Journal of Constructional Steel Research 88 (2013) 134–149

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Journal of Constructional Steel Research

Bolted shear connectors vs. headed studs behaviour in push-out tests

Marko Pavlović a,⁎, Zlatko Marković a, Milan Veljković b, Dragan Buđevac a

a Faculty of Civil Engineering, University of Belgrade, Serbiab Luleå University of Technology, Sweden

⁎ Corresponding author. Tel.: +381 641471748.E-mail address: marko@imk.grf.bg.ac.rs (M. Pavlović

0143-974X/$ – see front matter © 2013 Elsevier Ltd. Alhttp://dx.doi.org/10.1016/j.jcsr.2013.05.003

a b s t r a c t

a r t i c l e i n f o

Article history:Received 8 February 2013Accepted 4 May 2013Available online 2 June 2013

Keywords:Steel–concrete composite beamsPrefabricated structuresHigh strength boltsHeaded studsShear connector heightParametric studyPush-out testsFinite element analysisDamage plasticity

Prefabrication of concrete slabs reduces construction time for composite steel–concrete buildings and brid-ges. Different alternatives for shear connectors (bolts and headed studs) are analysed here to gain better in-sight in failure modes of shear connector in order to improve competiveness of prefabricated compositestructures. Casting of high strength bolted shear connectors in prefabricated concrete slabs offers the higherlevel of prefabrication comparing to a standard method of grouting welded headed studs in envisagedpockets of concrete slabs. In addition, bolted shear connectors can easily be dismantled together with theconcrete slab thus allowing the improved sustainability of the construction, simpler maintenance, and devel-opment of modular structural systems. Bolted shear connectors have been rarely used in construction, actu-ally just for rehabilitation works, because there is a lack of design recommendation. The first step towards thedesign recommendation is to understand the difference between the headed shear studs and the bolted shearconnectors in a push-out test. Push-out tests, according to EN1994-1-1, using 4 M16 — grade 8.8 bolts withembedded nut in the same layout and test set-up as for previously investigated headed studs wereperformed. Finite element models for both shear connectors were created, and good match with experimen-tal data was obtained. Basic shear connector properties such as: shear resistance, stiffness, ductility and fail-ure modes have been compared and discussed in detail by using experimental and FE results. Parametric FEanalyses of shear connector's height are carried out and shear resistance reduction factor has been proposedfor bolted shear connectors.

© 2013 Elsevier Ltd. All rights reserved.

1. Introduction

Steel–concrete composite beams have been used in buildings andbridges for decades. In-situ casted concrete requires often temporarysupports and formwork which leads to a longer construction timecompared to, recently established, prefabricated concrete slabs. Pre-fabrication of concrete slabs is a good way to reduce the constructiontime and optimize construction process. Composite action between asteel profile and a concrete slab is most commonly established bygrouting grouped headed studs welded to a flange of steel sectionin envisaged openings (pockets) of prefabricated concrete slabs.Moreover, if the replacement of concrete slabs is required either forstructural reasons (maintenance) or practical reasons (end of thelife time), bolted shear connectors has big advantages because ofeasier dismantling.

Prefabricated composite deck structures with bolted shear connec-tors may be used in residential and commercial buildings, car parksand modular building systems. They can also be competitive for shortspan overpass bridges and modular temporary bridge systems. Dry as-sembling and faster erection process are obtained by casting bolts in

).

l rights reserved.

prefabricated concrete slabs and by on-site assembling into predrilledflange of steel section part of composite member. In this case, low fabri-cation tolerances of prefabricated elements need to be achieved so as toensure assumed composite action of the structure.

Tolerances for the concrete slabs in prefabricated bridges are ratherstrict and very good state of the art on the requirements, achieved toler-ances and costs are provided in Hällmark licentiate thesis [1]. Referenceis made to amatch casting technique in order to get sufficient precision.This technique means that the first element can be cast in an ordinaryformwork, but from the second element and further, the previous castelement should be used as formwork on one side of the next element.By using this match-casting technique it has been shown that it is pos-sible to keep the mean joint-gap ≤ 0.4 mm as achieved in the singlespan L = 28 m, prefabricated composite road bridge AC 1684 built in2002 in Norrfors, Sweden. The total cost of the prefabricated bridgewas smaller than the in-situ cast bridge, in spite of such small executiontolerances achieved.

The construction costs with use of bolted shear connectors areexpected to be higher when compared to traditional headed studs.Still, the faster erection and life cycle cost analysis may lead, for cer-tain applications, that the total economy of the precast structures be-comes competitive. However, bolted shear connectors in compositestructures are rarely used. One of the possible reasons could be thelack of detailed research and design rules concerning their specific

135M. Pavlović et al. / Journal of Constructional Steel Research 88 (2013) 134–149

behaviour in contrast to, welded headed studs, as the most widelyused and studied shear connectors.

Possible uses of bolted shear connectors are shown in Fig. 1. Thecomposite action is established with or without nuts embedded inthe slab, either with or without preloading of bolts. Friction gripbolts shown in Fig. 1(a) transfer interface shear forces through fric-tion which are often used in construction of car parks [2]. The highstrength friction grip bolts, ASTM A325 and A449, have been investi-gated by Dallam [3], diameters of 12.7, 15.9 and 19.1 mm (1/5, 5/8, 3/4 in.), and height of 102 mm (4 in.). It was reported that bolts havezero slip at the serviceability stage and up to twice higher ultimateshear resistance compared to welded headed studs of same dimen-sions. Design shear resistance for friction grip bolts is defined in BS5400-5 [4], but notably lower values than those obtained by Dallam.Hawkins [5] conducted the large experimental research on anchorbolts without the embedded nut (Fig. 1(b)) in shear and tension. Var-iables for shear tests were the anchor bolt diameter (19 and 25 mm),embedment length (76, 127 and 178 mm) and concrete strength(20.7 and 34.5 MPa). He showed that such anchors have 80% shearresistance when compared to welded headed studs and only 15% ofshear stiffness. Other types of bolted shear connectors were partiallyanalysed by Dedic and Klaiber [6] and Kwon et al. [7] in terms ofrehabilitation work so as to strengthen the existing non compositebridges. Dedic and Klaiber [6] performed 4 experiments on 19 mmASTM A325 high strength bolts. They showed that shear resistanceand load–slip behaviour of bolted shear connectors, without or withsingle embedded nut shown in Fig. 1(b) and (c), are comparable towelded headed studs of same dimensions. Kwon et al. [7] examinedthe static and fatigue strength of 22 mm diameter friction grip bolts,as well as double embedded nut shear connectors shown inFig. 1(a) and (d). Similar static shear resistance is reported and evenbetter fatigue strength when compared to welded headed studs be-cause the connection is welding free. None of the mentioned researchon bolted shear connectors has analytically dealt with failure modesand behaviour of shear connectors, as it has been done for weldedheaded studs, neither the shear resistance of bolted connectors hasalso been thoroughly modelled with FEA.

The aim of this paper is to gain better understanding of the failuremodes of bolted and welded headed studs shear connectors by ad-vance FE analysis as the first step towards the design recommenda-tions for bolted shear connectors. High strength bolts M16, grade8.8, as shown in Fig. 1(c), and headed studs of same dimensionswere used in the standardized push-out test. Experiments aremodelled by advance 3D FE simulation based on explicit softwarewhich leads to the most realistic prediction of the failure modes forthese two shear connectors. The analysis is performed using damageplasticity parameters which are calibrated by cylinder coupon speci-mens taken from the bolt, headed stud and from the I section. Para-metric study of shear connector's height was also conducted, andresults are discussed.

a) frictiongrip bolt

b) withoutembedded nut

c) singleembedded nut

d) doubleembedded nut

Fig. 1. Bolted shear connectors.

2. Push-out tests

Four identical specimens of high strength bolted shear connectorswere prepared and tested in the Laboratory of Materials and Struc-tures at the Faculty of Civil Engineering in Belgrade according toEN1994-1-1 [8]. Layout and dimensions are shown in Fig. 2. Thesame connection layout, materials, testing procedure and equipmentwere used for comparative tests of headed studs with diameter d =16 mm and height above flange hsc = 105 mm, previously conductedby Spremić et al. [9] at the same Laboratory.

2.1. Test set-up

Concrete slabs (EC2 class: C30/37) with standard reinforcement lay-out (ribbed bars ø10 mm, grade R500) were prefabricated by castingthem in horizontal position. Openings with dimensions 240 × 240 mmwere left in the middle for later assembly of shear connectors. Highstrength bolts M16 × 140 mm, grade 8.8 (ISO 4014), were bolted toHEB260 (S235) steel section flanges with d0 = 17 mm holes. Distancesbetween bolts were 100 mm (see Fig. 2) in both directions. Thepreloading force of 40 kN (nearly 50% of full preloading force) was ap-plied by torque controlled wrench, see Fig. 1(c).

Assembling of the specimens was done in two phases, first oneside then another, by concreting openings as shown in Fig. 2.Connecting surfaces of steel flange were greased in order to avoidbond effects with concrete slab. Inner surfaces of openings werecleaned and treated with the layer of concrete glue. Openings werefilled with three-fraction concrete with shrinkage reduction admix-tures in horizontal position. To minimize initial shrinkage cracks,the specimens were kept in wet condition. After three days, half as-sembled specimens were turned and second phase was conductedin the same way as the first one.

During concreting of openings, concrete cubes and cylinders(minimum four specimens) were made out of the same concrete mix-ture. Characteristic compressive cube strength fck,cube = 40 MPa, andsplitting tensile strength fct,sp = 3.1 MPa were achieved for concretein openings. Standard tensile tests were conducted on 8 mm diame-ter coupons for steel section and bolts so as to obtain their materialproperties.

Each push-out specimen was equipped with 8 inductive displace-ment transducers with capacity of 20 mm to measure the slip andseparation between the concrete slab and steel profile, as shown inFig. 3. No strain measurements were made. Longitudinal slip wasmeasured on both sides of a steel section and on both slabs: transduc-ers V1–V4. Transversal separation between the steel section and bothslabs was measured only on the front side, as close to bolts groups aspossible: transducers H1 and H2. The separation of slabs was mea-sured on both sides of steel section: transducers S1 and S2. Forcewas measured by a load cell at the top, 1000 kN capacity. Data acquisi-tion and recording was done in 1 Hz frequency with multichannelacquisition device. Loading regime was adopted as specified in EC4 —

Annex B [8]. Force controlled cyclic load was applied in 26 cycles rang-ing from Fmin = 40 kN to Fmax = 280 kN, corresponding to 5% and 40%of expected failure load. Loading rate of 80 s/cycle (≈6.0 kN/s) was as-sumed to be small enough so as to act as the quasi-static loading. Aftercyclic loading, the load in a constant rate was applied in one step untilthe failure, in the displacement control, such that the failure did not ap-pear in less than 15 min.

2.2. Experimental results

Results of push-out tests of bolted shear connectors are presentedin Table 1 with ultimate total force Pult. Longitudinal slip is presentedas averaged value for transducers V1–V4 divided to the initial accu-mulated slip during cyclic loading δinit and additional slip to failureδu, as defined in Fig. 4(a). Total slip δu,tot = δinit + δu is also given.

layer of concrete glue

Fig. 2. Test specimen layout and assembling.

136 M. Pavlović et al. / Journal of Constructional Steel Research 88 (2013) 134–149

Slip to failure δu, as shear connector key property for classificationwith respect to ductility, will be used for comparisons with headedstuds and FEA results. Separation of concrete slabs (S1 and S2 fromFig. 3) and uplift of the concrete slab from the steel flange (H1 andH2) are given as averaged values. Statistical evaluation of experimen-tal results according to EN1990 – Annex D [10] is also given in Table 1for ultimate force Pult and slip δu. Force–slip curves for all four speci-mens are shown in Fig. 4(a), respect to additional slip to failure δu, to-gether with characteristic experimental curve for headed studs [9].Characteristic failure shape of bolted shear connector and threadand embedded nut penetration are shown in Fig. 4(b).

Comparison of the present study force–slip curves with previouslypublished experiment data on bolted shear connectors conducted byDedic and Klaiber [6], and Kwon et al. [7], with single embedded nutand double embedded nut, respectively, is shown in Fig. 5. Notablyhigher ductility of bolted shear connectors d = 22 mm investigatedby Kwon et al. [7], when compared to others, may be addressed to asingle shear tests used in experiments instead of push-out tests.

Failure patterns in the concrete are shown in Fig. 6 for three differ-ent characteristic cases of the tested specimens. Fig. 6(a) and (b)shows shear failure in 4 and 2 bolts, respectively, while Fig. 6(c)shows bolts prior to failure (2 bolts failed on the opposite slab). Re-gardless the number of bolts that failed in shear, damaged zones of

Fig. 3. Test

concrete were of the similar size and the crushing pattern. Concretecone pull-out failure did not occur in any of the specimens and noglobal cracking of concrete slabs was noticed. Therefore, no major dif-ferences in behaviour of specimens were noticed. This leads to theconclusion that failure of the concrete is not dominant and that theshear failure mode of bolts is governing for the size of bolt: the diam-eter and height, investigated here. This is confirmed by 4 force–slipcurves shown in Fig. 4(a). Those curves would scatter more in acase of dominant concrete failure mode (crushing, cracking, or conepull-out).

3. Numerical analyses

Extensive finite element analyses were conducted using ABAQUS/Explicit code. Two types of models were built for bolted shear connec-tors push-out tests, as shown in Fig. 7. Complete FEA model shown inFig. 7(a), completely representing push-out test specimens, was usedto narrow down initial uncertainties about analyses methods, bound-ary conditions, mesh, material models and model behaviour. Aftersatisfactory match of numerical and experimental results wasachieved more robust detail FEA model shown in Fig. 7(b) was devel-oped by downgrading model size to a zone around shear connectors.

set-up.

Table 1Experimental results for bolted shear connectors.

Totalforce (kN)

Slip — average (mm) Separation —

average (mm)

Specimen(8 bolts)

Ultimate Initial To failure Total Betweenslabs

Steel toconcrete

Pult δinit δu δu,tot

BT1 720.4 0.34 4.65 4.99 1.78 1.19BT2 702.3 1.37 5.01 6.38 1.82 1.19BT3 703.5 0.98 4.47 5.45 1.51 1.07BT4 741.7 1.12 3.90 5.02 1.23 0.99Mean 717.0 1.00 4.51 5.46 1.59 1.11Variation (%) 2.6 10.3Characteristic 668.5 3.3

0

50

100

150

200

0,0 1,0 2,0 3,0 4,0 5,0 6,0 7,0 8,0

For

ce p

er s

hear

con

nect

or (

mm

)

Slip (mm)

Present study: M16,h=105mm (average)

Dedic and Klaiber [6]:d=19mm, h=127mm

Kwon et al. [7]: d=22mm,h=127mm (average)

Fig. 5. Comparison to existing test data on bolted shear connectors.

137M. Pavlović et al. / Journal of Constructional Steel Research 88 (2013) 134–149

The corresponding detail FEA model was also built for headedstuds to match the test results obtained by Spremić et al. [9]. DetailFEA models of bolts and headed studs were used for studying the dif-ferences in behaviour of bolts and headed studs as shear connectors(shear resistance, stiffness and ductility). Parametric study of shearconnector height above the flange was conducted on detail FEAmodels.

3.1. Geometry, boundary conditions and loading

Complete FEA model consisted of all connection components usedin push-out tests: concrete slab, steel section, bolts, nuts, washers andreinforcement bars as shown in Fig. 7(a). One quarter of a real speci-men was modelled with double vertical symmetry condition. Bolt andnuts were modelled using the exact geometry of head and threads asshown in Fig. 7(c) so as to consider all complicated contact interac-tions and fracture mechanisms. Reinforcement bars were modelledas separate solid parts inside the concrete as shown in Fig. 7(a),since uniaxial rebar elements are not applicable with tetrahedron fi-nite elements of concrete slab.

General contact interaction procedurewas usedwith normal behav-iour (“hard” formulation) and tangential behaviour (“penalty” frictionformulation). Friction coefficient of 0.14 was set for preloaded highstrength bolts, for surface between the tread and the nut, according to[11]. No cohesion and same friction coefficient was used for the steel–concrete interface, since it was greased during specimen preparation.

The detail FEA models were built on same principles (double sym-metry, accurate geometry, contact and friction, etc.) but with fewsimplifications. Only the concrete slab around shear connectors was

a) Experimental force-slip curves.

0

100

200

300

400

500

600

700

800

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0

Tot

al f

orce

(kN

)

Slip (mm)

BT1

Headedstuds

BT2

BT4

BT3

0

700

0

Pult

δinit

δinit

δu,tot

0.05Pult

0.4Pult

slip δu

P

δ

Fig. 4. Experimental results of push-ou

modelled, since no global failure mode of the concrete slab was no-ticed either in experiments or in results of the complete FEA model.The size of concrete part considered in a detail FEA model, 180 mmwide and 280 mm high, (shown in Fig. 7(b)) was selected largeenough not to give additional constraint condition to concrete aroundshear connectors. It was done by checking the distribution of elasticand plastic strains and damage variables in the results of the completeFEA model. Surrounding surfaces of local concrete part were fullyconstrained to the “Support” reference point as shown in Fig. 7(b).Reference point is then assigned with a fully fixed boundary conditionexcept for lateral translation U3 (3 is designation for Z direction).Elastic stiffness ku3 was assigned for lateral translation U3 of “Sup-port” reference point in order to simulate equivalent boundary condi-tion of the rest parts of the concrete slab, not considered in detail FEAmodel. Influence of concrete slabs resisting separation in a push-outtest, due to its bending stiffness and contact–friction boundary condi-tion at the bottom surface, is taken into account in the detail FEAmodel. Moreover, two unknown boundary conditions (friction coeffi-cient and rotational rigidity) at the bottom surface of concrete slabs inthe complete FEA model are substituted by only one unknownboundary condition (lateral restraint stiffness ku3) in the detail FEAmodel. It was calibrated to a value of ku3 = 20 kN/mm to matchforce–slip curve of detail FEA model to tests results and completeFEA model as it is shown in Section 3.4. Reinforcement bars were

b) Characteristic failure and thread and embedded nut penetration.

t tests for bolted shear connectors.

a) 4 bolts failed in shear b) 2 bolts failed in shear c) opposite side (close to failure)

Fig. 6. Failure patterns in concrete slabs.

138 M. Pavlović et al. / Journal of Constructional Steel Research 88 (2013) 134–149

considered only in the complete FEA model. Preliminary analysesshowed that reinforcement did not influence results neither in com-plete nor the detail FEA model for the considered concrete strengthand shear connector diameter. Influence of the reinforcement maybe significant for global cracking of concrete slabs in a push-out testfor larger diameters of shear connectors and lower concretestrengths. An and Cederwall [12], experimentally showed that rein-forcement have none, or low, influence on local behaviour andshear resistance of welded headed stud. Spremić et al. [9] reportedsimilar behaviour for grouped headed studs. Therefore, reinforcementbars were not modelled in the detail FEA model.

Loading was defined in three subsequent steps. They correspondto experimental testing: bolt preloading, cyclic loading, and loadingup to failure. Bolts were preloaded by the “turn-of-nut method”, i.e.applying intermediate “wrenching” boundary conditions on nuts intheir local cylindrical coordinate system, see Fig. 8. Outer nuts weretorqued by defining appropriate tangential deformation (3.2 mm) toits six hexagon edges, clockwise, so as to achieve the same preloadingforce of Fp = 40 kN as used in push-out tests. Tangential deforma-tions of embedded nuts edges were restrained. Cyclic loading was

a) Complete push-out model. b) Detail–simp

Front view

X –

sym

met

ry(U

1=U

R2=

UR

3=0)

U1=U2„Supp

„Jack“ refereU1=U3=0; UR1=

U2

Fig. 7. FEA models geometry a

applied as force controlled in form of surface stress at the top of thesteel section to achieve total load of 280/4 = 70 kN. It was definedby time dependent amplitude function, with values ranging from0.12 to 1.0 in 26 cycles. Loading up to failure was applied as a verticaldisplacement U2 = 6 mm of the “Jack” reference point to which thetop surface of the steel section was constrained; see Fig. 6(b). Appro-priate smoothing was adopted for amplitude functions in all loadingsteps to avoid large inertia forces in quasi-static analysis.

3.2. Analyses method and mesh

Geometric and material nonlinear analysis was performed asquasi-static with dynamic explicit solver because it does not haveconvergence issues as implicit static solver. Mass scaling with desiredtime increment of 0.002 s was used in those analyses in order to in-crease speed of quasi-static analysis. Scaling was set to be variable(recomputed in every integration step) and non-uniform (differentfor each finite element) as it is the most efficient for those modelswith large spectra of elements sizes and damage included.

lified model. c) Bolt and nut.

Side view

Z –

sym

met

ry(U

3=U

R1=

UR

2=0)

Elastic lateral

restraintku3=0; UR1=UR2=UR3=0ort“ reference point

nce pointUR2=UR3=0

U2

nd boundary conditions.

Fig. 8. Bolts preloading by “turn-of-nut method”.

139M. Pavlović et al. / Journal of Constructional Steel Research 88 (2013) 134–149

Complex geometry of model parts (bolts and nuts) required tetra-hedron finite elements (C3D4) to be used for most parts. Mesh sizewas varied for different parts in terms of their size and importance.For example, thread area of bolts and nuts were meshed with1.2 mm elements, while head and shank had a mesh size of 2.4 mm,see Fig. 7(c). In expected failure zones of a bolt, mesh size was keptconstant because mesh size transitions would corrupt ductile andshear damage models used for bolt material.

3.3. Material models

Five different material models have been defined for modelledparts (steel section, concrete, bolt, headed stud and reinforcement.).The big attention has been paid to bolt, headed stud and concrete ma-terial models since the overall behaviour of shear connection FEAmodels was highly sensitive to their properties.

3.3.1. Steel materialsIsotropic plasticity with initial modulus of elasticity of E0 =

210 GPa, and Poisson's ratio of v = 0.3 was used for bolt, headedstud and steel section material. Experimental stress/strain curvesare shown in Fig. 9. Progressive damage models in ABAQUS wereused to account for failure modes and element removal. Ductile andshear damage models were used for bolt and headed stud material,while only ductile damage was used for steel section.

Parameters of ductile damage initiation criterions and damageevolution laws were derived observing basic behaviour of tensiletest coupons and implementing principles of progressive damagemodel described in [13]. Standard (round bar) tensile test modelswere built andmaterial parameters were calibrated by comparing nu-merical results to corresponding experimental data. A good match ofnumerical and experimental results of tensile tests was found asshown in Fig. 9. Subsequently those material models, and the samesize and mesh type were used for the complete and detail FEA modelsof push-out tests and good results were obtained.

0

100

200

300

400

500

600

700

800

900

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

Nominal strain (-)

Bolt (grade 8.8) - Test

Headed stud - Test

Steel section (S235) - Test

Bolt - FEA

Headed stud - FEA

Steel section - FEA

n

r

f

p

Nom

inal

str

ess

(MP

a)

Fig. 9. Experimental and numerical tensile tests results.

First, damage initiation criterion needs to be defined as equivalentplastic strain at the onset of damage εpl0 in function of stress triaxialityθ (strain rate is rolled out). For uniaxial tension (θ = 1/3), corre-sponding to standard tensile test, equivalent plastic strain at theonset of damage can be defined as εpl0 ¼ εpl0 ¼ εpln , where εnpl is definedin Fig. 10(a) as uniaxial true plastic strain at onset of necking obtainedfrom experimental results of standard tensile tests. Function of equiv-alent plastic strain at the onset of damage on triaxiality, will bedefined based on experimental and theoretical findings of someauthors. Trattnig et al. [14] conducted series of tests with differenttriaxiality on austenitic steels. Based on experimental results theyproposed exponential dependency of equivalent plastic strain at frac-ture εplf on triaxiality, as given by Eq. (1) in function of material con-stants α and β. Same fracture line was theoretically derived by Riceand Tracey [15] defining exponential dependency of the void growthrate on triaxiality.

εplf ¼ α⋅ exp −β⋅θð Þ ð1Þ

Divided by the same expression written for uniaxial strain state:εfpl = α ⋅ exp(−β ⋅ 1/3), the ratio of equivalent to uniaxial strain atfracture εplf =ε

plf is obtained in Eq. (2).

εplf =εplf ¼ exp −β⋅ θ−1=3ð Þ½ � ð2Þ

It is assumed that ratio of equivalent and uniaxial strain at fractureand at the onset of damage are the same: εplf =ε

plf ¼ εpl0 =ε

pl0 . Therefore

equivalent plastic strain at the onset of damage εpl0 is derived inEq. (3), in function of triaxiality, based on uniaxial plastic strain atthe onset of damage ε0pl.

εpl0 θð Þ ¼ εpl0 ⋅ exp −β⋅ θ−1=3ð Þ½ � ð3Þ

Material parameter β = 1.5 is adopted as proposed by Rice andTracey [15]. Finally with ε0pl = εnpl damage initiation criterionsaccording to Eq. (4) are shown in Fig. 10(b), based on values fromTable 2 for each steel material used.

εpl0 θð Þ ¼ εpln ⋅ exp −1:5⋅ θ−1=3ð Þ½ � ð4Þ

Once the damage initiation criterion is defined, plasticity curvesand damage evolution laws for use in ABAQUS material modelsare extracted from experimental results of standard tensile tests.The procedure developed here is based on engineering approachand is presented in recursive form, practical for use in spreadsheetcalculations and processing of raw tensile tests data. Followingcharacteristic points of nominal and true stress strain curves needto be identified for further manipulation: p — onset of plasticity;n — onset of necking (damage initiation); r — rapture point (criticaldamage); f — fracture point (total damage). Those points are shown inFigs. 9 and 10(a) and (c) for bolt material.

After onset of necking, longitudinal strains of test coupon start tolocalize in the necking zone [16], leaving other parts of coupon atthe same strain as they were at the onset of necking. To account forstrain localization, initial gauge length l0 (50 mm in this study), isfictively reduced to length lloc representing average necking zonelength, as illustrated in Fig. 10(a). Therefore, variable gauge length liis defined by Eq. (5) at every loading (elongation) stage “i” as functionof elongation Δli. Rate of gauge length reduction i.e. strain localizationis governed by power law through localization rate factor αL, given inTable 2.

li ¼l0; i b nl0 þ lloc−l0

� �Δli−Δlnð Þ= Δlr−Δlnð Þ½ �αL ; i≥ n

(ð5Þ

b) Damage initiation criterions. a) Plasticity curves and damage extraction procedure.

c) Damage evolution laws.

0

200

400

600

800

1000

1200

1400

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Tru

e st

ress

(M

Pa)

Localized true plastic strain (-)

Damage initiation,"necking" point(Dn=0)

undamaged response = plasticity curve

p

n

f

Total damage,"fracture" point(Df=1)

r

Criticaldamage,"rapture"point(Dr=Dcr)

l0lloc li

r'f'

accumulated plastic strain

Fi; Δli

Fi; Δli

0.00

0.10

0.20

0.30

-0.33 0.00 0.33 0.67 1.00 1.33 1.67 2.00

Equ

ival

ent

plas

tic

stra

inat

the

ons

et o

f da

mag

e (-

)

Stress triaxiality (-)

BoltHeaded studSteel section

unia

xial

te

nsio

n

0.0

0.2

0.4

0.6

0.8

1.00.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Dam

age

vari

able

(-)

Equivalent plastic displacement (mm)

Bolt

Headed stud

Steel section

r

f

n

Dcr

pl

n

pl

f

i

iiD

i

pl

n

Fig. 10. Plasticity and ductile damage parameters for steel materials.

140 M. Pavlović et al. / Journal of Constructional Steel Research 88 (2013) 134–149

Further, nominal strains εinom are obtained by Eq. (6), followingprevious assumption that increments of elongation after onset ofnecking are applied only to localized zone of test coupon.

εnomi ¼ Δli=li; i b n

εnomi−1 þ Δli−Δli−1ð Þ=li; i≥ n

(ð6Þ

Based on well-known relations, true strains εi = ln(1 + εinom)and true stresses σi = σi

nom(1 + εinom) localized in necking zoneare obtained. Those are shown in Fig. 10(a) with dashed lines as dam-aged material response (section p-n-r-f).

Undamaged material response is defined by Eq. (7) assuming per-fectly plastic behaviour after the onset of necking (point “n” inFig. 10(a)). Together with true plastic strains obtained in Eq. (8) itwas used as input data for plasticity curves in ABAQUS as shownwith solid lines in Fig. 10(a) (section p-n-r′-f′). Dashed extensions be-yond point “f′” were made to solve issues of discretising extremelyhigh strains in the necking zone by finite element method.

σ i ¼σ i; i b n

σnomn 1þ εnomi

� �; i≥ n

(ð7Þ

εpli ≅ εi−εp ð8Þ

Table 2Parameters for ductile damage calculation.

Damage Element type Element size Localization

Initiationstrain

Fact. Type Fact. Size(mm)

Fact. Length(mm)

Fact.

Material εnpl αD λE LE λS lloc αL

Boltgrade 8.8

0.078 1.7 C3D4 1.0 1.2 0.79 4.0 0.3

Headedstud

0.050 1.7 C3D4 1.0 1.2 0.79 6.0 0.5

FlangeS235

0.225 1.5 C3D8R 3.1 0.6 1 4.0 0.5

Damage variable is obtained as dimensionless difference betweenundamaged and damaged response of material as defined in Eq. (9). Itcan be noticed in Fig. 10(a) and (c) that at rapture point “r” materialundergoes critical value of damage Dcr immediately followed by frac-ture point “f”with total degradation of stiffness. This behaviour is alsonoticed by Lamaitre [16], defining value of critical damage as 1 −σr/σn in range of Dcr = 0.2–0.5 for most steels. Nevertheless thisis macro scale measure of damage variable, as average value acrossentire cross section at which fracture occurs. In the numerical anal-yses conducted here, significant nonuniform distribution of dam-age variable was noticed at the cross section at which fractureoccurs, affected by higher equivalent plastic strains in the core ofthe cross section. Some other authors, such as Bonora et al. [17]also observed that real values of critical damage for steel materialsare higher (0.55–0.65). For this purpose, damage eccentricity fac-tor αD was introduced in Eq. (9), with values ranging from 1.5 to1.7 for different steels used here, as given in Table 2. With thosevalues, good match of experimental and numerical rapture pointswere obtained, see Fig. 9.

Di ¼1−σ i=σ ið ÞαD;n≤ i≤ r

1; i ¼ f

�ð9Þ

Damage evolution laws were inputted in ABAQUS in tabular formas damage variable Di in function of equivalent plastic displacementupli . Values of u

pli corresponding to Di are defined by Eq. (10), as pro-

portional to evolution of plastic strains in necking zone.

upli ¼ upl

f εpli −εpln� �

= εplf −εpln� �

; i≥ n ð10Þ

Total equivalent plastic displacement at fractureuplf can be defined

by Eq. (11) as characteristic element length Lchar multiplied by plasticstrain accumulated during the necking (damage) process i.e. differ-ence between plastic displacement at fracture εfpl and at the onset ofnecking εnpl, see Fig. 10(a). Finite element size factor λS is introducedin Eq. (11) to take into account influence of actual mesh density,with element size LE, used in relation to refinedmesh density, with el-ement size LR, which could be considered as reference mesh. Different

141M. Pavlović et al. / Journal of Constructional Steel Research 88 (2013) 134–149

element sizes (mesh densities) were tried for each steel materialanalysed here in order to establish those factors. It has been foundthat element size factor follows the rule: λS ¼

ffiffiffiffiffiffiffiffiffiffiLR=L3

pE. Actual values

are presented in Table 2.

uplf ¼ λSLchar εplf −εpln

� �ð11Þ

Characteristic element length Lchar = λELE is defined as elementsize LE multiplied by element type factor λE which are presented inTable 2 for element type and size for each material as used later inpush-out models. Each steel material used here was analysed withtwo mesh types (C3D4 — tetrahedron and C3D8R — hexahedral) inorder to establish consistent value for element type factor λE. It hasbeen found that value of 1 is good match for tetrahedron C3D4 ele-ments, and that for hexahedral C3D8R elements it ranges from 2.5to 3.2 depending on ductility of material considered.

Parameters of shear damage were calibrated by comparing nu-merical results of the FEA models to experimental push-out testdata. Damage initiation criterion is function of shear stress ratio andequivalent plastic strain at onset of damage (strain rate is rolledout). It is assumed that in failure zones prevailing value of shear stressratio is 1.732. Therefore, shear damage initiation criterions were cali-brated to constant value of equivalent plastic strain at the onset ofdamage: εpls;bolt = 0.095 for bolts and εpls;stud = 0.200 for headedstuds. Such difference between two steel materials is addressed tofact that assumption of constant shear stress ratio is good approxima-tion for bolts with predominant shear failure mode, but rough ap-proximation for headed studs with larger influence of bending infailure zone. Displacement controlled shear damage evolution lawswere used with exponential softening and multiplicative degradation(interaction with ductile damage). Equivalent plastic displacementat failure for bolts upl

f ;s;bolt = 0.2 mm and uplf ;s;stud = 0.1 mm for

headed studs were set, while exponential law parameter of 0.7 wasused for both materials.

Material properties for reinforcement were set linear with E0 =210 GPa, and v = 0.3.

3.3.2. ConcreteConcrete damaged plasticity (CDP) model in ABAQUS was used to

describe concrete behaviour. CDP model consists of compressive andtensile behaviour, defined separately in terms of plasticity and dam-age parameters. Modulus of elasticity Ecm = 35.0 GPa was set asobtained from standard tests results. Mean compression cubestrength fcm = 40.0 MPa was determined through standard cubecompression tests. It was used to define the compressive stress σc

as function of uniaxial strain εc according to Eq. (12) from EC2 [18].

σ c ¼ f cmkη−η2

1þ k−2ð Þη ; η≤ εcu1=εc ð12Þ

where η = εc/εc1, and k = 1.05εc1Ecm/fcm are defined according toEC2. The strain at peak stress εc1 = 2.25∙10−3, and nominal ultimatestrain εcu1 = 3.5∙10−3 were adopted from EC2 for concrete with thesimilar mean compression strength. Unfortunately, plasticity curvein EC2 is defined only up to nominal ultimate strain εcu1. This is notan issue in case of standard reinforced concrete structures analyses,since compression strains in structural members are in generalbelow εcu1 at ultimate loads. Unlike, high crushing strains appear infront of shear connectors. Considering concrete compression behav-iour only up to strain εcu1 would lead to unreal overestimation ofconcrete crushing strength. For this reason, EC2 compression stress/strain curve was extended beyond nominal ultimate strain as shownin Fig. 11(a). Extension was made as defined by Eq. (13), with

sinusoidal part between points D–E and linear part between pointsE–F.

σc εcð Þ ¼ f cm1β− sin μαtD ⋅αtEπ=2

� �β⋅ sin αtEπ=2ð Þ þ μ

α

" #; εcuDb εc ≤ εcuE

f cuE εcuF−εcð Þ þ f cuF εc−εcuEð Þ½ �= εcuF−εcuEð Þ; εc > εcuE

8><>: ð13Þ

where μ = (εc − εcuD)/(εcuE − εcuD) is relative coordinate betweenpoints D–E and β = fcm/fcu1. Point D is defined as εcuD = εcu1 andfcuD = fcu1 = σc(εcu1) (Eq. (12)). Point E is the end of sinusoidal de-scending part at strain εcuE with concrete strength reduced to fcuE byfactor α = fcm/fcuE. Linear descending part (residual branch) ends inpoint F at strain εcuF with final residual strength of concrete fcuF. StrainεcuF = 0.10 was chosen large enough so as not to be achieved in theanalyses. Final residual strength of concrete fcuF = 0.4 MPa, reduc-tion factor α = 20 and strain εcuE = 0.03 were calibrated to matchexperimental push-out tests for bolts and headed studs. FactorsαtD = 0.5 and αtE = 1.0, governing tangents angles of sinusoidalpart at points D and E, were chosen so as to smooth overall shape ofstress/strain curve. Compression plasticity curve was defined depen-dent on inelastic strain starting from point B in Fig. 11(a) assumingthat the concrete acts elastically up to 0.4fcm according to EC2 [18].

Compression stress/strain curve according to Eq. (14) originatingfrom Chinese Code for Design of Concrete Structures, GB50010-2002[19], is also shown for comparison purposes in Fig. 11(a). It is theonly code found to define uniaxial concrete strength at high strains,among many design codes. This compressive stress/strain behaviourwas successfully used by Xu et al. [20] for FEA analysis of groupedheaded studs.

σc ¼f c αaηþ 3−2αað Þη2 þ αa−2ð Þη3h i

; η≤ 1

f cη= αd η−1ð Þ2 þ ηh i

; η> 1

8<: ð14Þ

Both ascending and descending parameters αa = 1.9 and αd =1.94 where obtained from [19] in terms of concrete strength fc =fcm = 40 MPa. Good match with the existing EC2 curve and proposedextension is evident.

Tension plasticity curve is defined as the function of crackingstrain and tensile stress. Tensile stress increases linearly along withmodulus of elasticity, up to the peak value fct. Characteristic tensilestrength was derived from EC2 relation: fct = 0.9fct,sp = 2.8 MPa,where fct,sp implies the splitting tensile strength. After this point,stress is degraded in sinusoidal manner and stress fct/20 is achievedat the cracking strain of εtu1 = 0.001.

Plasticity parameters: flow potential eccentricity ε = 0.1, andbiaxial/uniaxial compressive strength ratio σb0/σc0 = 1.16 were setas recommended by ABAQUS user manual [13]. Dilation angle ofψ = 36° was iteratively calibrated to match push-out tests results.The same value was used by Yang and Su [21], and it is close toJankowiak and Lodigowski [22] recommendation (ψ = 38°).

Damage evolution laws in ABAQUS were defined for concrete bothin compression and tension. They were derived from uniaxial stress/strain curves by comparing undamaged and damaged concrete re-sponses with the following expressions: Dc = 1 − fcm/σc and Dt =1 − fct/σt as functions of inelastic strain. Concrete compression dam-age curve is shown in Fig. 11(b).

3.4. Validation of numerical results

Numerical force–slip curves of complete and detail FEA models ofbolted shear connector with single embedded nut are compared withrepresentative experimental force–slip curve in Fig. 12(a). Data relatedto two extreme cases of lateral restraint stiffness ku3 (see Fig. 7(b)) inthe detail model are also shown. As for rigid lateral restraint ku3 = ∞detail FEA model showed higher shear resistance at smaller ultimate

Fig. 11. Parameters of concrete in compression.

142 M. Pavlović et al. / Journal of Constructional Steel Research 88 (2013) 134–149

slip when compared to a complete FEA model, whereas releasedlateral restraint ku3 = 0 resulted in lower shear resistance and largerultimate slip. With lateral restraint stiffness calibrated to value ku3 =20 kN/mm, detail FEAmodel showed good compatibilitywith completeFEA model and even better agreement with experimental data. Infurther comparative and parametric analyses, detail FEA models areused with the same lateral restraint stiffness for both bolts and headedstuds.

Detail models FEA force–slip curves for bolts and headed studs arecompared in Fig. 12(b) for loading up to failure with representativeexperimental curves. Numerical analyses performed on completeand detailed FEA models showed good agreement with experimentalresults. Results of numerical analysis will be used for further analysisof failure modes and behaviour of bolted shear connectors and head-ed studs.

4. Results and discussion

4.1. Shear connector stiffness and ductility

Representative experimental force–slip curves for bolted shearconnectors with single embedded nut and headed studs are shownin Fig. 13(a), together with deformed shapes at, or prior to, failure.Approximately the same shear resistance is achieved for bolts as the

a) Compatibility of complete and detail FEA models

0

100

200

300

400

500

600

700

800

0 1 2 3 4 5 6 7

Tot

al f

orce

(kN

)

Normalised slip (mm)

HS Bolts - Test (BT3)

Complete FEA model

Detail model - U3 fixed

Detail model - U3 free

Detail model - Ku3=20 kN/mmku3=20 kN/mm

ku3= 0

ku3= ∞

Fig. 12. Experimental and FEA force–slip

one for headed studs of the same diameter and height above flange,whereas the behaviour of those two shear connectors is different.Bolted shear connectors with single embedded nut showed lessstiffness at serviceability loads when compared to welded headedstuds. Lower initial tangential stiffness kinit (elastic behaviour), asshown in Fig. 13(b), is brought about by random distribution ofbolt-to-hole clearances within 8 bolts in one push-out specimen.Bolted shear connectors also showed earlier onset of nonlinearity asshown in Fig. 13(a), due to penetration of threads into the hole sur-face (see Fig. 4(b)) and reduced bearing capacity of the concrete infront of the embedded nut, explained in Section 4.2. This results in re-duced shear connector stiffness ksc of bolts when compared to weldedheaded studs at serviceability loads, as derived according to EC4 [8]and shown in Fig. 13(b). Full bearing in hole is achieved after the ini-tial closure of bolt-to-hole clearances and complete penetration ofthreads. This results in higher stiffness of bolted shear connectors atultimate loads (hardening part of force–slip curve) such that boltsachieve 95% of headed studs shear resistance.

Bolts with single embedded nut have reached ultimate load at slipof 4 mm which is lower when compared to headed studs. Accordingto EC4 [8], with characteristic ultimate slip lower than 6 mm, boltedshear connectors with single embedded nut would not be classifiedas ductile. This would exclude the possibility of their use in partialshear connection. The main reason for lower ductility is a shear at

b) Experimental vs. numerical force-slip curves for bolts and headed studs

0

100

200

300

400

500

600

700

800

0 1 2 3 4 5 6 7

Tot

al f

orce

(kN

)

Normalised slip (mm)

HS Bolts - Test (BT3)

HS Bolts - FEA

Headed studs - Test (STb)

Headed studs - FEA

curves for bolts and headed studs.

a) Shear resistance and deformed shapes of shear connectors. b) Shear connector stiffness.

0

20

40

60

80

100

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0

Slip (mm)

SLS:

slip

≈ 0

.5 m

m

UL

S: s

lip ≈

3.0

mm

ULS = 0.9Pult

SLS = 0.7Pult

Bolts

Headed studs

Fv,Rk,adj= 74.1 kN

PRk,adj=84.1 kNPb,ult Δb≈20%

Ps,ult

Δs≈10%

0

10

20

30

40

50

60

70

0.0 0.2 0.4 0.6 0.8 1.0

For

ce p

er s

hear

con

nect

or (

kN)

Slip (mm)

0.7Ps,ult 0.7Pb,ult

For

ce p

er s

hear

con

nect

or (

kN)

Fig. 13. Force–slip behaviour of bolted shear connectors with single embedded nut and headed studs.

zone 3

26.8 kN

para

lell

stre

sses

zone 3

para

lell

stre

sses

40 .7 kN

Fig. 14. Pry-out forces and parallel stresses for bolt and headed stud at 3.0 mm slip.

143M. Pavlović et al. / Journal of Constructional Steel Research 88 (2013) 134–149

the flange level; see details in Section 4.4 and Fig. 4(b). Hawkins [5]showed that ductility of bolted shear connectors without embeddednut is higher, whereas the stiffness and shear resistance of suchshear connector is remarkably reduced when compared to weldedheaded studs. Headed stud shear connectors can be treated as ductileonly for the limited range of stud diameters, height, distances andconcrete strengths, which is defined by EC4 [8] and confirmed byHegger et al. [23]. Similar, for bolts with single embedded nut, higherductility may be achieved by variation of these parameters as Nguyenand Kim [24] have shown for headed studs.

4.2. Bearing stresses in concrete

Earlier nonlinear behaviour is the most responsible one for re-duced stiffness of a bolted shear connector at serviceability loads.Most of it is addressed to reduced bearing capacity of concrete infront of embedded nut. Much higher bearing stresses than the con-crete strength fc, in zone of shear connector root, are needed to sus-tain ultimate shear forces, which is also concluded by Oehlers andBredford [25]. High bearing stresses can be developed by triaxialstress state producing confinement condition of concrete (Malecotet al. [26]). Local confinement condition in front of shear connectoris induced by pry-out force which produces stresses in concrete par-allel to shear connector shank. By comparing the distribution ofpry-out forces in bolts and headed studs, it will be shown here thatconfinement effects and bearing stresses are reduced in front of theembedded nut. This is illustrated in Fig. 14, together with plots ofstresses in concrete parallel to shear connector shank, on modelswith double scaled deformations. Slip of 3.0 mm was selected as itproduces approximately 90% of ultimate shear force (ULS) for bothshear connectors, see Fig. 13(a).

Pry-out force in the headed stud is the consequence of restrainedconcrete transverse expansion due to perpendicular local bearingstresses in front of a stud root and bending of stud. Concrete expan-sion is restrained between steel profile flange (zone 1 in Fig. 14)and a stud head (zone 3). This produces high compression stressesin concrete parallel to stud shank in zone 1, together with axial(pry-out) force in the stud shank. Triaxial compression stress stateis accomplished, and it results in a local confinement condition ofconcrete in a bearing zone 1 for the headed stud.

In case of bolts, main pry-out force is produced between the em-bedded nut and bolt head, as clearly displayed in distribution of

concrete parallel stresses in Fig. 14. Concrete above the nut (zone 2)is “pushed” due to nut inclination induced by reaction load in con-crete acting eccentrically on bolt. Concrete in front of the embeddednut (zone 1) is by the same principle “pulled” by a nut inclination.This reduces concrete compression stresses parallel to bolt shank inzone 1 produced by restrained transverse concrete expansion. Triaxi-al compression stress state (pressure) is reduced, affecting local con-finement effects and decrease of bearing stresses in front of theembedded nut. Axial force in both stud and bolt produced by inclina-tion of shear connector's root due to bending is small compared toaxial force produced by described phenomenon of restrained parallelstresses in concrete. This is proved by the fact that axial force in caseof bolt is higher than in stud, as shown in Fig. 14 even though thebending of bolt is lower.

Bearing stresses in concrete are shown in Fig. 15(a) and (b) forbolts and headed studs. Slip values of 0.5 mm and 3.0 mm are chosenso as to represent the serviceability and ultimate load level shown inFig. 13(a). Local confinement effects can be noticed as bearing

a) At slip of 0.5 mm – SLS b) At slip of 3.0 mm - ULS

-300

-250

-200

-150

-100

-50

00 10 20 30 40 50

Bea

ring

str

ess

in c

oncr

ete

(N

/mm

2 )

Bea

ring

str

ess

in c

oncr

ete

(N

/mm

2 )

Hight above flange - depth (mm)

Bolt

Headed Stud

zone 2shank

zone 1nut

-300

-250

-200

-150

-100

-50

00 10 20 30 40 50

Hight above flange - depth (mm)

Bolt

Headed Stud

A1

A2

A1≈A2

zone 2shank

zone 1nut

Fig. 15. Bearing stresses in concrete — S22 for bolts and headed studs at depth Z = 3 mm.

144 M. Pavlović et al. / Journal of Constructional Steel Research 88 (2013) 134–149

stresses are much higher than concrete compression capacity. CDPmodel capability to handle the confinement effects automatically isexplained by Yang and Su [21].

Bearing stresses for bolted shear connector in zone 1 (in front ofembedded nut) are limited by previously explained mechanism. At0.5 mm slip, bearing stresses in zone 1, shown in Fig. 15(a), are signif-icantly lower for bolt when compared to headed studs. Decrease of ashear force value for bolts at 0.5 mm slip, shown in Fig. 13(a), is rel-atively smaller when compared to a decrease of bearing stressesdue to larger effective width of the embedded nut when comparedto weld collar and shank in case of headed studs. Reduction of bearingstresses in front of the embedded nut is one of the reasons for earliernonlinear behaviour of bolted shear connectors. Other reason isthreads-to-hole penetration.

Higher local confinement effects of concrete in zone 2 in case ofbolts, produces higher bearing stresses compared to headed studs.At ultimate load level shown in Fig. 15 (b), areas of the shaded re-gions A1 and A2 are similar, which is the reason that approximatelythe same shear force is obtained for both shear connectors, seeFig. 13(a). Higher bearing stresses in zone 2 influence the large eccen-tricity acting on bolts. Increase in bearing stresses in zone 2 forbolts, is major contributor to the strength of the push out test, seeFig. 13(a).

4.3. Shear resistance of the connectors

Design resistance of bolted shear connectors is neither defined inEC4 [8], nor in other design codes [4, 27]. Characteristic shear resis-tance of high strength bolts in bolted connections of steel structures,according to EN1993-1-8 [28], adjusted to the measured bolt strengthfub = 787 MPa is given by Eq. (15). Since the shear plane is passingthrough the threaded portion of the bolt, tensile stress area of thebolt As = 157 mm2 is considered and αv = 0.6.

Fv;Rk;adj ¼ αvf ubAs ¼ 74:1kN ð15Þ

The characteristic shear resistance of headed studs according toEC4 [8], in terms of stud failure is specified by Eq. (16). It is also ad-justed to real material tensile strength used in tests fus = 523 MPa,see [9]. Gross cross sectional area A = 201 mm2 is used for headedstuds.

PRk;adj ¼ 0:8f usA ¼ 84:1kN ð16Þ

Those characteristic shear resistances are presented in Fig. 13(a)for comparison reasons. Eq. (16) provides good prediction of a realheaded studs shear resistance, as concluded in other researches [29]and [9], whereas shear resistance given by Eq. (15) is conservativefor bolted shear connectors with single embedded nut.

Resistance of the bolted shear connector obtained through testsand numerical analysis is 20% higher than pure shear resistance of abolt. Increase in load-bearing capacity, analysed here, comes fromfriction and contact forces acting on the embedded nut and concreteas well as the catenary effects in bolt. These effects are illustrated inFig. 16(a) on a deformed geometry at the ultimate load prior to fail-ure. Four internal force components have been defined: Fs — pureshear resistance of a bolt; Ft — catenary force; Fn — nut contact andfriction force; Fc — concrete friction force. Total shear resistance of abolted shear connector with the single embedded nut can be definedby Eq. (17)

Fult ¼ Fs þ Ft þ Fn þ Fc ð17Þ

Shear and axial forces in a bolt at ultimate load, obtained by inte-grating numerical results are shown in Fig. 16(b) together with vec-tors of tension principal stresses and contour plots of Von Missesstresses. Pure shear resistance of a bolt Fs is practically same as the ul-timate resistance given in EN1993-1-8 [28] (Eq. (15)) since plasticityand damage models were calibrated to match real bolt material. Boltaxial force Fx is generated by initial preloading and embedded nutpry-out effect already explained in Section 4.2. The initial boltpreloading is lost at the ultimate shear load as described by Wallaertand Fisher [30]. Prying force produced by the embedded nut inclina-tion at the interface layer reaches approximately 25% of a bolt tensileresistance. In case of bolted shear connectors with single embeddednut, axial force in bolt increases the ultimate shear resistance of theshear connector by catenary effects. Catenary effects arise from inter-nal force equilibrium defined on deformed geometry of the shear con-nector as shown in Fig. 16(a). Bolt axis and axial force Fx are inclinedat the interface layer under the angle α due to bending of a shear con-nector. Vertical projection of inclined axial force Ft = Fxsin(α) in-creases the bolt resistance to vertical shear. Required anchorage of abolt to a steel flange is provided by a thread penetrated into thehole surface as well as the presence of outer nut and washer. Shearresistance of a bolted shear connector with single embedded nut isincreased by 9% through catenary effects for bolt size and concretestrength studied here.

a) Improved shear resistance by contact and catenary effects.

b) Forces and principal stresses at failure.

Fs

Fult

Fn

Fc

Ft

α≈10°

Fx

Fx

Fig. 16. Load transfer mechanism for bolted shear connectors with single embedded nut.

145M. Pavlović et al. / Journal of Constructional Steel Research 88 (2013) 134–149

Due to described pry-out effects in Section 4.2, friction force atconcrete flange interface Fc is present as shown in Fig. 16(a). It is rel-atively small compared to other additional forces described here andshown in Fig. 17. Reasons lie in the reduction of contact stresses byembedded nut inclination (see zone 1 in Fig. 14) and reduction in fric-tion coefficient at interface layer by greasing the steel flange surfaceduring specimen preparation.

Inclination of the embedded nut results in high contact stresses atthe nut-flange interface, thus producing friction forces. Simple fric-tion at nut-flange interface is improved by the contact between thenut edge and the vault surface of flange (groove) produced by nut in-clination, as shown in Fig. 4(b), resulting in contact forces parallel toflange. Nut friction force Fn increases additionally at ultimate loads asthe nut grooves into the steel flange more deeper due to increasedbolt shank bending (see Fig. 17). Shear resistance of bolted shear con-nectors with single embedded nut is increased by 11% through theembedded nut friction force and groove contact for bolt size and con-crete strength studied here.

0

2

4

6

8

10

0.0 1.0 2.0 3.0 4.0 5.0

Slip (mm)

Fn - nut friction force

8.15 kN

Fc - concretefriction force

δ u =

4.2

6m

m

Fric

tion

forc

es p

er s

hear

con

nect

or (

kN)

Fig. 17. Friction forces acting on embedded nut and concrete.

4.4. Comparison of shear connector failure modes

Distribution of shear forces and bending moments in a bolt andstud prior to failure are shown in Fig. 18(a) and (b). Values of forcesand moments through shear connector's height are obtained throughintegrated cross section stresses in FEA models. Results for bolt areshown for bolt only and bolt and nut together in order to point outstrengthening role of the embedded nut. Portion of interface shearforce transferred directly by the embedded nut, already discussed inSection 4.3, can be seen as rise of 9% in shear force at the root crosssection.

In order to investigate failure modes of shear connectors studiedhere, failure criterion for interaction of axial force, bending momentand shear is established here for circular cross section. First, interac-tion of axial force and bending moment is obtained by plastic analysisof cross section capacity at ultimate load level, reaching full bearingcapacity of cross section for simultaneous action of axial force andbending moment. As shown in Fig. 19 outer parts of cross section,with area AM, are resisting bending moment while middle part witharea AN is carrying the axial force.

With ultimate stress fu reached in whole cross section, axial forceand bending moment capacities can be obtained in function of heighth, according to Eqs. (18) and (19).

M hð Þ ¼ 2zM hð ÞAM hð Þf u ð18Þ

N hð Þ ¼ AN hð Þf u ð19Þ

Varying height h from 0 to R, in previous expressions, correspond-ing limiting values of axial forces and bending moments are obtainedanalytically which is shown in Fig. 19 as normalized interaction curve.Simplified interaction curve is proposed in form of Eq. (20). Good fitto analytically obtained interaction curve is found with exponentsn = 2 and m = 1, which also matches interaction criterion for rect-angular solid section given in EN1993-1-1 [31].

N=NRuð Þn þ M=MRuð Þm ¼ 1 ð20Þ

Shear is introduced in given axial force and bending interactioncriteria with reduction of ultimate strength of material to value of

a) Bolt with single embedded nut.

b) Headed stud.

-1000

-500

0

500

1000

-100

-50

0

50

100

-10 0 10 20 30 40 50 60

Ben

ding

mom

ent

(kN

mm

)

Shea

r fo

rce

(kN

)

Hight above flange (mm)

Shear force - bolt

Shear force - bolt & nut

Bending moment - bolt

Bending moment - bolt & nut

failure of boltthrough threads

nut

ploted

-1000

-500

0

500

1000

-100

-50

0

50

100

-10 0 10 20 30 40 50 60

Ben

ding

mom

ent

(kN

mm

)

Shea

r fo

rce

(kN

)

Hight above flange (mm)

Shear force

Bending moment

failure of stud shank

weldcollar

ploted

Fig. 18. Distribution of shear forces and bending moments prior to failure.

146 M. Pavlović et al. / Journal of Constructional Steel Research 88 (2013) 134–149

(1 − ρ)fu, as defined in EN1993-1-1 [31], section 6.2.10. This leads toEq. (21) as illustrated in Fig. 19.

N=NRuð Þn þ M=MRuð Þm ¼ 1−ρð Þ ð21Þ

Reduction factor ρ = (2 V/VRu − 1)2, is valid for V ≥ 0.5VRu, asdefined by EN1993-1-1 [31]. Finally with n, m and ρ introduced as

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0

M/M

Ru

N/NRu

(N/NRu)n + (M/MRu)m = 1

(N/NRu)n + (M/MRu)m = 1-ρ

analitycal

ρ = (2V/VRu-1)2

Fig. 19. Multiple interaction criteria for circular cross section.

previously defined, multiple interaction criteria for axial force, bend-ing and shear for circular solid section is obtained in Eq. (22).

N=NRuð Þ2 þ M=MRuð Þ þ 2 V=VRu−1ð Þ2≤1; for V≥ 0:5VRu ð22Þ

The assessments of failure modes, based on FEA results and multi-ple interaction criteria established here, are given in Table 3 for boththe bolt and headed stud. The cross section of a bolt and stud at whichthe failure occurred are considered in order to investigate the partic-ipation of axial force, bending and shear in failure modes of shearconnectors. In addition, the cross section of a bolt above the embed-ded nut has been considered so as to investigate some possiblecombined shear/bending failure of a bolted shear connector with sin-gle embedded nut. Ultimate resistances are calculated with respect toreal material strengths fu,adj equal to true ultimate stresses σn shownon Fig. 10(a) taking into account influence of large stains occurring atultimate load level.

The failure of headed studs for static loads occurs due to combinedbending (56%) and shear (37%) at a shank above the weld collar. Atthe mentioned cross section, shear force in a stud shank is reducedwhen compared to ultimate shear force, since its portion is directlytransferred through the weld collar. This is the main reason for theimproved characteristic shear resistance of headed stud according toEC4 [8], or other design codes, when compared to theoretic pure shearfailure criterion of a stud shank which is presented in Eq. (23).

PRk;s ¼ 0:8f usA > f usA=ffiffiffi3

p¼ Fv;s ð23Þ

Table 3Failure criterions for bolts and headed studs.

Shear connector Hightaboveflange

Cross section properties(N; mm)

Ultimate resistances(kN; mm)

Ultimate forces — FEA(kN; mm)

Multiple interaction failure criterion

Strength Diameter Area SectionModulus

Axial Bending Shear Axial Bending Shear Axial Bending Shear Σ

(mm) fu,adj d A; As Wpl NRu MRu VRu N M V (N/NRu)2 (M/MRu) (2 V/VRu − 1)2 ≈1.0

Bolt at interface layer 0.0 852 14.1a 157 471 133.8 401.3 80.3 36.0 96.7 73.1 0.073 0.241 0.675 0.988Bolt above embedded nut 13.5 852 14.1a 157.0 471.0 133.8 401.3 80.3 34.6 181.9 51.0 0.067 0.453 0.073 0.594Stud above collar 6.5 556 16.0 201 682 111.8 379.6 67.1 26.1 212.0 54.0 0.055 0.559 0.372 0.985

a For threaded part of bolt: d = dnom − 0.938P = 14.12 mm.

147M. Pavlović et al. / Journal of Constructional Steel Research 88 (2013) 134–149

Shear at the interface layer is the dominant failure mode for thebolted shear connector with single embedded nut, with 67% partici-pation of a shear in multiple interaction failure criterion. Characteris-tic shearing shape of a failure area is shown in Fig. 4(b). Cross sectionat the shank above the nut is not critical, apart from an increasedbending, since the overall failure interaction criterion is low. Reasonfor this is the reduced shear force, meaning that one part of it is trans-ferred directly through the embedded nut.

The main consequence of a pure shear failure mode at a steel con-crete interface is the low ductility of bolted shear connectors with sin-gle embedded nut, mentioned before in Section 4.1. Also, this is thereason why they have either lower or the same shear resistance ascomparable headed studs even though their mechanical propertiesare nearly 50% higher.

5. Parametric study

Parametric study on shear connector height was conducted on de-tail FEA models for bolts with single embedded nut since it notably af-fects the unit price of bolted shear connectors. Verification parametricFEA study was conducted for headed studs as well, since it was com-parable to reduction factor α given in section 6.6.3.1 of EC4 [8].

To provide compatibility of the parametric study shown here tofurther parametric studies, nominal material properties for bothbolts and concrete were adopted. Nominal uniaxial stress–straincurve of parabolic shape was defined for high strength bolts grade8.8 with elongation after break A = 12%, fy = 640 MPa and fu =800 MPa as the minimum required by ISO 898-1 [32]. For concrete,material model parameters were set for class C35/45 according to

a) hsc=40 mm (hcs/d=2.50). b) hsc=60 mm

Fig. 20. Concrete compression damage at u

EC2 [18] with: fcm = 43 MPa, fctm = 3.2 MPa, Ecm = 34 Gpa, εc1 =2.25∙10−3 and εcu1 = 3.5∙10−3. Other parameters and principles ofconcrete material model definition were adopted as described inSection 3.3.2.

Deformed shapes and concrete damage plots for different boltedshear connector's height are shown in Fig. 20. As for 40 mm boltheight (hsc/d = 2.5), failure is governed by concrete cone pull-out,and not by bolts shear at the interface layer. Hawkins [5] foundsimilar behaviour for anchor bolts without embedded nut forheight-to-diameter ratio lower than 4. Force–slip curves for shearconnector's height ranging from 40 mm to 100 mm for bolts and48 mm to 100 mm for headed studs, are shown in Fig. 21.

Results concerning shear connector's height FEA parametric studyon bolts and headed studs are summarized in Table 4 and in Fig. 22.Shear connector resistance reduction factor αFEA was determinedwith regard to shear resistance of the highest connector examined.Values of this reduction factor for headed studs (Eq. (24)), as part ofconcrete failure criterion given by EC4 [8], were used for verificationof whole parametric analyses procedure. Good agreement wasachieved as shown in Table 4 and Fig. 22(b), which leads to conclu-sion that results relating to bolted shear connectors with single em-bedded nut can be trusted.

αs;EC4 ¼ 0:2 hsc=dþ 1ð Þ for 3≤ hsc=d b 4 ð24Þ

Bolted shear connectors with single embedded nut showed betterperformance compared to headed studs when it comes to reductionregarding height to diameter ratio. Based on results shown here,shear resistance reduction factor for bolted shear connectors with

(hcs/d=3.75). c) hsc=100 mm (hcs/d=6.25).

ltimate loads for different bolt heights.

Table 4Results of parametric study on shear connector's height.

Shearconn.

Height(mm)

Ratio(–)

Force(kN)

Slip(mm)

Failuremode

Reduction ofresistance (%)

Ratio (–)

hsc hsc/d Fult δu αFEA αb,prop;αs,EC4

αb,prop/αFEA;αs,EC4/αFEA

BoltsM16…8.8

40 2.50 71.4 6.5a Concrete 83.7 82.5 0.9950 3.13 81.5 5.8 Bolt 95.6 91.9 0.9660 3.75 84.4 5.1 Bolt 99.0 100 1.0164 4.00 84.9 5.0 Bolt 99.6 100 1.0080 5.00 85.2 4.9 Bolt 100.0 100 1.00100 6.25 85.2 4.8 Bolt 100.0 100 1.00

Studsd = 16 mm

48 3.00 74.9 8.0a Concrete 81.9 80.0 0.9864 4.00 88.9 6.7 Stud 97.1 100 1.03100 6.25 91.6 6.59 Stud 100.0 100 1.00

a Estimated values.

a) HS Bolts M16. b) Headed studs d=16mm.

40

50

60

70

80

90

0.0 1.0 2.0 3.0 4.0 5.0 6.0

For

ce p

er s

hear

con

nect

or (

kN)

Slip (mm)

h=40mm; h/d=2.50

h=50mm; h/d=3.12

h=60mm; h/d=3.75

h=64mm; h/d=4.00

h=80mm; h/d=5.00

h=10mm; h/d=6.2540

50

60

70

80

90

100

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0

For

ce p

er s

hear

con

nect

or (

kN)

Slip (mm)

h=48mm; h/d=3.00

h=64mm; h/d=4.00

h=100mm; h/d=6.25

Fig. 21. FEA force–slip curves for different shear connector's height.

148 M. Pavlović et al. / Journal of Constructional Steel Research 88 (2013) 134–149

single embedded nut αb,prop, similar to one given by EC4 [8] for head-ed studs is proposed in Eq. (25). Values and given and compared tonumerical results in Table 4 and Fig. 22(b).

αb;prop ¼ 0:15 hsc=dþ 3ð Þ≤ 1:0 ð25Þ

The ultimate slip at failure, which is important for the assessmentof shear connector ductility, is shown in Fig. 22(c) as function ofheight to diameter ratio, both for bolts and headed studs. It shows,

a) Shear connector resistance. b) Shear resistance redu

70

75

80

85

90

95

2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5

Shea

r c

onne

ctor

res

ista

nce

(kN

)

Hight to diameter ratio

HS BoltsM16...8.8

Headedstudsd=16mm

80

82

84

86

88

90

92

94

96

98

100

2.0 3.0 4.0

Red

ucti

on o

f sh

ear

resi

stan

ce (

%)

Hight to d

Fig. 22. Results of FEA parametric stu

as supposed earlier in Section 4.1, that limiting parameters of boltheight, diameter, distance and concrete strength may be found so asto achieve the ductile behaviour with the slip at failure which is great-er than 6 mm as stipulated by EC4 [8].

6. Conclusions

Standard push-out tests for M16, grade 8.8 bolted shear connec-tors with single embedded nut in the concrete slab, were performed

ction factors. c) Ultimate slip.

5.0 6.0 7.0iameter ratio

HS Bolts (FEA)

HS Bolts (proposed)

Headed studs (FEA)

Headed studs (EC4)

4.0

4.5

5.0

5.5

6.0

6.5

7.0

7.5

8.0

8.5

9.0

2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5

Slip

(m

m)

Hight to diameter ratio

HS BoltsM16...8.8

Headed studsd=16mm

dy on shear connector's height.

149M. Pavlović et al. / Journal of Constructional Steel Research 88 (2013) 134–149

and results are compared to adequate tests previously performed bySpremić et al. [9] for headed studs. Advanced FEA models for thepush-out test for both shear connectors were made and results arecompared to experimental results. Parametric FEA study on shearconnector's height was performed to investigate its influence andprovide justification of the FE model used. Following conclusionshave been drawn:

1.) Bolted shear connectors with single embedded nut (grade 8.8)achieve approximately 95% of shear resistance for static loads oftraditional arc welded headed studs shear connectors.

2.) Stiffness of single shear connector at serviceability loads ksc is re-duced to 50% for bolts when compared to headed studs, due to theslip in hole, threads-to-hole penetration and larger contributionof the shear force to the failure.

3.) Bolted shear connectors M16 with single embedded nut in fulldepth concrete slab, class C35/45, has showed brittle behaviour.

4.) Multiple axial/bending/shear failure criterion is established forbolted and headed studs shear connectors in Eq. (22). For staticloads, dominant failure mode of bolted shear connectors with sin-gle embedded nut is shear at the interface layer through threadedpart of a bolt with 67% participation of shear in multiple failurecriterion. Failure mode of headed studs for static loads isgoverned by interaction of 56% bending and 37% shear in shankzone above the welded collar.

5.) Shear resistance of bolts according to EN1993-1-8 given byEq. (15) turns out to be conservative in this particular case sinceshear resistance of bolted shear connectors with single embeddednut is increased up to 20% due to embedded nut-flange frictionand contact interaction and catenary effects in bolt.

6.) Bolted shear connectors with single embedded nut in the con-crete slab has showed a bit lower sensibility to reduction ofshear connector's height compared to welded headed studs.Shear resistance reduction factor is proposed by Eq. (25) similarto the one provided for welded headed studs by EC4 [8].

7.) At the lower bound of shear connector height to diameter ratio(hsc/d = 2.5) slip at failure is increased above 6 mm due to con-crete cone failure, leading to a ductile behaviour of a boltedshear connector.

The following conclusions are drawn for advanced FEA modelsbased on ABAQUS/Explicit code used here:

1.) Four node tetrahedron finite elements (C3D4) were successfullyused in quasi-static analyses of push-out tests.

2.) Continuous damagemodels for steel components may be calibrat-ed based on standard tensile tests and successfully used in FEanalyses of the push-out. Based on experimental and theoreticfindings of few authors, Eq. (4) was found appropriate for damageinitiation criterion. Engineering approach for determination of thedamage evolution law is presented in Section 3.3.1.

3.) Concrete damage plasticity (CDP) model was successfullyimplemented in FEA of push-out tests. Eq. (13) is proposed as an ex-tension of the existing EC2 [18] concrete compression stress/strainbehaviour.

4.) Variable non-uniform mass scaling method, used to reduce calcu-lation time in quasi-static FE analyses, showed much better per-formance compared to widely used time scaling method.

A major challenge for a wider use of bolted shear connectors withsingle embedded nut in prefabricated composite structures is the lackof design rules. Further investigation of the ductility and influence ofinitial slip in hole to the overall behaviour of prefabricated compositebeamwould be necessary for promotion of the prefabricated concretedecks in composite construction.

Acknowledgements

The writers would like to acknowledge the contribution of MilanSpremić for sharing data and experience in the previous phase of re-search. The writers are grateful for the support provided by “NB steel”Ltd. and “GEMAX” Concrete Production Ltd. from Belgrade.

References

[1] Hällmark R. Prefabricated Composite Bridges — a Study of Dry Deck Joints. LuleåUniversity of Technology; 2012228.

[2] Car Parks in Steel. Luxemburg: ArcelorMittal Corporation; 2008.[3] Dallam LN. High Strength Bolts Shear Connectors — Pushout Tests. ACI J Proc

1968(No. 9):767–9.[4] BS 5400-5: Steel, concrete and composite bridges. Part 5: Code of practice for design

of composite bridges. London, UK: British Standard Institution; 1979.[5] Hawkins N. Strength in shear and tension of cast-in-place anchor bolts. Anchorage

Concr 1987;SP-103:233–55.[6] Dedic DJ, Klaiber WF. High-Strength Bolts as Shear Connectors in Rehabilitation

Work. Concr Int 1984;6(7):41–6.[7] Kwon G, Engelhardt MD, Klingner RE. Behavior of post-installed shear connectors

under static and fatigue loading. J Constr Steel Res 2010;66(4):532–41.[8] EN1994-1-1: Eurocode 4 — Design of composite steel and concrete structures. Part

1-1: General rules and rules for buildings. Brussels, Belgium: European Committeefor Standardization (CEN); 2004.

[9] Spremić M, Marković Z, Veljković M, Budjevac D. Push–out experiments of headedshear studs in group arrangements. Adv Steel Constr 2013;9(2):170–91.

[10] EN1990: Eurocode — Basis of structural design. Brussels, Belgium: EuropeanCommittee for Standardization (CEN); 2002.

[11] ECCS Publication No38 — European Recommendations for Bolted Connections instructural steelwork. Brussels, Belgium: ECCS; 198563.

[12] An L, Cederwall K. Push-out tests on studs in high strength and normal strengthconcrete. J Constr Steel Res 1996;36(1):15–29.

[13] ABAQUS User Manual. Version 6.9. Providence, RI, USA: DS SIMULIA Corp; 2009.[14] Trattnig G, Antretter T, Pippan R. Fracture of austenitic steel subject to a wide

range of stress triaxiality ratios and crack deformation modes. Eng Fract Mech2008;75(2):223–35.

[15] Rice JR, Tracey DM. On the Ductile Enlargement of Voids in Triaxial Stress Fields.J Mech Phys Solids 1969;17:201–17.

[16] Lemaitre J. A Continuous Damage Mechanics Model for Ductile Fracture. J EngMater Technol 1985;107(1):83–90.

[17] Bonora N, Ruggiero A, Esposito L, Gentile D. CDM modeling of ductile failure inferritic steels: assessment of the geometry transferability of model parameters.Int J Plast November 2006;22(11):2015–47.

[18] EN1992-1-1: Eurocode 2 — Design of concrete structures. Part 1-1: General rulesand rules for buildings. Brussels, Belgium: European Committee for Standardization(CEN); 2004.

[19] GB50010-2002: Code for Design of Concrete Structures. Ministry of housing andurban–rural development of China; 2002.

[20] Xu C, Sugiura K, Wu C, Su Q. Parametrical static analysis on group studs withtypical push-out tests. J Constr Steel Res 2012;72:84–96.

[21] Yang G-T, Su Q-T. Discussion on “Numerical simulation of concrete encased steel com-posite columns” by Ehab Ellobody and Ben Young [J Constr Steel Res 2011;67(2):211–222]. J Constr Steel Res 2012;71:263–4.

[22] Jankowiak T, Lodigowski T. Identification of parameters of concrete damageplasticity constitutive model. Found Civil Environ Eng 2005;6:53–69.

[23] Hegger J, Sedlacek G, Döinghaus P, Trumpf H. Studies on the Ductility of ShearConnectors When Using High-Strength Steel and High-Strength Concrete. In:Eligehausen R, editor. International Symposium on Connections between Steeland Concrete. Stuttgart, Germany: RILEM Publications Sarl; 2001. p. 1025–46.

[24] Nguyen HT, Kim SE. Finite element modelling of push-out tests for large studshear connectors. J Constr Steel Res 2009;65(10–11):1909–20.

[25] Oehlers D, Bradford M. Elementary behaviour of composite steel and concretestructural members. Butterworth-Heinemann; 1999.

[26] Malecot Y, Daudeville L, Dupray F, Poinard C, Buzaud E. Strength and damageof concrete under high triaxial loading. Eur J Environ Civil Eng 2010;14(6–7):777–803.

[27] ANSI/AISC 360-05: Specification for structural steel buildings. Chicago, IL, USA:American Institute for Steel Construction (AISC); 2005.

[28] EN1993-1-8: Eurocode 3: Design of steel structures. Part 1-8: Design of joints.Brussels, Belgium: European Committee for Standardization (CEN); 2005.

[29] Shim C-S, Lee P-G, Yoon T-Y. Static behavior of large stud shear connectors. EngStruct 2004;26(12):1853–60.

[30] Wallaert JJ, Fisher JW. Shear Strength of High-Strength Bolts. J Struct Div ASCE1965;91(St3).

[31] EN1993-1-1: Eurocode 3 — Design of steel structures. Part 1-1: General rules andrules for buildings. Brussels, Belgium: European Committee for Standardization(CEN); 2005.

[32] ISO 898-1: Mechanical properties of fasteners made of carbon steel and alloysteel. Part 1: Bolts, screws and studs. Fourth ed. Brussels, Belgium: EuropeanCommittee for Standardization (CEN); 2009.