Size Effect on Shear Strength of Reinforced

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SIZE EFFECT ON SHEAR STRENGTH OF REINFORCEDCONCRETE BEAMS

byWassim M.Ghannoum

November 1998

Department of Civil Engineering ancl Applied MechanicsMcGill UniversityMontral, Canada


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Size Effect on Shear Strength of Reinforced Concrete Beams

Abstract

Given the great discord concerning the mechanisms that govern shear failure, the shearbehaviour of concrete bearn elements with no transverse reinforcement is investigated. Thevariables introduced in the experimental program are member depth, amount of longitudinalsteel reinforcement and concrete strength. The effects of these variables on the shear stress atfailure of the concrete are investigated. Two geometrically similar series of beams ofdifferent concrete strengths are compared. Beam heights in each of the series range from 90mm to 960 mm and al1 the beams have a constant a/d ratio of 2.5.

Results show a strong "size-effect" in the behaviour of concrete beam or one-way slabelements subjected to shear, where deeper members have smaller shear stresses at failurethan shallower ones. Increasing the amount of flexural reinforcement increases the shearstress at failure while increasing the concrete compressive strength has little or no effect onthe diagonal shear resistance of concrete.

The AC1 Code equations for shear are found to be unconsewative for large elements


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ToMy Parents


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Effet de taille sur la rsistance I 'effort tranchantde poutres en bton arm

Rsum

Etant donn le grand dsaccord concernant les mcanismes qui rgissent les ruptures encisaillement dans le bton, le comportement de poutres en bton, sans armatures l'efforttranchant. est tudi. Exprimentdement l'tude porte sur l'influence de la profondeur despoutres. la quantit d'armature flexionnelle et la rsistance du bton, sur la rsistance encisaillement du bton. Deux sries de poutres gomtriquement identiques, aux profondeursvariant entre 90 mm et 960 mm et possdant diffrentes rsistances de bton, sontcompares. Toutes les poutres testes ont un rapport d d de 2.5.

Les rsultats dmontrent un important "effet de taille" par lequel les lments les plusprofonds ont proportionnellement une moindre rsistance en cisaillement que les lmentsles moins profonds. L'augmentation de la quantit d'amature flexionnelle augmente larsistance l'effort tranchant des poutres alors que l'augmentation de la rsistance encompression du bton n'a presque aucun effet.

Les quations du code amricain AC1 donnant la rsistance en cisaillement du bton nesont pas scuritaires dans leurs prdictions pour les poutres de grande profondeur, alors queles expressions simplifies du code canadien CSA sont scuritaires dans la gamme desvaleurs des paramtres tests. Pour les poutres testes, dont le rapport a/d est de 2.5, la


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Acknowledgements

The author would like to express his deepest gratitude to Professor Denis Mitchell forhis continued encouragement and knowledgeable advise throughout this research program.Furthemore. the author would like to thank Dr. William Cook for his guidance and support.

The research was carried out in the Jamieson Stmctures Laboratory at McGilIUniversity. The author wishes to thank Ron Sheppard, Marek Przykorski, John Bartczak andDamon Kiperchuk for their assistance in the laboratory. The author wouid also like to thankCarla Ghannoum, Stuart Bristowe, Pierre Koch, Bryce Tupper, Emmet Poon, Kevin Li,Pedro Da Silva and Robert Zsigo for their assistance.

The cornpletion of this project would not have been possible without the patience andvaluable help of the secretaries of the Civil Engineering Department. particularly SandyShewchuk-Boyd, Lil ly Nardini. Ann Bless. and Donna Sears.

The financial assistance provided by the Natural Sciences and Engineering ResearchCouncil of Canada WSERC) is gratefully acknowledged. As well. the author would like toacknowledge Professor M. P. Collins and Evan Bentz for providing the software programRESPONSE 2000 used in this thesis.

Finally. the author would like to thank his friends and family especially his parents,for their constant support and encouragement during his years at McGill.


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Table of Contents

Abstract .................................................................................................................. i.Rsum ................................................................................................................................~lTable of Contents ............................................................................................................... ivList of Figures ..................................................................................................................... vi

..List of Tables .....................................................................................................................~II ......................................................................................................................ist of Symbols viii1 Introduction and Literature Review ........................................................................... 1

....................................................................................................... 1 introduction 13....................................................-2 Previous Size Effect Investigations ..............-....................................................................3 Shear and High-Strength Concrete 6

1 -4 Sliear Design Methods ...................................................................................... 7............................................................4.1 AC1 Shear Design Procedure 7

1 .4.2 CSA Simplified Shear Design Procedure .........................................81.4.3 Modified Compression Field Theory................................................ 9

1.5 Objectives of Research Program ....................................................................... 12

2 Experimental Program .................................................................................................. 132. Design and Details of the Beam Specimens ......................................... 13


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3. 5 Summary of kesults .......................................................................................... 443.6 interpretation and C ompari son of Results ........................................................ 46.........................................................................................................Analysis of Results 49

4.1 AC1Code Predictions ....................................................................................... 494.2 CSA Sirnplified Expressions ......................................................................... SI4 .3 Predictions Usin g th e M od ified Compression Field Theory and........................................................................................trut-and-Tie Models 54

5 Conclusions and Rccommeadations ............................................................................. 63References ........................................................................................................................... 65

0Appendix A-Response 2000 Input and Output .............................................................. 67


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List of FiguresChapter 1

1.1

Chapter 22.12.22.32-42.53.62.72.82.9

Chapter 33.13.23 -33-43 53.63.73 -83 93.103.1 13.123.133-14

Relative strength (ultimate moment/flexural moment) vs.a/d ratio '7(Kani 1967).......................................................................................................-Influence of member depth and aggregate size on shear stress at faiture fortests carried out by Shkya 1989, taken fiom Collins and Mitchell. 1997 ........5

Specirnen reinforcement details........................................................................ 14...................................ypical tensile stress-strain curves for reinforcing steel 16.....................................ypicai concrete compressive stress-strain responses 18

Concrete shrinkage readings............................................................................. 19............................................est setup and clamping of the failed weaker end 20..............................ne-point loading arrangement used for some specimens 21LVDT and concrete strain gauge locations ......................................................22Typicai steel strain gauge locations (top view) ................................................ 22Specimen strain target locations........................................................................ 23Test results for specimen N90............................................................................. 28Test results for specimen N 155 ..........................................................................29Test results for specirnen N220 .......................................................................... 30.....................................est results for specirnen N350 ............................... 31Test results for specimen N485 .......................................................................... 32.........................................................................est results for specimen N960 33....................................................................ormal-strength series afier failure 34

.............................................................................est results for specimen H90 37Test results for specimen H 1 55 .......................................................................... 38Test results for specimen H220 .......................................................................... 39Test results for specimen H350 ......................................................................... 40

.................................................................est results for specirnen H485 ... 41Test results for specimen H960 .......................................................................... 2High-strength series afier failure ........................................................................ 43


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List of TablesChapter2

2.12.2 ................................................................................einforcing steel properties 15Concrete mix designs .................................................................................. 17......................................................................3 Concrete properties forboth series 18Chapter3

3.1 Summaryof results ........................................................................................ 453.2 Shear strength difference between p=2% and p=l.2% ................................... 473.3 Shear strength difference between the high-strength and normal-strength

concrete series..................................................................................................... 48Chapter 4

4. Comparison of predictions using the AC1 simplified expressionwith test results ................................................................................................... 51

4.2 Comparison of predictions using the CSA simplified expressions...................................................................................................ith test results 53................... ............*.......3 Modi fied compression field theory predictions ... 604.4 Strut-and-tiemodelpredictions .......................................................................... 614.5 Combined predictions of themodified compression field theory andstrut-and-tie mode1 .............................................................................................. 62


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List of Symbols

shear spanarea of concretearea of longitudinal steel reinforcement in tension zoneoverall width of specimenminimum effective web width within depth ddistance frorn extreme compression fibre to centroid of tension reinforcementnominal diameter of reinforcing barsdistance measured perpendicular to the neutral axis between the resultants of the tensileand compressive force due to flexurelongitudinal steel reinforcement modulus of elasticityspecified compressive strength of concretelimiting compressive stress in concrete stmtmodulus of rupture of concretesplitting tensile stress of concreteultimate strength of reinforcementyield strength of reinforcementoverall thickness of specirnensmoment at sectionmoment at failureaxial load at sectioncrack spacing in the 8 directionshear force at sectionsliear stress resistance provided by concreteshear resistance of concreteshear force at failureaverage crack widthratio of average stress in rectangular compression block to the specified concretestrengthtensile stress factor which accounts for the shear resistance of cracked concrete


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Chapter 1

Introduction and Literature Review

1.1 Introductionin spite of the numerous research efforts directed at the shear capacity of concrete, there

is still great discord conceming the mechanisms that govern shear in concrete. Proposedtheories Vary radically from the simple 45" truss mode1 to the very complex non-linearfracture mechanics. Yet nearly al1 the resulting design procedures are empirical or semi-empirical at best and are obtained by a regression fit thrciugh experimental results.

Nowhere is this lack of understanding more evident than in the shear design provisionsof the AC1 Code (AC1 committee 318-1995) which consists of 43 empirical equations fordifferent types of members and different loading conditions. Moreover, there is greatdiscrepancy between design codes of different countries. Many of these codes do not evenaccount for some basic and proven factors affecting the shear capacity of concrete members.Of these factors, much confusion is expressed with regards to the effect of absolute membersize on the shear capacity of beam etements. On this subject, there is a lack of consensus inthe approach to the problem due to the limited amount of experiments dedicated to thiseffect, especially when it cornes to high-strength concrete elements.


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1.2 Previous Size Effect InvestigationsIn 1955, the Wilkins Air Force Depot warehouse in Shelby, Ohio, collapsed due to the

shear failure of 36 in. (914 mm) deep beams which did not contain any stirrups at thelocation of failure (Collins and Kuchma, 1997 and Collins and Mitchell, 1997). These beamshad a longitudinal steel ratio of only 0.45%. They failed at a shear stress of only about 0.5MPa whereas the AC1 Building Code of the time (AC1 Committee 318, 1951) permitted anallowable working stress of 0.62 MPa for the 20 MPa concrete used in the beams.Experirnents conducted at the Portland Cernent Association (Elstner and Hognestad, 1957)on 12 in. (305 mm) deep model beams indicated that the beams could resist about 1.0 MPa.However, the application of an axial tension stress of about 1.4 MPa reduced the shearcapacity by about 50%. It was thus concluded that tensile stresses caused by thermal andshrinkage rnovements were the reason for the beam failures.


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shear span-to-depth ratios, dd. He determined that member depth and steel percentage had agreat effect on shear strength and that there is a transition point at a/d=2.5 at which beamsare shear critical (Le. the value of the bending moment at failure was minimum)(see Fig.1.1).

Kani found this value of a/d to be the transition point between failure modes and is thesame for different member sizes and steel ratios. Below an d d value of about 2.5 the testbeams developed arch action and had a considerable reserve of strength beyond the firstcracking point. For a/d values greater than 2.5 failure was sudden, brittle and in diagonaltension soon atter the first diagonal cracks appeared. This transition point is moreernphasised in test beams containing higher reinforcement ratios and almost disappears inspecimens with lower reinforcement ratios. In addition. Kani found a ctearly definedenvelope bounded by limiting values of p and a/d. Inside this envelope diagonal shearfailures are predicted to occur and outside of this envelope flexural failures are predicted tooccur. These conclusions regarding the influence of both p and a/d were similar for al1 beamdepths tested. Kani also looked at the effect of beam width and found no significant effect onshear strength. Kani's work was summarised in the textbook "Kani on Shear in ReinforcedConcrete" (Kani et al. 1979).

More recently, Bazant and Kim (1984) derived a shear strength equation based on thetheory of fracture mechanics. This equation accounts for the size effect phenomenon as wellas the longitudinal steel ratio and incorporates the effect of aggregate size. This equation wascatibrated using 296 previous tests obtained from the literature and was compared with theAC1 Code equations. It was noted afler the comparison that the practice used in the AC1


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Later on, Bazant and Kazemi (1 991) performed tests on geometrically similar beamswith a size range of 1: 6 and having a constant a/d ratio of 3.0 and a constant longitudinalsteel ratio, p. Beams tested varied in depth from 1 inch (25 mm) to 16 inches (406 mm). Themain failure mode of the specimens tested was diagonal shear but the smallest specimenfailed in flexure. This study confirmed the size effect phenomenon and helped corroboratethe previously published formula. However, the deepest beam tested was relatively small andthe authors concluded that for beams larger than 16 inches (406 mm) additional reductions inshear strength due to size effect were likely.

Kim and Park (1994) performed tests on beams with a higher than normal concretestrength (53.7 MPa). Test variables were longitudinal steel ratio, p, shear span-to-depth ratio,a/d, and effective depth. d. Beam heights varied from 170 mm to 1000 mm while thelongitudinal steel ratio varied from 0.01 to 0.049 and d d varied from 1.5 to 6.0. Theirfindings were similar to Kani's from which it was concluded that the behaviour of the higherstrength concrete is similar to that of normal-strength concrete. However, since only oneconcrete strength was investigated no general conclusions could be made with respect toconcrete strength and shear capacity.

Shioya ( 1 989) conducted a number of tests on large-scale beams in which the influenceof member depth and aggregate size on shear strength was investigated. In this study, lightlyreinforced concrete beams containing no transverse reinforcement were tested under auniformly distributed load. The beam depths in this experimental program ranged from 100mm to 3000 mm. Shioya found that the shear stress at failure decreased as the member sizeincreased and as the aggregate size decreased. It is interesting to note that the beams tested


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(m)0.5 1O 1 5 20 25 3.0psiviits 4 . 1 1

1 m. (25 m lnu ^ r w r g a t r sur

Figure 1.2: Inf luence o f mem ber de pth and aggregate s ize on sh ear s t ress a t fa i lure for tes tscarried out by Shioya 1989. taken from Coll ins and Mitchell , 1997.

Stanik (1998) pe rf om ed tes ts on a wide range of beam specim ens a t the Univers i ty o fToronto. The specirnens tested had varying depths, d, ranging from 125 mm to 1000 mm,varying amounts of longi tudinal s tee l ( 0.76% to 1 .31%) as wel l a s varying concre te


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performed nearly as well a s the shallow members containing only bottom longitudinalrein forcement. As well, the wider members containing side distributed steel were weakerthan the narrower ones with similar side distributed steel. Stanik concluded that the sizeeffect is more related to measures controlling crack widths and crack spacing rather than theabsolute depth of the member. Moreover, Stanik found very little gain in shear strength withthe use of higher concrete strengths. In fact, he found that the shear strengths of the beamswith 100 MPa concrete were only marginally greater than the shear strength of the 40 MPabeams. Stanik used the modified compression field theory proposed by the CSA Standard(CSA 1994)to predict the response of his test beams. He found good agreement between hisexperirnental results and these predictions. He also proposed to use an effective aggregatesize of zero in the modified compression field theory method for the very high-strengthconcretes in order to account for the insignificant gain in shear strength from the lowerconcrete strengths. Stanik also performed a cornparison between his experimental results andthe AC1 Code (AC1 committee 318-1995) expressions. He found that the AC1 expressionssubstantially overestimate the shear contribution of concrete, notably in the deeper members.1.3 Shear and High-Strengtb Concrete

High-strength concrete is a more brittle material than normal-strength concrete. Thismeans that cracks that fonn in high-strength concrete will propagate more extensively thanin normal-strength concrete. Previous shear tests on high-strength concrete have shown asignificant difference between the failure planes of high-strength concrete and that ofiiormal-strength concrete. This is due to the fact that cracks tend to propagate through the


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Elzanaty et al. (1986) looked at the problem of shear in high-strength concrete andobserved a smoother failure plane in the higher strength concrete specimens. Their study wasperformed on a total of 18 beams with concrete strengths, f l , ranging from 2 1 to 83 MPa.Apart from concrete strength, test variables included p and the shear span-to-depth ratio, dd .The conclusions drawn from these tests were that the shear strength increased withincreasing f i but less than that predicted using the AC1 Code equations. These equationspredict an increase in shear strength in proportion to K . lzanaty et al. concluded that anincrease in the steel ratio led to an increase in the shear capacity of the specimens regardlessof concrete strength.

Ahmad et al. (1986) studied the effects of the a/d ratio and longitudinal steel percentageon the shear capacity of bezms without web reinforcement. For their tests, the concretestrength was maintained as constant as possible with f i in the range of 63 to 70 MPa.Findings were similar to previous experiments with a transition in the failure mode at an a/dratio of approximately 2.5. The envelope involving limits on a/d and p which separates shearfaiiures from flexural failures was found to be similar to the envelope for the normal-strengthconcrete. However, more longitudinal steel was required to prevent flexural failures. Ahmadet al. found that the shear capacity was proportional to f i0 .

1.4 ShearDesign Methods1.1.1 AC1 Shear Design Procedure

The AC1 Code (AC1 Committee 318-1995) shear design equations for non-prestressed


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In lieu of equation [1.1], the AC1 Code allows the foilowing simplet equation to beused:

V, = 0.1 66$7b,d with l?% mm] 11.21

These equations for predicting the shear strength of concrete beam elements are basedon the shear causing significant diagonal cracking. At the time these expressions werederived, the ACI-ASCE Committee 326 on shear and diagonal tension (ACI-ASCECommittee 326, 1962) concluded that for mentbers without stirrups, any increase in shearcapacity beyond the shear which caused significant diagonal cracking was unpredictable dueto the great variation in failure mechanisms and should thus be ignored. Bazant et al. (1984,1987, 1991 ) criticised this assumption since the diagonal cracking load is not proportional tothe ultimate load, and hence a uniform factor of safety against failure is not provided.1A.2 CSA Simplified Shear Design Procedure

The simplified expression in the 1994 CSA Standard (CSA 1994) for the evaluation ofthe contribution of the concrete, V,. to the shear capacity are given below:

a) For sections having either the minimum amount of transverse reinforcement required inthe Standard (CSA 1994), or an effective depth, d. not exceeding 300 mm :


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b) For sections with effective depths greater than 300 mm and with less transversereinforcement than the minimum required :

v, = ( 260 )d,,/F&d not Iess than 0 .10(~f ib ,d m.mm] [I.j]1000 + dSimilarly the nominal resistance can be written as:

not less than 0833Jf;;b,d IN,mm] [1.61

As can be seen from Equation [1.5], the CSA Concrete Standard (CSA 1994) includes aterm to account for the size effect in its simplified shear design expression but does not takeaccount of the reinforcing steel ratio, p. This shows the concern of this code regarding thesize effect phenomenon. However the linear nature of the te m added to the shear equationcannot account for the complexity of the problem. More research is needed to adjust thisequation to account for higher concrete strengths and amount of longitudinal reinforcement,p. Sorn limitations on the distribution of the longitudinal reinforcement may also berequited.1.4.3 Modified Compression Field Theory

In lieu of the latter simplified shear design equations, the CSA Standard (CSA 1994)proposes a more rational method of approach to the shear design "problem" based more on


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and by Collins et al. (1996) and yields the following design equations for predicting theconcrete contribution to the shear strength:

Where:b = Minimum effective web width within the depth of the sectiond, = Distance measured perpendicular to the neutral axis between th e resuitants of the tensile

and compressive force due to flexure, may be taken as O.9d for non-prestressed concretemembers

p = Tensi le stress factor which accounts for the shear resistance of cracked concrete

033 cot 8 0.18P = 24wl+J500E, 0 3 +a + I6

Where w is the average crack width which is taken as:

W here:


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For the case of a non-prestressed beam with bottom chord reinforcement thelongitudinal strain of the flexural tension chord can be taken as

M / d, + OS(N + V cot 8)Ex = EsAs

Where:M = Moment at sectionN = Axial load at section (positive in tension)V = Shear force at sectionEs = Modulus of elasticity of longitudinal steel reinforcernentA, = Area of Iongitudinal steel reinforcement in tension zone

In order to simpli@ the design procedure using the modified compression field theory, aset of tables and plots was developed (CSA 1994, Collins et al. 1996) with correspondingvalues of 0, B, E, and v/f& Applying the method requires an iterative process where a valueof E, is assumed and the corresponding8 value is calculated from which another value of E,is obtained. The process is repeated until the values of E,converge.

The method has given very accurate predictions of the shear response in beam elements(Collins et al. 1996, Vecchio and Collins 1988) especially when member size is involved.The method's predictions will be cornpared with the test results of this research.

The cornputer program "RESPONSE" has k en developed at the University of Toronto


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Collins 1982) and provides full graphical output of stresses and strains at key stages ofloading. A beta version of this program will be used in this research program to predict theresponse of the elements tested according to the modified compression field theory.

1.5 Objectivesof Research ProgramThe objective of this research program is to investigate a number of issues related to the

"size effect" in shear. An experimental program was planned to investigate the following:

1 ) The reduction in shear stress at failure as the size of beams or one-way slabsincreases.

2) The influence of concrete strength on the shear stress at failure.3) The effect of amount of longitudinal steel reinforcement on the shear stress at

fai ure.4) The combined effects of the three variables p, d and f l on the shear stress at failure

in beams or one-way slabs.

A comparison will also be performed between the test results and predictions given bycurrent shear design methods. The purpose being to evaluate the different approaches andtheories supporting these methods.


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Chapter 2

Experimental Program

2.1 Design and Details of the Beam SpecimensTwelve beam specimens were constructed and tested in the Structures Laboratory of the

Department of Civil Engineering at McGill University. The specimens were cast in twobatches of different concrete strengths producing two sets of geometrically identicalspecimens. Concrete strengths were 35 MPa for the "normal-strength" specimens and 60MPa for the "high-strength" specimens. The specimens al1 had a width of 400 mm and theirheights varied from 90 mm to 960 mm.

The specimens were designed according to the modified compression field theory to failin shear rather than bending. No transverse reinforcement was provided for any of thespecimens. The shear span-to-depth ratio, a/d, of al1 specimens was kept constant at a/d=2.5,in order to produce a shear critical specimen (Kani 1966,1967, 1979). AI1 of the beams weresubjected to a two-point loading arrangement as shown in Fig. 2.1.

Each specimen had two different iongitudinal steel ratios. The north end of the bearnscontained a larger number of reinforcing bars giving p=2% while the south end of the beamshad a smaller number of bars with p=1.2% (see Fig. 2.1). This was achieved by lapping the


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Southorth

North Shear Span Reinforcement Details ( ~ 2 % )

O BarsO Bars

NOTE:All dimensions in mmAll specimens 400 mmwideBars are evenly spreadAll side avers are 40 mm


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minimum c lear cover of 20 mm but the clear cover m us t at least equal the b ar diameter, d,.Hence for specimens with No. 20 bars and smaller, th e 20 mm cover was used and fo r largerdiameter bars, a cover equal to d, was used. It is noted that the AC1 Cod e (AC1 Com mittee3 18 , 1995) requires a constant minimum co ver of 20 m m for bars up to and including No. 35bars. A ll specimens had o ne layer of bottom steel excep t for the 960 mm d eep beams whichhad two layers (see Fig. 2.1). Two top bars were added in the three largest specimens. AI1reinforcement details are shown in Fig. 2.1.2.2 Specimen IdentificationA total o f twelve spe cimens were divided into two series: the normal-strength series (N),and the high-strength series (H). Both series have sim ila r geometry and steel reinforcement.Specimens were numbered according to their absolute height (in mm) as follows: N90,N 155, N220, N350, N485, N960, H90, H 155, H220, H350, H485 an d H960.

A further notation will be used in this report to disting uish the strong end from th e weakend o f the specimens. T he added notations wilt be (w) for the weak end and (s) for the s trongend. This notation will be added to the end o f the s pecim en name.

Table 2.1: Reinforcing steel propertiesSpecimenDesignation

N 9 0H 90

SteelLocationBottomBottom

Size Designation

No. 1O Grade 400No. t O Grade 500

f~

( M m477648

Area(mm2)

100100

&Y

( O h )

0.320.52

&sb

(%)0.400.55

fa


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2.3 Material Properties2.3.1 Reinforcing Steel Properties

Table 2.1 summarises the material properties of he deformed steel reinforcement usedin th e construction of the specimens. All of he reinforcement used was Grade 400 except forthe reinforcement of he smallest specimen in the high-strength series which was Grade 500.The values reported in Table 2.1 are the averages of three simples per bar sue chosenrandomly amongst the bars used. Figure 2.2 shows typical tensile stress-strain responses ofthe reinforcing bars-

No. 101

No. 20

No. 15Md

No. 25Ml01


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2.3.2 Concrete PropertiesThe concrete used to construct the specimens was provided by a local ready-rnix plant.

Table 2.2 summarises the mix designs provided by that plant. Following the cast, the normal-strength concrete was moist cured for three days and the high-strength concrete for sevendays.

Table 2.2: Concrete mix designsI 30 MPa 70 MPa

1 Strength 1 StrengthI 1 Concrete 1 ConcreteI 11 cernent (Type IO), kg/rn3 1 355 1 480'I I1 fine aggregates (sand) kg/m3 1 790 1 803

Coane aggregates, kg/m5 1040 1059I1 total water-, kg/m3 1 178 1 135

water-cernent ratio 0.50 0.28I water-reducing agent, ml/mJ 1110 1502

Iair-entraining agent, ml/m5 I 180 -1 1 -


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600 mm long. Four-point loadingwas applied over a span of 450mm. Tests were conductedonce at the beginning of series testing and once at the end to observe variations in theconcrete material properties during testing. It was observed however that no significantvariations in the material properties occurred from one testing date to another. The valuesshown in Table 2.3 are average values from three samples tested at the beginning of a seriesand three samples tested at the end of a series.

Table 2.3: Concrete properties for both series

Series

Normal-Strength Concretestd. Deviation

High-Strength Concretestd. deviation

fi

34.190.4958.552.56

EC'x 10-~4.090.2583.980.268

fwm a )3 O80.173.49O.17

fr(MPd4.890.334.670.25


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Figure 2.3 shows typical compressive stress-strain responses for both concrete strengthsand Fig. 2.4 shows the shrinkage readings taken on standard 75 mm by 75 mm by 280 mmlong shrinkage specimens. The values used to plot Fig. 2.4 are average values from twoshrinkage specirnens for each cast.

- malStrength Concrete- . - . High-StrengthConcrete

20 40 60 80 100 120Time (days)

Figure 2.4: Concrete shrinkage readings


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specimens creating a zero shear region between the two loading points. The load transferfrom the MTS machine to the specimens was through a ball-bearing joint, a steel spreaderbeam, a pair of rollen and a set of bearing plates that were grouted to the tops of thespecimens. The bearing plates at the supports and at the loading points for al1 the specimenswere one inch thick steel plates covering the entire width of the specirnen over a length of100mm,


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The loading was applied monotonically with load, deflection and strain values beingrecorded at small increments of loading. At key load stages, the crack pattern and crackwidths were recorded. After the failure of the weaker side, extemal HSS clamps and threadedrods were used to clamp the failed section (see Fig. 2.5), then the specimen was reloadeduntil the stronger side failed. For the smaller specimens, it was sometimes impossible toclamp the failed weaker side. ln these instances, the supports were moved to create a single-point loading scheme (see Fig. 2.6). This was possible since the shear spans of these smallerspecimens was smaller than the 500 mm distance separating the two initial loading points.

Figure 2.6: One-point loading arrangement used for some specimens


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to veriQ that no torsion was induced in the specimens. The reading of the target strains waspedonned using a 203 mm or 102 mm gauge length mechanical extensometer.

Figure2.7: LVDT and concrete strain gauge locations

a

Electrical resistance strain gauges were glued to the reinforcement bars of the bottomsteel as shown in Fig. 2.8. For the 960 mm high specimens with two layers of bottom ofreinforcement, the strain gauges were placed on the bottom layer. Two additional straineauges were giued to the concrete surface just below both loading points (see Fig. 2.7). TheCstrain readings obtained from the concrete strain gauges combined with those of the steelgauges enabled the calculation of the curvature of the specimens at the maximum momentand shear locations.

South Sn1 c h J North1m\ Ibncn(.-C.ugir r

i I


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Chapter 3

Experimental Results and Cornparisons

3.1 IntroductionIn this chapter, the observed behaviour of the 12 beam specimens is presented. Among

th e experimental results recorded were longitudinal steel strains, concrete strains and crackwidths at load stage intervals. These results are presented in Figs. 3.1 through 3.6 and Figs.3.8 through 3.1 3. Figs. 3.7 and 3.14 are photographs of the normal-strength and high-strengthconcrete specimens afier they have been tested.

A figure is given for each test beam. The response of the weak-end (p=1.2%) andstrong-end (p=2%) is plotted in each graph for comparison purposes. Each figure containsthe following:

a) A graph ploning the maximum applied moment versus the maximum flexural crackwidth.

b) A drawing showing the Iocation of the instrumentation.c) A graph plotting the maximum applied moment versus the longitudinal steel strain,measured on the reinforcing bars below the loading points.


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3.2 General BebaviourThe general behaviour of the four largest bearns was quite similar. First, the flexural

cracks initiated in the pure bending region. With further increase of Ioad new flexural cracksformed in the shear spans and curved toward the loading points. The failure in thesespecimen was always sudden and in diagonal tension shortly after diagonal shear cracksappeared. it was noted that the ultimate shear capacity of these beam elements was onlyslightly higher than the load which caused diagonal cracking. It is for this reason that nodiagonal tension cracks could be measured prior to failure.

As for the smaller sizes, the crack development was similar to that of the otherspecimens except where flexural yielding occured. This produced a different failuremechanism which will be discussed in detail for each specimen.

3.3 Normal-Streogth Coocrete Series$necben N90; In both the weak and strong ends of this specimen, the longitudinal

steel yielded before failure occurred due to the unexpectedly high shear resistance of thespecimen (Fig. 3.1 c)). Unfortunately, the strain gauge on the weak end was lost shortly afieryield. First cracking is observed in Fig. 3.1 c) at an approximate moment of 2.0 kN.m whichcorresponds to a modulus of rupture, f,, of 3.70 MPa. The principal tensile strain in theconcrete, obtained from the rosettes, changed very little prior to yielding of the longitudinalsteel. After y ielding, it Increased significantly (Fig. 3.1 d)) denoting large shear cracks beforefailure. The failure mode of both ends of the specimen was a combination of flexuralyielding and shear. The longitudinal steel yielded first and as it elongated, it increased the


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afier the first significant load drop at a shear force of 109.8 IrN, the specimen developed archaction and was able to reach a shear force of 134.5 kN. The principal tensile strains recordedfor the strong end denote large shear cracks before failure (Fig. 3.2 d)). Faiture shears were82.5 kN for the end with p=1.2% and 109.8kN for the end with p=2.0%.

m e n 22& First cracking in this specimen occurred at an approximate moment of12.5kN.m Fig. 3.3 c)) which corresponds to a modulus of rupture, f, of 3.87 MPa. Principaltensile strains remained small until about 90% of the failure load. At this load level thesestrains increased more significantly as very small shear cracks fonned causing the load todrop off (Fig. 3.3 d)). Failure of both ends was in shear and in a brittle fashion without anyyielding of the longitudinal steel (Fig. 3.3 c)). Failure shears were 100.6 kN for the end withp=1.2% and 1 19.7 kN for the end with p=2-0%.

N350; First cracking in this specimen occurred at an approximate moment of40 kN.m Fig. 3.4 c)) which corresponds to a modulus of rupture, f,, of 4.90 MPa. Principaltensile strains rernained small until about 90% of the failure load. At this load level thesestrains increased more significantly as very small shear cracks formed causing the load todrop off (Fig. 3 .4 dj). Failure of both ends was in shear and in a brinle fashion without anyyielding of the longitudinal steel (Fig. 3.4 c)). Failure shears were 152.6 kN for the end withp= 1 -2% and 173.1 kN for the end with p=2.0%.

S~ecimen485; First cracking in this specimen occurred at an approximate moment of


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en N960; First cracking in this specimen occurred a t an approximate moment of220 kN.m Fig. 3.6 c)) which corresponds to a modulus of rupture, f, of 3.58 MPa. Principaltensile strains remained small until very small shear cracks formed causing the load to dropoff (Fig. 3.6 d)). Failure of both ends was in shear and in a brittle fashion without anyyielding of the longitudinal steel (Fig. 3.6 c)). Failure shears were 340.5 khi for th e end withp=1.2% and 360.0 CcN for the end with p=2.0%.


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MaximumFkrunlCrackWidth (mm)Momenta. w. Fkxural Crack Wdtti

O 0.m2 0.004 0.006 0.008E* (mm/mm)

Moment vs. LongitudinalSteelStrain

Section 2-2 Section 1-1

O 0.002 0.004 0.006 0.W8 0.01 0.012E~ (mmlmm)

Shear vs. Principal Tensik Strain


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O 0.5 1 1.5 2 2.5Maximum FbxuralCrack Width (mm)MomentW. Max. FkwuralCrack Widai

1O 0002 0004 0006 0008 O 01

r, (mmlmm)Moment vs.LongitudinalSeel Strain


O 0.001 0.002 0.003 0.004 0.005E, (mmlmm)

Shear vs. PrincipalTensik Strain


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O 0.05 0.1 0.15 0.2 0.25 O 3Maximum Fkxuri l Crack W a mm)

Momentvs. Max. FlaxuraiCrack Width

IO 0.0005 O 001 0.0015 0 002

E* (mrnlmm)Momentvs. Longitudinal Steel Strain


O 0.001 0.002 0.003 0.004 D.W5 0.006E, (mrnlmm)

Shear vs. Principal Tensiie Strain


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O 0.05 0.1 0.15 0.2 0.25 0.3Maximum FkxuralCrack Width (mm)Momentvs. Max. FkxuralCracWdth

O 0.0005 0.001 00015 0.002 0.0025E, (mmlmm)

Moment vs. Longitudinal Steel Strain


O 0.005 0.01 0.015E, (mmlmm)

Shearvs. PrinapalTensik Strain


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O 0.0005 0.001 0 015 O 0.005 0.01 0.015 0.02Es (mmlmm) ~1 (mwmm)

Momentvs. LongitudinalSteelStmin Shearvs. PrincipalTensik Strain

300 -250

. . - - h ,L

2 Es2 Es1 1Section 2-2 Section 1-1

1O 0.05 0.1 0.15 0.2 0.25 0.3 O O O O DMaximumFkxunlC m k Mdth (mm) 0p=2% p=1.2%Moment vs. Max. FkxurolCnck Width

q=2%. -.

2 1-1


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O O. 0.2 0.3 0.4MaximumFkxuralCmckWdt (mm)Momentvs. Max fkxuralCrack Width

O 0.0002 OOOM O0006 0.0008 0001E, (mmlmm)

Momentvs. Longitudinal Steel Strain

Section 2-2. -Es1 1 E l - 1

Section 1-1

O 0.001 0 0 0 2 0.063 0.004 0.005 O 0 0 6E, (mmlmm)

Shear vs. PrincipalTensik Stmin


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3.4 High-StrengthConcreteSeries-90; In the weak-end of this specimen, the longitudinal steel yielded before

failure occurred due to the unexpectedly high shear resistance of the specimen (Fig. 3.8 c)).First cracking is observed in Fig. 3.8 c) at an approximate moment of 3.0 kN.m whichcorresponds to a modulus of rupture, f,., of 5.56 MPa. At the weak-end, the principal tensilestrain in the concrete, obtained from the rosettes, changed very little prior to yielding of thelongitudinal steel. Afier yielding, it increased significantly (Fig. 3.8 d)) denoting large shearcracks before failure. The failure mode of the weak-end was a combination of fiexuralyielding and shear. The longitudinal steel yielded first and as it elongated, the shear cracksincreased until a shear failure occurred. As for the strong-end, it failed in shear prior to theyielding of the steel (Fig. 3.8 c)). The principal tensile strains recorded for the strong enddenote large shear cracks before failure (Fig. 3.8 d)). Failure shears were 50.8 kN for the endwith p=1.2% and 76.0 kN for the end with p=2.0%.

Specirnedl55: First cracking in this specimen occurred at an approxirnate moment of12.0 kN.m (Fig. 3.9 c) ) which corresponds to a modulus of rupture. f, of 7.49 MPa- Principaltensile strains remained small until very small shear cracks formed causing the load to dropoff (Fig. 3.9 d)). Failure of both ends was in shear and in a brittle fashion without anyyielding of the longitudinal steel (Fig. 3.9 c)). Failure shears were 74.7 kN for the end withp=1.2% and 102.9kN for the end with p=2.0%.


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to drop off (Fig. 3.1 d)). Faiiure of both ends was in shear and in a brittle fashion withoutany yielding of the longitudinal steel (Fig. 3.1 1 c)). Failure shears were 151.8kN for the endwith p=1.2% and 184.2 kN for the end with p=2.0%.

485; First cracking in this specirnen occurred at an approxirnate moment of64.0 kN.m (Fig. 3.12 c)) which corresponds to a modulus of rupture, f, of 4.08 MPa.Principal tensile strains remained small until very smalt shear cracks formed causing the loadto drop off (Fig. 3.12 d)). Failure of both ends was due to diagonal tension cracking, with theshear failure forming in a brittle fashion, without any yielding of the longitudinal steel (Fig.3.12 c)). Failure shears were 189.8 kN for the end with p=1.2% and 190.3 kN for the endwith p=2.0%.

H960; First cracking in this specimen occurred at an approximate moment of260 kN.m (Fig. 3.13 c)) which corresponds to a moduhs of rupture, f,, of 4.23 MPa.Principal tensile strains remained small until very small shear cracks formed causing the loadto drop off (Fig. 3. 3 d)). Failure of both ends was in shear and in a brittle fashion withoutany yielding of the longitudinal steel (Fig. 3.13 c)). Failure shears were 290.7 kN for the endwith p=I -2%and 31 1.4 kN for the end with p=2.0%.-


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1O 0.2 0.4 0.0 0.8 1 1 2Maximum fkxunl CrackWidth (mm)

Moment vs. Max. FkxuralCradc Widtha)

O O O01 0.002 o.003E (mmtmm)Moment vs. LongitudinalSteel Strain

Section 2-2 Section 1-1T l

p=2% p=1.2%

O O002 0 . a 0.006 OO08 0.01E, (mrnlmm)

Shear vs. PrincipalTensiie Strain


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O 0.05 0.1 0.15 0.2 0.25 0.3Maximum Fkxural Crack Width (mm)

Moment vs. Max. FlexwalCrackWidFh

O 0.0002 O 0004 0.0006 0.0008 OM1E (mmlmm)

Moment vs. LongitudinalSteelStrain

Section 2-2rlp=2%

Section 1-1

O 0.002 0.004 0 . m 0.008 0.01 0.012cl (mdmm)

Shear vs. Principal Terisile Sain


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O 0.05 0.1 0.15 0.2 0.25 0.3 0.35Maximum Fkxural CrackWdth (mm)Momentvs. Max Fkxural Ca& Wdth

O 00002 00004 00006 00008 0001 00012 OW14E, (mmlmm)


Section 2-2 Section 1-1n

C 0.01 0.02 0.03 O M 0.05 0.06t, mmlmm)

Shear vs. PrincipalTensiie Strain


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Maximum FkrunlCrackWldth (mm)Momentvs.Max. FkxuralCrack With

a)

O 0.0002 0.0004 0.0006 0.0008 0.001 0.0012 0.0014E, (rnmlmm)



O 0.005 0.01 0.015 0.02E, (rnmlmm)

Shearvs. PrincipalTensik Strain


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Maximum Fkxu nl Crack Width (mm)Momentvs. Max. FlexuratCrackWidth

a)

O 0.0002 0.0004 0.0006 0.0008E (mmlmm)Momentvs. Longitudinal Steel Strain

Section2-2 Section 1-1

O O.Mi5 0.01 0.015 0.02E, (mmlmm)

Shear vs. PrincipalTende Strain


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. -Et-2 2 Es2 Es1 1 El-1Section2-2 Section 1-1

O O. 0.2 0.3 0.4 0.5 0.6 ..--.Maximum FhxunlCrackWdth (mm) ..--.Momentvs. Max. FkxuralCrack W m p=2%

p=2%

O 0.0002 0 . m 0.0006 0.0008E (mdrnrn)

Momentvs. Longitudinal Steel Straincl

O 0.005 0.01 0.015 0.02 0.025E, (mdmm)

Shear vs. Principal Tensiie Strain


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3.5 Summary ofResultsFig. 3.15 shows the failure shear stress versus specimen depth for both the normal and

high-strength concrete series. The failure shear stress has k e n detemined by adding theeffective member self-weight and the weight of the loading apparatus to the applied Ioads. Inthis figure it can be seen that, for the largest specimens, the high-strength concrete beamactually has a smaller failure shear stress than the cornpanion normal-strength concretebeam. Both series, regardless of the amount of reinforcement, had very comparable shearstrengths showing no significant gain in shear strength with increased concrete compressivestrength.


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TableSpecimen

N90

NI55

N220

N350

N485

N960

H90

Hl55

H220

SummaryP

(%)1-22.01.22.01.22.01.22.01.22.01.22.01.22 O1.22.01.2

3.1:' fl(MPa)

34.2

34.2

34.2

34.2

34.2

34.2

58.6

58.6

58.6

of resultsVmaX

(w42.575.984.61 1 1.9103.6122.7158.0178.6187.5215.4366.6386.152.177.476.7105

105.9

M m a x

(kN.m)10.819.434.745.959.069.9139.0157.0224.0257.4839.3883.913.319.731.543.060.3

V M

(MPa)1.632.921-662.191.361.611.261.431.O71-221.O51-102.002.981-502.061.39

~ M q f :

0.280.500.280.380.230.280.220.240.180.2 10.180.190.260.3 90.200.270.18

Mode ofFaiiure

Shear1FlexureS hear1FIexureShear1Flexure

S hearShearS hearShearShearShearShearShearShear

Shear l FlexureShearShearS hearShear


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Figure3.16: Normalised shear stress at failure versus specimen depth

3.6 Interpretation andCornparisonof ResultsIn Figs. 3.15 and 3.16. the size effect on shear strength is evident. In both the normal

and high-strength concrete. regardless of the steel ratio, the deeper rnembers had lower shearstresses at failure than the shallower ones. This effect is so pronounced that some of thesmailer specimens which have similar reinforcernent and geometries as the larger specimens,failed in flexure rather than shear.

The important influence of the longitudinal steel ratio, p, on the shear stress at faiture is

attenuation in the effect of p on shear strength, with increased specimen depth. This may be


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due to the fact that the longitudinal steel has a limited zone of influence in controllifig thewidth of diagonal cracks over the concrete cross section. Thus, the larger the specimen, thesmaller that zone of influence is with respect to the overall cross section.This effect indirectly contributes to the size effect as welt. The srnaller specimens, ki n galmost entirely in the zone of influence of the longitudinal steel, have their shear crackwidths controlled over most of their height whereas the larger specimens, whose cross-section is only partially influenced by the steel, have their shear cracks controlled over only alimited region.

The effect of concrete strength on shear capacity is summarised in Table 3.3. In thistable. a negative number implies that the high-strength specimen was weaker than thenormal-strength one. It can be seen from Table 3.3 that the normal-strength series and thehigh-strength series were very close in ternis of shear strength, since the biggest differencefound in the table is 18.5%. This can also be observed in Fig. 3.15 where the N S and HScurves are very close to each other. This is in great contradiction with current code equationswhich predict a relationship of E b e t w e e n concrete shear strength and concretecompressive strength.

Table 3.2: Shear strength difference between ends with ~'2% nd ends with p=1.2%

I I ends w ith p=l.2% (in %)Specimen Heigh t Difference in shear strength between ends with p=2% andNormal-Strength Series High-S trength Series

Table 3.3: Shear strength difference between the high-strength and normal-strength


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concrete series1 S p im en Height 1 Difference in shear strengh between high-strength and

I normal-strengtb concrete series (in %)

1 L IDifference = (V,, .,V,, , / (V,, , * 100

Chapter 4


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Analysis of Results

In this chapter, the experimental results are compared to the theoretical predictionsusing the design expressions of the AC1 Code (AC1 committee 3 18, 1995) and the CSAStandard (CSA 1994). For the CSA Standard, the simplified expressions, the general methodbased on the modified compression field theoty as well as th e strut-and-tie approach areinvestigated.

4.1 AC1Code Predictions

The AC1 Code (AC1 Committee 318, 1995) shear design equations for predicting theshear strength of concrete beam elements are:

VdVc = 0.15 8 K b w d + 17.24pw- wd 5 0.291Jr;bwd IN,mm]MIn lieu of equation [4.1], The AC1 Code allows the following simpler equation to be

used:

concrete beams. Hence. the more conservative Equation [4.2] is more appropriate for the


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prediction of the diagonal shear response of beam or one-way slab elements.Figure 4.1 compares Equation [4.2] with the experimental results obtained in terms of

the normalised shear stress ratio versus specimen depth. Results are also summarised inTable 4.1.

*. \ -AC[ Code

Figure 4.1: Cornparison of predictions using the AC1simplified expression with test results


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b) For sections with effective depths greater than 300 mm and with less transverse


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reinforcement than the minimum required :

215 8Vc = ( ) ~ ~ ; b . d not icss than 0.10&bWd [N, mm]1000 + d 14-41Note: to obtain the nominal shear strength, the original CSA equations were modified by

a factor of (0.16610.2) (see Chapter 1 for explanation).

Figure 4.2 compares the predictions of Equations 14.31 and 14-41with the experimentalresults obtained in terms of the norrnalised shear stress versus specimen depth. Results arealso summarised in Table 4.2.

0.50

0 -450.40:::: - 994 CSACode0.25_a,- 0.200.15o. 1O0.05

slightly unconservative by 1.8%.


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By observing the trends in Fig. 4.2, the concem anses that the predictions of theseequations might not be conservative for the following cases:

i . Specimens with depths greater than about 1000 mm especially since there is a limitof O. 1 on the normalised shear stress ratio given by Equation [4.4].

ii. Concrete strengths greater than about 60 MPa.iii. Beams and one-way slabs with a reinforcement ratio, p, less than about 1.2%.It can be noted as well, that these equations do not provide a uniform factor of safety

against diagonal shear failures, with very conservative predictions for srnall elements andslightly unconservative predictions for larger elements (see Fig. 4.2).

Table 4.2: Comparison of predictions using the CSA simplified expressions with test resultsSpccimen Normalised Shear CSA % Error

Stress at Failure Simplified Eq.~ 1 . 2 % p=2.0% ~ 1 . 2 % p=2.0h

N90 0.280 0.499 O. 166 40.6 1 66.75

N960 O. 179 0.189 0.1 15 35.78 39.03


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It is important to realise that for small shear span-to-depth ratios, a/d, sectional analysis


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may not be appropriate. For small aid ratios, the applied load is close to the support and thiscauses a disturbance in the flow of the stresses. There is a tendency for the forces to flowfrom the point of application of the load, directly into the support reaction. This "strutaction" creates a "disturbed region" in which the assumptions of plane sections and ofuniformly distributed shear stresses are inappropriate.

Figure 4.3 compares test results for a series of k s m s tested by Kani (Kani, 1967)withthe predictions using a strut-and-tie model and the sectional analysis predictions obtainedusing the modified compression field theory (Collins and Mitchell, 1997). From Fig. 4.3, itcan be seen that the sectional analysis method is more appropriate for aid ratios greater thanabout 2.5. For a/d smaller than 2.5, a strut-and-tie analysis is more appropriate for thisparticular series of tests.

For the predictions of the test results in this research program, the location chosen forthe sectional analysis was taken at a distance equal to the effective depth, d, from the edge ofthe loading plate. This section is just outside of the disturbed region around the loading pointand is the most critical section for combined shear and moment effects. The measuredmaterial properties were used for the predictions as well as the "as-built" cross-sectionaldimensions. The input and output values for each specimen are presented in Appendix A andthe results obtained from Response 2000~re summarised in Table 4.3 and Figs. 4.4 to 4.7.

The strut-and-tie model analysis was carried out for the series of beams tested. Thestrut-and-tie model consisted of a direct strut going from the loading plate to the reactionbearing plate. The bearings were sufficiently large to avoid crushing of the concrete at the


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O 100 200 300 400 500 600 700 800 900d (mm)

Figure 4.6: Predictions for the high-strength, p=1.2% series

*.. Experimental*. "- - - PredictionEnvelope


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Table43: Modified compression field theory predictionsbSpecimen

N90

NlSS

Nt20

N350

N485

N960

H90

Hl55

H220

p(%)

1.221-221.22

1.221 -27

1.22

1.22

1.221 -2

ExperimentalResu ts

va, (MPa)1-632.921-662.191.361.611.261.431 .O71.221-051-102.002.981.502.061.39

Response2000Results

Ypred(MPa)1.231.371.151.311.161.291.O51.220.981.1 10.880.981.351.551.311-491.33

Difference betweenthe predicted andexperimen a1resuits in%24.7 152.9630.7340.3914.7320.3416.9414.377.769.0315.9211.5132.4447.8012.9 127.8 14.58


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Table 4.5: Comb ined predictions of the modified compression field theory and the strut-and-tie mode1


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' ~ ~ e c i r n e n

N 90

N I 5 5

N220

N350

N485

N960

H g0

H l 5 5

p(%)

1.221.221.221.221.221.221.221.22

Experimen ta1Resultsv (MPa)

1.O32.921-662.19

Corn binedPredictioosvw @Pa)

1.571.861.171.35

Difference betweenthepredictedandexperirnentalresults in% *3 -7636.3629.2038.34

1.361.611.261-431.O71.221 .O51.102.002.981.502.06

Predictionmethod

Stnit-and-TieStmt-and-TieStrut-and-TieStrut-and-Tie

14.7320.3416.9414.377.769.0315.9211.510.0018.48-9.136.19

1 .161-291 O51-220.981.1 10.880.982.002.431-641.93

M. C. F. T.M. C. F.T.M. C. F. T.M. C. F. T.M. C. F. T.M. C. F. T.M. C. F. T .M. C. F. T.

Strut-and-TieStrut-and-TieStrut-and-TieStrut-and-Tie

Chapter 5


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Conclusions and Recommendations

Th e fol lowing conclusions we re drawn from the resul ts o f the experimental program onth e 12 bearn eiements:

1 ) The size effect is very evident in both the normal-strength and high-strengthconcrete ser ies . The shal lower specimens were consis tcnt ly able to res is t h ighershea r st resses than t he deep er ones .

2) High-strength and normal-strength specimens of the same s ize and samereinforcement ra t ios had a lmost equal shear s t resses a t fa i lure , showing nosignificant gain in sh ea r strength with increased concre te compressiv e strength. Th iscontradicts both the AC1 C o d e (AC1 Committee 318, 1995) and the CSA Standard(CSA 1994) assump tion that the concrete shear s trength, V,, is proport ional to thesquare root of the co ncrete compressive s t rength, fl-

3) Increasing the amount of longitudinal steel reinforcement increases the shear stressat failure in both the normal-strength and high-strength concrete series. Theinfluence of the longitudinal steel ratio, p, is found to a t tenuate with greaterspecimen depth. Th is is du e to the reduced effectiven ess of the longitudinal s teel in


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References


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AC Comm ittee 318, "BuildingCode Requirements for Reinforced Concrete ". ArnericanConcrete Institute. Detroit, 1951.AC1 Cornmittee 3 18, "Building Code Requirements or Structural Concrete (AC1 318-95}and Commentary (AC1 318R-95)". American Concrete Institute. Detroit, 1995, 369 pp .ACI-ASCE Commitee 326, "Shear and Diagonal Tension".AC1 Journal, v59, January-February-March 1962, p. 1-30,277-344 and 352-396.Ahrnad, S.H., Khaloo A.R., and Poveda A., "Shear Capacity of Reinforced High-StrengthConcrete Beams ". AC1 Journal, v83, March-April 1986, p. 297-305.Bazant, Z.P., and Kazemi,M.T., "Size E f i c r on Diagonal Shear Failure of Beams withoutStirrups". AC1 Structural Joumal, v88 No.3, May-June 1991, p. 268-276.Bazant, Z.P., and Kim, Jin-Keun, "Size ef/ect in Shear Failure of Longitudinally ReinforcedBeams ". ACI Journal, v8 1, September-October 1984, p. 456-468.Bazan , 2.P., and Sun, Hsu-Hue i, "Size Eflect in Diagonal Shear Failure: Influence ofAggregate Size and Stirrups ". AC1Materials Joumal, v84 No.4, July-August 1987, p. 259-272.Collins, M.P., Bentz. E.C.. "Response 2000. Reinforced Concrete Sectional Analysis usingthe Modified Compression field Theory". Version 0.7.5 (beta). University of Toronto,Toronto. Ont. 1998.CoIlins, M.P., Kuchma D.."How Safi Are Our Large, Lighrly Reinforced Concrete Beams,

E Izanaty,A.H.,Ni lson A.H.,and S ate F.O., "Shear Capaciv of Reinforced Concrete BeamsUsing High-Sfrength Concrete".AC1Journal, v83, March-April 1986, p. 290-296.


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Kani, G.N.J., "Basic Facts Concerning Shear Failure ".AC1 Journal, v63 , June 1966, p. 675-692.Kani, G.N.J., "How Sufe are our Large Reinforced Concrete Beams? ". AC1Joumal, v64,March 1967, p. 128- 141.Kani, M., et al, "Kani on Shear in Reinforced Concrete ". University of Toronto Press,Toronto, Ont. 1979. 225 pp.Kim. Jin-Keun. and Park. Yon-Dong, "Shear Strength of Reinforced Hr'ghStrcngth ConcrereBeams withour Web Reinforcement ". Magazine of Concrete Research, v46 No. 166, Marcht 994, p. 7- 16.Mphonde, A.G., and Frantz,G.C., "Shear Tests of High- and Low-Strength Concrete Beamsrvithout Stirrups ".AC1Journal, v8 1 , July-August 1984,p. 350-357.Sh ioya, T., "Skar Properties of Large Reinforced Concrete Members *- Special Report ofInstitute of Technology, Shimizu Corporation. No. 25, Feb. 1989.Stanik. B., "The influence of Concrete Sfrength. Distribution of Longitudinal Reinforcement,Amounr of Transverse Reinforcement and Member Size on Shear Strcngrh of ReinforcedConcrere Members ". Master's Thesis, Department of Civil Engineering, University ofToronto. Toronto, Ont.Vecchio, F.J., and Collins, M.P., "The Response of Reinforced Concrete to In-Plane Shearand Normal Stresses ". Department of Civil Engineering, University of Toronto, March 1982.Publication No. 82-03, ISBN 0-7727-7029-8.332 pp.Vecchio, F.J., and Collins, M.P., "Predicting the Response of Reinforced Concrete BeamsSubjccted ro Shear Using the Mod~pedCompression Field Theory". AC I Structural Journal,v85 No.3, May-June 1988,p. 258-268.


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RESPONSE 2000~nput and Output


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Response-2000 v 0.7.fN I55s1998lIOl28 - 1:57 prn

Control :V-Gxy

Transverse Strain


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I = 0.23 mmlm: 14.76 radlkm

y (avg) = 0.76 rnmlm-Y-_-Axial Load = 0.0 kN

Crack Diaaram

Vinci~al ompressive Stress

Shear StrainY

Shear on Crack

Shear Stress

PrincipalTensile Stre!

Moment:= 16.0 kNmShear = 66.7 kN


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Bearn Cross Section Longitudina l Strain Transverse Strain


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Control :M-Phi

9 = 7.77 adlkm lMoment:= 32.3 kNmShear = 97.7 kN

Crack Dianram Shear Strain

Shear on CrackrOP

potShear Stress

Principal Tensile Strei

i"


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Gross Conc. Tran(ln=16.49-- - - - - - ---- .I__


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220.6

5045.4

268

217

l883O.1

oadina (N.M.V + dN.dM,dV)0.00, 0.00, 0.00 + O,OO, 0.70, 1.00

Concrete Rebark = 578 MPa

h = 1.83MPa (aulo)

All units in millimetresClear cover to reinforcment= 30mm1 1 - --

Control :V-xy------ I

Beam Cross Section Transverse StrainOP


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IIIIIIIII

Control :Mah

y,(avg) = 2.39 mmlmAxial ~oad-=YoTk--Moment:= 121.9 kNmShear = 172.9 kN

Crack Diagram

'rinclpal Compressive Stress

Ybot

Shear StrainNP

Shear on Cracktop

Shear Stress

Principal Tensile Stress


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OZZ


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Size Effect on Shear Strength of Reinforced

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Transcript of Size Effect on Shear Strength of Reinforced