a r c h i v e s o f c i v i l a n d m e c h an i c a l e n g i n e e r i n g 1 9 ( 2 0 1 9 ) 3 7 5 – 3 9 0

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Original Research Article

An experimental and numerical study ofaluminium–concrete joints and composite beams

Łukasz Polus *[2_TD$DIFF], Maciej SzumigałaPoznan University of Technology, Institute of Structural Engineering, Poznań, Poland

a r t i c l e i n f o

Article history:

Received 16 January 2018

Accepted 23 November 2018

Available online 29 December 2018

Keywords:

Composite structures

Aluminium structures

Shear connectors

Concrete damaged plasticity

[7_td$diff]a b s t r a c t

The present study investigated the structural behaviour of aluminium–concrete composite

(ACC) beamswith profiled sheeting bymeans of conducting four-point bending tests on four

ACC beams. In the proposed ACC system, a concrete slab was connected to aluminium

girders by mechanical shear connectors developed by the authors of this article. The load-

slip behaviour of the connections was characterised in push-out tests of connectors. In

addition, non-linear 3D finite element (FE) models of the tested joints and composite beams

were developed and verified against the experimental results. The comparison between the

experimental and numerical results indicates that the adopted 3D model can capture the

response of the ACC joints and composite beams fairly well.

© 2018 Politechnika Wrocławska. Published by Elsevier B.V. All rights reserved.

Nomenclature

a h

* CorreE-ma

https://d1644-966

eight of compressive aluminium

b p art of the connector embedded in the concrete slab beff e ffective width of composite slab bf w idth of top flange d d iameter of the connector d1 d istance between the neutral axis of the aluminium

beam and its top

da m aximum aggregate size dc d amage variable dt d amage variable e e ccentricity

sponding author at: Poznan University of Technology, Institute oil addresses: lukasz.polus@put.poznan.pl (Ł. Polus), maciej.szoi.org/10.1016/j.acme.2018.11.0075/© 2018 Politechnika Wrocławska. Published by Elsevier B.V

fy y

f Structuumigala@

. All righ

ield strength

fc c ompressive cylinder strength fc,cube c ompressive cube strength fct t ensile strength of the concrete fb0/fc0 r atio of the strength in the biaxial state to the strength

in the uniaxial state

kt r eduction factor L s pan length n r ate of weakening nd n umber of studs in shear span q u niformly distributed load st t ransverse spacing of the connectors w v iscosity parameter Aa c ross section area of aluminium beam

ral Engineering, Piotrowo 5 Street, 60-965 Poznań, Poland.put.poznan.pl (M. Szumigała).

ts reserved.

a r ch i v e s o f c i v i l a n d m e ch an i c a l e n g i n e e r i n g 1 9 ( 2 0 1 9 ) 3 7 5 – 3 9 0376

E Y

oung's modulus Ec,0 in itial secant modulus of elasticity Ec,s s tabilised secant modulus of elasticity Fc c ompression force of concrete equal to the shear force

supplied by all the connectors

GF fr acture energy I m oment of inertia of the connector's cross-section [8_TD$DIFF]Mo m id-span moment corresponding to the first yielding

of the aluminium beam

Mcrack m id-span moment corresponding to the first cracking Mult m id-span ultimate strength of the composite section Nac d ouble compression force of aluminium Nat te nsile force capacity of the entire aluminium section Pult s hear capacity of a stud accounting for the effect of the

profiled sheeting and stud spacing

Rm u ltimate tensile strength a c oefficient b c oefficient gv p artial factor d[18_TD$DIFF]O m id-span deflection corresponding to M

[18_TD$DIFF]O

dcrack m

id-span deflection corresponding to [19_TD$DIFF]Mcrack

dult m

id-span deflection corresponding to [20_TD$DIFF]Mult

eeng e

ngineering strain eplasticln lo garithmic plastic strain ec c ompressive strain et te nsile strain ec1 s train at average compressive strength ecr c racking strain k p arameter used in the CDP model n P oisson's ratio r d ensity seng e ngineering stress strue tr ue stress c d ilatation angle

1. Introduction

1.1. Aluminium girder

The use of aluminium alloys in structural engineering is arelatively new practice [1,2]. Aluminium is lighter than steeland is corrosion-resistant [3,4]. The modulus of elasticity ofaluminium is approximately one third of that of steel, as aresult ofwhich aluminiummembersmay be damaged throughbuckling. To solve this problem, aluminium tubes can be filledwith concrete [5] and aluminium beams can be joined with aconcrete slab. Aluminium–concrete composite structures maybe used in composite bridges [6] and in structures located incorrosive or humid environments [7].

1.2. Shear connectors

In similar structures – steel and concrete structures – thereare many types of shear connectors: block connectors,welded studs and bars, composite dowels [8]. Shearconnection may also be based on friction [9]. To join analuminium beam with a concrete slab, a special connectorpresented in Ref. [10] and prepared by the authors of this

article may be used. This connector can be screwed to thealuminium beam. Welding studs are not recommended asshear connectors due to the problem with heat-affectedzones in the aluminium beam. These connectors may betested using the push-out standard test carried out inaccordance with the principles set out in Eurocode 4 [11].This test makes it possible to determine the load-bearingcapacity and ductility of the shear connection. The newpush-out test is presented in Ref. [12]. It makes it possible todetermine the stresses in the steel connector under condi-tions similar to those occurring in a composite beamsubjected to the positive bending moment. The results of269 tests of stud shear connectors used in profiled sheetingtroughs and seven modes of failure were analysed in Ref.[13]. Numerous premature concrete-related failure modesmay appear in composite beams with steel trapezoidaldecking [14]. They significantly reduce the strength anddeformation capacity of the shear connection. In this type ofbeams longitudinal cracking and debonding between theconcrete and the profiled sheeting may occur [15]. Theresistance of the connectors depends on: mesh position,transverse spacing, number of shear connectors per trough,slab depth [16] as well as diameter of the connector [17].

1.3. Concrete slab with profiled steel sheeting (PSS)

The advantages of using composite beams with PSS includereducing the height of the concrete slab and saving construc-tion time. The sheeting serves as a lost formwork as well as atension-bearing member [18]. There are two most populartypes of steel sheeting: open trough PSS and re-entrant PSS[19]. Due to the limitation of the ribwidth of PSS, the number ofshear connectors in a composite beam with PSS may be lowerthan the number required for a full composite design. For thisreason,many composite beamswith PSS are partial compositebeams [20].

1.4. Slip in bending composite beams

The results of the laboratory tests of the steel–concretecomposite beams with PSS presented in Ref. [21] showed thatthe failure mode of the aforementioned beams was connectedwith the longitudinal cracking due to the longitudinal shearsplitting force. The longitudinal cracking appeared in compos-ite beams with both open trough PSS [21] and re-entrant PSS[22]. Slip effects cause stiffness reduction in bending compos-ite beams, e.g. in steel plate–concrete composite beams [23]and steel–concrete composite beams [24]. The longitudinalshear may appear in the support zone, as it was analysed forthe composite concrete structures in Refs. [25,26]. Thelongitudinal reinforcing bars placed within the troughs mayimprove the resistance of composite slabs to longitudinalshear [27]. An analysis presented in Ref. [28] showed that thecomposite beams without full connection had lower resis-tance and stiffness than the composite beams with fullconnection. However, it is difficult to achieve full connection inthe composite beams with PSS. The mechanical character-istics of composite connections play an essential role in thebehaviour of composite beams [29]. The load-slip modelobtained from connector tests may be used for the numerical

[(Fig._1)TD$FIG]

Fig. 1 – Using load-slip diagram from the push-out test in FE analysis.

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analysis of composite beams [30]. Accordingly, this paperinvestigated the short-term mechanical behaviour of ACCjoints and beams. The stiffness of the connectors determinedin experiments was used both in the numerical simulation ofpush-out tests of ACC joints and four-point bending tests ofACC beams (see Fig. 1).

Fig. 2 – Force-slip diagrams from the push-out tests: 1 –

laboratory test [10] and 2 – FE analysis.

2. Materials and methods

2.1. Load-slip response of ACC joints from push-out tests,FE analysis and theoretical model

In this article, the results from the laboratory tests presentedin Ref. [10] are used to discuss the load-slip behaviour of theconnections. The tests were carried out on three modelshaving the same geometric configuration. An experimentalmodel consisted of: two concrete slabs made of C30/37concrete, two steel sheets made of 0.7 mm-thick S320GDsteel, eight shear connectors, two reinforcingmeshesmadeof6 mm S235JRG2 steel, round bars and an aluminium beammade of AW-6060 T6 alloy. The tests were performed 70 daysafter the casting, using the Instron 8500 Plus test machine.The load (between 30 kN and 70 kN) was applied cyclically 25times and subsequently the failure load was applied. Thelongitudinal slip between the concrete slabs and the alumini-um beam was measured continuously during loading usingLinear Voltage Displacement Transducers (LVDTs). Thepiston velocity was 0.5 mm/min. The results from these testsare presented in Fig. 2. ‘‘Mean of Experiments’’ presents themeanvalue of the force fromall tree tests. In Figs. 2 and 3 errorbars reflect the distance between the mean value and themax/min test values. The premature concrete-related failuremodes appeared during the tests and they had a negativeimpact on themargin of scatter of test results. ‘‘FEA analysis’’presents the results of numerical calculations. Thenon-linearload-slip response for one connector was obtained using themean value from the experiments (see Fig. 3, curve 1). Thisnon-linear load-slip model obtained from push-out tests wasused to reflect the behaviour of the connectors in numericalmodels of ACC joints and beams. The adopted 3D numericalmodel (described in Section 2.2) adequately captured theresponseof theACC joints inpush-out tests (compare curves 1and 2 in Fig. 2).

During the push-out test, the part of the connectorembedded in the concrete slab was subjected to bending.The stiffness of the connector was calculated using the beammodel and compared with the one determined experimental-ly. The deflection of the beam presented in Fig. 3 may becalculated using the following formula:

u ¼ Qb3

8EI(1)

where

Q ¼ q�b (2)

I ¼ pd4

64(3)

where q is the uniformly distributed load, b the part of theconnector embedded in the concrete slab, d the diameter of theconnector, I the moment of inertia of the connector's cross-section and E is the Young's modulus.

The stiffness of the connector may be assumed as:

k ¼ Qu

(4)

Using Eqs. (1) and (3) one obtains:[(Fig._2)TD$FIG]

[(Fig._3)TD$FIG]

Fig. 3 – Load-slip response for one connector: 1 – determinedexperimentally and used in numerical analysis and 2 –

obtained from theoretical model.

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k ¼ pEd4

8b3(5)

The presented beam model reflects only the elasticbehaviour of the connection. It does not take into accountthe formation of the plastic hinge within the connector. Intimber–concrete composite structures the stiffness of theconnector is determined as the slip modulus k0.4 for the loadequal to 40% of the estimated load-carrying capacity and isapproximately linearly proportional to the connector diameter[31]. In both numerical models (ACC joint – push out test; ACCbeam – four-point bending test) presented in this paper thenon-linear load-slipmodel from the laboratory tests (curve 1 inFig. 3) was used. This model was less accurate for theconnections used in the ACC beams tests, because therewas a different class of concrete than in the ACC joints tests.The concrete strength may have the greatest impact on thefinal section of the load-slip curve [32].

2.2. A numerical model of the aluminium–concretecomposite connection

The numerical model was prepared in the Abaqus program[33]. The results of its validation are presented in Fig. 2. It

[(Fig._4)TD$FIG]

Fig. 4 – The model of the connection in the Abaqus environmenslab, 2 – aluminium beam, 3 – steel plate, 4 – steel mesh and 5

consisted of an aluminium beam, steel meshes (6 mm indiameter), PSS and two concrete slabs. The model had twoaxes of symmetry. For this reason, the authors of this articleprepared only 1/4 of the model (see Fig. 4). The shearconnectors were modelled by a zero-length spring usingthe load-slip model from laboratory tests. This method(implicit modelling of connectors) was also used in Ref.[34]. PSS was the skin of the concrete slab. The concrete slabwas divided into eight-node cuboidal finite solid elements(C3D8R), the reinforcing meshes were modelled by means oftruss elements (T3D2), and an aluminium beam and PSS weredivided into four-node shell elements (S4R). The mesh sizewas 20 mm. Meshing elements should be larger than theaggregate size (16 mm), but not too large [35]. The totalnumber of all such elements was 3590. Surface-to-surface‘‘hard’’ contact and friction were defined between the flangeof the aluminiumbeamand the edge of the concrete slab. Thecoefficient of friction was 0.3. The meshes were embedded inthe concrete slab. The calculations were performed using theNewton-Raphson method in the Abaqus program. The loadwas applied in the form of displacement. Fig. 5 presents theboundary conditions used in the computermodel. In Fig. 6 thedotted lines represent the mean values of the engineeringstress–strain curves (ESS) from the static tensile tests of themetals used in the aluminium–concrete composite elements.The error bars reflect the distance between the mean valueand the max/min test values. These non-linear curves fromthe laboratory tests were approximated using piecewiselinear functions (PLF). Then, the engineering stress–strainwas converted to the true stress–strain (TSS). The true stressstrue and logarithmic plastic strain e

plasticln (see Table 1) used in

the Abaqus program were calculated using the followingformulas [33]:

strue ¼ sengð1þ eengÞ (6)

eplasticln ¼ lnð1þ eengÞ� strue

E(7)

where seng and eeng are the engineering stress and strain.

These equations were used up to the ultimate tensilestrength point. After the maximum tension stress there is thenecking region where these equations cannot be used.

t: (a) complete model; (b) quarter of the model; 1 – concrete– profiled steel sheeting (PSS).

[(Fig._5)TD$FIG]

Fig. 5 – Boundary conditions: 1 – displacement, 2 – displacement in x, y, z directions (blocked), 3 – displacement in x direction(blocked), 4 – displacement in z direction (blocked) and 5 – connector (zero-length spring).

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The behaviour of concretewas described using the concretedamaged plasticity (CDP) model available in the Abaqusprogram. The parameters needed to adequately modelconcrete using CDP model were described in Ref. [36].Jankowiak and Łodygowski discussed the CDP model togetherwith the parameters identification procedure [37]. Relevantinformation on how to use this model in practice was given inRefs. [38,39]. The stress–strain diagram for the analysis of theconcrete subjected to compression was adopted from Ref. [40].The compressive strength of the concrete was taken from thetest presented in Ref. [10]. Based on the strength of theconcrete, other strength parameters were calculated using[40].

Compressive stress was calculated using the followingformula:

[(Fig._6)TD$FIG]

Fig. 6 – Stress–strain re

sc ¼ f ckh�h2

1þ ðk�2Þh (8)

where

k ¼ 1:05Ecec1

f c(9)

h ¼ ec

ec1(10)

where fc is the average compressive strength, Ec the Young'smodulus of concrete, ec the compressive strain and ec1 is thestrain at average compressive strength.

In order to plot the curve (st–et), the formulas presented inRefs. [36,41] were used:

lations for metals.

Table 1 – Parameters of metals used in numerical analysis.

Metal

AW-6060 T6 S320GD S235JRG2 S235J2

E [MPa] n E [MPa] n E [MPa] n E [MPa] n

62 900 0.3 193 590 0.3 207 280 0.3 206 500 0.3

strue [MPa] eplasticln

strue [MPa] eplasticln

strue [MPa] eplasticln

strue [MPa] eplasticln

153.95 0.0 351.13 0.0 564.92 0.0 423.99 0.0166.79 0.00333 381.52 0.06942 600.36 0.00309 432.22 0.00389181.26 0.00509 388.10 0.07681 644.55 0.00486 437.57 0.00585190.37 0.00692 394.46 0.08414 671.43 0.00671 442.49 0.00781199.66 0.01663 400.07 0.09142 698.33 0.01447 459.57 0.01561204.67 0.02436 405.49 0.09866 706.79 0.02226 476.18 0.02336209.25 0.03204 410.51 0.10584 713.27 0.02999 492.04 0.03105213.27 0.03967 415.31 0.11297 506.85 0.03869216.69 0.04725 419.73 0.12005 521.02 0.04627219.48 0.05478 424.09 0.12708 534.54 0.05379221.67 0.06226 428.05 0.13407 547.3 0.06126223.34 0.06970 431.85 0.14100 558.75 0.06868

435.37 0.14789 570.08 0.07605438.66 0.15474 580.36 0.08337441.99 0.16153 589.96 0.09063445.05 0.16829 598.81 0.09785

607.31 0.10502615.25 0.11213622.34 0.11920628.84 0.12623634.83 0.13320640.20 0.14013644.93 0.14702

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st ¼ Ecet if et�ecr

st ¼ f ctecr

et

� �n

if et > ecr

9=; (11)

where n is the rate of weakening, ecr the cracking strain, fct thetensile strength of concrete and et is the tensile strain.

The value of fracture energy (GF is expressed in Newtonsper millimetre) was calculated using the following formula[42]:

GF ¼ ð0:0469da2�0:5da þ 26Þ� f c10

� �0:7

(12)

where da is the maximum aggregate size [mm].

The critical crack opening was calculated as follows [43]:

wc ¼ 5:14GF

f ct(13)

The constitutive laws for the concrete are shown in Figs. 7–9and Table 2.

2.3. Experimental behaviour of the aluminium–concretecomposite beams

The aluminium–concrete composite beams were subjected toa series of four-point bending tests. The geometric configura-

tions and details of the specimens are presented in Fig. 10. Thetests were conducted in the laboratory of the Institute ofStructural Engineering of the Poznan University of Technolo-gy, in an attempt to capture the short-term local and globalbehaviour of ACC beams.

The structural response of the ACC beams was used tovalidate non-linear FE models. The mid-span deflection of thebeams, the deflection under loads, the deflections of thesupports, and the slip between the concrete slab and thealuminium beam were measured using Linear VoltageDisplacement Transducers (LVDTs). Additionally, an observa-tion of the cracks arrangement on the surfaces of the beamswas performed. The first test was performed 100 days after thecasting and the last test was conducted 192 days after thecasting using the Instron 8500 Plus testmachine. The 0.7 mmT55P profiled sheeting was placed in an upward position. Thedegree of the shear connection was 0.79, as defined by the EC4[11] specifications, with two connectors screwed in eachtrough of the sheeting. The specimens were loaded symmet-rically at two points within the span of each beam, using aspreader beam. The beamswere located on roller supports (seeFig. 11a). Thanks to this test, the pure bending of the beamsbetween the two loading points was obtained. The tworeinforcingmeshes consisted of 6-mm bars (steel ratio � 1.0%)made of grade S235JRG2 steel. The spacing between the barswas 117.5 mm in longitudinal direction and 81.0 mm intransverse direction. The steel sheeting was made of gradeS320GD steel and the connectors were made of grade S235J2

[(Fig._7)TD$FIG]

Fig. 7 – Stress–strain relations for concrete subjected to compression (a) and tension (b) used in the numerical simulation ofthe push-out tests of ACC joints (1) and the four-point bending tests of ACC beams (2).

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steel. The mechanical properties of the metal elements wereobtained from the standard static tension tests according to[44]. The results of these tests are presented in Table 3. All theanalysed beams were made of strength class C50/60 concrete.The maximum aggregate size was 8 mm. The concrete cubesand cylinders specimensweremade at the time of casting. Themechanical properties of the concrete elementswere obtainedfrom the tests according to [45,46]. The results of these testsare presented in Table 4.

[(Fig._9)TD$FIG]

Fig. 9 – Damage parameter distribution used in the numerical sibeams (2): (a) as a function of crack width (dt–w); (b) as a functio

[(Fig._8)TD$FIG]

Fig. 8 – Stress-crack width relation used in the numericalsimulation of the tests of ACC joints (1) and the tests of ACCbeams (2).

Each test was divided into stages. In stage one, the loadwas applied cyclically (0.0–10.0 kN, 10.0–2.0 kN, 2.0–20.0 kN,20.0–2.0 kN, 2.0–30.0 kN, 30.0–2.0 kN). In stage two failureload was applied. The piston velocity was 1.0 mm/min(beam 1), 0.33 mm/min (beam 2) and 0.5 mm/min (beams 3and 4).

2.4. The numerical model of the aluminium–concretecomposite beams

The numerical model was prepared in the Abaqus programand it consisted of an aluminium beam, steel meshes, profiledsteel sheeting and a concrete slab. The authors of this articleprepared only 1/4 of themodel (see Fig. 12), because themodelhad two axes of symmetry.

The shear connectors were divided into eight-node cuboi-dal finite solid elements (C3D8R) and embedded in theconcrete slab. The connection between the aluminium beamand the shear connector was model by means of a zero lengthspring using load-slip model from the laboratory tests of theACC connections. The concrete slab was divided into eight-node cuboidal finite solid elements (C3D8R), the reinforcingmeshesweremodelled bymeans of truss elements (T3D2), thealuminium beam and PSS were divided into four-node shellelements (S4R) (see Fig. 13). The size of the mesh was largerthan the aggregate size (15 mm > 8 mm). The total number ofall elements was 12 481.

mulation of the tests of ACC joints (1) and the tests of ACCn of compressive stress (sc–dc).

Table 2 – Parameters of concrete used in numerical analysis.

Test of ACC joints

r [t/mm3] Ecm [MPa] n fc [MPa] fct [MPa] GF [N/m]

2.4 � 10�9 32 000 0.20 38.0 2.9 70.2

n c [8] e fb0/fc0 k w

1.2 40.0 0.1 1.16 0.667 0.001

Stress [MPa] Crushing strain dc Stress [MPa] Cracking strain dt

11.700 0.00000000 0.000 2.90000 0.000000 0.0000015.024 0.00003050 0.000 2.57689 0.000019 0.0208028.233 0.00021773 0.000 1.58411 0.000100 0.0847037.979 0.00096315 0.000 1.12166 0.000165 0.1144737.917 0.00111510 0.002 0.68953 0.000278 0.1820837.477 0.00127883 0.014 0.57308 0.000332 0.3202136.657 0.00145447 0.035 0.48823 0.000385 0.4208635.451 0.00164217 0.067 0.37354 0.000488 0.5569133.854 0.00184207 0.109 0.33317 0.000540 0.6048023.466 0.00276670 0.382 0.24945 0.000692 0.7041015.802 0.00330618 0.584 0.16259 0.000995 0.8071311.335 0.00359578 0.702 0.08307 0.001747 0.901464.708 0.00400287 0.876 0.04183 0.003099 0.950381.104 0.00421551 0.971 0.01736 0.006449 0.97940

Test of ACC beams

r [t/mm3] Ecm [MPa] n fc [MPa] fct [MPa] GF [N/m]

2.4 � 10�9 37 300 0.19 61.8 4.6 92.0

n c [8] e fb0/fc0 k w

3.0 40.0 0.1 1.16 0.667 0.050

Stress [MPa] Crushing strain dc Stress [MPa] Cracking strain dt

27.32 0.00000000 0.000 4.600000 0.0000000 0.0000042.59 0.00010819 0.000 1.078487 0.0001711 0.1934850.17 0.00020500 0.000 0.552185 0.0002352 0.5870660.27 0.00053406 0.000 0.319552 0.0002914 0.7610361.80 0.00079316 0.000 0.201234 0.0003446 0.8495161.61 0.00089833 0.003 0.134811 0.0003964 0.8991860.53 0.00107719 0.021 0.094682 0.0004475 0.9291957.37 0.00136196 0.072 0.069023 0.0004981 0.9483851.78 0.00171189 0.162 0.051858 0.0005486 0.9612247.87 0.00191665 0.225 0.039944 0.0005989 0.9701345.59 0.00202765 0.262 0.031417 0.0006492 0.9765143.08 0.00214492 0.303 0.025154 0.0006993 0.9811937.30 0.00240011 0.397 0.008628 0.0009998 0.99355

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Surface-to-surface ‘‘hard’’ contact and friction were definedbetween the flange of the aluminium beam and the edge of theconcrete slab. The friction coefficient was 0.3. The meshes wereembedded in the concrete slab. The calculations were performedusing the Newton-Raphson method. The authors of this articleused a three-step numerical analysis. In step one, the concreteslab was cooled down (DT =�23.4 K) to take into account theshrinkage of the concrete. The bearing strength of a connectionwithflexible connectors depended not only on the degree of shearconnection, but also on the value of shrinkage strain of concrete[47]. The shrinkage may have an impact on the ultimate loadcapacity and serviceability limit states [48]. The total shrinkagestrainwas the sumof thedrying shrinkage strain (0.140%) and theautogenous shrinkage strain (0.094%) [40,49]. The relationshipbetween temperature, strain and the linear coefficient of thermalexpansion (10� 10�6 1/K) was taken into account. In step two, thedead load of theACCbeamwas applied. In step three the loadwas

applied in the formof displacement. Fig. 14 presents the boundaryconditions used in the computer model.

Themodels of metals used in the numerical simulation arepresented in Fig. 6. The behaviour of concrete was describedusing a concrete damaged plasticity model. The stress–straindiagram for the analysis of the concrete subjected tocompression was adopted from Ref. [40]. The compressivestrength and the tensile strength of concrete were taken fromthe laboratory tests. The value of the fracture energy wascalculated using formula (12) and the critical crack openingwas calculated using formula (13). The constitutive laws forthe concrete are shown in Figs. 7–9 and Table 2. To validate thenumerical model of the push-out tests of the connectors, theparameters of C30/37 concrete were used. To validate thenumerical model of the four-point bending test of the ACCbeams, the parameters of C50/60 concrete were used. In bothnumerical models (the push-out tests and the four-point

[(Fig._11)TD$FIG]

Fig. 11 – (a) Bending test set-up, longitudinal view; (b) concrete rib: 1 – separation of sheeting; (c) failures: 2 – rib-shearing and 3– horizontal crack in the concrete slab.

[(Fig._10)TD$FIG]

Fig. 10 – Geometrical outline and details of the four-point bending tests conducted on the aluminium–concrete compositebeams: A1–3 – strain gauges on the aluminium beams, B1–3 – strain gauges on the concrete slab, 1–8 – LVDT and 9 –

inclinometer

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bending tests) the same non-linear load-slip model was usedto reflect the behaviour of the connectors.

The validation process of the computational model shouldconsist ofmany aspects such as the ones presented in Ref. [50].In this article, the validation process consisted of thepreliminary verification of the model and the selection ofthe elements with parameters having a significant influenceon the behaviour of the model. The rule presented in Ref. [51],according to which one should begin with the simplest modeland then build a more complex model, was used.

2.5. Calculation of the plastic flexural capacity of the ACCbeam

The plastic flexural capacity of the ACC beam Mult wascalculated based on the model for steel–concrete compositebeams presented in Ref. [21]. The authors of this paper madethe following assumptions:

� T

he reinforcement, the profiled sheeting and the concrete inthe ribs were not taken into account in the bending capacitycalculations.

� T

he ACC beam had two plastic neutral axes (in the concreteslab and in the aluminium beam).

� T

he calculations were made for a case where the plasticneutral axis of the aluminiumbeamwas located in itsflange.

From section equilibrium (see Fig. 15),

Nat ¼ Nac þ Fc (14)

Mult ¼ Nat d1� a2

� �þ Fc hc� xc

2þ hp þ a

2

� �(15)

where d1 is the distance between the neutral axis of thealuminium beam and its top, a the height of compressivealuminium, Nat the tensile force capacity of the entire alumin-ium section, Nac the double compression force of aluminiumand Fc is the compression force of concrete equal to shear forcesupplied by all the connectors.

Nat ¼ Aafy (16)

Fc ¼ f cbeffxc ¼ ndPult (17)

Nac ¼ 2abf f y (18)

where Aa is the cross section area of aluminium beam(28.8 cm2 in the analysed example), fy the yield strength of

Table 3 – Set of metal samples, measured mean values.

No. Material Samples fy [MPa] Rm [MPa] E [GPa]

1 4 samples of AW-6060 T6 aluminium alloy [TD$INLINE] 153.26 � 9.31 207.68 � 10.55 62.87 � 7.146.07%b 5.08%b 11.36%b

5.85SD 6.63SD 4.49SD

2 6 samples of S320GD grade steel [TD$INLINE] 350.43 � 3.44 374.42 � 0.96 193.59 � 12.40.98%d 0.26%d 6.40%d

3.28SD 0.91SD 11.80SD

3 5 samples of S235JRG2 grade steel [TD$INLINE] 562.11 � 7.39 689.88 � 14.95 207.28 � 2.381.31%c 2.17%c 1.15%c

5.95SD 12.04SD 1.92SD

4 3 samples of S235J2 grade steel [TD$INLINE] 422.3 � 9.40 557.2 � 4.72 206.50 � 19.432.23%a 0.85%a 9.41%a

3.79SD 1.90SD 7.82SD

SD, sample standard deviation.a Measurement errors were calculated according to Student's t-distribution using 2 degrees of freedom and a confidence level of 0.95.b Measurement errors were calculated according to Student's t-distribution using 3 degrees of freedom and a confidence level of 0.95.c Measurement errors were calculated according to Student's t-distribution using 4 degrees of freedom and a confidence level of 0.95.d Measurement errors were calculated according to Student's t-distribution using 5 degrees of freedom and a confidence level of 0.95.

a r ch i v e s o f c i v i l a n d m e ch an i c a l e n g i n e e r i n g 1 9 ( 2 0 1 9 ) 3 7 5 – 3 9 0384

aluminium (15.3 kN/cm2 in the analysed example), beff theeffective width of composite slab (37.0 cm in the analysedexample), bf the width of top flange (9.0 cm in the analysedexample), nd the number of connectors in shear span (8 in theanalysed example) and Pult is the shear capacity of a connectoraccounting for the effect of the profiled sheeting and connectorspacing.

Due to the fact, that the concrete strength significantlyaffected the resistance of the connectors and the authors ofthis paper used different concrete in laboratory tests ofconnectors and beams, the shear capacity of the connector(43.4 kN) was calculated using the following formula from Ref.[11] after adding coefficient b recommended in Ref. [21]:

Pult ¼ ktb0:29ad2

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffif ckEcm

pgv

(19)

where d is the diameter of the connector (16 mm in the ana-lysed example), gv the partial factor (1.0 in the analysed exam-ple), kt the reduction factor (0.52 in the analysed example), a

the coefficient (1.0 in the analysed example), fc and Ecm thecylindrical compressive strength (61.8 MPa for the analysedbeam) and mean secant modulus of concrete (37.3 GPa for theanalysed beam) and b is the coefficient recommended in Ref.[21] to be used when the transverse spacing of the connectors(st) is less than 4d (b = 0.74 in the analysed example):

b ¼ 0:95st4d

From Eqs. ( [21_TD$DIFF]14)–( [22_TD$DIFF]18),

Mult ¼Aaf y4bf

4bfd1�Aa þ 2Fcf y

!þ Fcðhc

þ hpÞ�F2c1

2f cbeffþ 14fybf

!(20)

The critical length was the distance between the supportand the force (900 mm). Therewere 4 troughs and 8 connectors

Table 4 – Set of concrete samples, measured mean values.

No. Material Samples fc,cube [MPa] fc [MPa] n Ec,0 [GPa] Ec,S [GPa] fct [MPa]

1 8 samples of C50/60 concrete [TD$INLINE] 65.71 � 1.67 – – – – –

2.54%d[1_TD$DIFF]

2.00SD

2 4 samples of C50/60 concrete [TD$INLINE] – – 0.19 � 0.03 33.51 � 1.53 37.33 � 1.44 –

15.24%b 4.58%b 3.86%b

0.02SD 0.96SD 0.91SD

3 5 samples of C50/60 concrete [TD$INLINE] – 61.82 � 3.85 – – – –

6.22%c

3.10SD

4 3 samples of C50/60 concrete [TD$INLINE] – – – – – 4.61 � 0.7516.19%a

0.30SD

5 12 samples of C30/37 concrete [TD$INLINE] 43.46 � 2.09 – – – – –

4.81%e[9_TD$DIFF]

2.69SD

SD, sample standard deviation.a[3_TD$DIFF]Measurement errors were calculated according to Student's t-distribution using [10_TD$DIFF]2 degrees of freedom and a confidence level of 0.95.

[11_TD$DIFF]b Measurement errors were calculated according to Student's t-distribution using [12_TD$DIFF]3 degrees of freedom and a confidence level of 0.95.[13_TD$DIFF]c Measurement errors were calculated according to Student's t-distribution using [14_TD$DIFF]4 degrees of freedom and a confidence level of 0.95.[15_TD$DIFF]d Measurement errors were calculated according to Student's t-distribution using [16_TD$DIFF]7 degrees of freedom and a confidence level of 0.95.[9_TD$DIFF]e Measurement errors were calculated according to Student's t-distribution using [17_TD$DIFF]11 degrees of freedom and a confidence level of 0.95.

a r c h i v e s o f c i v i l a n d m e c h an i c a l e n g i n e e r i n g 1 9 ( 2 0 1 9 ) 3 7 5 – 3 9 0 385

within the critical length. The reduced force transmitted to theslab by the connectors placed within the critical length wasFc = 8 � 43.3 = 347.0 kN. The plastic flexural capacityMut of theACC beam calculated from Eq. (20) was 71.4 kNm. This valuewas about 1.1% smaller than the measured mean ultimatestrength of the composite section (72.2 kNm) (see Table 5). Thetheoreticalmodel for ACC beams based on themodel for steel–concrete composite beams presented in Ref. [21] adequatelycaptured their plastic flexural capacity.

3. Results and discussion

3.1. Results of laboratory tests of ACC beams

When the load reached about 30% of the ultimate test load,the authors of the article observed little gaps (<1 mm)

between the profiled sheeting and troughs (see Fig. 11b). Thenumber of sheet metal screws was too small and thesheeting was detached from the concrete slab. When theload reached 47–69%, a horizontal crack occurred in theconcrete troughs near the support of the beams (see Fig. 11c).Its width and length continuously increased with theincrease of the load. When the load reached 81–94% of theultimate test load, the first longitudinal crack formedbetween the profiled sheeting and concrete troughs nearone of the supports (see Fig. 11c). When the crack appeared,the load decreased for a moment. Shortly after, the loadstarted to grow and the width and length of the crack werecontinuously increasing. At the collapse load, the profiledsheeting in the shear span detached from the concrete. Theshear studswere not broken off. The typical failuremodes ofthe ribs are presented in Fig. 11c. Due to a longitudinal shearsplitting force, longitudinal cracking appeared. Fig. 16 shows

[(Fig._13)TD$FIG]

Fig. 13 – The mesh used in the numerical calculations: 1 – quarter of the model, 2 – aluminium beam with steel meshes andconnectors, 3 – connector and 4 – profiled steel sheeting (PSS).

[(Fig._12)TD$FIG]

Fig. 12 – The model of the beam in the Abaqus environment: (a) complete model; (b) quarter of the model; 1 – concrete slab, 2 –

aluminium beam, 3 – steel plate, 4 – steel mesh, 5 – profiled steel sheeting (double thickness on sheet-to-sheet connection)and 6 – connectors.

a r ch i v e s o f c i v i l a n d m e ch an i c a l e n g i n e e r i n g 1 9 ( 2 0 1 9 ) 3 7 5 – 3 9 0386

the strain distribution across the specimen height alongsection 3-3.

Strain gauges had been placed in the upper part of the slaband on the aluminium beam. The strain in the bottom part ofthe slab was calculated with the assumption that thecurvature of the aluminium beam was the same as thecurvature of the concrete slab. One can observe the slip at theinterface. Due to the slip, two neutral axes were noted. At the

ultimate load, the beam specimens reached a deflection levelof about L/45 (beam 4) and L/60 (beams 1, 2 and 3). Once theload was removed, the residual deflections exceeded 40 mm(beam 4). The test results for the four composite beams weresummarised in Table 5. At the deflection level of L/250 the loadreached about 45% of the ultimate strength of the compositesection Mult. Because of the low value of the Young's modulusof the aluminium, the ACC beams showed big deflections.

[(Fig._15)TD$FIG]

Fig. 15 – Calculationmodel for the plastic flexural capacity ofthe ACC beam.

[(Fig._14)TD$FIG]

Fig. 14 – Boundary conditions: 1 – displacement, 2 – displacement in y direction (blocked), 3 – displacement in x direction(blocked), 4 – displacement in z direction (blocked) and rotation around x and y axes (blocked), 5 – connector (spring), 6 –

predefined field (temperature) and 7 – dead load.

Table 5 – Measured results from laboratory tests.

Result Beam 1 Beam 2 Beam 3 Beam 4 Mean

Mo [kN m] 52.6 54.7 53.8 53.9 53.8Mcrack [kN m] 62.0 67.9 68.6 59.6 64.5Mult [kN m] 71.3 70.6 73.6 73.4 72.2do [mm] 19.4 17.9 18.5 19.3 18.8dcrack [mm] 25.0 26.8 26.3 23.2 25.3dult [mm] 41.4 39.2 36.8 52.9 42.6Mult/Mo 1.36 1.29 1.37 1.36 1.35Mult/Mcrack 1.15 1.04 1.07 1.23 1.12dult/d[18_TD$DIFF]O 2.13 2.19 1.99 2.74 2.26

a r c h i v e s o f c i v i l a n d m e c h an i c a l e n g i n e e r i n g 1 9 ( 2 0 1 9 ) 3 7 5 – 3 9 0 387

3.2. Results of numerical analysis of ACC beams comparedwith laboratory tests

Fig. 17 shows the mid-span moment versus mid-spandeflection from the laboratory tests and [23_TD$DIFF]FE analysis. The errorbars reflect the distance between themean value and themax/min test values.

The adopted 3D model captured the response of the ACCbeams fairly well. The behaviour of the concrete was the most

challenging aspect in finite elementmodelling. In the course ofverification of the model, the authors of this article analysedthe impact of many parameters of concrete (e.g. parameter n,viscosity). Fig. 18 shows the mid-span moment versus the endslip of the beam, obtained from laboratory tests and numericalcalculations. The initial part of the ‘‘[23_TD$DIFF]FE analysis’’ curvepresents the slip caused by the shrinkage of the concrete.The lack of consistency between the moment-slip curves isvisible. The distance between the mean value and the max/min test values is greater in themoment-slip curve than in themoment-deflection curve (compare error bars in Figs. 17 and18). The big margin of scatter of test results for the slip may beconnected with the form of failure – the longitudinal crack

[(Fig._18)TD$FIG]

Fig. 18 – Mid-span moment versus end span slip: 1 – laboratory test, 2 – FE analysis, 3 – laboratory test 1 and 4 – slip innumerical analysis caused by the shrinkage of the concrete

[(Fig._16)TD$FIG]

Fig. 16 – Strain distribution across the specimen height along section 3-3 (mean values from the laboratory tests).

[(Fig._17)TD$FIG]

Fig. 17 – Mid-span moment versus mid-span deflection.

a r ch i v e s o f c i v i l a n d m e ch an i c a l e n g i n e e r i n g 1 9 ( 2 0 1 9 ) 3 7 5 – 3 9 0388

[(Fig._19)TD$FIG]

Fig. 19 – Failures: 1 – horizontal crack in the concrete slab and 2 – rib-shearing.

a r c h i v e s o f c i v i l a n d m e c h an i c a l e n g i n e e r i n g 1 9 ( 2 0 1 9 ) 3 7 5 – 3 9 0 389

formed between the profiled sheeting and the concretetroughs close to one of the supports. The slip was measuredonly close to one of the supports. Themoment-slip curve fromFE analysis had the best correlation with moment-slip curvefrom test 1. The failure modes of the ACC beams wereassociated with the horizontal cracking and the rib-shearingboth in FE analysis and laboratory tests (compare Fig. 11c andFig. 19).

4. Conclusions

The proposed connectors for the ACC beamswere successfullyused to join an aluminium beam with a concrete slab, but dueto the limitation of the rib width of the profiled sheeting, thenumber of shear connectors was lower than the numberrequired for a full composite design. The analysed beamswerepartial composite beams where the slip and the rib-shearingfailure appeared. The use of the waveform reinforcementpresented in Ref. [52] to prevent rib-shearing failure should betaken into consideration in the future. To adequately capturethe response of the partial composite beams, the load-slipmodel from the push-out tests of connectors was successfullyused in a non-linear analysis.

The plastic flexural capacity of the ACC beams was alsodiscussed. The results calculated using the model for steel–concrete composite beams presented in Ref. [21] for thepartial-composite beams corresponded to a large extent withthemeasured values. Therefore, this simplifiedmethod seemsto be suitable for application in practical design. The use ofcoefficient b, recommended in Ref. [21], was necessary toassure accuracy in predicting the plastic flexural capacity ofthe ACC beams.

Due to the significant deflections of the ACC beams, theserviceability limit statemay have an impact on the size of thecross-section of the ACC beam.

Conflict of interest

The equipment was delivered by Poznan University ofTechnology where authors are employed.

Ethical statement

Authors state that the research was conducted according toethical standards.

Acknowledgments

This research work was co-financed by the European Unionunder the European Social Fund and the project ‘‘Scholarshipsupport for Ph.D. students specialising in majors strategic forWielkopolska's development’’, Sub-measure 8.2.2 HumanCapital Operational Programme [24_TD$DIFF], [25_TD$DIFF]co-financed by EuropeanUnion under the [26_TD$DIFF]European [27_TD$DIFF]Social Fund.

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