash1417 1998

[6] R Park and T Paulay Reinforced Concrete Structures JohnWiley amp Sons Hoboken NJ USA 1975

[7] I F Kara ldquoPrediction of shear strength of FRP-reinforcedconcrete beams without stirrups based on genetic pro-grammingrdquo Advances in Engineering Software vol 42 no 6pp 295ndash304 2011

[8] R Bashir and A Ashour ldquoNeural networkmodelling for shearstrength of concrete members reinforced with FRP barsrdquoComposites Part B Engineering vol 43 no 8 pp 3198ndash32072012

[9] K Nasrollahzadeh and M M Basiri ldquoPrediction of shearstrength of FRP reinforced concrete beams using fuzzy in-ference systemrdquo Expert Systems with Applications vol 41no 4 pp 1006ndash1020 2014

[10] S Lee and C Lee ldquoPrediction of shear strength of FRP-reinforced concrete flexural members without stirrups usingartificial neural networksrdquo Engineering Structures vol 61pp 99ndash112 2014

[11] E M Golafshani and A Ashour ldquoA feasibility study of BBPfor predicting shear capacity of FRP reinforced concretebeams without stirrupsrdquo Advances in Engineering Softwarevol 97 pp 29ndash39 2016

[12] ACI-440 Guide for the Design and Construction of StructuralConcrete Reinforced with Fiber-Reinforced Polymer (FRP)ACI 440 1R-15 American Concrete Institute FarmingtonsHills MI USA 2015

[13] JSCE ldquoRecommendation for design and construction ofconcrete structures using continuous fiber reinforcing ma-terialsrdquo in Concrete Engineering Series 23 A Machida EdJapan Society of Civil Engineers Tokyo Japan 1997

[14] BISE Interim Guidance on the Design of Reinforced ConcreteStructures Using Fiber Composite Reinforcement British In-stitution of Structural Engineers Seto Ltd London UK1999

[15] CSA Canadian Highway Bridge Design Code SupplementNo 1 to CANCSA S6-06 (S61S1-10) Canadian StandardsAssociation (CSA) Mississauga ON Canada 2010

[16] ISIS Reinforced Concrete Structures with Fibre ReinforcedPolymersmdashDesign Manual No 3 University of Manitoba ISISCanada Corporation Winnipeg MB Canada 2007

[17] CNR-DT203 ldquoGuide for the design and construction ofconcrete structures reinforced with fiber-reinforced polymerbarsrdquo inAdvisory Committee on Technical Recommendations

for Construction CNR-DT 2032006 CNR Rome Italy2007

[18] CSA ldquoCode for the design and construction of buildingstructures with fibre-reinforced polymersrdquo in CANCSAS806-12 p 198 Canadian Standard Association TorontoON Canada 2012

[19] A Razaqpur and S Spadea ldquoResistenza a taglio di elementi dicalcestruzzzo reinforzatti e staffe di FRPrdquo in Proceedings ofAIAS Maratea Italy September 2010

[20] A F Ashour and I F Kara ldquoSize effect on shear strength ofFRP reinforced concrete beamsrdquo Composites Part B Engi-neering vol 60 pp 612ndash620 2014

[21] A R Yousif ldquoShear strength of large FRP-reinforced concretebeams without shear reinforcementrdquo Journal of Pure andApplied Sciences vol 27 pp 9ndash28 2015

[22] A K El-Sayed E F El-Salakawy and B Benmokrane ldquoShearcapacity of high-strength concrete beams reinforced with FRPbarsrdquo ACI Structural Journal vol 103 p 383 2006

[23] A G Razaqpur and O B Isgor ldquoProposed shear designmethod for FRP-reinforced concrete members without stir-rupsrdquo ACI Structural Journal vol 103 p 93 2006

[24] K Maruyama andW Zhao ldquoFlexural and shear behaviour ofconcrete beams reinforced with FRP rodsrdquo in Proceedings ofthe International Conference on Corrosion and CorrosionProtection of Steel in Concrete pp 24ndash28 Sheffield UK1994

[25] W Zhao K Maruyama and H Suzuki ldquoShear behavior ofconcrete beams reinforced by FRP rods as longitudinal andshear reinforcementrdquo in Proceedings of the Second In-ternational RILEM Symposium on Non-Metallic (FRP) Re-inforcement for Concrete Structures p 352 Ghent BelgiumAugust 1995

[26] H Nakamura and T Higai ldquoEvaluation of shear strength ofthe concrete beams reinforced with FRPrdquo in Proceedings ofJapan Society of Civil Engineers p 89 Ghent Belgium 1995

[27] K Maruyama and W Zhao ldquoSize effect in shear behavior ofFRP reinforced concrete beamrdquo in Advanced CompositeMaterials in Bridges and Structures pp 227ndash234 CanadianSociety for Civil Engineering Montreal QC Canada 1996

[28] Y Mizukawa Y Sato T Ueda and Y Kakuta ldquoA studyon shear fatigue behavior of concrete beams with FRP rodsrdquoin Proceedings of the Cird International Symposium onNon-Metallic (FRP) Reinforcement for Concrete Structures(FRPRCS-3) pp 309ndash316 Japan Concrete Institute SapporoJapan 1997

[29] N Duranovic K Pilakoutas and P Waldron ldquoTests onconcrete beams reinforced with glass fibre reinforced plasticbarsrdquo in Proceedings of the Cird International Symposium onNon-Metallic (FRP) Reinforcement for Concrete Structures(FRPRCS-3) pp 479ndash486 Sapporo Japan 1997

[30] N Swamy and M Aburawi ldquoStructural implications of usingGFRP bars as concrete reinforcementrdquo in Proceedings of 3rdInternational Symposium FRPRCS pp 503ndash510 SapporoJapan 1997

[31] C R Michaluk S H Rizkalla G Tadros and B BenmokraneldquoFlexural behavior of one-way concrete slabs reinforced byfiber reinforced plastic reinforcementsrdquo ACI StructuralJournal vol 95 pp 353ndash365 1998

[32] D Deitz I Harik and H Gesund ldquoOne-way slabs reinforcedwith glass fiber reinforced polymer reinforcing barsrdquo SpecialPublication vol 188 pp 279ndash286 1999

[33] T Alkhrdaji M Wideman A Belarbi and A Nanni ldquoShearstrength of GFRP RC beams and slabsrdquo in Proceedings of the

14 Advances in Civil Engineering

International Conference Composites in Construction-CCCpp 409ndash414 Porto Portugal 2001

[34] G S Melo and J A Rayol ldquoShear resistance of GFRPreinforced concrete beamsrdquo in Proceedings of the Rehabil-itating and Repairing the Buildings and Bridges of AmericasHemispheric Workshop on Future Directions Mayaguumlez PRUSA pp 47ndash64 2002

[35] A K Tureyen and R J Frosch ldquoShear tests of FRP-reinforcedconcrete beams without stirrupsrdquo ACI Structural Journalvol 99 pp 427ndash434 2002

[36] S P Gross J R Yost D W Dinehart E Svensen and N LiuldquoShear strength of normal and high strength concrete beamsreinforced with GFRP barsrdquo in Proceedings of InternationalConference on High Performance Materials in Bridgespp 426ndash437 ASCE Reston VA USA 2003

[37] M Tariq and J Newhook ldquoShear testing of FRP reinforcedconcrete without transverse reinforcementrdquo in Proceedings ofAnnual Conference of the Canadian Society for Civil Engi-neering pp 1330ndash1339 Moncton NB Canada June 2003

[38] S Gross D Dinehart J Yost and P -eisz ldquoExperimentaltests of high-strength concrete beams reinforced with CFRPbarsrdquo in Proceedings of the 4th International Conference onAdvanced Composite Materials in Bridges and Structures(ACMBS-4) Calgary AB Canada 2004

[39] A Lubell T Sherwood E Bentz and M P Collins ldquoSafe sheardesign of large wide beams adding shear reinforcement isrecommendedrdquoConcrete International vol 26 pp 66ndash78 2004

[40] J Yost S Gross G Masone and P Hamelin ldquoSustained loadeffects on deflection and ultimate strength of concrete beamsreinforced with GFRPrdquo in Proceedings of the InternationalConference Composites in Construction (CCC2005) LyonFrance July 2005

[41] A El-Sayed E El-Salakawy and B Benmokrane ldquoShearstrength of one-way concrete slabs reinforced with fiber-reinforced polymer composite barsrdquo Journal of Compositesfor Construction vol 9 no 2 pp 147ndash157 2005

[42] A E Kilpatrick and L Easden ldquoShear capacity of GFRPreinforced high strength concrete slabsrdquo in Proceedings of the18th Australasian Conference on the Mechanics of Structuresand Materials Perth Australia vol 1 pp 119ndash124 Taylor ampFrancis London UK 2005

[43] A K El-Sayed E F El-Salakawy and B BenmokraneldquoShear strength of FRP-reinforced concrete beams withouttransverse reinforcementrdquo ACI Structural Journal vol 103p 235 2006

[44] A Ashour ldquoFlexural and shear capacities of concrete beamsreinforced with GFRP barsrdquo Construction and BuildingMaterials vol 20 no 10 pp 1005ndash1015 2006

[45] M Guadagnini K Pilakoutas and P Waldron ldquoShear re-sistance of FRP RC beams experimental studyrdquo Journal ofComposites for Construction vol 10 no 6 pp 464ndash473 2006

[46] R Dawborn and A Kilpatrick Flexural Shear Capacity ofHigh Strength Concrete Slabs Reinforced with LongitudinalGFRP Bars 2006

[47] J Niewels ldquoZum Tragverhalten von Betonbauteilen mitFaserverbundkunststoffbewehrungrdquo Rheinisch-WestfalischeTechnische Hochschule Aachen Lehrstuhl und Institut furMassivbau Dissertation 2008

[48] A El-Sayed K Soudki and E Kling ldquoFlexural behaviour ofself-consolidating concrete slabs reinforced with GFRP barsrdquoin Proceedings of the 9th International Symposium on FiberReinforced Polymer Reinforcement for Reinforced ConcreteStructures pp 13ndash15 Sydney NSW Australia 2009

[49] A Caporale and R Luciano ldquoIndagine sperimentale enumerica sulla resistenza a taglio di travi di calcestruzzoarmate con barre di GFRPrdquo in Proceedings of XXXVIIIConvegno Nazionale AIAS Turin Italy September 2009

[50] R Olivito and F Zuccarello ldquoOn the shear behaviour ofconcrete beams reinforced by carbon fibre-reinforced poly-mer bars an experimental investigation by means of acousticemission techniquerdquo Strain vol 46 no 5 pp 470ndash481 2010

[51] E C Bentz L Massam and M P Collins ldquoShear strength oflarge concrete members with FRP reinforcementrdquo Journal ofComposites for Construction vol 14 no 6 pp 637ndash646 2010

[52] A G Razaqpur M Shedid and B Isgor ldquoShear strength offiber-reinforced polymer reinforced concrete beams subject tounsymmetric loadingrdquo Journal of Composites for Construc-tion vol 15 no 4 pp 500ndash512 2011

[53] M Alam and A Hussein ldquoEffect of member depth on shearstrength of high-strength fiber-reinforced polymerndashreinforced concrete beamsrdquo Journal of Composites for Con-struction vol 16 no 2 pp 119ndash126 2012

[54] F Matta A K El-Sayed A Nanni and B Benmokrane ldquoSizeeffect on concrete shear strength in beams reinforced withfiber-reinforced polymer barsrdquo ACI Structural Journalvol 110-S50 pp 617ndash628 2013

[55] B Abdul-Salam A Farghaly and B Benmokrane ldquoEvalua-tion of shear behavior for one-way concrete slabs reinforcedwith carbon-FRP barsrdquo GEN vol 243 p 1 2013

[56] C H Kim and H S Jang ldquoConcrete shear strength of normaland lightweight concrete beams reinforced with FRP barsrdquoJournal of Composites for Construction vol 18 no 2 article04013038 2014

[57] D Tomlinson and A Fam ldquoPerformance of concrete beamsreinforced with basalt FRP for flexure and shearrdquo Journal ofComposites for Construction vol 19 no 2 article 040140362014

[58] M A Issa T Ovitigala and M Ibrahim ldquoShear behavior ofbasalt fiber reinforced concrete beams with and without basaltFRP stirrupsrdquo Journal of Composites for Construction vol 20no 4 article 04015083 2015

[59] A El Refai and F Abed ldquoConcrete contribution to shearstrength of beams reinforced with basalt fiber-reinforcedbarsrdquo Journal of Composites for Construction vol 20 no 4article 04015082 2015

[60] G B Jumaa and A R Yuosif ldquoSize effect in shear failure ofhigh strength concrete beams without stirrups reinforcedwith basalt FRP barsrdquo KSCE Journal of Civil Engineering2018 In press

[61] M T Hagan H B Demuth and M H BealeNeural NetworkDesign (Electrical Engineering) -omson Learning BostonMA USA 1995

[62] S S Haykin S S Haykin S S Haykin and S S HaykinNeural Networks and Learning Machines Pearson Vol 3Pearson Upper Saddle River NJ USA 2009

[63] M Y Mansour M Dicleli J-Y Lee and J Zhang ldquoPredictingthe shear strength of reinforced concrete beams using artificialneural networksrdquo Engineering Structures vol 26 no 6pp 781ndash799 2004

[64] H Demuth M Beale and M Hagan Neural NetworkToolboxtrade 6 Userrsquos Guide -e MathWorks Inc vol 10 p 11Natick MA USA 2008

[65] A W Oreta and K Kawashima ldquoNeural network modeling ofconfined compressive strength and strain of circular concretecolumnsrdquo Journal of Structural Engineering vol 129 no 4pp 554ndash561 2003

Advances in Civil Engineering 15

[66] S Jung and K S Kim ldquoKnowledge-based predictionof shear strength of concrete beams without shear re-inforcementrdquo Engineering Structures vol 30 no 6pp 1515ndash1525 2008

[67] Z-H Duan S-C Kou and C-S Poon ldquoPrediction ofcompressive strength of recycled aggregate concrete usingartificial neural networksrdquo Construction and Building Mate-rials vol 40 pp 1200ndash1206 2013

[68] H El-Chabib M Nehdi and A Said ldquoPredicting shear ca-pacity of NSC and HSC slender beams without stirrups usingartificial intelligencerdquo Computers and Concrete vol 2 no 1pp 79ndash96 2005

[69] F Altun O Kisi and K Aydin ldquoPredicting the compressivestrength of steel fiber added lightweight concrete using neuralnetworkrdquo Computational Materials Science vol 42 no 2pp 259ndash265 2008

[70] J R Koza ldquoGenetic programming as a means for pro-gramming computers by natural selectionrdquo Statistics andComputing vol 4 no 2 pp 87ndash112 1994

[71] C Ferreira ldquoGene expression programming in problemsolvingrdquo in Soft Computing and Industry pp 635ndash653Springer Berlin Germany 2002

[72] C Kayadelen ldquoSoil liquefaction modeling by genetic ex-pression programming and neuro-fuzzyrdquo Expert Systems withApplications vol 38 no 4 pp 4080ndash4087 2011

[73] A H Gandomi A H Alavi and G J Yun ldquoFormulation ofuplift capacity of suction caissons using multi expressionprogrammingrdquo KSCE Journal of Civil Engineering vol 15no 2 pp 363ndash373 2011

[74] A H Gandomi A H Alavi and C RyanHandbook of GeneticProgramming Applications Springer Berlin Germany 2015

[75] A H Gandomi and A H Alavi ldquoA new multi-gene geneticprogramming approach to non-linear system modeling PartII geotechnical and earthquake engineering problemsrdquoNeural Computing and Applications vol 21 no 1 pp 189ndash201 2012

[76] A H Alavi and A H Gandomi ldquoEnergy-based numericalmodels for assessment of soil liquefactionrdquo GeoscienceFrontiers vol 3 no 4 pp 541ndash555 2012

[77] L Teodorescu and D Sherwood ldquoHigh energy physics eventselection with gene expression programmingrdquo ComputerPhysics Communications vol 178 no 6 pp 409ndash419 2008

[78] GEPSOFT GeneXproTools Version 50 GEPSOFT BristolUK 2013 httpwwwgepsoftcom

[79] S M Mousavi P Aminian A H Gandomi A H Alavi andH Bolandi ldquoA new predictive model for compressive strengthof HPC using gene expression programmingrdquo Advances inEngineering Software vol 45 no 1 pp 105ndash114 2012

[80] M Sarıdemir ldquoEmpirical modeling of splitting tensilestrength from cylinder compressive strength of concrete bygenetic programmingrdquo Expert Systems with Applicationsvol 38 no 11 pp 14257ndash14268 2011

[81] M Sonebi and A Cevik ldquoGenetic programming based for-mulation for fresh and hardened properties of self-compacting concrete containing pulverised fuel ashrdquo Con-struction and Building Materials vol 23 no 7 pp 2614ndash26222009

[82] A H Alavi P Aminian A H Gandomi and M A EsmaeilildquoGenetic-based modeling of uplift capacity of suction cais-sonsrdquo Expert Systems with Applications vol 38 no 10pp 12608ndash12618 2011

[83] T Zsutty ldquoShear strength prediction for separate catagories ofsimple beam testsrdquo ACI Journal Proceedings vol 68 no 2pp 138ndash143 1971

16 Advances in Civil Engineering

Vc absc3 + d5 lowastd3( ) d2 + d0( )2

4( )

13

lowast tanhd2d1( )

15 minus tanh d2 lowast d3( )4( )

5

lowast d2 +d153

max d1 c6( )c8 + d4( )( )

2

lowast tanhd2d1( )

15 minus

d1d0

radic

3

5

(6)

where d0 d1 d2 d3 d4 and d5 refer to d ad bρf fcprime and Ef respectively c2 656723946184092 c3 minus241413053630399 c4 minus121479701959083 c6 307014791103389 and c8 220241396443835

6 Nonlinear Regression Model (NLR)

Regression analysis is considered as an important toolthat can be used in the modeling process for solvingcomplicated problems of various engineering disciplines

However the proposed models based on nonlinear re-gression (NLR) are less accurate than the ANN and GEPhowever it is characterized by that it is simple and easy forapplication without the need of computers for calculationsA nonlinear regression model based on the experimentaldatabase collected from the literature was suggested eproposed equation was derived based on developinga model similar to that proposed by Zsutty [83] which is themost accurate and simple empirical equation that wasproposed for shear prediction of steel-RC members Inorder to predict the shear strength of FRP-RC beams moreaccurately considering the eect of all incentuencing pa-rameters the experimental shear strength was analyzedwith most common incentuencing parameters fcprime d b adEf and ρf Based on data tting analysis and after somesimplication the following equation was proposed

Vc 0321d( )

13 Efρfad( )

25fcprime( )15bwd (7)

It can be observed that the equation is simple rationaland more generalized than most codes and proposedequations from the literature as it considers the eect of allthe incentuencing parameters on the shear strength of FRP-RCmembers without stirrups

7 Results and Discussion

e shear strength results of FRP-reinforced concretemembers for the three proposed models the ANNs GEPand NLR are evaluated and compared with the commondesign provisions (ACI 440-15 JSCE-97 CSA 806-12) andseven proposed equations [1 4 7 10 19ndash21] e com-parison was examined based on statistical terms such as

Start

Initial population creation

Chromosome expression as ET

ET execution

Fitness evaluation

Stop

Chromosome selection

Reproduction

Terminate

New generation creation

Yes

No

Figure 5 Flowchart of GEP [77]

Table 3 Parameters used in the GEP Model

Parameters ValuesNumber of chromosomes 30ndash500Head size 3 5 8Number of genes 2 3 4Linking function Multiplication

Function set + minus lowast abs tanh x2 x12 x13 x15

Generation withoutchanges 2000

Number of tries 12Maximum complexity 10Fitness function RMSEMutation 0044Inversion 01One-pointrecombination 03

Two-pointrecombination 03

Gene recombination 01Gene transposition 01IS transposition 01RIS transposition 01Data type Floating pointConstants per gene 10

8 Advances in Civil Engineering

mean standard deviation (SD) and coelaquocient of variation(COV) in addition to error values such as mean absoluteerror (MAE) root mean square error (RMSE) and R2 asshown below

RMSE

sumN

i0 ei minuspi( )2

N

radic

MAE 1NsumN

i0ei minuspi∣∣∣∣

∣∣∣∣

R2 1minussumN

i0 ei minuspi( )2

sumN

i0 ei minus e( )2

(8)

where ei and pi are the experimental and predicted shearforce in kN respectively e is the average of the experimentalvalues andN is the total number of the considered samplese model that minimized the error values (MAE andRMSE) and maximized R2 is selected as the optimummodel

Figure 7 presents the scatter of the experimental shearforce Vexp versus the predicted shear strength Vpred for theproposed models codes and proposed equations from theliterature It is clear that the best models for predicting theshear strength are those suggested in this study which ina sequence are ANNs GEP and NLR as these modelspredict the shear strength very accurately with the optimumstatistical performance of R2 RMSE and MAE High cor-relation coelaquocients with low error rates indicate that theproposed three models are excellent models and exhibitgeneralization performance in predicting shear strength ofFRP-reinforced concrete beams without stirrups In con-trast the code design provisions and other proposedequations from the literature yielded dispersion results with

lower R2 and larger error rates as given in the scatterrelationships

Table 4 presents the statistical parameters (meanstandard deviation (SD) coelaquocient of variation (COV)minimum maximum range RMSE MAE and R2) of theratio of experimental shear strength to the predicted shearstrength VexpVpred for the proposed models in thisstudy seven well-known codes and seven proposedequations from literature based on the (269) collecteddatabase It is clear that the proposed equations yieldedsuperior accuracy between all the codes and proposedequation from the literature because their optimumstatistical parameters such as the mean SD range RMSEand R2 are 0998 0113 072 53 and 09877 respectivelyfor ANNs 1007 0162 088 82 and 0970 respectivelyfor GEP and 1003 0174 099 107 and 095 re-spectively for NLR

e ANNs and GEP models are articial intelligentmodels derived based on soft computing as veried abovethese models are accurate superior and highly elaquocient inpredicting the complicated problem such as shear strengthHowever the drawback of articial intelligent models is thatit cannot be calculated manually and it needs computers forcalculation Besides it is considered as a powerful and ef-cient tool which can be used in soft programs specializedfor analysis and design of reinforced concrete structures Onthe contrary the NLR model is simply accurate and rationalwhich can be used manually with sulaquocient accuracy morethan the design codes and previously proposed equationsNevertheless the regression equations cannot properlydene with the same level of elaquociency of articial intelligenttechniques the interactions between the input and outputparameters due to that the regression models usually areproduced based only on a few predened equations [79]

3Rt

c3 lowast

lowast

d0

d3d5

lowast Avg2 c2

c2 d0

Avg2

+

(a)

x5

lowast

ndash

5Rt

Tanh

x4

c4d3d2d1

Tanh

(b)

+

d2x2

+

d1d3

Max2d4

c6

c8

5Rt

lowast

(c)

x5

ndash

5Rt

x3

d0d1d2d1

Tanh

Sqrt

(d)

Figure 6 Expression trees ETs for the GEP model (a) Sub-ET 1 (b) Sub-ET 2 (c) Sub-ET 3 (d) Sub-ET 4

Advances in Civil Engineering 9

Finally it can be said that all the three proposed equationscan be considered as accurate efficient and useful modelswhich were trained on a largest collected database forpredicting the shear strength of FRP-reinforced concretemembers

8 Parametric Analyses

For further verification of the proposed ANNs GEP andNLR prediction models a parametric analysis was per-formed in this study -e main goal was to find the

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

ANNsR2 = 09877RMSE = 53MAE = 39

GEPR2 = 09709

RMSE = 82kNMAE = 59kN

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

ACI 440-06R2 = 0575

RMSE = 315MAE = 242

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

CSA 806-12R2 = 0783

RMSE = 225MAE = 117

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

R2 = 0805RMSE = 213MAE = 121

Nehdi et al (2007)

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

R2 = 0772RMSE = 231MAE = 144

Razaqpur and Spadea (2011)

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

R2 = 08347RMSE = 196MAE = 110

Kara (2011)

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

R2 = 0865RMSE = 177MAE = 109

Alam and Husein (2013)

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

R2 = 0885RMSE = 164MAE = 102

Ashour and Kara (2014)

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

R2 = 0902RMSE = 151MAE = 96

Lee (2014)

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

JSCE97R2 = 0792

RMSE = 220MAE = 149

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

NLR

Vexp (kN)

R2 = 0950RMSE = 107MAE = 73

Figure 7 Scatter of Vexp versus Vpred for ANN GEP NLR and different models from the literature

10 Advances in Civil Engineering

response of the three proposed models to predict the shearstrength for a set of input parameters which are selectedtaking into account the average value of each parame-ter in the collected database For further showing theperformance of the proposed models and for comparisonpurpose the response of three well-known codes (ACI1R440-15 JSCE-97 and CSA S806-12) was also considered-e approach depends on keeping all input parameters attheir selected values except that in each time a singleparameter value was changed incrementally within theexpected practical values Consequently an arrangementof manufactured data for the single considered parameteris produced this procedure was repeated for all parametersso that all models are examined for the entire input pa-rameters -e selected input parameters are fcprime 46MPabw 200mm d 400mm ad 4 ρf 0011 and Ef

74 GPa It is worthy to note that the ANNs model cannotproperly predict the shear strength for input parametersoutside the range of training data therefore it is only validfor prediction within the range of input parameters of thetraining data [8]

Figure 8 indicates the tendency of the predicted shearstrength by differentmodels to the varieties of themain designparameters (d fcprime ρf Ef ad and bw) Generally it can beobserved that the proposed models particularly the ANNsmodel yielded larger shear capacities for all parameters whileACI 440-15 yielded the lowest shear capacities which indicatethat the ACI 440-15 is very conservative

-e relationship of beam depth with the predicted shearstrength showed that all the proposed models and codesincreased with the increase in the beam depth throughoutthe range of 100ndash1000mm -e ACI 440-15 considers theeffect of beam depth linearly while all other models rep-resent the effect of depth nonlinearly the ANNs GEP andNLR models consider the depth raised to a power of 083067 and 066 respectively Also it can be observed that theGEP and NLR yield almost the same results All the pro-posed models and codes showed an increase in shearstrength with the increase in the concrete compressive

strength but in different rates It was found that fcprime is raisedto a power of 066 030 and 02 for ANNs GEP and NLRrespectively

-e effect of the flexure reinforcement ratio on shearstrength indicates a similar trend of the NLR model and thedesign codes but the ANNs and GEP models showeda slightly decreased trend for reinforcement ratios greaterthan 003 this is not in agreement with codes and previousstudies because of that only few data were available with ρflarger than 003 and these data actually showed decreasingshear capacity Additionally these models were derivedbased only on the artificial technology of data trainingwithout manually choosing the general mathematical shapeof the model in contrary to the NLRmodel and design codeswhich was derived based on the theoretical or semiempiricalcriteria

-e shear strength also increased with the increase inthe elastic modulus of the flexure reinforcement ratio Itcan be observed that all models showed a similar trend linefor the entire range of data while the ANNs model showedan increased rate up to about 110 GPa and then the in-crease rate reduced significantly similar results also ob-tained by Bashir and Ashour [8] On the contrary thetrend lines of the shear span to depth ratio are decreasedfor GEP and NLR models for the entire range of datameanwhile for ANNs model it decreases up to ad of 5and then it started to increase slightly -is behavior is inagreement with the few available experimental results[32 52 56] which were studied as ad greater than 5However other codes do not consider the effect of ad asthe trend lines for ACI 440-15 and JSCE-97 are constantwhile the CSA S806 trend line remains constant beyondthe ad value of 5 Finally the effect of beam width on shearstrength is linear as indicated by trend lines for all modelsexcept the ANNs model which showed a lower increaserate beyond 700mm width

To investigate how the proposed models consider thesize effect on shear capacity the same parametric data usedfor studying the beam depth are used Figure 9 presents

Table 4 Statistical parameters of (VexpVpred) for the proposed models and different design equations

Design equations Mean (VexpVpred) SD COV Minimum Maximum Range RMSE MAE R2

[12] 1813 0416 2306 113 374 261 315 242 0575[13] 1302 0282 2163 046 251 205 220 149 0792[18] 1091 0227 2085 047 185 137 225 117 0783[16] 1193 0386 3249 044 248 203 2633 1758 0703[17] 0948 0265 2799 039 174 134 2257 1403 0782[14] 1072 0247 231 054 192 138 1470 980 0908[15] 1393 0254 1835 070 248 178 2456 1661 0742[4] 1113 0219 1967 055 192 136 213 121 0805[19] 1305 0235 1801 084 214 129 231 184 0772[7] 1025 0205 2003 054 191 136 196 110 0835[1] 1148 0227 1981 059 172 113 177 109 0865[20] 0965 0174 1806 063 168 105 164 102 0885[10] 1015 0229 2251 053 196 143 151 96 0905[21] 1096 0283 2587 056 212 156 1915 1180 0843NLR 1003 0174 1732 062 161 099 107 73 0950GEP 1007 0162 1608 066 155 088 82 59 09709ANNs 0998 0113 1131 071 144 072 53 39 09877

Advances in Civil Engineering 11

0

30

60

90

120

150

180

0 150 300 450 600 750 900 1050

V pre

d (k

N)

d (mm)

ANNGEPJSCE 97

NLRACI 440CSA S806

0

20

40

60

80

100

120

0 10 20 30 40 50 60 70 80 90 100 110

V pre

d (k

N)

fcprime (MPa)

ANNGEPJSCE 97

NLRACI 440SCA S806

0

20

40

60

80

100

120

0 001 002 003 004 005

V pre

d (k

N)

ρf

ANNGEPJSCE 97

NLRACI 440CSA S806

0

20

40

60

80

100

120

0 25 50 75 100 125 150 175

V pre

d (k

N)

Ef (MPa)

ANNGEPJSCE 97

NLRACI 440CSA S806

0

20

40

60

80

100

120

0 2 4 6 8 10

V pre

d (k

N)

ad

ANNGEPJSCE 97

NLRACI 440CSA S806

0

60

120

180

240

300

360

0 200 400 600 800 1000 1200

V pre

d (k

N)

b (mm)

ANNGEPJSCE 97

NLRACI 440CSA S806

Figure 8 Eect of the parameters (d fcprime ρf Ef ad and bw) on shear capacity predicted by ANNs GEP NLR and three design codes(ACI1R 440-06 JSCE-97 and CSA S806-12)

12 Advances in Civil Engineering

the relationship between normalized shear strength as(Vpredbwd

fcprime1113969

) and beam depth It is clear that the nor-malized shear strength is decreased with the increase in thebeam depth for ANNs GEP and NLR showing that the sizeeffect is efficiently presented in these models -e trends ofGEP and NLR are very close and compatible and decreasedfrom a depth of 100mm to 1000mm while the ANNsmodelseems to be more accurate as it shows an increase in thetrend up to the depth of 200mm and then it decreasedsimilarly to that of GEP and NLR after that the trend startsto increase slightly

It can be summed up to that the artificial intelligentmodels due to their efficiency and powerful ability in rec-ognizing the parameters interaction demonstrate variousrates of change and fluctuation for the entire scope of inputparameters -e ANNs and GEP models define accurately theinteraction of each parameter on shear strength predictionand have a great ability to represent the actual response ofeach parameter in spite of its complexity and fluctuationnature Furthermore these models are evolved by trainingnumerous preliminary linear and nonlinear models withoutany prior assumption regarding the shape and structure of themathematical model

9 Conclusions

An experimental database including 269 shear test results ofFRP-reinforced concrete members without stirrups availablein the literature was established to propose three predictionmodels to estimate the shear capacity of FRP-RC membersusing three powerful tools which are ANNs GEP and NLR-e following conclusions can be drawn from this study

(i) -e proposed models for predicting the shear ca-pacity of FRP-RC members based on ANNs andGEP techniques showed excellent performancegreat efficiency and high level of accuracy andyielded consistent results throughout a wide rangeof influencing parameters moreover the ANNsmodel is more superior than the GEP as the SD andR2 for ANNs are 0113 and 09877 and for GEP are0162 and 097 respectively

(ii) A simple rational and yet accurate empiricalequation was proposed for predicting shearstrength of FRP-RC members by NLR -e equa-tion considers all the important influencing pa-rameters and simplified to be easy for use Inaddition it gives consistent and accurate resultswith SD and R2 of 0173 and 095 respectively

(iii) -rough a comparative statistical analysis for theproposed models with seven shear design codes andsix proposed equations from the literature it hasbeen found that the most accurate and efficientmodels are ANNs and GEP and to a lower dgreeNLR Among the codes and available proposals theCSA S806-12 and Ashour and Kara [20] equationswere appearing to be more accurate than the others

(iv) From a parametric study considering all the influ-encing parameters on shear capacity it was found thatthe ANNs model and to a lower level GEP modeldefines accurately the interaction of each parameteron shear capacity prediction and has a great ability torepresent the actual response of each parameter inspite of its complexity and fluctuation nature

(v) -e ANNs and GEP models demonstrate that theeffect of flexure reinforcement ratio on shear ca-pacity decreased beyond 003 as a real response tothe available few data in this range therefore morestudies are needed to confirm this case

(vi) -e ANNs model demonstrated that the effect ofad does not absolutely reduce the shear capacitywhile beyond the ad value of 5 its effect couldbecome reverse and contribute to increase in theshear capacity as confirmed by few previous studies

(vii) -e size effect is considered properly by the pro-posed models particularly the ANNs model whichyields more accurate shear capacity prediction tothe experimental results

Data Availability

-e (database of shear strength of beams without stirrups)data used to support the findings of this study are includedwithin the article

Conflicts of Interest

-e authors declare that they have no conflicts of interest

0

004

008

012

016

02

024

0 200 400 600 800 1000 1200

ANNNLRGEP

d (mm)

V pre

db wd

fc

Figure 9 Normalized shear strength (Vpredbwd

fcprime1113969

) versus beamdepth

Advances in Civil Engineering 13

References

[1] M S Alam and A Hussein ldquoSize effect on shear strength ofFRP reinforced concrete beams without stirrupsrdquo Journal ofComposites for Construction vol 17 no 4 pp 507ndash516 2013

[2] J R Yost S P Gross and D W Dinehart ldquoShear strength ofnormal strength concrete beams reinforced with deformedGFRP barsrdquo Journal of Composites for Construction vol 5no 4 pp 268ndash275 2001

[3] A G Razaqpur B O Isgor S Greenaway and A SelleyldquoConcrete contribution to the shear resistance of fiber rein-forced polymer reinforced concrete membersrdquo Journal ofComposites for Construction vol 8 no 5 pp 452ndash460 2004

[4] M Nehdi H El Chabib and A A Saıd ldquoProposed sheardesign equations for FRP-reinforced concrete beams based ongenetic algorithms approachrdquo Journal of Materials in CivilEngineering vol 19 no 12 pp 1033ndash1042 2007

[5] ASCE-ACI445 ldquoRecent approaches to shear design ofstructural concreterdquo Journal of Structural Engineeringvol 124 no 12 pp 1375ndash1417 1998

[6] R Park and T Paulay Reinforced Concrete Structures JohnWiley amp Sons Hoboken NJ USA 1975

[7] I F Kara ldquoPrediction of shear strength of FRP-reinforcedconcrete beams without stirrups based on genetic pro-grammingrdquo Advances in Engineering Software vol 42 no 6pp 295ndash304 2011

[8] R Bashir and A Ashour ldquoNeural networkmodelling for shearstrength of concrete members reinforced with FRP barsrdquoComposites Part B Engineering vol 43 no 8 pp 3198ndash32072012

[9] K Nasrollahzadeh and M M Basiri ldquoPrediction of shearstrength of FRP reinforced concrete beams using fuzzy in-ference systemrdquo Expert Systems with Applications vol 41no 4 pp 1006ndash1020 2014

[10] S Lee and C Lee ldquoPrediction of shear strength of FRP-reinforced concrete flexural members without stirrups usingartificial neural networksrdquo Engineering Structures vol 61pp 99ndash112 2014

[11] E M Golafshani and A Ashour ldquoA feasibility study of BBPfor predicting shear capacity of FRP reinforced concretebeams without stirrupsrdquo Advances in Engineering Softwarevol 97 pp 29ndash39 2016

[12] ACI-440 Guide for the Design and Construction of StructuralConcrete Reinforced with Fiber-Reinforced Polymer (FRP)ACI 440 1R-15 American Concrete Institute FarmingtonsHills MI USA 2015

[13] JSCE ldquoRecommendation for design and construction ofconcrete structures using continuous fiber reinforcing ma-terialsrdquo in Concrete Engineering Series 23 A Machida EdJapan Society of Civil Engineers Tokyo Japan 1997

[14] BISE Interim Guidance on the Design of Reinforced ConcreteStructures Using Fiber Composite Reinforcement British In-stitution of Structural Engineers Seto Ltd London UK1999

[15] CSA Canadian Highway Bridge Design Code SupplementNo 1 to CANCSA S6-06 (S61S1-10) Canadian StandardsAssociation (CSA) Mississauga ON Canada 2010

[16] ISIS Reinforced Concrete Structures with Fibre ReinforcedPolymersmdashDesign Manual No 3 University of Manitoba ISISCanada Corporation Winnipeg MB Canada 2007

[17] CNR-DT203 ldquoGuide for the design and construction ofconcrete structures reinforced with fiber-reinforced polymerbarsrdquo inAdvisory Committee on Technical Recommendations

for Construction CNR-DT 2032006 CNR Rome Italy2007

[18] CSA ldquoCode for the design and construction of buildingstructures with fibre-reinforced polymersrdquo in CANCSAS806-12 p 198 Canadian Standard Association TorontoON Canada 2012

[19] A Razaqpur and S Spadea ldquoResistenza a taglio di elementi dicalcestruzzzo reinforzatti e staffe di FRPrdquo in Proceedings ofAIAS Maratea Italy September 2010

[20] A F Ashour and I F Kara ldquoSize effect on shear strength ofFRP reinforced concrete beamsrdquo Composites Part B Engi-neering vol 60 pp 612ndash620 2014

[21] A R Yousif ldquoShear strength of large FRP-reinforced concretebeams without shear reinforcementrdquo Journal of Pure andApplied Sciences vol 27 pp 9ndash28 2015

[22] A K El-Sayed E F El-Salakawy and B Benmokrane ldquoShearcapacity of high-strength concrete beams reinforced with FRPbarsrdquo ACI Structural Journal vol 103 p 383 2006

[23] A G Razaqpur and O B Isgor ldquoProposed shear designmethod for FRP-reinforced concrete members without stir-rupsrdquo ACI Structural Journal vol 103 p 93 2006

[24] K Maruyama andW Zhao ldquoFlexural and shear behaviour ofconcrete beams reinforced with FRP rodsrdquo in Proceedings ofthe International Conference on Corrosion and CorrosionProtection of Steel in Concrete pp 24ndash28 Sheffield UK1994

[25] W Zhao K Maruyama and H Suzuki ldquoShear behavior ofconcrete beams reinforced by FRP rods as longitudinal andshear reinforcementrdquo in Proceedings of the Second In-ternational RILEM Symposium on Non-Metallic (FRP) Re-inforcement for Concrete Structures p 352 Ghent BelgiumAugust 1995

[26] H Nakamura and T Higai ldquoEvaluation of shear strength ofthe concrete beams reinforced with FRPrdquo in Proceedings ofJapan Society of Civil Engineers p 89 Ghent Belgium 1995

[27] K Maruyama and W Zhao ldquoSize effect in shear behavior ofFRP reinforced concrete beamrdquo in Advanced CompositeMaterials in Bridges and Structures pp 227ndash234 CanadianSociety for Civil Engineering Montreal QC Canada 1996

[28] Y Mizukawa Y Sato T Ueda and Y Kakuta ldquoA studyon shear fatigue behavior of concrete beams with FRP rodsrdquoin Proceedings of the Cird International Symposium onNon-Metallic (FRP) Reinforcement for Concrete Structures(FRPRCS-3) pp 309ndash316 Japan Concrete Institute SapporoJapan 1997

[29] N Duranovic K Pilakoutas and P Waldron ldquoTests onconcrete beams reinforced with glass fibre reinforced plasticbarsrdquo in Proceedings of the Cird International Symposium onNon-Metallic (FRP) Reinforcement for Concrete Structures(FRPRCS-3) pp 479ndash486 Sapporo Japan 1997

[30] N Swamy and M Aburawi ldquoStructural implications of usingGFRP bars as concrete reinforcementrdquo in Proceedings of 3rdInternational Symposium FRPRCS pp 503ndash510 SapporoJapan 1997

[31] C R Michaluk S H Rizkalla G Tadros and B BenmokraneldquoFlexural behavior of one-way concrete slabs reinforced byfiber reinforced plastic reinforcementsrdquo ACI StructuralJournal vol 95 pp 353ndash365 1998

[32] D Deitz I Harik and H Gesund ldquoOne-way slabs reinforcedwith glass fiber reinforced polymer reinforcing barsrdquo SpecialPublication vol 188 pp 279ndash286 1999

[33] T Alkhrdaji M Wideman A Belarbi and A Nanni ldquoShearstrength of GFRP RC beams and slabsrdquo in Proceedings of the

14 Advances in Civil Engineering

International Conference Composites in Construction-CCCpp 409ndash414 Porto Portugal 2001

[34] G S Melo and J A Rayol ldquoShear resistance of GFRPreinforced concrete beamsrdquo in Proceedings of the Rehabil-itating and Repairing the Buildings and Bridges of AmericasHemispheric Workshop on Future Directions Mayaguumlez PRUSA pp 47ndash64 2002

[35] A K Tureyen and R J Frosch ldquoShear tests of FRP-reinforcedconcrete beams without stirrupsrdquo ACI Structural Journalvol 99 pp 427ndash434 2002

[36] S P Gross J R Yost D W Dinehart E Svensen and N LiuldquoShear strength of normal and high strength concrete beamsreinforced with GFRP barsrdquo in Proceedings of InternationalConference on High Performance Materials in Bridgespp 426ndash437 ASCE Reston VA USA 2003

[37] M Tariq and J Newhook ldquoShear testing of FRP reinforcedconcrete without transverse reinforcementrdquo in Proceedings ofAnnual Conference of the Canadian Society for Civil Engi-neering pp 1330ndash1339 Moncton NB Canada June 2003

[38] S Gross D Dinehart J Yost and P -eisz ldquoExperimentaltests of high-strength concrete beams reinforced with CFRPbarsrdquo in Proceedings of the 4th International Conference onAdvanced Composite Materials in Bridges and Structures(ACMBS-4) Calgary AB Canada 2004

[39] A Lubell T Sherwood E Bentz and M P Collins ldquoSafe sheardesign of large wide beams adding shear reinforcement isrecommendedrdquoConcrete International vol 26 pp 66ndash78 2004

[40] J Yost S Gross G Masone and P Hamelin ldquoSustained loadeffects on deflection and ultimate strength of concrete beamsreinforced with GFRPrdquo in Proceedings of the InternationalConference Composites in Construction (CCC2005) LyonFrance July 2005

[41] A El-Sayed E El-Salakawy and B Benmokrane ldquoShearstrength of one-way concrete slabs reinforced with fiber-reinforced polymer composite barsrdquo Journal of Compositesfor Construction vol 9 no 2 pp 147ndash157 2005

[42] A E Kilpatrick and L Easden ldquoShear capacity of GFRPreinforced high strength concrete slabsrdquo in Proceedings of the18th Australasian Conference on the Mechanics of Structuresand Materials Perth Australia vol 1 pp 119ndash124 Taylor ampFrancis London UK 2005

[43] A K El-Sayed E F El-Salakawy and B BenmokraneldquoShear strength of FRP-reinforced concrete beams withouttransverse reinforcementrdquo ACI Structural Journal vol 103p 235 2006

[44] A Ashour ldquoFlexural and shear capacities of concrete beamsreinforced with GFRP barsrdquo Construction and BuildingMaterials vol 20 no 10 pp 1005ndash1015 2006

[45] M Guadagnini K Pilakoutas and P Waldron ldquoShear re-sistance of FRP RC beams experimental studyrdquo Journal ofComposites for Construction vol 10 no 6 pp 464ndash473 2006

[46] R Dawborn and A Kilpatrick Flexural Shear Capacity ofHigh Strength Concrete Slabs Reinforced with LongitudinalGFRP Bars 2006

[47] J Niewels ldquoZum Tragverhalten von Betonbauteilen mitFaserverbundkunststoffbewehrungrdquo Rheinisch-WestfalischeTechnische Hochschule Aachen Lehrstuhl und Institut furMassivbau Dissertation 2008

[48] A El-Sayed K Soudki and E Kling ldquoFlexural behaviour ofself-consolidating concrete slabs reinforced with GFRP barsrdquoin Proceedings of the 9th International Symposium on FiberReinforced Polymer Reinforcement for Reinforced ConcreteStructures pp 13ndash15 Sydney NSW Australia 2009

[49] A Caporale and R Luciano ldquoIndagine sperimentale enumerica sulla resistenza a taglio di travi di calcestruzzoarmate con barre di GFRPrdquo in Proceedings of XXXVIIIConvegno Nazionale AIAS Turin Italy September 2009

[50] R Olivito and F Zuccarello ldquoOn the shear behaviour ofconcrete beams reinforced by carbon fibre-reinforced poly-mer bars an experimental investigation by means of acousticemission techniquerdquo Strain vol 46 no 5 pp 470ndash481 2010

[51] E C Bentz L Massam and M P Collins ldquoShear strength oflarge concrete members with FRP reinforcementrdquo Journal ofComposites for Construction vol 14 no 6 pp 637ndash646 2010

[52] A G Razaqpur M Shedid and B Isgor ldquoShear strength offiber-reinforced polymer reinforced concrete beams subject tounsymmetric loadingrdquo Journal of Composites for Construc-tion vol 15 no 4 pp 500ndash512 2011

[53] M Alam and A Hussein ldquoEffect of member depth on shearstrength of high-strength fiber-reinforced polymerndashreinforced concrete beamsrdquo Journal of Composites for Con-struction vol 16 no 2 pp 119ndash126 2012

[54] F Matta A K El-Sayed A Nanni and B Benmokrane ldquoSizeeffect on concrete shear strength in beams reinforced withfiber-reinforced polymer barsrdquo ACI Structural Journalvol 110-S50 pp 617ndash628 2013

[55] B Abdul-Salam A Farghaly and B Benmokrane ldquoEvalua-tion of shear behavior for one-way concrete slabs reinforcedwith carbon-FRP barsrdquo GEN vol 243 p 1 2013

[56] C H Kim and H S Jang ldquoConcrete shear strength of normaland lightweight concrete beams reinforced with FRP barsrdquoJournal of Composites for Construction vol 18 no 2 article04013038 2014

[57] D Tomlinson and A Fam ldquoPerformance of concrete beamsreinforced with basalt FRP for flexure and shearrdquo Journal ofComposites for Construction vol 19 no 2 article 040140362014

[58] M A Issa T Ovitigala and M Ibrahim ldquoShear behavior ofbasalt fiber reinforced concrete beams with and without basaltFRP stirrupsrdquo Journal of Composites for Construction vol 20no 4 article 04015083 2015

[59] A El Refai and F Abed ldquoConcrete contribution to shearstrength of beams reinforced with basalt fiber-reinforcedbarsrdquo Journal of Composites for Construction vol 20 no 4article 04015082 2015

[60] G B Jumaa and A R Yuosif ldquoSize effect in shear failure ofhigh strength concrete beams without stirrups reinforcedwith basalt FRP barsrdquo KSCE Journal of Civil Engineering2018 In press

[61] M T Hagan H B Demuth and M H BealeNeural NetworkDesign (Electrical Engineering) -omson Learning BostonMA USA 1995

[62] S S Haykin S S Haykin S S Haykin and S S HaykinNeural Networks and Learning Machines Pearson Vol 3Pearson Upper Saddle River NJ USA 2009

[63] M Y Mansour M Dicleli J-Y Lee and J Zhang ldquoPredictingthe shear strength of reinforced concrete beams using artificialneural networksrdquo Engineering Structures vol 26 no 6pp 781ndash799 2004

[64] H Demuth M Beale and M Hagan Neural NetworkToolboxtrade 6 Userrsquos Guide -e MathWorks Inc vol 10 p 11Natick MA USA 2008

[65] A W Oreta and K Kawashima ldquoNeural network modeling ofconfined compressive strength and strain of circular concretecolumnsrdquo Journal of Structural Engineering vol 129 no 4pp 554ndash561 2003

Advances in Civil Engineering 15

[66] S Jung and K S Kim ldquoKnowledge-based predictionof shear strength of concrete beams without shear re-inforcementrdquo Engineering Structures vol 30 no 6pp 1515ndash1525 2008

[67] Z-H Duan S-C Kou and C-S Poon ldquoPrediction ofcompressive strength of recycled aggregate concrete usingartificial neural networksrdquo Construction and Building Mate-rials vol 40 pp 1200ndash1206 2013

[68] H El-Chabib M Nehdi and A Said ldquoPredicting shear ca-pacity of NSC and HSC slender beams without stirrups usingartificial intelligencerdquo Computers and Concrete vol 2 no 1pp 79ndash96 2005

[69] F Altun O Kisi and K Aydin ldquoPredicting the compressivestrength of steel fiber added lightweight concrete using neuralnetworkrdquo Computational Materials Science vol 42 no 2pp 259ndash265 2008

[70] J R Koza ldquoGenetic programming as a means for pro-gramming computers by natural selectionrdquo Statistics andComputing vol 4 no 2 pp 87ndash112 1994

[71] C Ferreira ldquoGene expression programming in problemsolvingrdquo in Soft Computing and Industry pp 635ndash653Springer Berlin Germany 2002

[72] C Kayadelen ldquoSoil liquefaction modeling by genetic ex-pression programming and neuro-fuzzyrdquo Expert Systems withApplications vol 38 no 4 pp 4080ndash4087 2011

[73] A H Gandomi A H Alavi and G J Yun ldquoFormulation ofuplift capacity of suction caissons using multi expressionprogrammingrdquo KSCE Journal of Civil Engineering vol 15no 2 pp 363ndash373 2011

[74] A H Gandomi A H Alavi and C RyanHandbook of GeneticProgramming Applications Springer Berlin Germany 2015

[75] A H Gandomi and A H Alavi ldquoA new multi-gene geneticprogramming approach to non-linear system modeling PartII geotechnical and earthquake engineering problemsrdquoNeural Computing and Applications vol 21 no 1 pp 189ndash201 2012

[76] A H Alavi and A H Gandomi ldquoEnergy-based numericalmodels for assessment of soil liquefactionrdquo GeoscienceFrontiers vol 3 no 4 pp 541ndash555 2012

[77] L Teodorescu and D Sherwood ldquoHigh energy physics eventselection with gene expression programmingrdquo ComputerPhysics Communications vol 178 no 6 pp 409ndash419 2008

[78] GEPSOFT GeneXproTools Version 50 GEPSOFT BristolUK 2013 httpwwwgepsoftcom

[79] S M Mousavi P Aminian A H Gandomi A H Alavi andH Bolandi ldquoA new predictive model for compressive strengthof HPC using gene expression programmingrdquo Advances inEngineering Software vol 45 no 1 pp 105ndash114 2012

[80] M Sarıdemir ldquoEmpirical modeling of splitting tensilestrength from cylinder compressive strength of concrete bygenetic programmingrdquo Expert Systems with Applicationsvol 38 no 11 pp 14257ndash14268 2011

[81] M Sonebi and A Cevik ldquoGenetic programming based for-mulation for fresh and hardened properties of self-compacting concrete containing pulverised fuel ashrdquo Con-struction and Building Materials vol 23 no 7 pp 2614ndash26222009

[82] A H Alavi P Aminian A H Gandomi and M A EsmaeilildquoGenetic-based modeling of uplift capacity of suction cais-sonsrdquo Expert Systems with Applications vol 38 no 10pp 12608ndash12618 2011

[83] T Zsutty ldquoShear strength prediction for separate catagories ofsimple beam testsrdquo ACI Journal Proceedings vol 68 no 2pp 138ndash143 1971

16 Advances in Civil Engineering

mean standard deviation (SD) and coelaquocient of variation(COV) in addition to error values such as mean absoluteerror (MAE) root mean square error (RMSE) and R2 asshown below

RMSE

sumN

i0 ei minuspi( )2

N

radic

MAE 1NsumN

i0ei minuspi∣∣∣∣

∣∣∣∣

R2 1minussumN

i0 ei minuspi( )2

sumN

i0 ei minus e( )2

(8)

where ei and pi are the experimental and predicted shearforce in kN respectively e is the average of the experimentalvalues andN is the total number of the considered samplese model that minimized the error values (MAE andRMSE) and maximized R2 is selected as the optimummodel

Figure 7 presents the scatter of the experimental shearforce Vexp versus the predicted shear strength Vpred for theproposed models codes and proposed equations from theliterature It is clear that the best models for predicting theshear strength are those suggested in this study which ina sequence are ANNs GEP and NLR as these modelspredict the shear strength very accurately with the optimumstatistical performance of R2 RMSE and MAE High cor-relation coelaquocients with low error rates indicate that theproposed three models are excellent models and exhibitgeneralization performance in predicting shear strength ofFRP-reinforced concrete beams without stirrups In con-trast the code design provisions and other proposedequations from the literature yielded dispersion results with

lower R2 and larger error rates as given in the scatterrelationships

Table 4 presents the statistical parameters (meanstandard deviation (SD) coelaquocient of variation (COV)minimum maximum range RMSE MAE and R2) of theratio of experimental shear strength to the predicted shearstrength VexpVpred for the proposed models in thisstudy seven well-known codes and seven proposedequations from literature based on the (269) collecteddatabase It is clear that the proposed equations yieldedsuperior accuracy between all the codes and proposedequation from the literature because their optimumstatistical parameters such as the mean SD range RMSEand R2 are 0998 0113 072 53 and 09877 respectivelyfor ANNs 1007 0162 088 82 and 0970 respectivelyfor GEP and 1003 0174 099 107 and 095 re-spectively for NLR

e ANNs and GEP models are articial intelligentmodels derived based on soft computing as veried abovethese models are accurate superior and highly elaquocient inpredicting the complicated problem such as shear strengthHowever the drawback of articial intelligent models is thatit cannot be calculated manually and it needs computers forcalculation Besides it is considered as a powerful and ef-cient tool which can be used in soft programs specializedfor analysis and design of reinforced concrete structures Onthe contrary the NLR model is simply accurate and rationalwhich can be used manually with sulaquocient accuracy morethan the design codes and previously proposed equationsNevertheless the regression equations cannot properlydene with the same level of elaquociency of articial intelligenttechniques the interactions between the input and outputparameters due to that the regression models usually areproduced based only on a few predened equations [79]

3Rt

c3 lowast

lowast

d0

d3d5

lowast Avg2 c2

c2 d0

Avg2

+

(a)

x5

lowast

ndash

5Rt

Tanh

x4

c4d3d2d1

Tanh

(b)

+

d2x2

+

d1d3

Max2d4

c6

c8

5Rt

lowast

(c)

x5

ndash

5Rt

x3

d0d1d2d1

Tanh

Sqrt

(d)

Figure 6 Expression trees ETs for the GEP model (a) Sub-ET 1 (b) Sub-ET 2 (c) Sub-ET 3 (d) Sub-ET 4

Advances in Civil Engineering 9

Finally it can be said that all the three proposed equationscan be considered as accurate efficient and useful modelswhich were trained on a largest collected database forpredicting the shear strength of FRP-reinforced concretemembers

8 Parametric Analyses

For further verification of the proposed ANNs GEP andNLR prediction models a parametric analysis was per-formed in this study -e main goal was to find the

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

ANNsR2 = 09877RMSE = 53MAE = 39

GEPR2 = 09709

RMSE = 82kNMAE = 59kN

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

ACI 440-06R2 = 0575

RMSE = 315MAE = 242

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

CSA 806-12R2 = 0783

RMSE = 225MAE = 117

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

R2 = 0805RMSE = 213MAE = 121

Nehdi et al (2007)

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

R2 = 0772RMSE = 231MAE = 144

Razaqpur and Spadea (2011)

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

R2 = 08347RMSE = 196MAE = 110

Kara (2011)

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

R2 = 0865RMSE = 177MAE = 109

Alam and Husein (2013)

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

R2 = 0885RMSE = 164MAE = 102

Ashour and Kara (2014)

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

R2 = 0902RMSE = 151MAE = 96

Lee (2014)

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

JSCE97R2 = 0792

RMSE = 220MAE = 149

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

NLR

Vexp (kN)

R2 = 0950RMSE = 107MAE = 73

Figure 7 Scatter of Vexp versus Vpred for ANN GEP NLR and different models from the literature

10 Advances in Civil Engineering

response of the three proposed models to predict the shearstrength for a set of input parameters which are selectedtaking into account the average value of each parame-ter in the collected database For further showing theperformance of the proposed models and for comparisonpurpose the response of three well-known codes (ACI1R440-15 JSCE-97 and CSA S806-12) was also considered-e approach depends on keeping all input parameters attheir selected values except that in each time a singleparameter value was changed incrementally within theexpected practical values Consequently an arrangementof manufactured data for the single considered parameteris produced this procedure was repeated for all parametersso that all models are examined for the entire input pa-rameters -e selected input parameters are fcprime 46MPabw 200mm d 400mm ad 4 ρf 0011 and Ef

74 GPa It is worthy to note that the ANNs model cannotproperly predict the shear strength for input parametersoutside the range of training data therefore it is only validfor prediction within the range of input parameters of thetraining data [8]

Figure 8 indicates the tendency of the predicted shearstrength by differentmodels to the varieties of themain designparameters (d fcprime ρf Ef ad and bw) Generally it can beobserved that the proposed models particularly the ANNsmodel yielded larger shear capacities for all parameters whileACI 440-15 yielded the lowest shear capacities which indicatethat the ACI 440-15 is very conservative

-e relationship of beam depth with the predicted shearstrength showed that all the proposed models and codesincreased with the increase in the beam depth throughoutthe range of 100ndash1000mm -e ACI 440-15 considers theeffect of beam depth linearly while all other models rep-resent the effect of depth nonlinearly the ANNs GEP andNLR models consider the depth raised to a power of 083067 and 066 respectively Also it can be observed that theGEP and NLR yield almost the same results All the pro-posed models and codes showed an increase in shearstrength with the increase in the concrete compressive

strength but in different rates It was found that fcprime is raisedto a power of 066 030 and 02 for ANNs GEP and NLRrespectively

-e effect of the flexure reinforcement ratio on shearstrength indicates a similar trend of the NLR model and thedesign codes but the ANNs and GEP models showeda slightly decreased trend for reinforcement ratios greaterthan 003 this is not in agreement with codes and previousstudies because of that only few data were available with ρflarger than 003 and these data actually showed decreasingshear capacity Additionally these models were derivedbased only on the artificial technology of data trainingwithout manually choosing the general mathematical shapeof the model in contrary to the NLRmodel and design codeswhich was derived based on the theoretical or semiempiricalcriteria

-e shear strength also increased with the increase inthe elastic modulus of the flexure reinforcement ratio Itcan be observed that all models showed a similar trend linefor the entire range of data while the ANNs model showedan increased rate up to about 110 GPa and then the in-crease rate reduced significantly similar results also ob-tained by Bashir and Ashour [8] On the contrary thetrend lines of the shear span to depth ratio are decreasedfor GEP and NLR models for the entire range of datameanwhile for ANNs model it decreases up to ad of 5and then it started to increase slightly -is behavior is inagreement with the few available experimental results[32 52 56] which were studied as ad greater than 5However other codes do not consider the effect of ad asthe trend lines for ACI 440-15 and JSCE-97 are constantwhile the CSA S806 trend line remains constant beyondthe ad value of 5 Finally the effect of beam width on shearstrength is linear as indicated by trend lines for all modelsexcept the ANNs model which showed a lower increaserate beyond 700mm width

To investigate how the proposed models consider thesize effect on shear capacity the same parametric data usedfor studying the beam depth are used Figure 9 presents

Table 4 Statistical parameters of (VexpVpred) for the proposed models and different design equations

Design equations Mean (VexpVpred) SD COV Minimum Maximum Range RMSE MAE R2

[12] 1813 0416 2306 113 374 261 315 242 0575[13] 1302 0282 2163 046 251 205 220 149 0792[18] 1091 0227 2085 047 185 137 225 117 0783[16] 1193 0386 3249 044 248 203 2633 1758 0703[17] 0948 0265 2799 039 174 134 2257 1403 0782[14] 1072 0247 231 054 192 138 1470 980 0908[15] 1393 0254 1835 070 248 178 2456 1661 0742[4] 1113 0219 1967 055 192 136 213 121 0805[19] 1305 0235 1801 084 214 129 231 184 0772[7] 1025 0205 2003 054 191 136 196 110 0835[1] 1148 0227 1981 059 172 113 177 109 0865[20] 0965 0174 1806 063 168 105 164 102 0885[10] 1015 0229 2251 053 196 143 151 96 0905[21] 1096 0283 2587 056 212 156 1915 1180 0843NLR 1003 0174 1732 062 161 099 107 73 0950GEP 1007 0162 1608 066 155 088 82 59 09709ANNs 0998 0113 1131 071 144 072 53 39 09877

Advances in Civil Engineering 11

0

30

60

90

120

150

180

0 150 300 450 600 750 900 1050

V pre

d (k

N)

d (mm)

ANNGEPJSCE 97

NLRACI 440CSA S806

0

20

40

60

80

100

120

0 10 20 30 40 50 60 70 80 90 100 110

V pre

d (k

N)

fcprime (MPa)

ANNGEPJSCE 97

NLRACI 440SCA S806

0

20

40

60

80

100

120

0 001 002 003 004 005

V pre

d (k

N)

ρf

ANNGEPJSCE 97

NLRACI 440CSA S806

0

20

40

60

80

100

120

0 25 50 75 100 125 150 175

V pre

d (k

N)

Ef (MPa)

ANNGEPJSCE 97

NLRACI 440CSA S806

0

20

40

60

80

100

120

0 2 4 6 8 10

V pre

d (k

N)

ad

ANNGEPJSCE 97

NLRACI 440CSA S806

0

60

120

180

240

300

360

0 200 400 600 800 1000 1200

V pre

d (k

N)

b (mm)

ANNGEPJSCE 97

NLRACI 440CSA S806

Figure 8 Eect of the parameters (d fcprime ρf Ef ad and bw) on shear capacity predicted by ANNs GEP NLR and three design codes(ACI1R 440-06 JSCE-97 and CSA S806-12)

12 Advances in Civil Engineering

the relationship between normalized shear strength as(Vpredbwd

fcprime1113969

) and beam depth It is clear that the nor-malized shear strength is decreased with the increase in thebeam depth for ANNs GEP and NLR showing that the sizeeffect is efficiently presented in these models -e trends ofGEP and NLR are very close and compatible and decreasedfrom a depth of 100mm to 1000mm while the ANNsmodelseems to be more accurate as it shows an increase in thetrend up to the depth of 200mm and then it decreasedsimilarly to that of GEP and NLR after that the trend startsto increase slightly

It can be summed up to that the artificial intelligentmodels due to their efficiency and powerful ability in rec-ognizing the parameters interaction demonstrate variousrates of change and fluctuation for the entire scope of inputparameters -e ANNs and GEP models define accurately theinteraction of each parameter on shear strength predictionand have a great ability to represent the actual response ofeach parameter in spite of its complexity and fluctuationnature Furthermore these models are evolved by trainingnumerous preliminary linear and nonlinear models withoutany prior assumption regarding the shape and structure of themathematical model

9 Conclusions

An experimental database including 269 shear test results ofFRP-reinforced concrete members without stirrups availablein the literature was established to propose three predictionmodels to estimate the shear capacity of FRP-RC membersusing three powerful tools which are ANNs GEP and NLR-e following conclusions can be drawn from this study

(i) -e proposed models for predicting the shear ca-pacity of FRP-RC members based on ANNs andGEP techniques showed excellent performancegreat efficiency and high level of accuracy andyielded consistent results throughout a wide rangeof influencing parameters moreover the ANNsmodel is more superior than the GEP as the SD andR2 for ANNs are 0113 and 09877 and for GEP are0162 and 097 respectively

(ii) A simple rational and yet accurate empiricalequation was proposed for predicting shearstrength of FRP-RC members by NLR -e equa-tion considers all the important influencing pa-rameters and simplified to be easy for use Inaddition it gives consistent and accurate resultswith SD and R2 of 0173 and 095 respectively

(iii) -rough a comparative statistical analysis for theproposed models with seven shear design codes andsix proposed equations from the literature it hasbeen found that the most accurate and efficientmodels are ANNs and GEP and to a lower dgreeNLR Among the codes and available proposals theCSA S806-12 and Ashour and Kara [20] equationswere appearing to be more accurate than the others

(iv) From a parametric study considering all the influ-encing parameters on shear capacity it was found thatthe ANNs model and to a lower level GEP modeldefines accurately the interaction of each parameteron shear capacity prediction and has a great ability torepresent the actual response of each parameter inspite of its complexity and fluctuation nature

(v) -e ANNs and GEP models demonstrate that theeffect of flexure reinforcement ratio on shear ca-pacity decreased beyond 003 as a real response tothe available few data in this range therefore morestudies are needed to confirm this case

(vi) -e ANNs model demonstrated that the effect ofad does not absolutely reduce the shear capacitywhile beyond the ad value of 5 its effect couldbecome reverse and contribute to increase in theshear capacity as confirmed by few previous studies

(vii) -e size effect is considered properly by the pro-posed models particularly the ANNs model whichyields more accurate shear capacity prediction tothe experimental results

Data Availability

-e (database of shear strength of beams without stirrups)data used to support the findings of this study are includedwithin the article

Conflicts of Interest

-e authors declare that they have no conflicts of interest

0

004

008

012

016

02

024

0 200 400 600 800 1000 1200

ANNNLRGEP

d (mm)

V pre

db wd

fc

Figure 9 Normalized shear strength (Vpredbwd

fcprime1113969

) versus beamdepth

Advances in Civil Engineering 13

References

[1] M S Alam and A Hussein ldquoSize effect on shear strength ofFRP reinforced concrete beams without stirrupsrdquo Journal ofComposites for Construction vol 17 no 4 pp 507ndash516 2013

[2] J R Yost S P Gross and D W Dinehart ldquoShear strength ofnormal strength concrete beams reinforced with deformedGFRP barsrdquo Journal of Composites for Construction vol 5no 4 pp 268ndash275 2001

[3] A G Razaqpur B O Isgor S Greenaway and A SelleyldquoConcrete contribution to the shear resistance of fiber rein-forced polymer reinforced concrete membersrdquo Journal ofComposites for Construction vol 8 no 5 pp 452ndash460 2004

[4] M Nehdi H El Chabib and A A Saıd ldquoProposed sheardesign equations for FRP-reinforced concrete beams based ongenetic algorithms approachrdquo Journal of Materials in CivilEngineering vol 19 no 12 pp 1033ndash1042 2007

[5] ASCE-ACI445 ldquoRecent approaches to shear design ofstructural concreterdquo Journal of Structural Engineeringvol 124 no 12 pp 1375ndash1417 1998

[6] R Park and T Paulay Reinforced Concrete Structures JohnWiley amp Sons Hoboken NJ USA 1975

[7] I F Kara ldquoPrediction of shear strength of FRP-reinforcedconcrete beams without stirrups based on genetic pro-grammingrdquo Advances in Engineering Software vol 42 no 6pp 295ndash304 2011

[8] R Bashir and A Ashour ldquoNeural networkmodelling for shearstrength of concrete members reinforced with FRP barsrdquoComposites Part B Engineering vol 43 no 8 pp 3198ndash32072012

[9] K Nasrollahzadeh and M M Basiri ldquoPrediction of shearstrength of FRP reinforced concrete beams using fuzzy in-ference systemrdquo Expert Systems with Applications vol 41no 4 pp 1006ndash1020 2014

[10] S Lee and C Lee ldquoPrediction of shear strength of FRP-reinforced concrete flexural members without stirrups usingartificial neural networksrdquo Engineering Structures vol 61pp 99ndash112 2014

[11] E M Golafshani and A Ashour ldquoA feasibility study of BBPfor predicting shear capacity of FRP reinforced concretebeams without stirrupsrdquo Advances in Engineering Softwarevol 97 pp 29ndash39 2016

[12] ACI-440 Guide for the Design and Construction of StructuralConcrete Reinforced with Fiber-Reinforced Polymer (FRP)ACI 440 1R-15 American Concrete Institute FarmingtonsHills MI USA 2015

[13] JSCE ldquoRecommendation for design and construction ofconcrete structures using continuous fiber reinforcing ma-terialsrdquo in Concrete Engineering Series 23 A Machida EdJapan Society of Civil Engineers Tokyo Japan 1997

[14] BISE Interim Guidance on the Design of Reinforced ConcreteStructures Using Fiber Composite Reinforcement British In-stitution of Structural Engineers Seto Ltd London UK1999

[15] CSA Canadian Highway Bridge Design Code SupplementNo 1 to CANCSA S6-06 (S61S1-10) Canadian StandardsAssociation (CSA) Mississauga ON Canada 2010

[16] ISIS Reinforced Concrete Structures with Fibre ReinforcedPolymersmdashDesign Manual No 3 University of Manitoba ISISCanada Corporation Winnipeg MB Canada 2007

[17] CNR-DT203 ldquoGuide for the design and construction ofconcrete structures reinforced with fiber-reinforced polymerbarsrdquo inAdvisory Committee on Technical Recommendations

for Construction CNR-DT 2032006 CNR Rome Italy2007

[18] CSA ldquoCode for the design and construction of buildingstructures with fibre-reinforced polymersrdquo in CANCSAS806-12 p 198 Canadian Standard Association TorontoON Canada 2012

[19] A Razaqpur and S Spadea ldquoResistenza a taglio di elementi dicalcestruzzzo reinforzatti e staffe di FRPrdquo in Proceedings ofAIAS Maratea Italy September 2010

[20] A F Ashour and I F Kara ldquoSize effect on shear strength ofFRP reinforced concrete beamsrdquo Composites Part B Engi-neering vol 60 pp 612ndash620 2014

[21] A R Yousif ldquoShear strength of large FRP-reinforced concretebeams without shear reinforcementrdquo Journal of Pure andApplied Sciences vol 27 pp 9ndash28 2015

[22] A K El-Sayed E F El-Salakawy and B Benmokrane ldquoShearcapacity of high-strength concrete beams reinforced with FRPbarsrdquo ACI Structural Journal vol 103 p 383 2006

[23] A G Razaqpur and O B Isgor ldquoProposed shear designmethod for FRP-reinforced concrete members without stir-rupsrdquo ACI Structural Journal vol 103 p 93 2006

[24] K Maruyama andW Zhao ldquoFlexural and shear behaviour ofconcrete beams reinforced with FRP rodsrdquo in Proceedings ofthe International Conference on Corrosion and CorrosionProtection of Steel in Concrete pp 24ndash28 Sheffield UK1994

[25] W Zhao K Maruyama and H Suzuki ldquoShear behavior ofconcrete beams reinforced by FRP rods as longitudinal andshear reinforcementrdquo in Proceedings of the Second In-ternational RILEM Symposium on Non-Metallic (FRP) Re-inforcement for Concrete Structures p 352 Ghent BelgiumAugust 1995

[26] H Nakamura and T Higai ldquoEvaluation of shear strength ofthe concrete beams reinforced with FRPrdquo in Proceedings ofJapan Society of Civil Engineers p 89 Ghent Belgium 1995

[27] K Maruyama and W Zhao ldquoSize effect in shear behavior ofFRP reinforced concrete beamrdquo in Advanced CompositeMaterials in Bridges and Structures pp 227ndash234 CanadianSociety for Civil Engineering Montreal QC Canada 1996

[28] Y Mizukawa Y Sato T Ueda and Y Kakuta ldquoA studyon shear fatigue behavior of concrete beams with FRP rodsrdquoin Proceedings of the Cird International Symposium onNon-Metallic (FRP) Reinforcement for Concrete Structures(FRPRCS-3) pp 309ndash316 Japan Concrete Institute SapporoJapan 1997

[29] N Duranovic K Pilakoutas and P Waldron ldquoTests onconcrete beams reinforced with glass fibre reinforced plasticbarsrdquo in Proceedings of the Cird International Symposium onNon-Metallic (FRP) Reinforcement for Concrete Structures(FRPRCS-3) pp 479ndash486 Sapporo Japan 1997

[30] N Swamy and M Aburawi ldquoStructural implications of usingGFRP bars as concrete reinforcementrdquo in Proceedings of 3rdInternational Symposium FRPRCS pp 503ndash510 SapporoJapan 1997

[31] C R Michaluk S H Rizkalla G Tadros and B BenmokraneldquoFlexural behavior of one-way concrete slabs reinforced byfiber reinforced plastic reinforcementsrdquo ACI StructuralJournal vol 95 pp 353ndash365 1998

[32] D Deitz I Harik and H Gesund ldquoOne-way slabs reinforcedwith glass fiber reinforced polymer reinforcing barsrdquo SpecialPublication vol 188 pp 279ndash286 1999

[33] T Alkhrdaji M Wideman A Belarbi and A Nanni ldquoShearstrength of GFRP RC beams and slabsrdquo in Proceedings of the

14 Advances in Civil Engineering

International Conference Composites in Construction-CCCpp 409ndash414 Porto Portugal 2001

[34] G S Melo and J A Rayol ldquoShear resistance of GFRPreinforced concrete beamsrdquo in Proceedings of the Rehabil-itating and Repairing the Buildings and Bridges of AmericasHemispheric Workshop on Future Directions Mayaguumlez PRUSA pp 47ndash64 2002

[35] A K Tureyen and R J Frosch ldquoShear tests of FRP-reinforcedconcrete beams without stirrupsrdquo ACI Structural Journalvol 99 pp 427ndash434 2002

[36] S P Gross J R Yost D W Dinehart E Svensen and N LiuldquoShear strength of normal and high strength concrete beamsreinforced with GFRP barsrdquo in Proceedings of InternationalConference on High Performance Materials in Bridgespp 426ndash437 ASCE Reston VA USA 2003

[37] M Tariq and J Newhook ldquoShear testing of FRP reinforcedconcrete without transverse reinforcementrdquo in Proceedings ofAnnual Conference of the Canadian Society for Civil Engi-neering pp 1330ndash1339 Moncton NB Canada June 2003

[38] S Gross D Dinehart J Yost and P -eisz ldquoExperimentaltests of high-strength concrete beams reinforced with CFRPbarsrdquo in Proceedings of the 4th International Conference onAdvanced Composite Materials in Bridges and Structures(ACMBS-4) Calgary AB Canada 2004

[39] A Lubell T Sherwood E Bentz and M P Collins ldquoSafe sheardesign of large wide beams adding shear reinforcement isrecommendedrdquoConcrete International vol 26 pp 66ndash78 2004

[40] J Yost S Gross G Masone and P Hamelin ldquoSustained loadeffects on deflection and ultimate strength of concrete beamsreinforced with GFRPrdquo in Proceedings of the InternationalConference Composites in Construction (CCC2005) LyonFrance July 2005

[41] A El-Sayed E El-Salakawy and B Benmokrane ldquoShearstrength of one-way concrete slabs reinforced with fiber-reinforced polymer composite barsrdquo Journal of Compositesfor Construction vol 9 no 2 pp 147ndash157 2005

[42] A E Kilpatrick and L Easden ldquoShear capacity of GFRPreinforced high strength concrete slabsrdquo in Proceedings of the18th Australasian Conference on the Mechanics of Structuresand Materials Perth Australia vol 1 pp 119ndash124 Taylor ampFrancis London UK 2005

[43] A K El-Sayed E F El-Salakawy and B BenmokraneldquoShear strength of FRP-reinforced concrete beams withouttransverse reinforcementrdquo ACI Structural Journal vol 103p 235 2006

[44] A Ashour ldquoFlexural and shear capacities of concrete beamsreinforced with GFRP barsrdquo Construction and BuildingMaterials vol 20 no 10 pp 1005ndash1015 2006

[45] M Guadagnini K Pilakoutas and P Waldron ldquoShear re-sistance of FRP RC beams experimental studyrdquo Journal ofComposites for Construction vol 10 no 6 pp 464ndash473 2006

[46] R Dawborn and A Kilpatrick Flexural Shear Capacity ofHigh Strength Concrete Slabs Reinforced with LongitudinalGFRP Bars 2006

[47] J Niewels ldquoZum Tragverhalten von Betonbauteilen mitFaserverbundkunststoffbewehrungrdquo Rheinisch-WestfalischeTechnische Hochschule Aachen Lehrstuhl und Institut furMassivbau Dissertation 2008

[48] A El-Sayed K Soudki and E Kling ldquoFlexural behaviour ofself-consolidating concrete slabs reinforced with GFRP barsrdquoin Proceedings of the 9th International Symposium on FiberReinforced Polymer Reinforcement for Reinforced ConcreteStructures pp 13ndash15 Sydney NSW Australia 2009

[49] A Caporale and R Luciano ldquoIndagine sperimentale enumerica sulla resistenza a taglio di travi di calcestruzzoarmate con barre di GFRPrdquo in Proceedings of XXXVIIIConvegno Nazionale AIAS Turin Italy September 2009

[50] R Olivito and F Zuccarello ldquoOn the shear behaviour ofconcrete beams reinforced by carbon fibre-reinforced poly-mer bars an experimental investigation by means of acousticemission techniquerdquo Strain vol 46 no 5 pp 470ndash481 2010

[51] E C Bentz L Massam and M P Collins ldquoShear strength oflarge concrete members with FRP reinforcementrdquo Journal ofComposites for Construction vol 14 no 6 pp 637ndash646 2010

[52] A G Razaqpur M Shedid and B Isgor ldquoShear strength offiber-reinforced polymer reinforced concrete beams subject tounsymmetric loadingrdquo Journal of Composites for Construc-tion vol 15 no 4 pp 500ndash512 2011

[53] M Alam and A Hussein ldquoEffect of member depth on shearstrength of high-strength fiber-reinforced polymerndashreinforced concrete beamsrdquo Journal of Composites for Con-struction vol 16 no 2 pp 119ndash126 2012

[54] F Matta A K El-Sayed A Nanni and B Benmokrane ldquoSizeeffect on concrete shear strength in beams reinforced withfiber-reinforced polymer barsrdquo ACI Structural Journalvol 110-S50 pp 617ndash628 2013

[55] B Abdul-Salam A Farghaly and B Benmokrane ldquoEvalua-tion of shear behavior for one-way concrete slabs reinforcedwith carbon-FRP barsrdquo GEN vol 243 p 1 2013

[56] C H Kim and H S Jang ldquoConcrete shear strength of normaland lightweight concrete beams reinforced with FRP barsrdquoJournal of Composites for Construction vol 18 no 2 article04013038 2014

[57] D Tomlinson and A Fam ldquoPerformance of concrete beamsreinforced with basalt FRP for flexure and shearrdquo Journal ofComposites for Construction vol 19 no 2 article 040140362014

[58] M A Issa T Ovitigala and M Ibrahim ldquoShear behavior ofbasalt fiber reinforced concrete beams with and without basaltFRP stirrupsrdquo Journal of Composites for Construction vol 20no 4 article 04015083 2015

[59] A El Refai and F Abed ldquoConcrete contribution to shearstrength of beams reinforced with basalt fiber-reinforcedbarsrdquo Journal of Composites for Construction vol 20 no 4article 04015082 2015

[60] G B Jumaa and A R Yuosif ldquoSize effect in shear failure ofhigh strength concrete beams without stirrups reinforcedwith basalt FRP barsrdquo KSCE Journal of Civil Engineering2018 In press

[61] M T Hagan H B Demuth and M H BealeNeural NetworkDesign (Electrical Engineering) -omson Learning BostonMA USA 1995

[62] S S Haykin S S Haykin S S Haykin and S S HaykinNeural Networks and Learning Machines Pearson Vol 3Pearson Upper Saddle River NJ USA 2009

[63] M Y Mansour M Dicleli J-Y Lee and J Zhang ldquoPredictingthe shear strength of reinforced concrete beams using artificialneural networksrdquo Engineering Structures vol 26 no 6pp 781ndash799 2004

[64] H Demuth M Beale and M Hagan Neural NetworkToolboxtrade 6 Userrsquos Guide -e MathWorks Inc vol 10 p 11Natick MA USA 2008

[65] A W Oreta and K Kawashima ldquoNeural network modeling ofconfined compressive strength and strain of circular concretecolumnsrdquo Journal of Structural Engineering vol 129 no 4pp 554ndash561 2003

Advances in Civil Engineering 15

[66] S Jung and K S Kim ldquoKnowledge-based predictionof shear strength of concrete beams without shear re-inforcementrdquo Engineering Structures vol 30 no 6pp 1515ndash1525 2008

[67] Z-H Duan S-C Kou and C-S Poon ldquoPrediction ofcompressive strength of recycled aggregate concrete usingartificial neural networksrdquo Construction and Building Mate-rials vol 40 pp 1200ndash1206 2013

[68] H El-Chabib M Nehdi and A Said ldquoPredicting shear ca-pacity of NSC and HSC slender beams without stirrups usingartificial intelligencerdquo Computers and Concrete vol 2 no 1pp 79ndash96 2005

[69] F Altun O Kisi and K Aydin ldquoPredicting the compressivestrength of steel fiber added lightweight concrete using neuralnetworkrdquo Computational Materials Science vol 42 no 2pp 259ndash265 2008

[70] J R Koza ldquoGenetic programming as a means for pro-gramming computers by natural selectionrdquo Statistics andComputing vol 4 no 2 pp 87ndash112 1994

[71] C Ferreira ldquoGene expression programming in problemsolvingrdquo in Soft Computing and Industry pp 635ndash653Springer Berlin Germany 2002

[72] C Kayadelen ldquoSoil liquefaction modeling by genetic ex-pression programming and neuro-fuzzyrdquo Expert Systems withApplications vol 38 no 4 pp 4080ndash4087 2011

[73] A H Gandomi A H Alavi and G J Yun ldquoFormulation ofuplift capacity of suction caissons using multi expressionprogrammingrdquo KSCE Journal of Civil Engineering vol 15no 2 pp 363ndash373 2011

[74] A H Gandomi A H Alavi and C RyanHandbook of GeneticProgramming Applications Springer Berlin Germany 2015

[75] A H Gandomi and A H Alavi ldquoA new multi-gene geneticprogramming approach to non-linear system modeling PartII geotechnical and earthquake engineering problemsrdquoNeural Computing and Applications vol 21 no 1 pp 189ndash201 2012

[76] A H Alavi and A H Gandomi ldquoEnergy-based numericalmodels for assessment of soil liquefactionrdquo GeoscienceFrontiers vol 3 no 4 pp 541ndash555 2012

[77] L Teodorescu and D Sherwood ldquoHigh energy physics eventselection with gene expression programmingrdquo ComputerPhysics Communications vol 178 no 6 pp 409ndash419 2008

[78] GEPSOFT GeneXproTools Version 50 GEPSOFT BristolUK 2013 httpwwwgepsoftcom

[79] S M Mousavi P Aminian A H Gandomi A H Alavi andH Bolandi ldquoA new predictive model for compressive strengthof HPC using gene expression programmingrdquo Advances inEngineering Software vol 45 no 1 pp 105ndash114 2012

[80] M Sarıdemir ldquoEmpirical modeling of splitting tensilestrength from cylinder compressive strength of concrete bygenetic programmingrdquo Expert Systems with Applicationsvol 38 no 11 pp 14257ndash14268 2011

[81] M Sonebi and A Cevik ldquoGenetic programming based for-mulation for fresh and hardened properties of self-compacting concrete containing pulverised fuel ashrdquo Con-struction and Building Materials vol 23 no 7 pp 2614ndash26222009

[82] A H Alavi P Aminian A H Gandomi and M A EsmaeilildquoGenetic-based modeling of uplift capacity of suction cais-sonsrdquo Expert Systems with Applications vol 38 no 10pp 12608ndash12618 2011

[83] T Zsutty ldquoShear strength prediction for separate catagories ofsimple beam testsrdquo ACI Journal Proceedings vol 68 no 2pp 138ndash143 1971

16 Advances in Civil Engineering

Finally it can be said that all the three proposed equationscan be considered as accurate efficient and useful modelswhich were trained on a largest collected database forpredicting the shear strength of FRP-reinforced concretemembers

8 Parametric Analyses

For further verification of the proposed ANNs GEP andNLR prediction models a parametric analysis was per-formed in this study -e main goal was to find the

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

ANNsR2 = 09877RMSE = 53MAE = 39

GEPR2 = 09709

RMSE = 82kNMAE = 59kN

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

ACI 440-06R2 = 0575

RMSE = 315MAE = 242

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

CSA 806-12R2 = 0783

RMSE = 225MAE = 117

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

R2 = 0805RMSE = 213MAE = 121

Nehdi et al (2007)

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

R2 = 0772RMSE = 231MAE = 144

Razaqpur and Spadea (2011)

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

R2 = 08347RMSE = 196MAE = 110

Kara (2011)

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

R2 = 0865RMSE = 177MAE = 109

Alam and Husein (2013)

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

R2 = 0885RMSE = 164MAE = 102

Ashour and Kara (2014)

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

R2 = 0902RMSE = 151MAE = 96

Lee (2014)

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

JSCE97R2 = 0792

RMSE = 220MAE = 149

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

Vexp (kN)

0

50

100

150

200

250

300

0 50 100 150 200 250 300

V pre

d (kN

)

NLR

Vexp (kN)

R2 = 0950RMSE = 107MAE = 73

Figure 7 Scatter of Vexp versus Vpred for ANN GEP NLR and different models from the literature

10 Advances in Civil Engineering

response of the three proposed models to predict the shearstrength for a set of input parameters which are selectedtaking into account the average value of each parame-ter in the collected database For further showing theperformance of the proposed models and for comparisonpurpose the response of three well-known codes (ACI1R440-15 JSCE-97 and CSA S806-12) was also considered-e approach depends on keeping all input parameters attheir selected values except that in each time a singleparameter value was changed incrementally within theexpected practical values Consequently an arrangementof manufactured data for the single considered parameteris produced this procedure was repeated for all parametersso that all models are examined for the entire input pa-rameters -e selected input parameters are fcprime 46MPabw 200mm d 400mm ad 4 ρf 0011 and Ef

74 GPa It is worthy to note that the ANNs model cannotproperly predict the shear strength for input parametersoutside the range of training data therefore it is only validfor prediction within the range of input parameters of thetraining data [8]

Figure 8 indicates the tendency of the predicted shearstrength by differentmodels to the varieties of themain designparameters (d fcprime ρf Ef ad and bw) Generally it can beobserved that the proposed models particularly the ANNsmodel yielded larger shear capacities for all parameters whileACI 440-15 yielded the lowest shear capacities which indicatethat the ACI 440-15 is very conservative

-e relationship of beam depth with the predicted shearstrength showed that all the proposed models and codesincreased with the increase in the beam depth throughoutthe range of 100ndash1000mm -e ACI 440-15 considers theeffect of beam depth linearly while all other models rep-resent the effect of depth nonlinearly the ANNs GEP andNLR models consider the depth raised to a power of 083067 and 066 respectively Also it can be observed that theGEP and NLR yield almost the same results All the pro-posed models and codes showed an increase in shearstrength with the increase in the concrete compressive

strength but in different rates It was found that fcprime is raisedto a power of 066 030 and 02 for ANNs GEP and NLRrespectively

-e effect of the flexure reinforcement ratio on shearstrength indicates a similar trend of the NLR model and thedesign codes but the ANNs and GEP models showeda slightly decreased trend for reinforcement ratios greaterthan 003 this is not in agreement with codes and previousstudies because of that only few data were available with ρflarger than 003 and these data actually showed decreasingshear capacity Additionally these models were derivedbased only on the artificial technology of data trainingwithout manually choosing the general mathematical shapeof the model in contrary to the NLRmodel and design codeswhich was derived based on the theoretical or semiempiricalcriteria

-e shear strength also increased with the increase inthe elastic modulus of the flexure reinforcement ratio Itcan be observed that all models showed a similar trend linefor the entire range of data while the ANNs model showedan increased rate up to about 110 GPa and then the in-crease rate reduced significantly similar results also ob-tained by Bashir and Ashour [8] On the contrary thetrend lines of the shear span to depth ratio are decreasedfor GEP and NLR models for the entire range of datameanwhile for ANNs model it decreases up to ad of 5and then it started to increase slightly -is behavior is inagreement with the few available experimental results[32 52 56] which were studied as ad greater than 5However other codes do not consider the effect of ad asthe trend lines for ACI 440-15 and JSCE-97 are constantwhile the CSA S806 trend line remains constant beyondthe ad value of 5 Finally the effect of beam width on shearstrength is linear as indicated by trend lines for all modelsexcept the ANNs model which showed a lower increaserate beyond 700mm width

To investigate how the proposed models consider thesize effect on shear capacity the same parametric data usedfor studying the beam depth are used Figure 9 presents

Table 4 Statistical parameters of (VexpVpred) for the proposed models and different design equations

Design equations Mean (VexpVpred) SD COV Minimum Maximum Range RMSE MAE R2

[12] 1813 0416 2306 113 374 261 315 242 0575[13] 1302 0282 2163 046 251 205 220 149 0792[18] 1091 0227 2085 047 185 137 225 117 0783[16] 1193 0386 3249 044 248 203 2633 1758 0703[17] 0948 0265 2799 039 174 134 2257 1403 0782[14] 1072 0247 231 054 192 138 1470 980 0908[15] 1393 0254 1835 070 248 178 2456 1661 0742[4] 1113 0219 1967 055 192 136 213 121 0805[19] 1305 0235 1801 084 214 129 231 184 0772[7] 1025 0205 2003 054 191 136 196 110 0835[1] 1148 0227 1981 059 172 113 177 109 0865[20] 0965 0174 1806 063 168 105 164 102 0885[10] 1015 0229 2251 053 196 143 151 96 0905[21] 1096 0283 2587 056 212 156 1915 1180 0843NLR 1003 0174 1732 062 161 099 107 73 0950GEP 1007 0162 1608 066 155 088 82 59 09709ANNs 0998 0113 1131 071 144 072 53 39 09877

Advances in Civil Engineering 11

0

30

60

90

120

150

180

0 150 300 450 600 750 900 1050

V pre

d (k

N)

d (mm)

ANNGEPJSCE 97

NLRACI 440CSA S806

0

20

40

60

80

100

120

0 10 20 30 40 50 60 70 80 90 100 110

V pre

d (k

N)

fcprime (MPa)

ANNGEPJSCE 97

NLRACI 440SCA S806

0

20

40

60

80

100

120

0 001 002 003 004 005

V pre

d (k

N)

ρf

ANNGEPJSCE 97

NLRACI 440CSA S806

0

20

40

60

80

100

120

0 25 50 75 100 125 150 175

V pre

d (k

N)

Ef (MPa)

ANNGEPJSCE 97

NLRACI 440CSA S806

0

20

40

60

80

100

120

0 2 4 6 8 10

V pre

d (k

N)

ad

ANNGEPJSCE 97

NLRACI 440CSA S806

0

60

120

180

240

300

360

0 200 400 600 800 1000 1200

V pre

d (k

N)

b (mm)

ANNGEPJSCE 97

NLRACI 440CSA S806

Figure 8 Eect of the parameters (d fcprime ρf Ef ad and bw) on shear capacity predicted by ANNs GEP NLR and three design codes(ACI1R 440-06 JSCE-97 and CSA S806-12)

12 Advances in Civil Engineering

the relationship between normalized shear strength as(Vpredbwd

fcprime1113969

) and beam depth It is clear that the nor-malized shear strength is decreased with the increase in thebeam depth for ANNs GEP and NLR showing that the sizeeffect is efficiently presented in these models -e trends ofGEP and NLR are very close and compatible and decreasedfrom a depth of 100mm to 1000mm while the ANNsmodelseems to be more accurate as it shows an increase in thetrend up to the depth of 200mm and then it decreasedsimilarly to that of GEP and NLR after that the trend startsto increase slightly

It can be summed up to that the artificial intelligentmodels due to their efficiency and powerful ability in rec-ognizing the parameters interaction demonstrate variousrates of change and fluctuation for the entire scope of inputparameters -e ANNs and GEP models define accurately theinteraction of each parameter on shear strength predictionand have a great ability to represent the actual response ofeach parameter in spite of its complexity and fluctuationnature Furthermore these models are evolved by trainingnumerous preliminary linear and nonlinear models withoutany prior assumption regarding the shape and structure of themathematical model

9 Conclusions

An experimental database including 269 shear test results ofFRP-reinforced concrete members without stirrups availablein the literature was established to propose three predictionmodels to estimate the shear capacity of FRP-RC membersusing three powerful tools which are ANNs GEP and NLR-e following conclusions can be drawn from this study

(i) -e proposed models for predicting the shear ca-pacity of FRP-RC members based on ANNs andGEP techniques showed excellent performancegreat efficiency and high level of accuracy andyielded consistent results throughout a wide rangeof influencing parameters moreover the ANNsmodel is more superior than the GEP as the SD andR2 for ANNs are 0113 and 09877 and for GEP are0162 and 097 respectively

(ii) A simple rational and yet accurate empiricalequation was proposed for predicting shearstrength of FRP-RC members by NLR -e equa-tion considers all the important influencing pa-rameters and simplified to be easy for use Inaddition it gives consistent and accurate resultswith SD and R2 of 0173 and 095 respectively

(iii) -rough a comparative statistical analysis for theproposed models with seven shear design codes andsix proposed equations from the literature it hasbeen found that the most accurate and efficientmodels are ANNs and GEP and to a lower dgreeNLR Among the codes and available proposals theCSA S806-12 and Ashour and Kara [20] equationswere appearing to be more accurate than the others

(iv) From a parametric study considering all the influ-encing parameters on shear capacity it was found thatthe ANNs model and to a lower level GEP modeldefines accurately the interaction of each parameteron shear capacity prediction and has a great ability torepresent the actual response of each parameter inspite of its complexity and fluctuation nature

(v) -e ANNs and GEP models demonstrate that theeffect of flexure reinforcement ratio on shear ca-pacity decreased beyond 003 as a real response tothe available few data in this range therefore morestudies are needed to confirm this case

(vi) -e ANNs model demonstrated that the effect ofad does not absolutely reduce the shear capacitywhile beyond the ad value of 5 its effect couldbecome reverse and contribute to increase in theshear capacity as confirmed by few previous studies

(vii) -e size effect is considered properly by the pro-posed models particularly the ANNs model whichyields more accurate shear capacity prediction tothe experimental results

Data Availability

-e (database of shear strength of beams without stirrups)data used to support the findings of this study are includedwithin the article

Conflicts of Interest

-e authors declare that they have no conflicts of interest

0

004

008

012

016

02

024

0 200 400 600 800 1000 1200

ANNNLRGEP

d (mm)

V pre

db wd

fc

Figure 9 Normalized shear strength (Vpredbwd

fcprime1113969

) versus beamdepth

Advances in Civil Engineering 13

References

[1] M S Alam and A Hussein ldquoSize effect on shear strength ofFRP reinforced concrete beams without stirrupsrdquo Journal ofComposites for Construction vol 17 no 4 pp 507ndash516 2013

[2] J R Yost S P Gross and D W Dinehart ldquoShear strength ofnormal strength concrete beams reinforced with deformedGFRP barsrdquo Journal of Composites for Construction vol 5no 4 pp 268ndash275 2001

[3] A G Razaqpur B O Isgor S Greenaway and A SelleyldquoConcrete contribution to the shear resistance of fiber rein-forced polymer reinforced concrete membersrdquo Journal ofComposites for Construction vol 8 no 5 pp 452ndash460 2004

[4] M Nehdi H El Chabib and A A Saıd ldquoProposed sheardesign equations for FRP-reinforced concrete beams based ongenetic algorithms approachrdquo Journal of Materials in CivilEngineering vol 19 no 12 pp 1033ndash1042 2007

[5] ASCE-ACI445 ldquoRecent approaches to shear design ofstructural concreterdquo Journal of Structural Engineeringvol 124 no 12 pp 1375ndash1417 1998

[6] R Park and T Paulay Reinforced Concrete Structures JohnWiley amp Sons Hoboken NJ USA 1975

[7] I F Kara ldquoPrediction of shear strength of FRP-reinforcedconcrete beams without stirrups based on genetic pro-grammingrdquo Advances in Engineering Software vol 42 no 6pp 295ndash304 2011

[8] R Bashir and A Ashour ldquoNeural networkmodelling for shearstrength of concrete members reinforced with FRP barsrdquoComposites Part B Engineering vol 43 no 8 pp 3198ndash32072012

[9] K Nasrollahzadeh and M M Basiri ldquoPrediction of shearstrength of FRP reinforced concrete beams using fuzzy in-ference systemrdquo Expert Systems with Applications vol 41no 4 pp 1006ndash1020 2014

[10] S Lee and C Lee ldquoPrediction of shear strength of FRP-reinforced concrete flexural members without stirrups usingartificial neural networksrdquo Engineering Structures vol 61pp 99ndash112 2014

[11] E M Golafshani and A Ashour ldquoA feasibility study of BBPfor predicting shear capacity of FRP reinforced concretebeams without stirrupsrdquo Advances in Engineering Softwarevol 97 pp 29ndash39 2016

[12] ACI-440 Guide for the Design and Construction of StructuralConcrete Reinforced with Fiber-Reinforced Polymer (FRP)ACI 440 1R-15 American Concrete Institute FarmingtonsHills MI USA 2015

[13] JSCE ldquoRecommendation for design and construction ofconcrete structures using continuous fiber reinforcing ma-terialsrdquo in Concrete Engineering Series 23 A Machida EdJapan Society of Civil Engineers Tokyo Japan 1997

[14] BISE Interim Guidance on the Design of Reinforced ConcreteStructures Using Fiber Composite Reinforcement British In-stitution of Structural Engineers Seto Ltd London UK1999

[15] CSA Canadian Highway Bridge Design Code SupplementNo 1 to CANCSA S6-06 (S61S1-10) Canadian StandardsAssociation (CSA) Mississauga ON Canada 2010

[16] ISIS Reinforced Concrete Structures with Fibre ReinforcedPolymersmdashDesign Manual No 3 University of Manitoba ISISCanada Corporation Winnipeg MB Canada 2007

[17] CNR-DT203 ldquoGuide for the design and construction ofconcrete structures reinforced with fiber-reinforced polymerbarsrdquo inAdvisory Committee on Technical Recommendations

for Construction CNR-DT 2032006 CNR Rome Italy2007

[18] CSA ldquoCode for the design and construction of buildingstructures with fibre-reinforced polymersrdquo in CANCSAS806-12 p 198 Canadian Standard Association TorontoON Canada 2012

[19] A Razaqpur and S Spadea ldquoResistenza a taglio di elementi dicalcestruzzzo reinforzatti e staffe di FRPrdquo in Proceedings ofAIAS Maratea Italy September 2010

[20] A F Ashour and I F Kara ldquoSize effect on shear strength ofFRP reinforced concrete beamsrdquo Composites Part B Engi-neering vol 60 pp 612ndash620 2014

[21] A R Yousif ldquoShear strength of large FRP-reinforced concretebeams without shear reinforcementrdquo Journal of Pure andApplied Sciences vol 27 pp 9ndash28 2015

[22] A K El-Sayed E F El-Salakawy and B Benmokrane ldquoShearcapacity of high-strength concrete beams reinforced with FRPbarsrdquo ACI Structural Journal vol 103 p 383 2006

[23] A G Razaqpur and O B Isgor ldquoProposed shear designmethod for FRP-reinforced concrete members without stir-rupsrdquo ACI Structural Journal vol 103 p 93 2006

[24] K Maruyama andW Zhao ldquoFlexural and shear behaviour ofconcrete beams reinforced with FRP rodsrdquo in Proceedings ofthe International Conference on Corrosion and CorrosionProtection of Steel in Concrete pp 24ndash28 Sheffield UK1994

[25] W Zhao K Maruyama and H Suzuki ldquoShear behavior ofconcrete beams reinforced by FRP rods as longitudinal andshear reinforcementrdquo in Proceedings of the Second In-ternational RILEM Symposium on Non-Metallic (FRP) Re-inforcement for Concrete Structures p 352 Ghent BelgiumAugust 1995

[26] H Nakamura and T Higai ldquoEvaluation of shear strength ofthe concrete beams reinforced with FRPrdquo in Proceedings ofJapan Society of Civil Engineers p 89 Ghent Belgium 1995

[27] K Maruyama and W Zhao ldquoSize effect in shear behavior ofFRP reinforced concrete beamrdquo in Advanced CompositeMaterials in Bridges and Structures pp 227ndash234 CanadianSociety for Civil Engineering Montreal QC Canada 1996

[28] Y Mizukawa Y Sato T Ueda and Y Kakuta ldquoA studyon shear fatigue behavior of concrete beams with FRP rodsrdquoin Proceedings of the Cird International Symposium onNon-Metallic (FRP) Reinforcement for Concrete Structures(FRPRCS-3) pp 309ndash316 Japan Concrete Institute SapporoJapan 1997

[29] N Duranovic K Pilakoutas and P Waldron ldquoTests onconcrete beams reinforced with glass fibre reinforced plasticbarsrdquo in Proceedings of the Cird International Symposium onNon-Metallic (FRP) Reinforcement for Concrete Structures(FRPRCS-3) pp 479ndash486 Sapporo Japan 1997

[30] N Swamy and M Aburawi ldquoStructural implications of usingGFRP bars as concrete reinforcementrdquo in Proceedings of 3rdInternational Symposium FRPRCS pp 503ndash510 SapporoJapan 1997

[31] C R Michaluk S H Rizkalla G Tadros and B BenmokraneldquoFlexural behavior of one-way concrete slabs reinforced byfiber reinforced plastic reinforcementsrdquo ACI StructuralJournal vol 95 pp 353ndash365 1998

[32] D Deitz I Harik and H Gesund ldquoOne-way slabs reinforcedwith glass fiber reinforced polymer reinforcing barsrdquo SpecialPublication vol 188 pp 279ndash286 1999

[33] T Alkhrdaji M Wideman A Belarbi and A Nanni ldquoShearstrength of GFRP RC beams and slabsrdquo in Proceedings of the

14 Advances in Civil Engineering

International Conference Composites in Construction-CCCpp 409ndash414 Porto Portugal 2001

[34] G S Melo and J A Rayol ldquoShear resistance of GFRPreinforced concrete beamsrdquo in Proceedings of the Rehabil-itating and Repairing the Buildings and Bridges of AmericasHemispheric Workshop on Future Directions Mayaguumlez PRUSA pp 47ndash64 2002

[35] A K Tureyen and R J Frosch ldquoShear tests of FRP-reinforcedconcrete beams without stirrupsrdquo ACI Structural Journalvol 99 pp 427ndash434 2002

[36] S P Gross J R Yost D W Dinehart E Svensen and N LiuldquoShear strength of normal and high strength concrete beamsreinforced with GFRP barsrdquo in Proceedings of InternationalConference on High Performance Materials in Bridgespp 426ndash437 ASCE Reston VA USA 2003

[37] M Tariq and J Newhook ldquoShear testing of FRP reinforcedconcrete without transverse reinforcementrdquo in Proceedings ofAnnual Conference of the Canadian Society for Civil Engi-neering pp 1330ndash1339 Moncton NB Canada June 2003

[38] S Gross D Dinehart J Yost and P -eisz ldquoExperimentaltests of high-strength concrete beams reinforced with CFRPbarsrdquo in Proceedings of the 4th International Conference onAdvanced Composite Materials in Bridges and Structures(ACMBS-4) Calgary AB Canada 2004

[39] A Lubell T Sherwood E Bentz and M P Collins ldquoSafe sheardesign of large wide beams adding shear reinforcement isrecommendedrdquoConcrete International vol 26 pp 66ndash78 2004

[40] J Yost S Gross G Masone and P Hamelin ldquoSustained loadeffects on deflection and ultimate strength of concrete beamsreinforced with GFRPrdquo in Proceedings of the InternationalConference Composites in Construction (CCC2005) LyonFrance July 2005

[41] A El-Sayed E El-Salakawy and B Benmokrane ldquoShearstrength of one-way concrete slabs reinforced with fiber-reinforced polymer composite barsrdquo Journal of Compositesfor Construction vol 9 no 2 pp 147ndash157 2005

[42] A E Kilpatrick and L Easden ldquoShear capacity of GFRPreinforced high strength concrete slabsrdquo in Proceedings of the18th Australasian Conference on the Mechanics of Structuresand Materials Perth Australia vol 1 pp 119ndash124 Taylor ampFrancis London UK 2005

[43] A K El-Sayed E F El-Salakawy and B BenmokraneldquoShear strength of FRP-reinforced concrete beams withouttransverse reinforcementrdquo ACI Structural Journal vol 103p 235 2006

[44] A Ashour ldquoFlexural and shear capacities of concrete beamsreinforced with GFRP barsrdquo Construction and BuildingMaterials vol 20 no 10 pp 1005ndash1015 2006

[45] M Guadagnini K Pilakoutas and P Waldron ldquoShear re-sistance of FRP RC beams experimental studyrdquo Journal ofComposites for Construction vol 10 no 6 pp 464ndash473 2006

[46] R Dawborn and A Kilpatrick Flexural Shear Capacity ofHigh Strength Concrete Slabs Reinforced with LongitudinalGFRP Bars 2006

[47] J Niewels ldquoZum Tragverhalten von Betonbauteilen mitFaserverbundkunststoffbewehrungrdquo Rheinisch-WestfalischeTechnische Hochschule Aachen Lehrstuhl und Institut furMassivbau Dissertation 2008

[48] A El-Sayed K Soudki and E Kling ldquoFlexural behaviour ofself-consolidating concrete slabs reinforced with GFRP barsrdquoin Proceedings of the 9th International Symposium on FiberReinforced Polymer Reinforcement for Reinforced ConcreteStructures pp 13ndash15 Sydney NSW Australia 2009

[49] A Caporale and R Luciano ldquoIndagine sperimentale enumerica sulla resistenza a taglio di travi di calcestruzzoarmate con barre di GFRPrdquo in Proceedings of XXXVIIIConvegno Nazionale AIAS Turin Italy September 2009

[50] R Olivito and F Zuccarello ldquoOn the shear behaviour ofconcrete beams reinforced by carbon fibre-reinforced poly-mer bars an experimental investigation by means of acousticemission techniquerdquo Strain vol 46 no 5 pp 470ndash481 2010

[51] E C Bentz L Massam and M P Collins ldquoShear strength oflarge concrete members with FRP reinforcementrdquo Journal ofComposites for Construction vol 14 no 6 pp 637ndash646 2010

[52] A G Razaqpur M Shedid and B Isgor ldquoShear strength offiber-reinforced polymer reinforced concrete beams subject tounsymmetric loadingrdquo Journal of Composites for Construc-tion vol 15 no 4 pp 500ndash512 2011

[53] M Alam and A Hussein ldquoEffect of member depth on shearstrength of high-strength fiber-reinforced polymerndashreinforced concrete beamsrdquo Journal of Composites for Con-struction vol 16 no 2 pp 119ndash126 2012

[54] F Matta A K El-Sayed A Nanni and B Benmokrane ldquoSizeeffect on concrete shear strength in beams reinforced withfiber-reinforced polymer barsrdquo ACI Structural Journalvol 110-S50 pp 617ndash628 2013

[55] B Abdul-Salam A Farghaly and B Benmokrane ldquoEvalua-tion of shear behavior for one-way concrete slabs reinforcedwith carbon-FRP barsrdquo GEN vol 243 p 1 2013

[56] C H Kim and H S Jang ldquoConcrete shear strength of normaland lightweight concrete beams reinforced with FRP barsrdquoJournal of Composites for Construction vol 18 no 2 article04013038 2014

[57] D Tomlinson and A Fam ldquoPerformance of concrete beamsreinforced with basalt FRP for flexure and shearrdquo Journal ofComposites for Construction vol 19 no 2 article 040140362014

[58] M A Issa T Ovitigala and M Ibrahim ldquoShear behavior ofbasalt fiber reinforced concrete beams with and without basaltFRP stirrupsrdquo Journal of Composites for Construction vol 20no 4 article 04015083 2015

[59] A El Refai and F Abed ldquoConcrete contribution to shearstrength of beams reinforced with basalt fiber-reinforcedbarsrdquo Journal of Composites for Construction vol 20 no 4article 04015082 2015

[60] G B Jumaa and A R Yuosif ldquoSize effect in shear failure ofhigh strength concrete beams without stirrups reinforcedwith basalt FRP barsrdquo KSCE Journal of Civil Engineering2018 In press

[61] M T Hagan H B Demuth and M H BealeNeural NetworkDesign (Electrical Engineering) -omson Learning BostonMA USA 1995

[62] S S Haykin S S Haykin S S Haykin and S S HaykinNeural Networks and Learning Machines Pearson Vol 3Pearson Upper Saddle River NJ USA 2009

[63] M Y Mansour M Dicleli J-Y Lee and J Zhang ldquoPredictingthe shear strength of reinforced concrete beams using artificialneural networksrdquo Engineering Structures vol 26 no 6pp 781ndash799 2004

[64] H Demuth M Beale and M Hagan Neural NetworkToolboxtrade 6 Userrsquos Guide -e MathWorks Inc vol 10 p 11Natick MA USA 2008

[65] A W Oreta and K Kawashima ldquoNeural network modeling ofconfined compressive strength and strain of circular concretecolumnsrdquo Journal of Structural Engineering vol 129 no 4pp 554ndash561 2003

Advances in Civil Engineering 15

[66] S Jung and K S Kim ldquoKnowledge-based predictionof shear strength of concrete beams without shear re-inforcementrdquo Engineering Structures vol 30 no 6pp 1515ndash1525 2008

[67] Z-H Duan S-C Kou and C-S Poon ldquoPrediction ofcompressive strength of recycled aggregate concrete usingartificial neural networksrdquo Construction and Building Mate-rials vol 40 pp 1200ndash1206 2013

[68] H El-Chabib M Nehdi and A Said ldquoPredicting shear ca-pacity of NSC and HSC slender beams without stirrups usingartificial intelligencerdquo Computers and Concrete vol 2 no 1pp 79ndash96 2005

[69] F Altun O Kisi and K Aydin ldquoPredicting the compressivestrength of steel fiber added lightweight concrete using neuralnetworkrdquo Computational Materials Science vol 42 no 2pp 259ndash265 2008

[70] J R Koza ldquoGenetic programming as a means for pro-gramming computers by natural selectionrdquo Statistics andComputing vol 4 no 2 pp 87ndash112 1994

[71] C Ferreira ldquoGene expression programming in problemsolvingrdquo in Soft Computing and Industry pp 635ndash653Springer Berlin Germany 2002

[72] C Kayadelen ldquoSoil liquefaction modeling by genetic ex-pression programming and neuro-fuzzyrdquo Expert Systems withApplications vol 38 no 4 pp 4080ndash4087 2011

[73] A H Gandomi A H Alavi and G J Yun ldquoFormulation ofuplift capacity of suction caissons using multi expressionprogrammingrdquo KSCE Journal of Civil Engineering vol 15no 2 pp 363ndash373 2011

[74] A H Gandomi A H Alavi and C RyanHandbook of GeneticProgramming Applications Springer Berlin Germany 2015

[75] A H Gandomi and A H Alavi ldquoA new multi-gene geneticprogramming approach to non-linear system modeling PartII geotechnical and earthquake engineering problemsrdquoNeural Computing and Applications vol 21 no 1 pp 189ndash201 2012

[76] A H Alavi and A H Gandomi ldquoEnergy-based numericalmodels for assessment of soil liquefactionrdquo GeoscienceFrontiers vol 3 no 4 pp 541ndash555 2012

[77] L Teodorescu and D Sherwood ldquoHigh energy physics eventselection with gene expression programmingrdquo ComputerPhysics Communications vol 178 no 6 pp 409ndash419 2008

[78] GEPSOFT GeneXproTools Version 50 GEPSOFT BristolUK 2013 httpwwwgepsoftcom

[79] S M Mousavi P Aminian A H Gandomi A H Alavi andH Bolandi ldquoA new predictive model for compressive strengthof HPC using gene expression programmingrdquo Advances inEngineering Software vol 45 no 1 pp 105ndash114 2012

[80] M Sarıdemir ldquoEmpirical modeling of splitting tensilestrength from cylinder compressive strength of concrete bygenetic programmingrdquo Expert Systems with Applicationsvol 38 no 11 pp 14257ndash14268 2011

[81] M Sonebi and A Cevik ldquoGenetic programming based for-mulation for fresh and hardened properties of self-compacting concrete containing pulverised fuel ashrdquo Con-struction and Building Materials vol 23 no 7 pp 2614ndash26222009

[82] A H Alavi P Aminian A H Gandomi and M A EsmaeilildquoGenetic-based modeling of uplift capacity of suction cais-sonsrdquo Expert Systems with Applications vol 38 no 10pp 12608ndash12618 2011

[83] T Zsutty ldquoShear strength prediction for separate catagories ofsimple beam testsrdquo ACI Journal Proceedings vol 68 no 2pp 138ndash143 1971

16 Advances in Civil Engineering

response of the three proposed models to predict the shearstrength for a set of input parameters which are selectedtaking into account the average value of each parame-ter in the collected database For further showing theperformance of the proposed models and for comparisonpurpose the response of three well-known codes (ACI1R440-15 JSCE-97 and CSA S806-12) was also considered-e approach depends on keeping all input parameters attheir selected values except that in each time a singleparameter value was changed incrementally within theexpected practical values Consequently an arrangementof manufactured data for the single considered parameteris produced this procedure was repeated for all parametersso that all models are examined for the entire input pa-rameters -e selected input parameters are fcprime 46MPabw 200mm d 400mm ad 4 ρf 0011 and Ef

74 GPa It is worthy to note that the ANNs model cannotproperly predict the shear strength for input parametersoutside the range of training data therefore it is only validfor prediction within the range of input parameters of thetraining data [8]

Figure 8 indicates the tendency of the predicted shearstrength by differentmodels to the varieties of themain designparameters (d fcprime ρf Ef ad and bw) Generally it can beobserved that the proposed models particularly the ANNsmodel yielded larger shear capacities for all parameters whileACI 440-15 yielded the lowest shear capacities which indicatethat the ACI 440-15 is very conservative

-e relationship of beam depth with the predicted shearstrength showed that all the proposed models and codesincreased with the increase in the beam depth throughoutthe range of 100ndash1000mm -e ACI 440-15 considers theeffect of beam depth linearly while all other models rep-resent the effect of depth nonlinearly the ANNs GEP andNLR models consider the depth raised to a power of 083067 and 066 respectively Also it can be observed that theGEP and NLR yield almost the same results All the pro-posed models and codes showed an increase in shearstrength with the increase in the concrete compressive

strength but in different rates It was found that fcprime is raisedto a power of 066 030 and 02 for ANNs GEP and NLRrespectively

-e effect of the flexure reinforcement ratio on shearstrength indicates a similar trend of the NLR model and thedesign codes but the ANNs and GEP models showeda slightly decreased trend for reinforcement ratios greaterthan 003 this is not in agreement with codes and previousstudies because of that only few data were available with ρflarger than 003 and these data actually showed decreasingshear capacity Additionally these models were derivedbased only on the artificial technology of data trainingwithout manually choosing the general mathematical shapeof the model in contrary to the NLRmodel and design codeswhich was derived based on the theoretical or semiempiricalcriteria

-e shear strength also increased with the increase inthe elastic modulus of the flexure reinforcement ratio Itcan be observed that all models showed a similar trend linefor the entire range of data while the ANNs model showedan increased rate up to about 110 GPa and then the in-crease rate reduced significantly similar results also ob-tained by Bashir and Ashour [8] On the contrary thetrend lines of the shear span to depth ratio are decreasedfor GEP and NLR models for the entire range of datameanwhile for ANNs model it decreases up to ad of 5and then it started to increase slightly -is behavior is inagreement with the few available experimental results[32 52 56] which were studied as ad greater than 5However other codes do not consider the effect of ad asthe trend lines for ACI 440-15 and JSCE-97 are constantwhile the CSA S806 trend line remains constant beyondthe ad value of 5 Finally the effect of beam width on shearstrength is linear as indicated by trend lines for all modelsexcept the ANNs model which showed a lower increaserate beyond 700mm width

To investigate how the proposed models consider thesize effect on shear capacity the same parametric data usedfor studying the beam depth are used Figure 9 presents

Table 4 Statistical parameters of (VexpVpred) for the proposed models and different design equations

Design equations Mean (VexpVpred) SD COV Minimum Maximum Range RMSE MAE R2

[12] 1813 0416 2306 113 374 261 315 242 0575[13] 1302 0282 2163 046 251 205 220 149 0792[18] 1091 0227 2085 047 185 137 225 117 0783[16] 1193 0386 3249 044 248 203 2633 1758 0703[17] 0948 0265 2799 039 174 134 2257 1403 0782[14] 1072 0247 231 054 192 138 1470 980 0908[15] 1393 0254 1835 070 248 178 2456 1661 0742[4] 1113 0219 1967 055 192 136 213 121 0805[19] 1305 0235 1801 084 214 129 231 184 0772[7] 1025 0205 2003 054 191 136 196 110 0835[1] 1148 0227 1981 059 172 113 177 109 0865[20] 0965 0174 1806 063 168 105 164 102 0885[10] 1015 0229 2251 053 196 143 151 96 0905[21] 1096 0283 2587 056 212 156 1915 1180 0843NLR 1003 0174 1732 062 161 099 107 73 0950GEP 1007 0162 1608 066 155 088 82 59 09709ANNs 0998 0113 1131 071 144 072 53 39 09877

Advances in Civil Engineering 11

0

30

60

90

120

150

180

0 150 300 450 600 750 900 1050

V pre

d (k

N)

d (mm)

ANNGEPJSCE 97

NLRACI 440CSA S806

0

20

40

60

80

100

120

0 10 20 30 40 50 60 70 80 90 100 110

V pre

d (k

N)

fcprime (MPa)

ANNGEPJSCE 97

NLRACI 440SCA S806

0

20

40

60

80

100

120

0 001 002 003 004 005

V pre

d (k

N)

ρf

ANNGEPJSCE 97

NLRACI 440CSA S806

0

20

40

60

80

100

120

0 25 50 75 100 125 150 175

V pre

d (k

N)

Ef (MPa)

ANNGEPJSCE 97

NLRACI 440CSA S806

0

20

40

60

80

100

120

0 2 4 6 8 10

V pre

d (k

N)

ad

ANNGEPJSCE 97

NLRACI 440CSA S806

0

60

120

180

240

300

360

0 200 400 600 800 1000 1200

V pre

d (k

N)

b (mm)

ANNGEPJSCE 97

NLRACI 440CSA S806

Figure 8 Eect of the parameters (d fcprime ρf Ef ad and bw) on shear capacity predicted by ANNs GEP NLR and three design codes(ACI1R 440-06 JSCE-97 and CSA S806-12)

12 Advances in Civil Engineering

the relationship between normalized shear strength as(Vpredbwd

fcprime1113969

) and beam depth It is clear that the nor-malized shear strength is decreased with the increase in thebeam depth for ANNs GEP and NLR showing that the sizeeffect is efficiently presented in these models -e trends ofGEP and NLR are very close and compatible and decreasedfrom a depth of 100mm to 1000mm while the ANNsmodelseems to be more accurate as it shows an increase in thetrend up to the depth of 200mm and then it decreasedsimilarly to that of GEP and NLR after that the trend startsto increase slightly

It can be summed up to that the artificial intelligentmodels due to their efficiency and powerful ability in rec-ognizing the parameters interaction demonstrate variousrates of change and fluctuation for the entire scope of inputparameters -e ANNs and GEP models define accurately theinteraction of each parameter on shear strength predictionand have a great ability to represent the actual response ofeach parameter in spite of its complexity and fluctuationnature Furthermore these models are evolved by trainingnumerous preliminary linear and nonlinear models withoutany prior assumption regarding the shape and structure of themathematical model

9 Conclusions

An experimental database including 269 shear test results ofFRP-reinforced concrete members without stirrups availablein the literature was established to propose three predictionmodels to estimate the shear capacity of FRP-RC membersusing three powerful tools which are ANNs GEP and NLR-e following conclusions can be drawn from this study

(i) -e proposed models for predicting the shear ca-pacity of FRP-RC members based on ANNs andGEP techniques showed excellent performancegreat efficiency and high level of accuracy andyielded consistent results throughout a wide rangeof influencing parameters moreover the ANNsmodel is more superior than the GEP as the SD andR2 for ANNs are 0113 and 09877 and for GEP are0162 and 097 respectively

(ii) A simple rational and yet accurate empiricalequation was proposed for predicting shearstrength of FRP-RC members by NLR -e equa-tion considers all the important influencing pa-rameters and simplified to be easy for use Inaddition it gives consistent and accurate resultswith SD and R2 of 0173 and 095 respectively

(iii) -rough a comparative statistical analysis for theproposed models with seven shear design codes andsix proposed equations from the literature it hasbeen found that the most accurate and efficientmodels are ANNs and GEP and to a lower dgreeNLR Among the codes and available proposals theCSA S806-12 and Ashour and Kara [20] equationswere appearing to be more accurate than the others

(iv) From a parametric study considering all the influ-encing parameters on shear capacity it was found thatthe ANNs model and to a lower level GEP modeldefines accurately the interaction of each parameteron shear capacity prediction and has a great ability torepresent the actual response of each parameter inspite of its complexity and fluctuation nature

(v) -e ANNs and GEP models demonstrate that theeffect of flexure reinforcement ratio on shear ca-pacity decreased beyond 003 as a real response tothe available few data in this range therefore morestudies are needed to confirm this case

(vi) -e ANNs model demonstrated that the effect ofad does not absolutely reduce the shear capacitywhile beyond the ad value of 5 its effect couldbecome reverse and contribute to increase in theshear capacity as confirmed by few previous studies

(vii) -e size effect is considered properly by the pro-posed models particularly the ANNs model whichyields more accurate shear capacity prediction tothe experimental results

Data Availability

-e (database of shear strength of beams without stirrups)data used to support the findings of this study are includedwithin the article

Conflicts of Interest

-e authors declare that they have no conflicts of interest

0

004

008

012

016

02

024

0 200 400 600 800 1000 1200

ANNNLRGEP

d (mm)

V pre

db wd

fc

Figure 9 Normalized shear strength (Vpredbwd

fcprime1113969

) versus beamdepth

Advances in Civil Engineering 13

References

[1] M S Alam and A Hussein ldquoSize effect on shear strength ofFRP reinforced concrete beams without stirrupsrdquo Journal ofComposites for Construction vol 17 no 4 pp 507ndash516 2013

[2] J R Yost S P Gross and D W Dinehart ldquoShear strength ofnormal strength concrete beams reinforced with deformedGFRP barsrdquo Journal of Composites for Construction vol 5no 4 pp 268ndash275 2001

[3] A G Razaqpur B O Isgor S Greenaway and A SelleyldquoConcrete contribution to the shear resistance of fiber rein-forced polymer reinforced concrete membersrdquo Journal ofComposites for Construction vol 8 no 5 pp 452ndash460 2004

[4] M Nehdi H El Chabib and A A Saıd ldquoProposed sheardesign equations for FRP-reinforced concrete beams based ongenetic algorithms approachrdquo Journal of Materials in CivilEngineering vol 19 no 12 pp 1033ndash1042 2007

[5] ASCE-ACI445 ldquoRecent approaches to shear design ofstructural concreterdquo Journal of Structural Engineeringvol 124 no 12 pp 1375ndash1417 1998

[6] R Park and T Paulay Reinforced Concrete Structures JohnWiley amp Sons Hoboken NJ USA 1975

[7] I F Kara ldquoPrediction of shear strength of FRP-reinforcedconcrete beams without stirrups based on genetic pro-grammingrdquo Advances in Engineering Software vol 42 no 6pp 295ndash304 2011

[8] R Bashir and A Ashour ldquoNeural networkmodelling for shearstrength of concrete members reinforced with FRP barsrdquoComposites Part B Engineering vol 43 no 8 pp 3198ndash32072012

[9] K Nasrollahzadeh and M M Basiri ldquoPrediction of shearstrength of FRP reinforced concrete beams using fuzzy in-ference systemrdquo Expert Systems with Applications vol 41no 4 pp 1006ndash1020 2014

[10] S Lee and C Lee ldquoPrediction of shear strength of FRP-reinforced concrete flexural members without stirrups usingartificial neural networksrdquo Engineering Structures vol 61pp 99ndash112 2014

[11] E M Golafshani and A Ashour ldquoA feasibility study of BBPfor predicting shear capacity of FRP reinforced concretebeams without stirrupsrdquo Advances in Engineering Softwarevol 97 pp 29ndash39 2016

[12] ACI-440 Guide for the Design and Construction of StructuralConcrete Reinforced with Fiber-Reinforced Polymer (FRP)ACI 440 1R-15 American Concrete Institute FarmingtonsHills MI USA 2015

[13] JSCE ldquoRecommendation for design and construction ofconcrete structures using continuous fiber reinforcing ma-terialsrdquo in Concrete Engineering Series 23 A Machida EdJapan Society of Civil Engineers Tokyo Japan 1997

[14] BISE Interim Guidance on the Design of Reinforced ConcreteStructures Using Fiber Composite Reinforcement British In-stitution of Structural Engineers Seto Ltd London UK1999

[15] CSA Canadian Highway Bridge Design Code SupplementNo 1 to CANCSA S6-06 (S61S1-10) Canadian StandardsAssociation (CSA) Mississauga ON Canada 2010

[16] ISIS Reinforced Concrete Structures with Fibre ReinforcedPolymersmdashDesign Manual No 3 University of Manitoba ISISCanada Corporation Winnipeg MB Canada 2007

[17] CNR-DT203 ldquoGuide for the design and construction ofconcrete structures reinforced with fiber-reinforced polymerbarsrdquo inAdvisory Committee on Technical Recommendations

for Construction CNR-DT 2032006 CNR Rome Italy2007

[18] CSA ldquoCode for the design and construction of buildingstructures with fibre-reinforced polymersrdquo in CANCSAS806-12 p 198 Canadian Standard Association TorontoON Canada 2012

[19] A Razaqpur and S Spadea ldquoResistenza a taglio di elementi dicalcestruzzzo reinforzatti e staffe di FRPrdquo in Proceedings ofAIAS Maratea Italy September 2010

[20] A F Ashour and I F Kara ldquoSize effect on shear strength ofFRP reinforced concrete beamsrdquo Composites Part B Engi-neering vol 60 pp 612ndash620 2014

[21] A R Yousif ldquoShear strength of large FRP-reinforced concretebeams without shear reinforcementrdquo Journal of Pure andApplied Sciences vol 27 pp 9ndash28 2015

[22] A K El-Sayed E F El-Salakawy and B Benmokrane ldquoShearcapacity of high-strength concrete beams reinforced with FRPbarsrdquo ACI Structural Journal vol 103 p 383 2006

[23] A G Razaqpur and O B Isgor ldquoProposed shear designmethod for FRP-reinforced concrete members without stir-rupsrdquo ACI Structural Journal vol 103 p 93 2006

[24] K Maruyama andW Zhao ldquoFlexural and shear behaviour ofconcrete beams reinforced with FRP rodsrdquo in Proceedings ofthe International Conference on Corrosion and CorrosionProtection of Steel in Concrete pp 24ndash28 Sheffield UK1994

[25] W Zhao K Maruyama and H Suzuki ldquoShear behavior ofconcrete beams reinforced by FRP rods as longitudinal andshear reinforcementrdquo in Proceedings of the Second In-ternational RILEM Symposium on Non-Metallic (FRP) Re-inforcement for Concrete Structures p 352 Ghent BelgiumAugust 1995

[26] H Nakamura and T Higai ldquoEvaluation of shear strength ofthe concrete beams reinforced with FRPrdquo in Proceedings ofJapan Society of Civil Engineers p 89 Ghent Belgium 1995

[27] K Maruyama and W Zhao ldquoSize effect in shear behavior ofFRP reinforced concrete beamrdquo in Advanced CompositeMaterials in Bridges and Structures pp 227ndash234 CanadianSociety for Civil Engineering Montreal QC Canada 1996

[28] Y Mizukawa Y Sato T Ueda and Y Kakuta ldquoA studyon shear fatigue behavior of concrete beams with FRP rodsrdquoin Proceedings of the Cird International Symposium onNon-Metallic (FRP) Reinforcement for Concrete Structures(FRPRCS-3) pp 309ndash316 Japan Concrete Institute SapporoJapan 1997

[29] N Duranovic K Pilakoutas and P Waldron ldquoTests onconcrete beams reinforced with glass fibre reinforced plasticbarsrdquo in Proceedings of the Cird International Symposium onNon-Metallic (FRP) Reinforcement for Concrete Structures(FRPRCS-3) pp 479ndash486 Sapporo Japan 1997

[30] N Swamy and M Aburawi ldquoStructural implications of usingGFRP bars as concrete reinforcementrdquo in Proceedings of 3rdInternational Symposium FRPRCS pp 503ndash510 SapporoJapan 1997

[31] C R Michaluk S H Rizkalla G Tadros and B BenmokraneldquoFlexural behavior of one-way concrete slabs reinforced byfiber reinforced plastic reinforcementsrdquo ACI StructuralJournal vol 95 pp 353ndash365 1998

[32] D Deitz I Harik and H Gesund ldquoOne-way slabs reinforcedwith glass fiber reinforced polymer reinforcing barsrdquo SpecialPublication vol 188 pp 279ndash286 1999

[33] T Alkhrdaji M Wideman A Belarbi and A Nanni ldquoShearstrength of GFRP RC beams and slabsrdquo in Proceedings of the

14 Advances in Civil Engineering

International Conference Composites in Construction-CCCpp 409ndash414 Porto Portugal 2001

[34] G S Melo and J A Rayol ldquoShear resistance of GFRPreinforced concrete beamsrdquo in Proceedings of the Rehabil-itating and Repairing the Buildings and Bridges of AmericasHemispheric Workshop on Future Directions Mayaguumlez PRUSA pp 47ndash64 2002

[35] A K Tureyen and R J Frosch ldquoShear tests of FRP-reinforcedconcrete beams without stirrupsrdquo ACI Structural Journalvol 99 pp 427ndash434 2002

[36] S P Gross J R Yost D W Dinehart E Svensen and N LiuldquoShear strength of normal and high strength concrete beamsreinforced with GFRP barsrdquo in Proceedings of InternationalConference on High Performance Materials in Bridgespp 426ndash437 ASCE Reston VA USA 2003

[37] M Tariq and J Newhook ldquoShear testing of FRP reinforcedconcrete without transverse reinforcementrdquo in Proceedings ofAnnual Conference of the Canadian Society for Civil Engi-neering pp 1330ndash1339 Moncton NB Canada June 2003

[38] S Gross D Dinehart J Yost and P -eisz ldquoExperimentaltests of high-strength concrete beams reinforced with CFRPbarsrdquo in Proceedings of the 4th International Conference onAdvanced Composite Materials in Bridges and Structures(ACMBS-4) Calgary AB Canada 2004

[39] A Lubell T Sherwood E Bentz and M P Collins ldquoSafe sheardesign of large wide beams adding shear reinforcement isrecommendedrdquoConcrete International vol 26 pp 66ndash78 2004

[40] J Yost S Gross G Masone and P Hamelin ldquoSustained loadeffects on deflection and ultimate strength of concrete beamsreinforced with GFRPrdquo in Proceedings of the InternationalConference Composites in Construction (CCC2005) LyonFrance July 2005

[41] A El-Sayed E El-Salakawy and B Benmokrane ldquoShearstrength of one-way concrete slabs reinforced with fiber-reinforced polymer composite barsrdquo Journal of Compositesfor Construction vol 9 no 2 pp 147ndash157 2005

[42] A E Kilpatrick and L Easden ldquoShear capacity of GFRPreinforced high strength concrete slabsrdquo in Proceedings of the18th Australasian Conference on the Mechanics of Structuresand Materials Perth Australia vol 1 pp 119ndash124 Taylor ampFrancis London UK 2005

[43] A K El-Sayed E F El-Salakawy and B BenmokraneldquoShear strength of FRP-reinforced concrete beams withouttransverse reinforcementrdquo ACI Structural Journal vol 103p 235 2006

[44] A Ashour ldquoFlexural and shear capacities of concrete beamsreinforced with GFRP barsrdquo Construction and BuildingMaterials vol 20 no 10 pp 1005ndash1015 2006

[45] M Guadagnini K Pilakoutas and P Waldron ldquoShear re-sistance of FRP RC beams experimental studyrdquo Journal ofComposites for Construction vol 10 no 6 pp 464ndash473 2006

[46] R Dawborn and A Kilpatrick Flexural Shear Capacity ofHigh Strength Concrete Slabs Reinforced with LongitudinalGFRP Bars 2006

[47] J Niewels ldquoZum Tragverhalten von Betonbauteilen mitFaserverbundkunststoffbewehrungrdquo Rheinisch-WestfalischeTechnische Hochschule Aachen Lehrstuhl und Institut furMassivbau Dissertation 2008

[48] A El-Sayed K Soudki and E Kling ldquoFlexural behaviour ofself-consolidating concrete slabs reinforced with GFRP barsrdquoin Proceedings of the 9th International Symposium on FiberReinforced Polymer Reinforcement for Reinforced ConcreteStructures pp 13ndash15 Sydney NSW Australia 2009

[49] A Caporale and R Luciano ldquoIndagine sperimentale enumerica sulla resistenza a taglio di travi di calcestruzzoarmate con barre di GFRPrdquo in Proceedings of XXXVIIIConvegno Nazionale AIAS Turin Italy September 2009

[50] R Olivito and F Zuccarello ldquoOn the shear behaviour ofconcrete beams reinforced by carbon fibre-reinforced poly-mer bars an experimental investigation by means of acousticemission techniquerdquo Strain vol 46 no 5 pp 470ndash481 2010

[51] E C Bentz L Massam and M P Collins ldquoShear strength oflarge concrete members with FRP reinforcementrdquo Journal ofComposites for Construction vol 14 no 6 pp 637ndash646 2010

[52] A G Razaqpur M Shedid and B Isgor ldquoShear strength offiber-reinforced polymer reinforced concrete beams subject tounsymmetric loadingrdquo Journal of Composites for Construc-tion vol 15 no 4 pp 500ndash512 2011

[53] M Alam and A Hussein ldquoEffect of member depth on shearstrength of high-strength fiber-reinforced polymerndashreinforced concrete beamsrdquo Journal of Composites for Con-struction vol 16 no 2 pp 119ndash126 2012

[54] F Matta A K El-Sayed A Nanni and B Benmokrane ldquoSizeeffect on concrete shear strength in beams reinforced withfiber-reinforced polymer barsrdquo ACI Structural Journalvol 110-S50 pp 617ndash628 2013

[55] B Abdul-Salam A Farghaly and B Benmokrane ldquoEvalua-tion of shear behavior for one-way concrete slabs reinforcedwith carbon-FRP barsrdquo GEN vol 243 p 1 2013

[56] C H Kim and H S Jang ldquoConcrete shear strength of normaland lightweight concrete beams reinforced with FRP barsrdquoJournal of Composites for Construction vol 18 no 2 article04013038 2014

[57] D Tomlinson and A Fam ldquoPerformance of concrete beamsreinforced with basalt FRP for flexure and shearrdquo Journal ofComposites for Construction vol 19 no 2 article 040140362014

[58] M A Issa T Ovitigala and M Ibrahim ldquoShear behavior ofbasalt fiber reinforced concrete beams with and without basaltFRP stirrupsrdquo Journal of Composites for Construction vol 20no 4 article 04015083 2015

[59] A El Refai and F Abed ldquoConcrete contribution to shearstrength of beams reinforced with basalt fiber-reinforcedbarsrdquo Journal of Composites for Construction vol 20 no 4article 04015082 2015

[60] G B Jumaa and A R Yuosif ldquoSize effect in shear failure ofhigh strength concrete beams without stirrups reinforcedwith basalt FRP barsrdquo KSCE Journal of Civil Engineering2018 In press

[61] M T Hagan H B Demuth and M H BealeNeural NetworkDesign (Electrical Engineering) -omson Learning BostonMA USA 1995

[62] S S Haykin S S Haykin S S Haykin and S S HaykinNeural Networks and Learning Machines Pearson Vol 3Pearson Upper Saddle River NJ USA 2009

[63] M Y Mansour M Dicleli J-Y Lee and J Zhang ldquoPredictingthe shear strength of reinforced concrete beams using artificialneural networksrdquo Engineering Structures vol 26 no 6pp 781ndash799 2004

[64] H Demuth M Beale and M Hagan Neural NetworkToolboxtrade 6 Userrsquos Guide -e MathWorks Inc vol 10 p 11Natick MA USA 2008

[65] A W Oreta and K Kawashima ldquoNeural network modeling ofconfined compressive strength and strain of circular concretecolumnsrdquo Journal of Structural Engineering vol 129 no 4pp 554ndash561 2003

Advances in Civil Engineering 15

[66] S Jung and K S Kim ldquoKnowledge-based predictionof shear strength of concrete beams without shear re-inforcementrdquo Engineering Structures vol 30 no 6pp 1515ndash1525 2008

[67] Z-H Duan S-C Kou and C-S Poon ldquoPrediction ofcompressive strength of recycled aggregate concrete usingartificial neural networksrdquo Construction and Building Mate-rials vol 40 pp 1200ndash1206 2013

[68] H El-Chabib M Nehdi and A Said ldquoPredicting shear ca-pacity of NSC and HSC slender beams without stirrups usingartificial intelligencerdquo Computers and Concrete vol 2 no 1pp 79ndash96 2005

[69] F Altun O Kisi and K Aydin ldquoPredicting the compressivestrength of steel fiber added lightweight concrete using neuralnetworkrdquo Computational Materials Science vol 42 no 2pp 259ndash265 2008

[70] J R Koza ldquoGenetic programming as a means for pro-gramming computers by natural selectionrdquo Statistics andComputing vol 4 no 2 pp 87ndash112 1994

[71] C Ferreira ldquoGene expression programming in problemsolvingrdquo in Soft Computing and Industry pp 635ndash653Springer Berlin Germany 2002

[72] C Kayadelen ldquoSoil liquefaction modeling by genetic ex-pression programming and neuro-fuzzyrdquo Expert Systems withApplications vol 38 no 4 pp 4080ndash4087 2011

[73] A H Gandomi A H Alavi and G J Yun ldquoFormulation ofuplift capacity of suction caissons using multi expressionprogrammingrdquo KSCE Journal of Civil Engineering vol 15no 2 pp 363ndash373 2011

[74] A H Gandomi A H Alavi and C RyanHandbook of GeneticProgramming Applications Springer Berlin Germany 2015

[75] A H Gandomi and A H Alavi ldquoA new multi-gene geneticprogramming approach to non-linear system modeling PartII geotechnical and earthquake engineering problemsrdquoNeural Computing and Applications vol 21 no 1 pp 189ndash201 2012

[76] A H Alavi and A H Gandomi ldquoEnergy-based numericalmodels for assessment of soil liquefactionrdquo GeoscienceFrontiers vol 3 no 4 pp 541ndash555 2012

[77] L Teodorescu and D Sherwood ldquoHigh energy physics eventselection with gene expression programmingrdquo ComputerPhysics Communications vol 178 no 6 pp 409ndash419 2008

[78] GEPSOFT GeneXproTools Version 50 GEPSOFT BristolUK 2013 httpwwwgepsoftcom

[79] S M Mousavi P Aminian A H Gandomi A H Alavi andH Bolandi ldquoA new predictive model for compressive strengthof HPC using gene expression programmingrdquo Advances inEngineering Software vol 45 no 1 pp 105ndash114 2012

[80] M Sarıdemir ldquoEmpirical modeling of splitting tensilestrength from cylinder compressive strength of concrete bygenetic programmingrdquo Expert Systems with Applicationsvol 38 no 11 pp 14257ndash14268 2011

[81] M Sonebi and A Cevik ldquoGenetic programming based for-mulation for fresh and hardened properties of self-compacting concrete containing pulverised fuel ashrdquo Con-struction and Building Materials vol 23 no 7 pp 2614ndash26222009

[82] A H Alavi P Aminian A H Gandomi and M A EsmaeilildquoGenetic-based modeling of uplift capacity of suction cais-sonsrdquo Expert Systems with Applications vol 38 no 10pp 12608ndash12618 2011

[83] T Zsutty ldquoShear strength prediction for separate catagories ofsimple beam testsrdquo ACI Journal Proceedings vol 68 no 2pp 138ndash143 1971

16 Advances in Civil Engineering

0

30

60

90

120

150

180

0 150 300 450 600 750 900 1050

V pre

d (k

N)

d (mm)

ANNGEPJSCE 97

NLRACI 440CSA S806

0

20

40

60

80

100

120

0 10 20 30 40 50 60 70 80 90 100 110

V pre

d (k

N)

fcprime (MPa)

ANNGEPJSCE 97

NLRACI 440SCA S806

0

20

40

60

80

100

120

0 001 002 003 004 005

V pre

d (k

N)

ρf

ANNGEPJSCE 97

NLRACI 440CSA S806

0

20

40

60

80

100

120

0 25 50 75 100 125 150 175

V pre

d (k

N)

Ef (MPa)

ANNGEPJSCE 97

NLRACI 440CSA S806

0

20

40

60

80

100

120

0 2 4 6 8 10

V pre

d (k

N)

ad

ANNGEPJSCE 97

NLRACI 440CSA S806

0

60

120

180

240

300

360

0 200 400 600 800 1000 1200

V pre

d (k

N)

b (mm)

ANNGEPJSCE 97

NLRACI 440CSA S806

Figure 8 Eect of the parameters (d fcprime ρf Ef ad and bw) on shear capacity predicted by ANNs GEP NLR and three design codes(ACI1R 440-06 JSCE-97 and CSA S806-12)

12 Advances in Civil Engineering

the relationship between normalized shear strength as(Vpredbwd

fcprime1113969

) and beam depth It is clear that the nor-malized shear strength is decreased with the increase in thebeam depth for ANNs GEP and NLR showing that the sizeeffect is efficiently presented in these models -e trends ofGEP and NLR are very close and compatible and decreasedfrom a depth of 100mm to 1000mm while the ANNsmodelseems to be more accurate as it shows an increase in thetrend up to the depth of 200mm and then it decreasedsimilarly to that of GEP and NLR after that the trend startsto increase slightly

It can be summed up to that the artificial intelligentmodels due to their efficiency and powerful ability in rec-ognizing the parameters interaction demonstrate variousrates of change and fluctuation for the entire scope of inputparameters -e ANNs and GEP models define accurately theinteraction of each parameter on shear strength predictionand have a great ability to represent the actual response ofeach parameter in spite of its complexity and fluctuationnature Furthermore these models are evolved by trainingnumerous preliminary linear and nonlinear models withoutany prior assumption regarding the shape and structure of themathematical model

9 Conclusions

An experimental database including 269 shear test results ofFRP-reinforced concrete members without stirrups availablein the literature was established to propose three predictionmodels to estimate the shear capacity of FRP-RC membersusing three powerful tools which are ANNs GEP and NLR-e following conclusions can be drawn from this study

(i) -e proposed models for predicting the shear ca-pacity of FRP-RC members based on ANNs andGEP techniques showed excellent performancegreat efficiency and high level of accuracy andyielded consistent results throughout a wide rangeof influencing parameters moreover the ANNsmodel is more superior than the GEP as the SD andR2 for ANNs are 0113 and 09877 and for GEP are0162 and 097 respectively

(ii) A simple rational and yet accurate empiricalequation was proposed for predicting shearstrength of FRP-RC members by NLR -e equa-tion considers all the important influencing pa-rameters and simplified to be easy for use Inaddition it gives consistent and accurate resultswith SD and R2 of 0173 and 095 respectively

(iii) -rough a comparative statistical analysis for theproposed models with seven shear design codes andsix proposed equations from the literature it hasbeen found that the most accurate and efficientmodels are ANNs and GEP and to a lower dgreeNLR Among the codes and available proposals theCSA S806-12 and Ashour and Kara [20] equationswere appearing to be more accurate than the others

(iv) From a parametric study considering all the influ-encing parameters on shear capacity it was found thatthe ANNs model and to a lower level GEP modeldefines accurately the interaction of each parameteron shear capacity prediction and has a great ability torepresent the actual response of each parameter inspite of its complexity and fluctuation nature

(v) -e ANNs and GEP models demonstrate that theeffect of flexure reinforcement ratio on shear ca-pacity decreased beyond 003 as a real response tothe available few data in this range therefore morestudies are needed to confirm this case

(vi) -e ANNs model demonstrated that the effect ofad does not absolutely reduce the shear capacitywhile beyond the ad value of 5 its effect couldbecome reverse and contribute to increase in theshear capacity as confirmed by few previous studies

(vii) -e size effect is considered properly by the pro-posed models particularly the ANNs model whichyields more accurate shear capacity prediction tothe experimental results

Data Availability

-e (database of shear strength of beams without stirrups)data used to support the findings of this study are includedwithin the article

Conflicts of Interest

-e authors declare that they have no conflicts of interest

0

004

008

012

016

02

024

0 200 400 600 800 1000 1200

ANNNLRGEP

d (mm)

V pre

db wd

fc

Figure 9 Normalized shear strength (Vpredbwd

fcprime1113969

) versus beamdepth

Advances in Civil Engineering 13

References

[1] M S Alam and A Hussein ldquoSize effect on shear strength ofFRP reinforced concrete beams without stirrupsrdquo Journal ofComposites for Construction vol 17 no 4 pp 507ndash516 2013

[2] J R Yost S P Gross and D W Dinehart ldquoShear strength ofnormal strength concrete beams reinforced with deformedGFRP barsrdquo Journal of Composites for Construction vol 5no 4 pp 268ndash275 2001

[3] A G Razaqpur B O Isgor S Greenaway and A SelleyldquoConcrete contribution to the shear resistance of fiber rein-forced polymer reinforced concrete membersrdquo Journal ofComposites for Construction vol 8 no 5 pp 452ndash460 2004

[4] M Nehdi H El Chabib and A A Saıd ldquoProposed sheardesign equations for FRP-reinforced concrete beams based ongenetic algorithms approachrdquo Journal of Materials in CivilEngineering vol 19 no 12 pp 1033ndash1042 2007

[5] ASCE-ACI445 ldquoRecent approaches to shear design ofstructural concreterdquo Journal of Structural Engineeringvol 124 no 12 pp 1375ndash1417 1998

[6] R Park and T Paulay Reinforced Concrete Structures JohnWiley amp Sons Hoboken NJ USA 1975

[7] I F Kara ldquoPrediction of shear strength of FRP-reinforcedconcrete beams without stirrups based on genetic pro-grammingrdquo Advances in Engineering Software vol 42 no 6pp 295ndash304 2011

[8] R Bashir and A Ashour ldquoNeural networkmodelling for shearstrength of concrete members reinforced with FRP barsrdquoComposites Part B Engineering vol 43 no 8 pp 3198ndash32072012

[9] K Nasrollahzadeh and M M Basiri ldquoPrediction of shearstrength of FRP reinforced concrete beams using fuzzy in-ference systemrdquo Expert Systems with Applications vol 41no 4 pp 1006ndash1020 2014

[10] S Lee and C Lee ldquoPrediction of shear strength of FRP-reinforced concrete flexural members without stirrups usingartificial neural networksrdquo Engineering Structures vol 61pp 99ndash112 2014

[11] E M Golafshani and A Ashour ldquoA feasibility study of BBPfor predicting shear capacity of FRP reinforced concretebeams without stirrupsrdquo Advances in Engineering Softwarevol 97 pp 29ndash39 2016

[12] ACI-440 Guide for the Design and Construction of StructuralConcrete Reinforced with Fiber-Reinforced Polymer (FRP)ACI 440 1R-15 American Concrete Institute FarmingtonsHills MI USA 2015

[13] JSCE ldquoRecommendation for design and construction ofconcrete structures using continuous fiber reinforcing ma-terialsrdquo in Concrete Engineering Series 23 A Machida EdJapan Society of Civil Engineers Tokyo Japan 1997

[14] BISE Interim Guidance on the Design of Reinforced ConcreteStructures Using Fiber Composite Reinforcement British In-stitution of Structural Engineers Seto Ltd London UK1999

[15] CSA Canadian Highway Bridge Design Code SupplementNo 1 to CANCSA S6-06 (S61S1-10) Canadian StandardsAssociation (CSA) Mississauga ON Canada 2010

[16] ISIS Reinforced Concrete Structures with Fibre ReinforcedPolymersmdashDesign Manual No 3 University of Manitoba ISISCanada Corporation Winnipeg MB Canada 2007

[17] CNR-DT203 ldquoGuide for the design and construction ofconcrete structures reinforced with fiber-reinforced polymerbarsrdquo inAdvisory Committee on Technical Recommendations

for Construction CNR-DT 2032006 CNR Rome Italy2007

[18] CSA ldquoCode for the design and construction of buildingstructures with fibre-reinforced polymersrdquo in CANCSAS806-12 p 198 Canadian Standard Association TorontoON Canada 2012

[19] A Razaqpur and S Spadea ldquoResistenza a taglio di elementi dicalcestruzzzo reinforzatti e staffe di FRPrdquo in Proceedings ofAIAS Maratea Italy September 2010

[20] A F Ashour and I F Kara ldquoSize effect on shear strength ofFRP reinforced concrete beamsrdquo Composites Part B Engi-neering vol 60 pp 612ndash620 2014

[21] A R Yousif ldquoShear strength of large FRP-reinforced concretebeams without shear reinforcementrdquo Journal of Pure andApplied Sciences vol 27 pp 9ndash28 2015

[22] A K El-Sayed E F El-Salakawy and B Benmokrane ldquoShearcapacity of high-strength concrete beams reinforced with FRPbarsrdquo ACI Structural Journal vol 103 p 383 2006

[23] A G Razaqpur and O B Isgor ldquoProposed shear designmethod for FRP-reinforced concrete members without stir-rupsrdquo ACI Structural Journal vol 103 p 93 2006

[24] K Maruyama andW Zhao ldquoFlexural and shear behaviour ofconcrete beams reinforced with FRP rodsrdquo in Proceedings ofthe International Conference on Corrosion and CorrosionProtection of Steel in Concrete pp 24ndash28 Sheffield UK1994

[25] W Zhao K Maruyama and H Suzuki ldquoShear behavior ofconcrete beams reinforced by FRP rods as longitudinal andshear reinforcementrdquo in Proceedings of the Second In-ternational RILEM Symposium on Non-Metallic (FRP) Re-inforcement for Concrete Structures p 352 Ghent BelgiumAugust 1995

[26] H Nakamura and T Higai ldquoEvaluation of shear strength ofthe concrete beams reinforced with FRPrdquo in Proceedings ofJapan Society of Civil Engineers p 89 Ghent Belgium 1995

[27] K Maruyama and W Zhao ldquoSize effect in shear behavior ofFRP reinforced concrete beamrdquo in Advanced CompositeMaterials in Bridges and Structures pp 227ndash234 CanadianSociety for Civil Engineering Montreal QC Canada 1996

[28] Y Mizukawa Y Sato T Ueda and Y Kakuta ldquoA studyon shear fatigue behavior of concrete beams with FRP rodsrdquoin Proceedings of the Cird International Symposium onNon-Metallic (FRP) Reinforcement for Concrete Structures(FRPRCS-3) pp 309ndash316 Japan Concrete Institute SapporoJapan 1997

[29] N Duranovic K Pilakoutas and P Waldron ldquoTests onconcrete beams reinforced with glass fibre reinforced plasticbarsrdquo in Proceedings of the Cird International Symposium onNon-Metallic (FRP) Reinforcement for Concrete Structures(FRPRCS-3) pp 479ndash486 Sapporo Japan 1997

[30] N Swamy and M Aburawi ldquoStructural implications of usingGFRP bars as concrete reinforcementrdquo in Proceedings of 3rdInternational Symposium FRPRCS pp 503ndash510 SapporoJapan 1997

[31] C R Michaluk S H Rizkalla G Tadros and B BenmokraneldquoFlexural behavior of one-way concrete slabs reinforced byfiber reinforced plastic reinforcementsrdquo ACI StructuralJournal vol 95 pp 353ndash365 1998

[32] D Deitz I Harik and H Gesund ldquoOne-way slabs reinforcedwith glass fiber reinforced polymer reinforcing barsrdquo SpecialPublication vol 188 pp 279ndash286 1999

[33] T Alkhrdaji M Wideman A Belarbi and A Nanni ldquoShearstrength of GFRP RC beams and slabsrdquo in Proceedings of the

14 Advances in Civil Engineering

International Conference Composites in Construction-CCCpp 409ndash414 Porto Portugal 2001

[34] G S Melo and J A Rayol ldquoShear resistance of GFRPreinforced concrete beamsrdquo in Proceedings of the Rehabil-itating and Repairing the Buildings and Bridges of AmericasHemispheric Workshop on Future Directions Mayaguumlez PRUSA pp 47ndash64 2002

[35] A K Tureyen and R J Frosch ldquoShear tests of FRP-reinforcedconcrete beams without stirrupsrdquo ACI Structural Journalvol 99 pp 427ndash434 2002

[36] S P Gross J R Yost D W Dinehart E Svensen and N LiuldquoShear strength of normal and high strength concrete beamsreinforced with GFRP barsrdquo in Proceedings of InternationalConference on High Performance Materials in Bridgespp 426ndash437 ASCE Reston VA USA 2003

[37] M Tariq and J Newhook ldquoShear testing of FRP reinforcedconcrete without transverse reinforcementrdquo in Proceedings ofAnnual Conference of the Canadian Society for Civil Engi-neering pp 1330ndash1339 Moncton NB Canada June 2003

[38] S Gross D Dinehart J Yost and P -eisz ldquoExperimentaltests of high-strength concrete beams reinforced with CFRPbarsrdquo in Proceedings of the 4th International Conference onAdvanced Composite Materials in Bridges and Structures(ACMBS-4) Calgary AB Canada 2004

[39] A Lubell T Sherwood E Bentz and M P Collins ldquoSafe sheardesign of large wide beams adding shear reinforcement isrecommendedrdquoConcrete International vol 26 pp 66ndash78 2004

[40] J Yost S Gross G Masone and P Hamelin ldquoSustained loadeffects on deflection and ultimate strength of concrete beamsreinforced with GFRPrdquo in Proceedings of the InternationalConference Composites in Construction (CCC2005) LyonFrance July 2005

[41] A El-Sayed E El-Salakawy and B Benmokrane ldquoShearstrength of one-way concrete slabs reinforced with fiber-reinforced polymer composite barsrdquo Journal of Compositesfor Construction vol 9 no 2 pp 147ndash157 2005

[42] A E Kilpatrick and L Easden ldquoShear capacity of GFRPreinforced high strength concrete slabsrdquo in Proceedings of the18th Australasian Conference on the Mechanics of Structuresand Materials Perth Australia vol 1 pp 119ndash124 Taylor ampFrancis London UK 2005

[43] A K El-Sayed E F El-Salakawy and B BenmokraneldquoShear strength of FRP-reinforced concrete beams withouttransverse reinforcementrdquo ACI Structural Journal vol 103p 235 2006

[44] A Ashour ldquoFlexural and shear capacities of concrete beamsreinforced with GFRP barsrdquo Construction and BuildingMaterials vol 20 no 10 pp 1005ndash1015 2006

[45] M Guadagnini K Pilakoutas and P Waldron ldquoShear re-sistance of FRP RC beams experimental studyrdquo Journal ofComposites for Construction vol 10 no 6 pp 464ndash473 2006

[46] R Dawborn and A Kilpatrick Flexural Shear Capacity ofHigh Strength Concrete Slabs Reinforced with LongitudinalGFRP Bars 2006

[47] J Niewels ldquoZum Tragverhalten von Betonbauteilen mitFaserverbundkunststoffbewehrungrdquo Rheinisch-WestfalischeTechnische Hochschule Aachen Lehrstuhl und Institut furMassivbau Dissertation 2008

[48] A El-Sayed K Soudki and E Kling ldquoFlexural behaviour ofself-consolidating concrete slabs reinforced with GFRP barsrdquoin Proceedings of the 9th International Symposium on FiberReinforced Polymer Reinforcement for Reinforced ConcreteStructures pp 13ndash15 Sydney NSW Australia 2009

[49] A Caporale and R Luciano ldquoIndagine sperimentale enumerica sulla resistenza a taglio di travi di calcestruzzoarmate con barre di GFRPrdquo in Proceedings of XXXVIIIConvegno Nazionale AIAS Turin Italy September 2009

[50] R Olivito and F Zuccarello ldquoOn the shear behaviour ofconcrete beams reinforced by carbon fibre-reinforced poly-mer bars an experimental investigation by means of acousticemission techniquerdquo Strain vol 46 no 5 pp 470ndash481 2010

[51] E C Bentz L Massam and M P Collins ldquoShear strength oflarge concrete members with FRP reinforcementrdquo Journal ofComposites for Construction vol 14 no 6 pp 637ndash646 2010

[52] A G Razaqpur M Shedid and B Isgor ldquoShear strength offiber-reinforced polymer reinforced concrete beams subject tounsymmetric loadingrdquo Journal of Composites for Construc-tion vol 15 no 4 pp 500ndash512 2011

[53] M Alam and A Hussein ldquoEffect of member depth on shearstrength of high-strength fiber-reinforced polymerndashreinforced concrete beamsrdquo Journal of Composites for Con-struction vol 16 no 2 pp 119ndash126 2012

[54] F Matta A K El-Sayed A Nanni and B Benmokrane ldquoSizeeffect on concrete shear strength in beams reinforced withfiber-reinforced polymer barsrdquo ACI Structural Journalvol 110-S50 pp 617ndash628 2013

[55] B Abdul-Salam A Farghaly and B Benmokrane ldquoEvalua-tion of shear behavior for one-way concrete slabs reinforcedwith carbon-FRP barsrdquo GEN vol 243 p 1 2013

[56] C H Kim and H S Jang ldquoConcrete shear strength of normaland lightweight concrete beams reinforced with FRP barsrdquoJournal of Composites for Construction vol 18 no 2 article04013038 2014

[57] D Tomlinson and A Fam ldquoPerformance of concrete beamsreinforced with basalt FRP for flexure and shearrdquo Journal ofComposites for Construction vol 19 no 2 article 040140362014

[58] M A Issa T Ovitigala and M Ibrahim ldquoShear behavior ofbasalt fiber reinforced concrete beams with and without basaltFRP stirrupsrdquo Journal of Composites for Construction vol 20no 4 article 04015083 2015

[59] A El Refai and F Abed ldquoConcrete contribution to shearstrength of beams reinforced with basalt fiber-reinforcedbarsrdquo Journal of Composites for Construction vol 20 no 4article 04015082 2015

[60] G B Jumaa and A R Yuosif ldquoSize effect in shear failure ofhigh strength concrete beams without stirrups reinforcedwith basalt FRP barsrdquo KSCE Journal of Civil Engineering2018 In press

[61] M T Hagan H B Demuth and M H BealeNeural NetworkDesign (Electrical Engineering) -omson Learning BostonMA USA 1995

[62] S S Haykin S S Haykin S S Haykin and S S HaykinNeural Networks and Learning Machines Pearson Vol 3Pearson Upper Saddle River NJ USA 2009

[63] M Y Mansour M Dicleli J-Y Lee and J Zhang ldquoPredictingthe shear strength of reinforced concrete beams using artificialneural networksrdquo Engineering Structures vol 26 no 6pp 781ndash799 2004

[64] H Demuth M Beale and M Hagan Neural NetworkToolboxtrade 6 Userrsquos Guide -e MathWorks Inc vol 10 p 11Natick MA USA 2008

[65] A W Oreta and K Kawashima ldquoNeural network modeling ofconfined compressive strength and strain of circular concretecolumnsrdquo Journal of Structural Engineering vol 129 no 4pp 554ndash561 2003

Advances in Civil Engineering 15

[66] S Jung and K S Kim ldquoKnowledge-based predictionof shear strength of concrete beams without shear re-inforcementrdquo Engineering Structures vol 30 no 6pp 1515ndash1525 2008

[67] Z-H Duan S-C Kou and C-S Poon ldquoPrediction ofcompressive strength of recycled aggregate concrete usingartificial neural networksrdquo Construction and Building Mate-rials vol 40 pp 1200ndash1206 2013

[68] H El-Chabib M Nehdi and A Said ldquoPredicting shear ca-pacity of NSC and HSC slender beams without stirrups usingartificial intelligencerdquo Computers and Concrete vol 2 no 1pp 79ndash96 2005

[69] F Altun O Kisi and K Aydin ldquoPredicting the compressivestrength of steel fiber added lightweight concrete using neuralnetworkrdquo Computational Materials Science vol 42 no 2pp 259ndash265 2008

[70] J R Koza ldquoGenetic programming as a means for pro-gramming computers by natural selectionrdquo Statistics andComputing vol 4 no 2 pp 87ndash112 1994

[71] C Ferreira ldquoGene expression programming in problemsolvingrdquo in Soft Computing and Industry pp 635ndash653Springer Berlin Germany 2002

[72] C Kayadelen ldquoSoil liquefaction modeling by genetic ex-pression programming and neuro-fuzzyrdquo Expert Systems withApplications vol 38 no 4 pp 4080ndash4087 2011

[73] A H Gandomi A H Alavi and G J Yun ldquoFormulation ofuplift capacity of suction caissons using multi expressionprogrammingrdquo KSCE Journal of Civil Engineering vol 15no 2 pp 363ndash373 2011

[74] A H Gandomi A H Alavi and C RyanHandbook of GeneticProgramming Applications Springer Berlin Germany 2015

[75] A H Gandomi and A H Alavi ldquoA new multi-gene geneticprogramming approach to non-linear system modeling PartII geotechnical and earthquake engineering problemsrdquoNeural Computing and Applications vol 21 no 1 pp 189ndash201 2012

[76] A H Alavi and A H Gandomi ldquoEnergy-based numericalmodels for assessment of soil liquefactionrdquo GeoscienceFrontiers vol 3 no 4 pp 541ndash555 2012

[77] L Teodorescu and D Sherwood ldquoHigh energy physics eventselection with gene expression programmingrdquo ComputerPhysics Communications vol 178 no 6 pp 409ndash419 2008

[78] GEPSOFT GeneXproTools Version 50 GEPSOFT BristolUK 2013 httpwwwgepsoftcom

[79] S M Mousavi P Aminian A H Gandomi A H Alavi andH Bolandi ldquoA new predictive model for compressive strengthof HPC using gene expression programmingrdquo Advances inEngineering Software vol 45 no 1 pp 105ndash114 2012

[80] M Sarıdemir ldquoEmpirical modeling of splitting tensilestrength from cylinder compressive strength of concrete bygenetic programmingrdquo Expert Systems with Applicationsvol 38 no 11 pp 14257ndash14268 2011

[81] M Sonebi and A Cevik ldquoGenetic programming based for-mulation for fresh and hardened properties of self-compacting concrete containing pulverised fuel ashrdquo Con-struction and Building Materials vol 23 no 7 pp 2614ndash26222009

[82] A H Alavi P Aminian A H Gandomi and M A EsmaeilildquoGenetic-based modeling of uplift capacity of suction cais-sonsrdquo Expert Systems with Applications vol 38 no 10pp 12608ndash12618 2011

[83] T Zsutty ldquoShear strength prediction for separate catagories ofsimple beam testsrdquo ACI Journal Proceedings vol 68 no 2pp 138ndash143 1971

16 Advances in Civil Engineering

the relationship between normalized shear strength as(Vpredbwd

fcprime1113969

) and beam depth It is clear that the nor-malized shear strength is decreased with the increase in thebeam depth for ANNs GEP and NLR showing that the sizeeffect is efficiently presented in these models -e trends ofGEP and NLR are very close and compatible and decreasedfrom a depth of 100mm to 1000mm while the ANNsmodelseems to be more accurate as it shows an increase in thetrend up to the depth of 200mm and then it decreasedsimilarly to that of GEP and NLR after that the trend startsto increase slightly

It can be summed up to that the artificial intelligentmodels due to their efficiency and powerful ability in rec-ognizing the parameters interaction demonstrate variousrates of change and fluctuation for the entire scope of inputparameters -e ANNs and GEP models define accurately theinteraction of each parameter on shear strength predictionand have a great ability to represent the actual response ofeach parameter in spite of its complexity and fluctuationnature Furthermore these models are evolved by trainingnumerous preliminary linear and nonlinear models withoutany prior assumption regarding the shape and structure of themathematical model

9 Conclusions

An experimental database including 269 shear test results ofFRP-reinforced concrete members without stirrups availablein the literature was established to propose three predictionmodels to estimate the shear capacity of FRP-RC membersusing three powerful tools which are ANNs GEP and NLR-e following conclusions can be drawn from this study

(i) -e proposed models for predicting the shear ca-pacity of FRP-RC members based on ANNs andGEP techniques showed excellent performancegreat efficiency and high level of accuracy andyielded consistent results throughout a wide rangeof influencing parameters moreover the ANNsmodel is more superior than the GEP as the SD andR2 for ANNs are 0113 and 09877 and for GEP are0162 and 097 respectively

(ii) A simple rational and yet accurate empiricalequation was proposed for predicting shearstrength of FRP-RC members by NLR -e equa-tion considers all the important influencing pa-rameters and simplified to be easy for use Inaddition it gives consistent and accurate resultswith SD and R2 of 0173 and 095 respectively

(iii) -rough a comparative statistical analysis for theproposed models with seven shear design codes andsix proposed equations from the literature it hasbeen found that the most accurate and efficientmodels are ANNs and GEP and to a lower dgreeNLR Among the codes and available proposals theCSA S806-12 and Ashour and Kara [20] equationswere appearing to be more accurate than the others

(iv) From a parametric study considering all the influ-encing parameters on shear capacity it was found thatthe ANNs model and to a lower level GEP modeldefines accurately the interaction of each parameteron shear capacity prediction and has a great ability torepresent the actual response of each parameter inspite of its complexity and fluctuation nature

(v) -e ANNs and GEP models demonstrate that theeffect of flexure reinforcement ratio on shear ca-pacity decreased beyond 003 as a real response tothe available few data in this range therefore morestudies are needed to confirm this case

(vi) -e ANNs model demonstrated that the effect ofad does not absolutely reduce the shear capacitywhile beyond the ad value of 5 its effect couldbecome reverse and contribute to increase in theshear capacity as confirmed by few previous studies

(vii) -e size effect is considered properly by the pro-posed models particularly the ANNs model whichyields more accurate shear capacity prediction tothe experimental results

Data Availability

-e (database of shear strength of beams without stirrups)data used to support the findings of this study are includedwithin the article

Conflicts of Interest

-e authors declare that they have no conflicts of interest

0

004

008

012

016

02

024

0 200 400 600 800 1000 1200

ANNNLRGEP

d (mm)

V pre

db wd

fc

Figure 9 Normalized shear strength (Vpredbwd

fcprime1113969

) versus beamdepth

Advances in Civil Engineering 13

References

[1] M S Alam and A Hussein ldquoSize effect on shear strength ofFRP reinforced concrete beams without stirrupsrdquo Journal ofComposites for Construction vol 17 no 4 pp 507ndash516 2013

[2] J R Yost S P Gross and D W Dinehart ldquoShear strength ofnormal strength concrete beams reinforced with deformedGFRP barsrdquo Journal of Composites for Construction vol 5no 4 pp 268ndash275 2001

[3] A G Razaqpur B O Isgor S Greenaway and A SelleyldquoConcrete contribution to the shear resistance of fiber rein-forced polymer reinforced concrete membersrdquo Journal ofComposites for Construction vol 8 no 5 pp 452ndash460 2004

[4] M Nehdi H El Chabib and A A Saıd ldquoProposed sheardesign equations for FRP-reinforced concrete beams based ongenetic algorithms approachrdquo Journal of Materials in CivilEngineering vol 19 no 12 pp 1033ndash1042 2007

[5] ASCE-ACI445 ldquoRecent approaches to shear design ofstructural concreterdquo Journal of Structural Engineeringvol 124 no 12 pp 1375ndash1417 1998

[6] R Park and T Paulay Reinforced Concrete Structures JohnWiley amp Sons Hoboken NJ USA 1975

[7] I F Kara ldquoPrediction of shear strength of FRP-reinforcedconcrete beams without stirrups based on genetic pro-grammingrdquo Advances in Engineering Software vol 42 no 6pp 295ndash304 2011

[8] R Bashir and A Ashour ldquoNeural networkmodelling for shearstrength of concrete members reinforced with FRP barsrdquoComposites Part B Engineering vol 43 no 8 pp 3198ndash32072012

[9] K Nasrollahzadeh and M M Basiri ldquoPrediction of shearstrength of FRP reinforced concrete beams using fuzzy in-ference systemrdquo Expert Systems with Applications vol 41no 4 pp 1006ndash1020 2014

[10] S Lee and C Lee ldquoPrediction of shear strength of FRP-reinforced concrete flexural members without stirrups usingartificial neural networksrdquo Engineering Structures vol 61pp 99ndash112 2014

[11] E M Golafshani and A Ashour ldquoA feasibility study of BBPfor predicting shear capacity of FRP reinforced concretebeams without stirrupsrdquo Advances in Engineering Softwarevol 97 pp 29ndash39 2016

[12] ACI-440 Guide for the Design and Construction of StructuralConcrete Reinforced with Fiber-Reinforced Polymer (FRP)ACI 440 1R-15 American Concrete Institute FarmingtonsHills MI USA 2015

[13] JSCE ldquoRecommendation for design and construction ofconcrete structures using continuous fiber reinforcing ma-terialsrdquo in Concrete Engineering Series 23 A Machida EdJapan Society of Civil Engineers Tokyo Japan 1997

[14] BISE Interim Guidance on the Design of Reinforced ConcreteStructures Using Fiber Composite Reinforcement British In-stitution of Structural Engineers Seto Ltd London UK1999

[15] CSA Canadian Highway Bridge Design Code SupplementNo 1 to CANCSA S6-06 (S61S1-10) Canadian StandardsAssociation (CSA) Mississauga ON Canada 2010

[16] ISIS Reinforced Concrete Structures with Fibre ReinforcedPolymersmdashDesign Manual No 3 University of Manitoba ISISCanada Corporation Winnipeg MB Canada 2007

[17] CNR-DT203 ldquoGuide for the design and construction ofconcrete structures reinforced with fiber-reinforced polymerbarsrdquo inAdvisory Committee on Technical Recommendations

for Construction CNR-DT 2032006 CNR Rome Italy2007

[18] CSA ldquoCode for the design and construction of buildingstructures with fibre-reinforced polymersrdquo in CANCSAS806-12 p 198 Canadian Standard Association TorontoON Canada 2012

[19] A Razaqpur and S Spadea ldquoResistenza a taglio di elementi dicalcestruzzzo reinforzatti e staffe di FRPrdquo in Proceedings ofAIAS Maratea Italy September 2010

[20] A F Ashour and I F Kara ldquoSize effect on shear strength ofFRP reinforced concrete beamsrdquo Composites Part B Engi-neering vol 60 pp 612ndash620 2014

[21] A R Yousif ldquoShear strength of large FRP-reinforced concretebeams without shear reinforcementrdquo Journal of Pure andApplied Sciences vol 27 pp 9ndash28 2015

[22] A K El-Sayed E F El-Salakawy and B Benmokrane ldquoShearcapacity of high-strength concrete beams reinforced with FRPbarsrdquo ACI Structural Journal vol 103 p 383 2006

[23] A G Razaqpur and O B Isgor ldquoProposed shear designmethod for FRP-reinforced concrete members without stir-rupsrdquo ACI Structural Journal vol 103 p 93 2006

[24] K Maruyama andW Zhao ldquoFlexural and shear behaviour ofconcrete beams reinforced with FRP rodsrdquo in Proceedings ofthe International Conference on Corrosion and CorrosionProtection of Steel in Concrete pp 24ndash28 Sheffield UK1994

[25] W Zhao K Maruyama and H Suzuki ldquoShear behavior ofconcrete beams reinforced by FRP rods as longitudinal andshear reinforcementrdquo in Proceedings of the Second In-ternational RILEM Symposium on Non-Metallic (FRP) Re-inforcement for Concrete Structures p 352 Ghent BelgiumAugust 1995

[26] H Nakamura and T Higai ldquoEvaluation of shear strength ofthe concrete beams reinforced with FRPrdquo in Proceedings ofJapan Society of Civil Engineers p 89 Ghent Belgium 1995

[27] K Maruyama and W Zhao ldquoSize effect in shear behavior ofFRP reinforced concrete beamrdquo in Advanced CompositeMaterials in Bridges and Structures pp 227ndash234 CanadianSociety for Civil Engineering Montreal QC Canada 1996

[28] Y Mizukawa Y Sato T Ueda and Y Kakuta ldquoA studyon shear fatigue behavior of concrete beams with FRP rodsrdquoin Proceedings of the Cird International Symposium onNon-Metallic (FRP) Reinforcement for Concrete Structures(FRPRCS-3) pp 309ndash316 Japan Concrete Institute SapporoJapan 1997

[29] N Duranovic K Pilakoutas and P Waldron ldquoTests onconcrete beams reinforced with glass fibre reinforced plasticbarsrdquo in Proceedings of the Cird International Symposium onNon-Metallic (FRP) Reinforcement for Concrete Structures(FRPRCS-3) pp 479ndash486 Sapporo Japan 1997

[30] N Swamy and M Aburawi ldquoStructural implications of usingGFRP bars as concrete reinforcementrdquo in Proceedings of 3rdInternational Symposium FRPRCS pp 503ndash510 SapporoJapan 1997

[31] C R Michaluk S H Rizkalla G Tadros and B BenmokraneldquoFlexural behavior of one-way concrete slabs reinforced byfiber reinforced plastic reinforcementsrdquo ACI StructuralJournal vol 95 pp 353ndash365 1998

[32] D Deitz I Harik and H Gesund ldquoOne-way slabs reinforcedwith glass fiber reinforced polymer reinforcing barsrdquo SpecialPublication vol 188 pp 279ndash286 1999

[33] T Alkhrdaji M Wideman A Belarbi and A Nanni ldquoShearstrength of GFRP RC beams and slabsrdquo in Proceedings of the

14 Advances in Civil Engineering

International Conference Composites in Construction-CCCpp 409ndash414 Porto Portugal 2001

[34] G S Melo and J A Rayol ldquoShear resistance of GFRPreinforced concrete beamsrdquo in Proceedings of the Rehabil-itating and Repairing the Buildings and Bridges of AmericasHemispheric Workshop on Future Directions Mayaguumlez PRUSA pp 47ndash64 2002

[35] A K Tureyen and R J Frosch ldquoShear tests of FRP-reinforcedconcrete beams without stirrupsrdquo ACI Structural Journalvol 99 pp 427ndash434 2002

[36] S P Gross J R Yost D W Dinehart E Svensen and N LiuldquoShear strength of normal and high strength concrete beamsreinforced with GFRP barsrdquo in Proceedings of InternationalConference on High Performance Materials in Bridgespp 426ndash437 ASCE Reston VA USA 2003

[37] M Tariq and J Newhook ldquoShear testing of FRP reinforcedconcrete without transverse reinforcementrdquo in Proceedings ofAnnual Conference of the Canadian Society for Civil Engi-neering pp 1330ndash1339 Moncton NB Canada June 2003

[38] S Gross D Dinehart J Yost and P -eisz ldquoExperimentaltests of high-strength concrete beams reinforced with CFRPbarsrdquo in Proceedings of the 4th International Conference onAdvanced Composite Materials in Bridges and Structures(ACMBS-4) Calgary AB Canada 2004

[39] A Lubell T Sherwood E Bentz and M P Collins ldquoSafe sheardesign of large wide beams adding shear reinforcement isrecommendedrdquoConcrete International vol 26 pp 66ndash78 2004

[40] J Yost S Gross G Masone and P Hamelin ldquoSustained loadeffects on deflection and ultimate strength of concrete beamsreinforced with GFRPrdquo in Proceedings of the InternationalConference Composites in Construction (CCC2005) LyonFrance July 2005

[41] A El-Sayed E El-Salakawy and B Benmokrane ldquoShearstrength of one-way concrete slabs reinforced with fiber-reinforced polymer composite barsrdquo Journal of Compositesfor Construction vol 9 no 2 pp 147ndash157 2005

[42] A E Kilpatrick and L Easden ldquoShear capacity of GFRPreinforced high strength concrete slabsrdquo in Proceedings of the18th Australasian Conference on the Mechanics of Structuresand Materials Perth Australia vol 1 pp 119ndash124 Taylor ampFrancis London UK 2005

[43] A K El-Sayed E F El-Salakawy and B BenmokraneldquoShear strength of FRP-reinforced concrete beams withouttransverse reinforcementrdquo ACI Structural Journal vol 103p 235 2006

[44] A Ashour ldquoFlexural and shear capacities of concrete beamsreinforced with GFRP barsrdquo Construction and BuildingMaterials vol 20 no 10 pp 1005ndash1015 2006

[45] M Guadagnini K Pilakoutas and P Waldron ldquoShear re-sistance of FRP RC beams experimental studyrdquo Journal ofComposites for Construction vol 10 no 6 pp 464ndash473 2006

[46] R Dawborn and A Kilpatrick Flexural Shear Capacity ofHigh Strength Concrete Slabs Reinforced with LongitudinalGFRP Bars 2006

[47] J Niewels ldquoZum Tragverhalten von Betonbauteilen mitFaserverbundkunststoffbewehrungrdquo Rheinisch-WestfalischeTechnische Hochschule Aachen Lehrstuhl und Institut furMassivbau Dissertation 2008

[48] A El-Sayed K Soudki and E Kling ldquoFlexural behaviour ofself-consolidating concrete slabs reinforced with GFRP barsrdquoin Proceedings of the 9th International Symposium on FiberReinforced Polymer Reinforcement for Reinforced ConcreteStructures pp 13ndash15 Sydney NSW Australia 2009

[49] A Caporale and R Luciano ldquoIndagine sperimentale enumerica sulla resistenza a taglio di travi di calcestruzzoarmate con barre di GFRPrdquo in Proceedings of XXXVIIIConvegno Nazionale AIAS Turin Italy September 2009

[50] R Olivito and F Zuccarello ldquoOn the shear behaviour ofconcrete beams reinforced by carbon fibre-reinforced poly-mer bars an experimental investigation by means of acousticemission techniquerdquo Strain vol 46 no 5 pp 470ndash481 2010

[51] E C Bentz L Massam and M P Collins ldquoShear strength oflarge concrete members with FRP reinforcementrdquo Journal ofComposites for Construction vol 14 no 6 pp 637ndash646 2010

[52] A G Razaqpur M Shedid and B Isgor ldquoShear strength offiber-reinforced polymer reinforced concrete beams subject tounsymmetric loadingrdquo Journal of Composites for Construc-tion vol 15 no 4 pp 500ndash512 2011

[53] M Alam and A Hussein ldquoEffect of member depth on shearstrength of high-strength fiber-reinforced polymerndashreinforced concrete beamsrdquo Journal of Composites for Con-struction vol 16 no 2 pp 119ndash126 2012

[54] F Matta A K El-Sayed A Nanni and B Benmokrane ldquoSizeeffect on concrete shear strength in beams reinforced withfiber-reinforced polymer barsrdquo ACI Structural Journalvol 110-S50 pp 617ndash628 2013

[55] B Abdul-Salam A Farghaly and B Benmokrane ldquoEvalua-tion of shear behavior for one-way concrete slabs reinforcedwith carbon-FRP barsrdquo GEN vol 243 p 1 2013

[56] C H Kim and H S Jang ldquoConcrete shear strength of normaland lightweight concrete beams reinforced with FRP barsrdquoJournal of Composites for Construction vol 18 no 2 article04013038 2014

[57] D Tomlinson and A Fam ldquoPerformance of concrete beamsreinforced with basalt FRP for flexure and shearrdquo Journal ofComposites for Construction vol 19 no 2 article 040140362014

[58] M A Issa T Ovitigala and M Ibrahim ldquoShear behavior ofbasalt fiber reinforced concrete beams with and without basaltFRP stirrupsrdquo Journal of Composites for Construction vol 20no 4 article 04015083 2015

[59] A El Refai and F Abed ldquoConcrete contribution to shearstrength of beams reinforced with basalt fiber-reinforcedbarsrdquo Journal of Composites for Construction vol 20 no 4article 04015082 2015

[60] G B Jumaa and A R Yuosif ldquoSize effect in shear failure ofhigh strength concrete beams without stirrups reinforcedwith basalt FRP barsrdquo KSCE Journal of Civil Engineering2018 In press

[61] M T Hagan H B Demuth and M H BealeNeural NetworkDesign (Electrical Engineering) -omson Learning BostonMA USA 1995

[62] S S Haykin S S Haykin S S Haykin and S S HaykinNeural Networks and Learning Machines Pearson Vol 3Pearson Upper Saddle River NJ USA 2009

[63] M Y Mansour M Dicleli J-Y Lee and J Zhang ldquoPredictingthe shear strength of reinforced concrete beams using artificialneural networksrdquo Engineering Structures vol 26 no 6pp 781ndash799 2004

[64] H Demuth M Beale and M Hagan Neural NetworkToolboxtrade 6 Userrsquos Guide -e MathWorks Inc vol 10 p 11Natick MA USA 2008

[65] A W Oreta and K Kawashima ldquoNeural network modeling ofconfined compressive strength and strain of circular concretecolumnsrdquo Journal of Structural Engineering vol 129 no 4pp 554ndash561 2003

Advances in Civil Engineering 15

[66] S Jung and K S Kim ldquoKnowledge-based predictionof shear strength of concrete beams without shear re-inforcementrdquo Engineering Structures vol 30 no 6pp 1515ndash1525 2008

[67] Z-H Duan S-C Kou and C-S Poon ldquoPrediction ofcompressive strength of recycled aggregate concrete usingartificial neural networksrdquo Construction and Building Mate-rials vol 40 pp 1200ndash1206 2013

[68] H El-Chabib M Nehdi and A Said ldquoPredicting shear ca-pacity of NSC and HSC slender beams without stirrups usingartificial intelligencerdquo Computers and Concrete vol 2 no 1pp 79ndash96 2005

[69] F Altun O Kisi and K Aydin ldquoPredicting the compressivestrength of steel fiber added lightweight concrete using neuralnetworkrdquo Computational Materials Science vol 42 no 2pp 259ndash265 2008

[70] J R Koza ldquoGenetic programming as a means for pro-gramming computers by natural selectionrdquo Statistics andComputing vol 4 no 2 pp 87ndash112 1994

[71] C Ferreira ldquoGene expression programming in problemsolvingrdquo in Soft Computing and Industry pp 635ndash653Springer Berlin Germany 2002

[72] C Kayadelen ldquoSoil liquefaction modeling by genetic ex-pression programming and neuro-fuzzyrdquo Expert Systems withApplications vol 38 no 4 pp 4080ndash4087 2011

[73] A H Gandomi A H Alavi and G J Yun ldquoFormulation ofuplift capacity of suction caissons using multi expressionprogrammingrdquo KSCE Journal of Civil Engineering vol 15no 2 pp 363ndash373 2011

[74] A H Gandomi A H Alavi and C RyanHandbook of GeneticProgramming Applications Springer Berlin Germany 2015

[75] A H Gandomi and A H Alavi ldquoA new multi-gene geneticprogramming approach to non-linear system modeling PartII geotechnical and earthquake engineering problemsrdquoNeural Computing and Applications vol 21 no 1 pp 189ndash201 2012

[76] A H Alavi and A H Gandomi ldquoEnergy-based numericalmodels for assessment of soil liquefactionrdquo GeoscienceFrontiers vol 3 no 4 pp 541ndash555 2012

[77] L Teodorescu and D Sherwood ldquoHigh energy physics eventselection with gene expression programmingrdquo ComputerPhysics Communications vol 178 no 6 pp 409ndash419 2008

[78] GEPSOFT GeneXproTools Version 50 GEPSOFT BristolUK 2013 httpwwwgepsoftcom

[79] S M Mousavi P Aminian A H Gandomi A H Alavi andH Bolandi ldquoA new predictive model for compressive strengthof HPC using gene expression programmingrdquo Advances inEngineering Software vol 45 no 1 pp 105ndash114 2012

[80] M Sarıdemir ldquoEmpirical modeling of splitting tensilestrength from cylinder compressive strength of concrete bygenetic programmingrdquo Expert Systems with Applicationsvol 38 no 11 pp 14257ndash14268 2011

[81] M Sonebi and A Cevik ldquoGenetic programming based for-mulation for fresh and hardened properties of self-compacting concrete containing pulverised fuel ashrdquo Con-struction and Building Materials vol 23 no 7 pp 2614ndash26222009

[82] A H Alavi P Aminian A H Gandomi and M A EsmaeilildquoGenetic-based modeling of uplift capacity of suction cais-sonsrdquo Expert Systems with Applications vol 38 no 10pp 12608ndash12618 2011

[83] T Zsutty ldquoShear strength prediction for separate catagories ofsimple beam testsrdquo ACI Journal Proceedings vol 68 no 2pp 138ndash143 1971

16 Advances in Civil Engineering

References

[1] M S Alam and A Hussein ldquoSize effect on shear strength ofFRP reinforced concrete beams without stirrupsrdquo Journal ofComposites for Construction vol 17 no 4 pp 507ndash516 2013

[2] J R Yost S P Gross and D W Dinehart ldquoShear strength ofnormal strength concrete beams reinforced with deformedGFRP barsrdquo Journal of Composites for Construction vol 5no 4 pp 268ndash275 2001

[3] A G Razaqpur B O Isgor S Greenaway and A SelleyldquoConcrete contribution to the shear resistance of fiber rein-forced polymer reinforced concrete membersrdquo Journal ofComposites for Construction vol 8 no 5 pp 452ndash460 2004

[4] M Nehdi H El Chabib and A A Saıd ldquoProposed sheardesign equations for FRP-reinforced concrete beams based ongenetic algorithms approachrdquo Journal of Materials in CivilEngineering vol 19 no 12 pp 1033ndash1042 2007

[5] ASCE-ACI445 ldquoRecent approaches to shear design ofstructural concreterdquo Journal of Structural Engineeringvol 124 no 12 pp 1375ndash1417 1998

[6] R Park and T Paulay Reinforced Concrete Structures JohnWiley amp Sons Hoboken NJ USA 1975

[7] I F Kara ldquoPrediction of shear strength of FRP-reinforcedconcrete beams without stirrups based on genetic pro-grammingrdquo Advances in Engineering Software vol 42 no 6pp 295ndash304 2011

[8] R Bashir and A Ashour ldquoNeural networkmodelling for shearstrength of concrete members reinforced with FRP barsrdquoComposites Part B Engineering vol 43 no 8 pp 3198ndash32072012

[9] K Nasrollahzadeh and M M Basiri ldquoPrediction of shearstrength of FRP reinforced concrete beams using fuzzy in-ference systemrdquo Expert Systems with Applications vol 41no 4 pp 1006ndash1020 2014

[10] S Lee and C Lee ldquoPrediction of shear strength of FRP-reinforced concrete flexural members without stirrups usingartificial neural networksrdquo Engineering Structures vol 61pp 99ndash112 2014

[11] E M Golafshani and A Ashour ldquoA feasibility study of BBPfor predicting shear capacity of FRP reinforced concretebeams without stirrupsrdquo Advances in Engineering Softwarevol 97 pp 29ndash39 2016

[12] ACI-440 Guide for the Design and Construction of StructuralConcrete Reinforced with Fiber-Reinforced Polymer (FRP)ACI 440 1R-15 American Concrete Institute FarmingtonsHills MI USA 2015

[13] JSCE ldquoRecommendation for design and construction ofconcrete structures using continuous fiber reinforcing ma-terialsrdquo in Concrete Engineering Series 23 A Machida EdJapan Society of Civil Engineers Tokyo Japan 1997

[14] BISE Interim Guidance on the Design of Reinforced ConcreteStructures Using Fiber Composite Reinforcement British In-stitution of Structural Engineers Seto Ltd London UK1999

[15] CSA Canadian Highway Bridge Design Code SupplementNo 1 to CANCSA S6-06 (S61S1-10) Canadian StandardsAssociation (CSA) Mississauga ON Canada 2010

[16] ISIS Reinforced Concrete Structures with Fibre ReinforcedPolymersmdashDesign Manual No 3 University of Manitoba ISISCanada Corporation Winnipeg MB Canada 2007

[17] CNR-DT203 ldquoGuide for the design and construction ofconcrete structures reinforced with fiber-reinforced polymerbarsrdquo inAdvisory Committee on Technical Recommendations

for Construction CNR-DT 2032006 CNR Rome Italy2007

[18] CSA ldquoCode for the design and construction of buildingstructures with fibre-reinforced polymersrdquo in CANCSAS806-12 p 198 Canadian Standard Association TorontoON Canada 2012

[19] A Razaqpur and S Spadea ldquoResistenza a taglio di elementi dicalcestruzzzo reinforzatti e staffe di FRPrdquo in Proceedings ofAIAS Maratea Italy September 2010

[20] A F Ashour and I F Kara ldquoSize effect on shear strength ofFRP reinforced concrete beamsrdquo Composites Part B Engi-neering vol 60 pp 612ndash620 2014

[21] A R Yousif ldquoShear strength of large FRP-reinforced concretebeams without shear reinforcementrdquo Journal of Pure andApplied Sciences vol 27 pp 9ndash28 2015

[22] A K El-Sayed E F El-Salakawy and B Benmokrane ldquoShearcapacity of high-strength concrete beams reinforced with FRPbarsrdquo ACI Structural Journal vol 103 p 383 2006

[23] A G Razaqpur and O B Isgor ldquoProposed shear designmethod for FRP-reinforced concrete members without stir-rupsrdquo ACI Structural Journal vol 103 p 93 2006

[24] K Maruyama andW Zhao ldquoFlexural and shear behaviour ofconcrete beams reinforced with FRP rodsrdquo in Proceedings ofthe International Conference on Corrosion and CorrosionProtection of Steel in Concrete pp 24ndash28 Sheffield UK1994

[25] W Zhao K Maruyama and H Suzuki ldquoShear behavior ofconcrete beams reinforced by FRP rods as longitudinal andshear reinforcementrdquo in Proceedings of the Second In-ternational RILEM Symposium on Non-Metallic (FRP) Re-inforcement for Concrete Structures p 352 Ghent BelgiumAugust 1995

[26] H Nakamura and T Higai ldquoEvaluation of shear strength ofthe concrete beams reinforced with FRPrdquo in Proceedings ofJapan Society of Civil Engineers p 89 Ghent Belgium 1995

[27] K Maruyama and W Zhao ldquoSize effect in shear behavior ofFRP reinforced concrete beamrdquo in Advanced CompositeMaterials in Bridges and Structures pp 227ndash234 CanadianSociety for Civil Engineering Montreal QC Canada 1996

[28] Y Mizukawa Y Sato T Ueda and Y Kakuta ldquoA studyon shear fatigue behavior of concrete beams with FRP rodsrdquoin Proceedings of the Cird International Symposium onNon-Metallic (FRP) Reinforcement for Concrete Structures(FRPRCS-3) pp 309ndash316 Japan Concrete Institute SapporoJapan 1997

[29] N Duranovic K Pilakoutas and P Waldron ldquoTests onconcrete beams reinforced with glass fibre reinforced plasticbarsrdquo in Proceedings of the Cird International Symposium onNon-Metallic (FRP) Reinforcement for Concrete Structures(FRPRCS-3) pp 479ndash486 Sapporo Japan 1997

[30] N Swamy and M Aburawi ldquoStructural implications of usingGFRP bars as concrete reinforcementrdquo in Proceedings of 3rdInternational Symposium FRPRCS pp 503ndash510 SapporoJapan 1997

[31] C R Michaluk S H Rizkalla G Tadros and B BenmokraneldquoFlexural behavior of one-way concrete slabs reinforced byfiber reinforced plastic reinforcementsrdquo ACI StructuralJournal vol 95 pp 353ndash365 1998

[32] D Deitz I Harik and H Gesund ldquoOne-way slabs reinforcedwith glass fiber reinforced polymer reinforcing barsrdquo SpecialPublication vol 188 pp 279ndash286 1999

[33] T Alkhrdaji M Wideman A Belarbi and A Nanni ldquoShearstrength of GFRP RC beams and slabsrdquo in Proceedings of the

14 Advances in Civil Engineering

International Conference Composites in Construction-CCCpp 409ndash414 Porto Portugal 2001

[34] G S Melo and J A Rayol ldquoShear resistance of GFRPreinforced concrete beamsrdquo in Proceedings of the Rehabil-itating and Repairing the Buildings and Bridges of AmericasHemispheric Workshop on Future Directions Mayaguumlez PRUSA pp 47ndash64 2002

[35] A K Tureyen and R J Frosch ldquoShear tests of FRP-reinforcedconcrete beams without stirrupsrdquo ACI Structural Journalvol 99 pp 427ndash434 2002

[36] S P Gross J R Yost D W Dinehart E Svensen and N LiuldquoShear strength of normal and high strength concrete beamsreinforced with GFRP barsrdquo in Proceedings of InternationalConference on High Performance Materials in Bridgespp 426ndash437 ASCE Reston VA USA 2003

[37] M Tariq and J Newhook ldquoShear testing of FRP reinforcedconcrete without transverse reinforcementrdquo in Proceedings ofAnnual Conference of the Canadian Society for Civil Engi-neering pp 1330ndash1339 Moncton NB Canada June 2003

[38] S Gross D Dinehart J Yost and P -eisz ldquoExperimentaltests of high-strength concrete beams reinforced with CFRPbarsrdquo in Proceedings of the 4th International Conference onAdvanced Composite Materials in Bridges and Structures(ACMBS-4) Calgary AB Canada 2004

[39] A Lubell T Sherwood E Bentz and M P Collins ldquoSafe sheardesign of large wide beams adding shear reinforcement isrecommendedrdquoConcrete International vol 26 pp 66ndash78 2004

[40] J Yost S Gross G Masone and P Hamelin ldquoSustained loadeffects on deflection and ultimate strength of concrete beamsreinforced with GFRPrdquo in Proceedings of the InternationalConference Composites in Construction (CCC2005) LyonFrance July 2005

[41] A El-Sayed E El-Salakawy and B Benmokrane ldquoShearstrength of one-way concrete slabs reinforced with fiber-reinforced polymer composite barsrdquo Journal of Compositesfor Construction vol 9 no 2 pp 147ndash157 2005

[42] A E Kilpatrick and L Easden ldquoShear capacity of GFRPreinforced high strength concrete slabsrdquo in Proceedings of the18th Australasian Conference on the Mechanics of Structuresand Materials Perth Australia vol 1 pp 119ndash124 Taylor ampFrancis London UK 2005

[43] A K El-Sayed E F El-Salakawy and B BenmokraneldquoShear strength of FRP-reinforced concrete beams withouttransverse reinforcementrdquo ACI Structural Journal vol 103p 235 2006

[44] A Ashour ldquoFlexural and shear capacities of concrete beamsreinforced with GFRP barsrdquo Construction and BuildingMaterials vol 20 no 10 pp 1005ndash1015 2006

[45] M Guadagnini K Pilakoutas and P Waldron ldquoShear re-sistance of FRP RC beams experimental studyrdquo Journal ofComposites for Construction vol 10 no 6 pp 464ndash473 2006

[46] R Dawborn and A Kilpatrick Flexural Shear Capacity ofHigh Strength Concrete Slabs Reinforced with LongitudinalGFRP Bars 2006

[47] J Niewels ldquoZum Tragverhalten von Betonbauteilen mitFaserverbundkunststoffbewehrungrdquo Rheinisch-WestfalischeTechnische Hochschule Aachen Lehrstuhl und Institut furMassivbau Dissertation 2008

[48] A El-Sayed K Soudki and E Kling ldquoFlexural behaviour ofself-consolidating concrete slabs reinforced with GFRP barsrdquoin Proceedings of the 9th International Symposium on FiberReinforced Polymer Reinforcement for Reinforced ConcreteStructures pp 13ndash15 Sydney NSW Australia 2009

[49] A Caporale and R Luciano ldquoIndagine sperimentale enumerica sulla resistenza a taglio di travi di calcestruzzoarmate con barre di GFRPrdquo in Proceedings of XXXVIIIConvegno Nazionale AIAS Turin Italy September 2009

[50] R Olivito and F Zuccarello ldquoOn the shear behaviour ofconcrete beams reinforced by carbon fibre-reinforced poly-mer bars an experimental investigation by means of acousticemission techniquerdquo Strain vol 46 no 5 pp 470ndash481 2010

[51] E C Bentz L Massam and M P Collins ldquoShear strength oflarge concrete members with FRP reinforcementrdquo Journal ofComposites for Construction vol 14 no 6 pp 637ndash646 2010

[52] A G Razaqpur M Shedid and B Isgor ldquoShear strength offiber-reinforced polymer reinforced concrete beams subject tounsymmetric loadingrdquo Journal of Composites for Construc-tion vol 15 no 4 pp 500ndash512 2011

[53] M Alam and A Hussein ldquoEffect of member depth on shearstrength of high-strength fiber-reinforced polymerndashreinforced concrete beamsrdquo Journal of Composites for Con-struction vol 16 no 2 pp 119ndash126 2012

[54] F Matta A K El-Sayed A Nanni and B Benmokrane ldquoSizeeffect on concrete shear strength in beams reinforced withfiber-reinforced polymer barsrdquo ACI Structural Journalvol 110-S50 pp 617ndash628 2013

[55] B Abdul-Salam A Farghaly and B Benmokrane ldquoEvalua-tion of shear behavior for one-way concrete slabs reinforcedwith carbon-FRP barsrdquo GEN vol 243 p 1 2013

[56] C H Kim and H S Jang ldquoConcrete shear strength of normaland lightweight concrete beams reinforced with FRP barsrdquoJournal of Composites for Construction vol 18 no 2 article04013038 2014

[57] D Tomlinson and A Fam ldquoPerformance of concrete beamsreinforced with basalt FRP for flexure and shearrdquo Journal ofComposites for Construction vol 19 no 2 article 040140362014

[58] M A Issa T Ovitigala and M Ibrahim ldquoShear behavior ofbasalt fiber reinforced concrete beams with and without basaltFRP stirrupsrdquo Journal of Composites for Construction vol 20no 4 article 04015083 2015

[59] A El Refai and F Abed ldquoConcrete contribution to shearstrength of beams reinforced with basalt fiber-reinforcedbarsrdquo Journal of Composites for Construction vol 20 no 4article 04015082 2015

[60] G B Jumaa and A R Yuosif ldquoSize effect in shear failure ofhigh strength concrete beams without stirrups reinforcedwith basalt FRP barsrdquo KSCE Journal of Civil Engineering2018 In press

[61] M T Hagan H B Demuth and M H BealeNeural NetworkDesign (Electrical Engineering) -omson Learning BostonMA USA 1995

[62] S S Haykin S S Haykin S S Haykin and S S HaykinNeural Networks and Learning Machines Pearson Vol 3Pearson Upper Saddle River NJ USA 2009

[63] M Y Mansour M Dicleli J-Y Lee and J Zhang ldquoPredictingthe shear strength of reinforced concrete beams using artificialneural networksrdquo Engineering Structures vol 26 no 6pp 781ndash799 2004

[64] H Demuth M Beale and M Hagan Neural NetworkToolboxtrade 6 Userrsquos Guide -e MathWorks Inc vol 10 p 11Natick MA USA 2008

[65] A W Oreta and K Kawashima ldquoNeural network modeling ofconfined compressive strength and strain of circular concretecolumnsrdquo Journal of Structural Engineering vol 129 no 4pp 554ndash561 2003

Advances in Civil Engineering 15

[66] S Jung and K S Kim ldquoKnowledge-based predictionof shear strength of concrete beams without shear re-inforcementrdquo Engineering Structures vol 30 no 6pp 1515ndash1525 2008

[67] Z-H Duan S-C Kou and C-S Poon ldquoPrediction ofcompressive strength of recycled aggregate concrete usingartificial neural networksrdquo Construction and Building Mate-rials vol 40 pp 1200ndash1206 2013

[68] H El-Chabib M Nehdi and A Said ldquoPredicting shear ca-pacity of NSC and HSC slender beams without stirrups usingartificial intelligencerdquo Computers and Concrete vol 2 no 1pp 79ndash96 2005

[69] F Altun O Kisi and K Aydin ldquoPredicting the compressivestrength of steel fiber added lightweight concrete using neuralnetworkrdquo Computational Materials Science vol 42 no 2pp 259ndash265 2008

[70] J R Koza ldquoGenetic programming as a means for pro-gramming computers by natural selectionrdquo Statistics andComputing vol 4 no 2 pp 87ndash112 1994

[71] C Ferreira ldquoGene expression programming in problemsolvingrdquo in Soft Computing and Industry pp 635ndash653Springer Berlin Germany 2002

[72] C Kayadelen ldquoSoil liquefaction modeling by genetic ex-pression programming and neuro-fuzzyrdquo Expert Systems withApplications vol 38 no 4 pp 4080ndash4087 2011

[73] A H Gandomi A H Alavi and G J Yun ldquoFormulation ofuplift capacity of suction caissons using multi expressionprogrammingrdquo KSCE Journal of Civil Engineering vol 15no 2 pp 363ndash373 2011

[74] A H Gandomi A H Alavi and C RyanHandbook of GeneticProgramming Applications Springer Berlin Germany 2015

[75] A H Gandomi and A H Alavi ldquoA new multi-gene geneticprogramming approach to non-linear system modeling PartII geotechnical and earthquake engineering problemsrdquoNeural Computing and Applications vol 21 no 1 pp 189ndash201 2012

[76] A H Alavi and A H Gandomi ldquoEnergy-based numericalmodels for assessment of soil liquefactionrdquo GeoscienceFrontiers vol 3 no 4 pp 541ndash555 2012

[77] L Teodorescu and D Sherwood ldquoHigh energy physics eventselection with gene expression programmingrdquo ComputerPhysics Communications vol 178 no 6 pp 409ndash419 2008

[78] GEPSOFT GeneXproTools Version 50 GEPSOFT BristolUK 2013 httpwwwgepsoftcom

[79] S M Mousavi P Aminian A H Gandomi A H Alavi andH Bolandi ldquoA new predictive model for compressive strengthof HPC using gene expression programmingrdquo Advances inEngineering Software vol 45 no 1 pp 105ndash114 2012

[80] M Sarıdemir ldquoEmpirical modeling of splitting tensilestrength from cylinder compressive strength of concrete bygenetic programmingrdquo Expert Systems with Applicationsvol 38 no 11 pp 14257ndash14268 2011

[81] M Sonebi and A Cevik ldquoGenetic programming based for-mulation for fresh and hardened properties of self-compacting concrete containing pulverised fuel ashrdquo Con-struction and Building Materials vol 23 no 7 pp 2614ndash26222009

[82] A H Alavi P Aminian A H Gandomi and M A EsmaeilildquoGenetic-based modeling of uplift capacity of suction cais-sonsrdquo Expert Systems with Applications vol 38 no 10pp 12608ndash12618 2011

[83] T Zsutty ldquoShear strength prediction for separate catagories ofsimple beam testsrdquo ACI Journal Proceedings vol 68 no 2pp 138ndash143 1971

16 Advances in Civil Engineering

International Conference Composites in Construction-CCCpp 409ndash414 Porto Portugal 2001

[34] G S Melo and J A Rayol ldquoShear resistance of GFRPreinforced concrete beamsrdquo in Proceedings of the Rehabil-itating and Repairing the Buildings and Bridges of AmericasHemispheric Workshop on Future Directions Mayaguumlez PRUSA pp 47ndash64 2002

[35] A K Tureyen and R J Frosch ldquoShear tests of FRP-reinforcedconcrete beams without stirrupsrdquo ACI Structural Journalvol 99 pp 427ndash434 2002

[36] S P Gross J R Yost D W Dinehart E Svensen and N LiuldquoShear strength of normal and high strength concrete beamsreinforced with GFRP barsrdquo in Proceedings of InternationalConference on High Performance Materials in Bridgespp 426ndash437 ASCE Reston VA USA 2003

[37] M Tariq and J Newhook ldquoShear testing of FRP reinforcedconcrete without transverse reinforcementrdquo in Proceedings ofAnnual Conference of the Canadian Society for Civil Engi-neering pp 1330ndash1339 Moncton NB Canada June 2003

[38] S Gross D Dinehart J Yost and P -eisz ldquoExperimentaltests of high-strength concrete beams reinforced with CFRPbarsrdquo in Proceedings of the 4th International Conference onAdvanced Composite Materials in Bridges and Structures(ACMBS-4) Calgary AB Canada 2004

[39] A Lubell T Sherwood E Bentz and M P Collins ldquoSafe sheardesign of large wide beams adding shear reinforcement isrecommendedrdquoConcrete International vol 26 pp 66ndash78 2004

[40] J Yost S Gross G Masone and P Hamelin ldquoSustained loadeffects on deflection and ultimate strength of concrete beamsreinforced with GFRPrdquo in Proceedings of the InternationalConference Composites in Construction (CCC2005) LyonFrance July 2005

[41] A El-Sayed E El-Salakawy and B Benmokrane ldquoShearstrength of one-way concrete slabs reinforced with fiber-reinforced polymer composite barsrdquo Journal of Compositesfor Construction vol 9 no 2 pp 147ndash157 2005

[42] A E Kilpatrick and L Easden ldquoShear capacity of GFRPreinforced high strength concrete slabsrdquo in Proceedings of the18th Australasian Conference on the Mechanics of Structuresand Materials Perth Australia vol 1 pp 119ndash124 Taylor ampFrancis London UK 2005

[43] A K El-Sayed E F El-Salakawy and B BenmokraneldquoShear strength of FRP-reinforced concrete beams withouttransverse reinforcementrdquo ACI Structural Journal vol 103p 235 2006

[44] A Ashour ldquoFlexural and shear capacities of concrete beamsreinforced with GFRP barsrdquo Construction and BuildingMaterials vol 20 no 10 pp 1005ndash1015 2006

[45] M Guadagnini K Pilakoutas and P Waldron ldquoShear re-sistance of FRP RC beams experimental studyrdquo Journal ofComposites for Construction vol 10 no 6 pp 464ndash473 2006

[46] R Dawborn and A Kilpatrick Flexural Shear Capacity ofHigh Strength Concrete Slabs Reinforced with LongitudinalGFRP Bars 2006

[47] J Niewels ldquoZum Tragverhalten von Betonbauteilen mitFaserverbundkunststoffbewehrungrdquo Rheinisch-WestfalischeTechnische Hochschule Aachen Lehrstuhl und Institut furMassivbau Dissertation 2008

[48] A El-Sayed K Soudki and E Kling ldquoFlexural behaviour ofself-consolidating concrete slabs reinforced with GFRP barsrdquoin Proceedings of the 9th International Symposium on FiberReinforced Polymer Reinforcement for Reinforced ConcreteStructures pp 13ndash15 Sydney NSW Australia 2009

[49] A Caporale and R Luciano ldquoIndagine sperimentale enumerica sulla resistenza a taglio di travi di calcestruzzoarmate con barre di GFRPrdquo in Proceedings of XXXVIIIConvegno Nazionale AIAS Turin Italy September 2009

[50] R Olivito and F Zuccarello ldquoOn the shear behaviour ofconcrete beams reinforced by carbon fibre-reinforced poly-mer bars an experimental investigation by means of acousticemission techniquerdquo Strain vol 46 no 5 pp 470ndash481 2010

[51] E C Bentz L Massam and M P Collins ldquoShear strength oflarge concrete members with FRP reinforcementrdquo Journal ofComposites for Construction vol 14 no 6 pp 637ndash646 2010

[52] A G Razaqpur M Shedid and B Isgor ldquoShear strength offiber-reinforced polymer reinforced concrete beams subject tounsymmetric loadingrdquo Journal of Composites for Construc-tion vol 15 no 4 pp 500ndash512 2011

[53] M Alam and A Hussein ldquoEffect of member depth on shearstrength of high-strength fiber-reinforced polymerndashreinforced concrete beamsrdquo Journal of Composites for Con-struction vol 16 no 2 pp 119ndash126 2012

[54] F Matta A K El-Sayed A Nanni and B Benmokrane ldquoSizeeffect on concrete shear strength in beams reinforced withfiber-reinforced polymer barsrdquo ACI Structural Journalvol 110-S50 pp 617ndash628 2013

[55] B Abdul-Salam A Farghaly and B Benmokrane ldquoEvalua-tion of shear behavior for one-way concrete slabs reinforcedwith carbon-FRP barsrdquo GEN vol 243 p 1 2013

[56] C H Kim and H S Jang ldquoConcrete shear strength of normaland lightweight concrete beams reinforced with FRP barsrdquoJournal of Composites for Construction vol 18 no 2 article04013038 2014

[57] D Tomlinson and A Fam ldquoPerformance of concrete beamsreinforced with basalt FRP for flexure and shearrdquo Journal ofComposites for Construction vol 19 no 2 article 040140362014

[58] M A Issa T Ovitigala and M Ibrahim ldquoShear behavior ofbasalt fiber reinforced concrete beams with and without basaltFRP stirrupsrdquo Journal of Composites for Construction vol 20no 4 article 04015083 2015

[59] A El Refai and F Abed ldquoConcrete contribution to shearstrength of beams reinforced with basalt fiber-reinforcedbarsrdquo Journal of Composites for Construction vol 20 no 4article 04015082 2015

[60] G B Jumaa and A R Yuosif ldquoSize effect in shear failure ofhigh strength concrete beams without stirrups reinforcedwith basalt FRP barsrdquo KSCE Journal of Civil Engineering2018 In press

[61] M T Hagan H B Demuth and M H BealeNeural NetworkDesign (Electrical Engineering) -omson Learning BostonMA USA 1995

[62] S S Haykin S S Haykin S S Haykin and S S HaykinNeural Networks and Learning Machines Pearson Vol 3Pearson Upper Saddle River NJ USA 2009

[63] M Y Mansour M Dicleli J-Y Lee and J Zhang ldquoPredictingthe shear strength of reinforced concrete beams using artificialneural networksrdquo Engineering Structures vol 26 no 6pp 781ndash799 2004

[64] H Demuth M Beale and M Hagan Neural NetworkToolboxtrade 6 Userrsquos Guide -e MathWorks Inc vol 10 p 11Natick MA USA 2008

[65] A W Oreta and K Kawashima ldquoNeural network modeling ofconfined compressive strength and strain of circular concretecolumnsrdquo Journal of Structural Engineering vol 129 no 4pp 554ndash561 2003

Advances in Civil Engineering 15

[66] S Jung and K S Kim ldquoKnowledge-based predictionof shear strength of concrete beams without shear re-inforcementrdquo Engineering Structures vol 30 no 6pp 1515ndash1525 2008

[67] Z-H Duan S-C Kou and C-S Poon ldquoPrediction ofcompressive strength of recycled aggregate concrete usingartificial neural networksrdquo Construction and Building Mate-rials vol 40 pp 1200ndash1206 2013

[68] H El-Chabib M Nehdi and A Said ldquoPredicting shear ca-pacity of NSC and HSC slender beams without stirrups usingartificial intelligencerdquo Computers and Concrete vol 2 no 1pp 79ndash96 2005

[69] F Altun O Kisi and K Aydin ldquoPredicting the compressivestrength of steel fiber added lightweight concrete using neuralnetworkrdquo Computational Materials Science vol 42 no 2pp 259ndash265 2008

[70] J R Koza ldquoGenetic programming as a means for pro-gramming computers by natural selectionrdquo Statistics andComputing vol 4 no 2 pp 87ndash112 1994

[71] C Ferreira ldquoGene expression programming in problemsolvingrdquo in Soft Computing and Industry pp 635ndash653Springer Berlin Germany 2002

[72] C Kayadelen ldquoSoil liquefaction modeling by genetic ex-pression programming and neuro-fuzzyrdquo Expert Systems withApplications vol 38 no 4 pp 4080ndash4087 2011

[73] A H Gandomi A H Alavi and G J Yun ldquoFormulation ofuplift capacity of suction caissons using multi expressionprogrammingrdquo KSCE Journal of Civil Engineering vol 15no 2 pp 363ndash373 2011

[74] A H Gandomi A H Alavi and C RyanHandbook of GeneticProgramming Applications Springer Berlin Germany 2015

[75] A H Gandomi and A H Alavi ldquoA new multi-gene geneticprogramming approach to non-linear system modeling PartII geotechnical and earthquake engineering problemsrdquoNeural Computing and Applications vol 21 no 1 pp 189ndash201 2012

[76] A H Alavi and A H Gandomi ldquoEnergy-based numericalmodels for assessment of soil liquefactionrdquo GeoscienceFrontiers vol 3 no 4 pp 541ndash555 2012

[77] L Teodorescu and D Sherwood ldquoHigh energy physics eventselection with gene expression programmingrdquo ComputerPhysics Communications vol 178 no 6 pp 409ndash419 2008

[78] GEPSOFT GeneXproTools Version 50 GEPSOFT BristolUK 2013 httpwwwgepsoftcom

[79] S M Mousavi P Aminian A H Gandomi A H Alavi andH Bolandi ldquoA new predictive model for compressive strengthof HPC using gene expression programmingrdquo Advances inEngineering Software vol 45 no 1 pp 105ndash114 2012

[80] M Sarıdemir ldquoEmpirical modeling of splitting tensilestrength from cylinder compressive strength of concrete bygenetic programmingrdquo Expert Systems with Applicationsvol 38 no 11 pp 14257ndash14268 2011

[81] M Sonebi and A Cevik ldquoGenetic programming based for-mulation for fresh and hardened properties of self-compacting concrete containing pulverised fuel ashrdquo Con-struction and Building Materials vol 23 no 7 pp 2614ndash26222009

[82] A H Alavi P Aminian A H Gandomi and M A EsmaeilildquoGenetic-based modeling of uplift capacity of suction cais-sonsrdquo Expert Systems with Applications vol 38 no 10pp 12608ndash12618 2011

[83] T Zsutty ldquoShear strength prediction for separate catagories ofsimple beam testsrdquo ACI Journal Proceedings vol 68 no 2pp 138ndash143 1971

16 Advances in Civil Engineering

[66] S Jung and K S Kim ldquoKnowledge-based predictionof shear strength of concrete beams without shear re-inforcementrdquo Engineering Structures vol 30 no 6pp 1515ndash1525 2008

[67] Z-H Duan S-C Kou and C-S Poon ldquoPrediction ofcompressive strength of recycled aggregate concrete usingartificial neural networksrdquo Construction and Building Mate-rials vol 40 pp 1200ndash1206 2013

[68] H El-Chabib M Nehdi and A Said ldquoPredicting shear ca-pacity of NSC and HSC slender beams without stirrups usingartificial intelligencerdquo Computers and Concrete vol 2 no 1pp 79ndash96 2005

[69] F Altun O Kisi and K Aydin ldquoPredicting the compressivestrength of steel fiber added lightweight concrete using neuralnetworkrdquo Computational Materials Science vol 42 no 2pp 259ndash265 2008

[70] J R Koza ldquoGenetic programming as a means for pro-gramming computers by natural selectionrdquo Statistics andComputing vol 4 no 2 pp 87ndash112 1994

[71] C Ferreira ldquoGene expression programming in problemsolvingrdquo in Soft Computing and Industry pp 635ndash653Springer Berlin Germany 2002

[72] C Kayadelen ldquoSoil liquefaction modeling by genetic ex-pression programming and neuro-fuzzyrdquo Expert Systems withApplications vol 38 no 4 pp 4080ndash4087 2011

[73] A H Gandomi A H Alavi and G J Yun ldquoFormulation ofuplift capacity of suction caissons using multi expressionprogrammingrdquo KSCE Journal of Civil Engineering vol 15no 2 pp 363ndash373 2011

[74] A H Gandomi A H Alavi and C RyanHandbook of GeneticProgramming Applications Springer Berlin Germany 2015

[75] A H Gandomi and A H Alavi ldquoA new multi-gene geneticprogramming approach to non-linear system modeling PartII geotechnical and earthquake engineering problemsrdquoNeural Computing and Applications vol 21 no 1 pp 189ndash201 2012

[76] A H Alavi and A H Gandomi ldquoEnergy-based numericalmodels for assessment of soil liquefactionrdquo GeoscienceFrontiers vol 3 no 4 pp 541ndash555 2012

[77] L Teodorescu and D Sherwood ldquoHigh energy physics eventselection with gene expression programmingrdquo ComputerPhysics Communications vol 178 no 6 pp 409ndash419 2008

[78] GEPSOFT GeneXproTools Version 50 GEPSOFT BristolUK 2013 httpwwwgepsoftcom

[79] S M Mousavi P Aminian A H Gandomi A H Alavi andH Bolandi ldquoA new predictive model for compressive strengthof HPC using gene expression programmingrdquo Advances inEngineering Software vol 45 no 1 pp 105ndash114 2012

[80] M Sarıdemir ldquoEmpirical modeling of splitting tensilestrength from cylinder compressive strength of concrete bygenetic programmingrdquo Expert Systems with Applicationsvol 38 no 11 pp 14257ndash14268 2011

[81] M Sonebi and A Cevik ldquoGenetic programming based for-mulation for fresh and hardened properties of self-compacting concrete containing pulverised fuel ashrdquo Con-struction and Building Materials vol 23 no 7 pp 2614ndash26222009

[82] A H Alavi P Aminian A H Gandomi and M A EsmaeilildquoGenetic-based modeling of uplift capacity of suction cais-sonsrdquo Expert Systems with Applications vol 38 no 10pp 12608ndash12618 2011

[83] T Zsutty ldquoShear strength prediction for separate catagories ofsimple beam testsrdquo ACI Journal Proceedings vol 68 no 2pp 138ndash143 1971

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