Engineering Structures 77 (2014) 65–83

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Engineering Structures

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Finite element analysis of new composite floors having cold-formed steeland concrete slab

http://dx.doi.org/10.1016/j.engstruct.2014.07.0300141-0296/� 2014 Elsevier Ltd. All rights reserved.

⇑ Corresponding author. Tel.: +1 (212) 896 3000.E-mail addresses: ym34@njit.edu (Y. Majdi), hsuc@adm.njit.edu (C.-T.T. Hsu),

mz42@njit.edu (M. Zarei).

Yazdan Majdi a,⇑, Cheng-Tzu Thomas Hsu b, Mehdi Zarei b

a Arup, 77 Water Street, New York, NY 10005, United Statesb Department of Civil and Environmental Engineering, New Jersey Institute of Technology, University Heights, Newark, NJ 07102, United States

a r t i c l e i n f o a b s t r a c t

Article history:Received 17 November 2013Revised 22 July 2014Accepted 23 July 2014Available online 15 August 2014

Keywords:Composite floor systemCold-formed steelLight-gauge steelConcrete slabContinuous shear connectorFinite element modeling

In this research, the structural behavior of a new type of composite floor system is explored through finiteelement modeling. The new composite floor incorporates cold-formed (light-gauge) steel profiles as thejoist on bottom, a corrugated steel deck as the formwork for concrete, a continuous hat channel (furringchannel) as the shear connector and finally a concrete slab on top. All steel parts in the system are cold-formed and connected together by self-drilling fasteners.

In the present study, a comprehensive three-dimensional finite element modeling is performed for thiscomposite floor system. A local bond-slip model is applied to simulate the slip of the shear connectorinside the concrete slab. A nonlinear analysis is performed on the composite floor considering all differenttypes of structural nonlinearities and the behavior of the system is monitored from beginning of loadingall the way to a defined point of failure. Results of finite element analyses are compared with experimen-tal data.

Further, parametric studies are conducted to determine the effect of shear connector’s slip on reducingultimate strength and initial stiffness of such a floor system.

� 2014 Elsevier Ltd. All rights reserved.

1. Introduction

The basic idea in composite construction is to use the advanta-ges of both steel and concrete materials while avoiding their inher-ent disadvantages. In order for this idea to work, steel and concreteparts should be fully connected so that no delamination and/or slipcan occur between the two parts. This research focuses on numer-ically studying a new type of composite floor system with cold-formed steel having an innovative type of shear connector. Thefloor system is illustrated in Fig. 1.

In this composite floor system [1,2], a continuous furringchannel has been used instead of shear studs, as the shear con-nector (Fig. 2). The structural system consists of: steel joistscomprising two back-to-back C-sections, a corrugated steel deck(which acts as formwork for the concrete slab), furring channelas the shear connector and a cast-in-place concrete slab withtransverse reinforcement. Self-drilling fasteners are used for con-necting all the steel parts. The furring channel is expected totransfer shear flow from the steel joist to the slab through its

bond-slip behavior with concrete [31]. Thus, the bond-slip mech-anism is the key parameter in studying the effectiveness of thefurring channel.

In numerical simulation of structures having steel embedded inconcrete, it is customary to assume that there is a perfect connec-tivity between the two materials (i.e., no slip condition). Such anassumption is accepted to be appropriate where the shear transferis provided by shear studs or other similar interlocking mecha-nisms [3]. However, in the composite system discussed above,the shear transfer relies on the bond-slip behavior of the smoothsteel surface with concrete which is a new idea never used before.Thus, it is important to investigate the performance of such sheartransfer mechanism.

This research uses computer modeling (simulation) to study thestructural behavior of such a composite floor system up to adefined point of failure. Finite element method has been used forstructural modeling and analysis. Results of the analyses are com-pared with experimental data for the purpose of verification.Further, capability of the newly introduced continuous shearconnector in maintaining composite action between steel joistand concrete slab has been studied and the effect of shear connec-tor’s slip on behavior of the system has been numericallyevaluated.

Fig. 1. The cold-formed composite floor system, subject of the current research.

Fig. 2. Proposed continuous furring channel as the shear transfer member [1].

66 Y. Majdi et al. / Engineering Structures 77 (2014) 65–83

2. Literature review

A composite floor system conventionally consists of a rein-forced concrete slab that is supported on a set of steel joists. Steeland concrete parts should be fully connected such that shear flowcan be transferred between them. The composite integrity is pro-vided by shear connectors. Types of shear connectors include:studs, channels, stiffened angles and flat bars as illustrated inFig. 3. The most-often used connectors are shear studs [4].

Cold-formed steel sections are made by directly shaping thinsteel sheets, strips, plates or flat bars with no heating involved.The thickness of these sections usually ranges from 0.014900 to0.2500 [4]. Cold-formed steel sections generally have the advantageof being lighter, cheaper and environmentally greener, while equalin stiffness and strength compared to regular hot-rolled sections. Itshould be noted that cold-formed steel shows a gradual yielding instress–strain curve as compared to hot-rolled steel with sharpyielding.

Due to the mentioned advantages, use of cold-formed steelbeams as joists in composite floor systems instead of their hot-rolled counterparts has come into interest in recent years. How-ever, as the cold-formed steel sections are light gauge (small inthickness), it is impractical to weld shear studs to them as it wastraditionally done to hot-rolled joists [5]. This especially raisesthe problem of shear transfer between steel joists and the concreteslab. Various types of shear connectors suggested up to this dateare shown to be costly and there is little information in open tech-nical literature about the performance and capacities of them [6,5].

2.1. Past experimental studies

Maximiliano et al. [7] were the first researchers who studiedcomposite beams consisting of cold-formed double channel shapeconnected to a concrete slab by shear connectors made of cold-formed steel. Push-out tests were performed to find the load-slipbehavior of them. According to the results from composite beamtests, ultimate moments were in average 30% higher than the val-ues obtained from elastic section analysis and 9% lower than thevalues obtained from plastic section analysis.

Hanaor [5] conducted tests on composite beams with cold-formed double channels and tried different types of connectingtechnologies between the steel beam and concrete slab which con-sisted of cold-formed channel sections in both screwed and weldedconditions, powder actuated nails, expansion anchors, throughbolts and concrete screws. These connecting technologies were pri-marily studied in push-out tests and then were used in testing ofcomposite beams with cold-formed double channels. The resultsshowed that the response of such composite beams, if designedand executed properly, is highly ductile. The researcher also con-cluded that the capacity of cold-formed shear connectors can beconservatively determined according to cold-formed section designcodes. Fig. 4 shows the shear connectors developed by Hanaor.

Lakkavalli and Liu [6] conducted experiments on compositebeams with cold-formed double channel joists through manylarge-scale tests. In their configuration, joist flanges were cast intothe concrete slab. Four types of shear transfer mechanisms weretried in their work: (1) natural surface bond between steel andconcrete, (2) shear transfer enhancements in forms of pre-fabri-cated bent-up tabs, (3) pre-drilled holes and (4) self-drillingscrews. Test results by these researchers indicated that specimensemployed with shear transfer enhancements showed a markedincrease in strength and reduced deflection as compared withthose relying only on a natural bond between steel and concreteto resist shear. Among the shear-transfer enhancements investi-gated (Fig. 5), bent-up tabs provided the best performance at boththe strength and serviceability limit states, followed by drilledholes in the embedded flanges. The use of self-drilling screwsresulted in the lowest strength.

Punurai [8] conducted a series of bending tests on the compos-ite beam configuration discussed in this research and obtainedexperimental load–displacement graphs for them.

2.2. Past finite element work

Barbosa and Ribeiro [9] investigated modeling of simply-supported reinforced concrete beams using ANSYS concrete

Fig. 3. Different types of shear connectors for composite beams [4].

Fig. 4. Hanaor’s shear connectors [5].

Y. Majdi et al. / Engineering Structures 77 (2014) 65–83 67

elements. They tried different types of plasticity models combinedwith concrete cracking/crushing features. Their results suggest thatusing Von Mises plasticity and isotropic work hardening ruletogether with no crushing feature in concrete elements can leadto a much better solution convergence and longer load–deforma-tion path in finite element modeling of structures involvingconcrete in ANSYS.

Salari et al. [10] used the basic governing equations with theforce method to develop a new composite beam element for thepurpose of modeling composite beams with deformable shear con-nectors under small displacement.

Sebastian and McConnel [11] developed a Finite Elements (FE)program for the analysis of general composite structures withthe ability to model ribbed composite slabs on profiled steel sheet-ing. They used a specialized stub element with empirical nonlinearshear force-slip relationships at the concrete–steel beam interfaceto permit the modeling of either full or partial shear connectoraction.

Ayoub and Filippou [12] presented an inelastic beam elementfor the analysis of steel–concrete girders with partial compositeaction under monotonic and cyclic loads. Their element wasderived from a two-field mixed formulation with independentapproximation of internal forces and transverse displacements.

Using the displacement formulation and the finite elementstechnique, Dall’Asta and Zona [13] performed non-linear analysisof composite steel–concrete beams and illustrated some aspectsrelated to the convergence issues by comparing solutionsderiving from finite elements with 8, 10 and 16 degrees offreedom.

Amadio and Fragiacomo [14] focused on the effective widthevaluation for analysis of steel–concrete composite beams. Usinga parametric study carried out through the ABAQUS code, theresearchers analyzed the most important parameters that influ-ence the effective width and presented some preliminary criteriafor an adequate design.

Baskar et al. [15] used ABAQUS software for nonlinear finite ele-ment analysis on steel–concrete plate girders subjected to negativebending. The researchers used thin shell elements for the girderand solid elements for the concrete slab while shear studs wereused as shear connectors. In order to model the shear connectionbetween steel and concrete, two attempts were made: In the firstattempt, bond strength at the interface of steel and concrete andthe shear strength of studs were combined and modeled as a hor-izontal shear friction between the two materials using ABAQUSsurface interaction technique. According to the researchers, thismethod had resulted in larger deflections in comparison to theexperimental data and also had resulted in severe discontinuitiesbetween the steel and concrete surfaces. In a second attempt, theresearchers used beam elements to model the studs into the

Fig. 5. Shear transfer mechanisms used by Lakkavalli and Liu [6].

68 Y. Majdi et al. / Engineering Structures 77 (2014) 65–83

concrete slab. The results from the second attempt were closer tothe experimental values and the model behaved more consistently.

Faella et al. [16] used a finite element procedure to study theeffect of nonlinearity of the shear connection in composite beams.The results showed that a significant increase in deformation ofsteel–concrete composite beams occurs due to the nonlinearityof shear connection.

Fragiacomo et al. [17] developed of a numerical procedure forstudying steel–concrete composite beams with regard to boththe collapse analysis and long-term behavior at the serviceabilitylimit state. The researchers specially considered rheological phe-nomena of concrete (creep and shrinkage). Later, in a related work,Macorini et al. [18] presented a finite element model suitable forlong-term analysis of steel–concrete composite beams. Theresearchers used one-dimensional beam elements for the steelprofile and two-dimensional shell elements for the concrete slabwhere the two types of elements were interconnected by meansof link elements to account for deformability of the connection.

Cas et al. [19] presented a new finite element formulation fornon-linear analysis of two-layer composite beams and columnswith an interlayer slip. They introduced a layered frame elementwhich could account for geometrical and material nonlinearitiesand also time-dependent shrinkage and creep in concrete. How-ever the element could only take small amount of slip betweenthe layers.

Chung and Sotelino [20] studied different finite element model-ing techniques for composite beams consisting of a steel girder anda steel deck. In order to evaluate the accuracy of each technique,results from each model were compared to the experimental datafrom full-scale laboratory and field tests. Fig. 6 shows all of thosemodeling techniques. Having assumed a full composite action,rigid link elements were used to connect the two steel parts inall models. The researchers concluded that if shell elements areused for modeling of the girder, a high level of mesh refinementis required to achieve convergence due to the displacement incom-patibility between the drilling Degree of Freedom (DOF) of the webelement and the rotational DOF of the flange element. They alsoconcluded that the economical eccentric beam model (model no.4 in Fig. 6) is accurate enough for prediction of flexural behaviorof the composite beam.

Barth and Wu [21] conducted nonlinear finite element analysesto study the behavior of concrete slab on steel stringers. They usedABAQUS software and the results of simulation were verified by

comparison with experimental data. Having assumed a full com-posite action between the steel girder and concrete slab, multi-point contacts were used between the nodes of two materials tomodel the shear transfer mechanism.

Queiroz et al. [22] conducted finite element modeling of compos-ite beams with shear studs using ANSYS software. The researchersperformed modeling for both flexible and rigid shear connectionsbetween steel and concrete using links and springs as shown inFig. 7 (bond link elements). The reliability of their models was dem-onstrated by comparisons with experimental data. They concludedthat their simulation was able to successfully predict load–deflection response of composite beams subjected to concentratedor uniformly distributed loading. The researchers also concludedthat the continuation of the shear connection beyond the beam sup-ports of simply-supported beams can favorably affect not only theoverall system response, but also the slip and the stud force distribu-tions along the beam. Furthermore, they showed that partial interac-tion in shear connection between steel and concrete can significantlyaffect both strength and deflection of the composite beam.

Zhao and Li [23] studied the nonlinear mechanical behavior andfailure process of a bonded steel–concrete composite beam byusing finite element method. The researchers used a three-dimensional FE model and discussed major reasons for failure ofcomposite beams.

Nguyen et al. [24] investigated the behavior of continuous com-posite beams with discrete shear connection using a nonlinearmixed finite element model. The researchers paid special attentionto the hogging moment regions where cracking occurs.

Queiroz et al. [25] used a simplified two-dimensional finite ele-ment modeling for evaluation of composite beams by ANSYS soft-ware. They used plastic beam elements to model steel beam andconcrete slab and a collection of links to model the shear studs(see Fig. 8). Their model was capable of simulating both full andpartial composite action between steel and concrete. The resultswere validated by comparison with experimental data and moresophisticated three-dimensional models. The conclusion was thatthis type of modeling, with fewer numerical convergence prob-lems, faster time of analysis and far more simplicity, is accurateenough for prediction of the behavior of a composite beam system

Tsavdaridis et al. [26] performed finite element modeling ofcomposite ultra-shallow floor beams (USFB) using ANSYS. In theirsystem, concrete slab lies within the steel flanges and is connectedthrough the web opening providing enhanced longitudinal and

Fig. 6. Different techniques in finite element modeling of girder-steel deck composite [20].

Y. Majdi et al. / Engineering Structures 77 (2014) 65–83 69

vertical shear resistance. The researchers compared their resultsfrom ANSYS finite element modeling to experimental data and avery well agreement was observed. In that research, the bondbetween steel and concrete was accounted for in computer modelsusing various Mohr–Coulomb friction coefficients.

3. Modeling assumptions

3.1. General considerations

In finite element modeling of the floor system, a single steeljoist plus an effective width of the concrete slab and steel deckare considered. The effective width is chosen based on AISC

recommendations [3]. In geometry of the models, concrete ribs,steel deck ribs and joist openings are included. Concrete slab ismodeled using 3D solid elements while all steel parts, due to theirsmall thicknesses, are modeled using 2D shell elements. All steelmembers are represented with their mid-planes and corner curvesof the steel joist are approximated with sharp edges. Due to thesymmetry, only one quarter of the system is required to be mod-eled. In all models, steel joist is made of two AISI standard C sec-tions (introduced in Table 1 for each model) and steel deck is anAISI standard 9/1600 cold-formed deck (gauge 20) with proof stressof 33 ksi (proof stress is defined in section 3.4). The continuousshear connector is a cold-formed hat channel developed by Hsuet al. [1] as shown in Fig. 2 and has a proof stress of 33 ksi.

Fig. 7. Finite element modeling of a composite beam with shear studs as shear connectors [22].

Fig. 8. Two-dimensional finite element modeling of a composite beam using beam elements [25].

Fig. 9. Support conditions and loading pattern in the models.

70 Y. Majdi et al. / Engineering Structures 77 (2014) 65–83

3.2. Support conditions and loading pattern

Support conditions and loading pattern are chosen as follows(see Fig. 9):

1. All models are assumed to be simply-supported in both ends. Inorder to create such condition, the nodes at the bottom of steeljoist are prevented from vertical translation, yet they are free torotate and are allowed to have horizontal translations.

2. All models are loaded with two vertical concentrated loads(equal to P/2) in one third and two third of the span. This typeof loading will cause a pure bending condition between theapplied forces. Total loading on the model will be equal to thesummation of the two applied forces (=P).

3. It is assumed that self-weight of the system also appears as twoequivalent concentrated loads in one third and two third of thespan. This idealization causes minor error in the results as theeffect of self-weight is insignificant. Thus, in ANSYS models,the total load, P, comprises two portions: the self-weight (deadload) and the piston load (live load).

3.3. Elements meshing

Finer mesh is used around the furring channel where high stressgradient is expected. The meshing becomes coarser in horizontaldirection at far concrete edges where stress gradient is expectedto be very low. Since high stress gradient is expected in verticaldirection all long the beam section, a fine meshing is consideredvertically for the concrete slab and the steel joist.

Fig. 10. Uniaxial stress–strain model for cold-formed steel (Fy = proof stress).

Fig. 11. Uniaxial compressive stress–strain model for concrete with f 0c ¼ 3200 psi.

Fig. 12. Local bond-slip model for cold-formed steel embedded in concrete.

Y. Majdi et al. / Engineering Structures 77 (2014) 65–83 71

On the faces where different parts are in contact or attached byscrews, a perfect node to node matching is performed in meshing.General meshing of the models are refined in multiple steps untilfurther refinement does not significantly affect the analysis results.Refer to Figs. 17 and 18 for general meshing of the system.

3.4. Modeling cold-formed steel material

In the present modeling, the cold-formed steel material isassumed to follow a multi-linear stress–strain pattern in uniaxialtension. The pattern is chosen to agree with actual stress–strain

Fig. 13. Visualization of slip between steel and concrete.

Fig. 14. Distribution of bond stress over the embedded steel in general case.

Fig. 15. Test set-up introduced by Majdi et al. [31] to study bond-sli

Fig. 16. Parameters of Cohesive Zone Material as used by ANSYS [27].

72 Y. Majdi et al. / Engineering Structures 77 (2014) 65–83

curves obtained from tension tests on material coupons. Fig. 10depicts the assumed multi-linear patterns for the cold-formedsteel. Note since cold-formed steel typically does not show a clearyield point in its stress–strain graph, an ‘‘offset yield stress’’ (alsoknown as ‘‘proof stress’’) is defined instead of yield stress for thatby intersecting an offset line with the stress–strain curve. The off-set line is drawn from the 0.2% strain value with a slope parallel tothe initial slope of the curve [4] (see Fig. 10).

For all cold-formed steel materials, von Mises yield criterion isused with associative flow rule and isotropic (work) hardening rule[27]. Poisson’s ratio for cold-formed steel is assumed to be equal to0.3.

3.5. Modeling concrete material

A multi-linear uniaxial stress–strain relationship in compres-sion is assumed for concrete based on the following numericalexpression as suggested by Desayi and Krishnan [28]:

p behavior between the proposed furring channel and concrete.

Fig. 17. ANSYS finite element modeling of the proposed composite floor system –3D view.

Fig. 18. ANSYS finite element modeling of the proposed composite floor system –3D view of steel parts only.

Fig. 19. ANSYS finite element modeling of contacts between concrete slab and steelparts.

Y. Majdi et al. / Engineering Structures 77 (2014) 65–83 73

f ¼ Ece

1þ ee0

� �2 ð1Þ

e0 ¼2f 0cEc

ð2Þ

where f is the stress at strain e, e the strain at stress f, e0 the strain atthe ultimate compressive strength, f 0c and Ec is the concrete modulusof elasticity (equal to initial slope of the curve), determined fromthe equation suggested in ACI code [29]:

Ec ¼ 57;000ffiffiffiffif 0c

qð3Þ

In which f 0c is in psi, or:

Ec ¼ 47;000ffiffiffiffif 0c

q

In which f 0c is in MPa.The assumed multi-linear model is depicted in Fig. 11 for

f 0c ¼ 3200 psi (22.06 MPa). As seen in this figure, the model consistsof 6 linear portions. The softening branch of stress–strain curve isapproximated by a perfectly plastic behavior beyond the point ofultimate stress to overcome convergence problems. Similarmulti-linear models with 6 lines are used for other f 0c values.

Plasticity is considered in the concrete model using von Misesyield criterion, associative flow rule and isotropic (work) hardening[27]. No crushing is assumed for the concrete.

When tensile principal stress in a point attains the value of fct

(splitting tensile strength), concrete is assumed to crack perpendic-ular to the direction of stress in that point. The tensile stress inpoint of crack will suddenly be dropped to zero. Tensile behaviorof concrete is assumed to be linear before cracking. The value offct is assumed equal to the average splitting tensile strength sug-gested in the commentary of ACI code [29] section R8.6.1:

fct ¼ 6:7ffiffiffiffif 0c

qð4Þ

In which f 0c is in psi, or:

fct ¼ 0:56ffiffiffiffif 0c

q

In which f 0c is in MPa.Poisson’s ratio for concrete is assumed equal to 0.2.

3.6. Modeling structural components

Concrete slab is modeled using SOLID65 element in ANSYS [30].The element is defined by eight nodes having three degrees of free-dom at each node: translations in the nodal x, y, and z directions.The element is capable of considering reinforcement and crackingin the concrete. The reinforcement and cracks are assumedsmeared in the element.

Cold-formed steel parts are the furring channel, steel deck andthe steel joist. Since these parts all consist of thin steel sheets,SHELL181 element is found to be suitable to model them [30].SHELL181 is a four node element with six degrees of freedom ateach node: translations in the x, y, and z directions, and rotationsabout the x, y, and z-axes. The element is well-suited for linear,large rotation, and/or large strain nonlinear applications. Changein shell thickness as a result of large-deformation is accountedfor in nonlinear analyses.

Refer to Figs. 17 and 18 for elements meshing and types of ele-ments used for steel and concrete parts.

3.7. Bond-slip behavior between furring channel and concrete

In the proposed composite floor system, shear transfer betweenthe steel joist and concrete slab relies on the bond-slip behaviorbetween the faces of the continuous furring channel and concrete.A local bond-slip model is required to simulate such behavior inFinite Element Analysis. Local bond-slip model is referred to a

Fig. 20. ANSYS finite element modeling of self-drilling fasteners.

Fig. 21. ANSYS finite element modeling of the furring channel with bent ribs on thelips.

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graph or function which at any arbitrary point of contact, expressesbond stress (shear stress transferred over the steel and concretefaces, s) in terms of the slip between the contact faces (d).

Majdi et al. [31] developed and verified such a local bond-slipmodel. The researchers began their work with setting up and solv-ing the bond-slip governing differential equation based on a bi-linear behavior (Fig. 12) to obtain the necessary mathematicalequations. Then a new test set-up was introduced for the experi-mental studies followed by a new innovative procedure to cali-brate the mathematical equations based on selected points fromthe test data. Subsequently, a local bond-slip model was developedby curve fitting through four sets of results. Finally, the researchersverified validity of their proposed model.

Fig. 13 depicts how the slip (d) between two materials is definedas the difference between deformation of steel (us) and deforma-tion of concrete (uc). In Fig. 14, bond stress distribution is shownover a portion of embedded steel in a general case as a result ofthe assumed bi-linear model. Further, the test set-up to obtainexperimental bond-slip data is shown in Fig. 15. Note the furringchannel shown in the set-up is identical to the furring channelused as shear transfer member in the current study.

Eventually, the following equations were proposed to deter-mine the parameters of the bi-linear bond-slip model based onthe concrete strength, f 0c [31,32]:

d1 ¼ 0:001100ð0:279 mmÞ ð5Þ

sf ¼ �0:054f 0c þ 8:433ffiffiffiffif 0c

q� 173 ð6Þ

df ¼ 0:369 lnðf 0c Þ � 0:595 ð7Þ

where d1 and df are in inches, f 0c and sf are in psi and2000 psi 6 f 0c 6 6000 psi.

In SI units, the above equations will take the form:

sf ¼ �0:054f 0c þ 0:7ffiffiffiffif 0c

q� 1:193

df ¼ 9:373 lnffiffiffiffif 0c

q� �þ 8:213

where f 0c and sf are in MPa and df is in mm.In the Finite Element Models, the concrete deck is connected to

the furring channel through surface-to-surface contact and targetelements, CONTA173 and TARGET170 [30], to simulate the bond-slip condition between the two materials (see Fig. 19).

A series of contact elements are created over the surface ofembedded steel shell elements sharing common nodes with them.Similarly, a series of target elements are considered over thesurface of concrete solid elements which are in contact with steelelements. Thus the actual behavior between steel and concretesurfaces can be represented through the interaction of contactand target elements [33]. This interaction can be programmed tofollow a special constitutive law equivalent to the developed localbond-slip models.

ANSYS Bilinear Cohesive Zone Material Model [27] can beemployed to simulate the constitutive law between steel and con-crete surfaces. In this model it can be assumed that contact ele-ments can have tangential slip over the target elementsaccording to the rule shown in Fig. 16. ANSYS Bilinear CohesiveZone Material Model is based on the model proposed by Alfanoand Crisfield [34]. According to that model (referring to Fig. 16),debonding begins at point A and is completed at point C. After deb-onding has been initiated in point A, it is assumed to be cumulativeand any unloading and subsequent reloading occurs in a linearelastic manner along line OB at a more gradual slope. Parameterdt is obtained from:

dt ¼ ut � �ut

ut

� �uc

t

uct � �ut

� �ð8Þ

And is used to determine the Bond Stress at any point from:

st ¼ Ktutð1� dtÞ: ð9Þ

3.8. Contact between concrete slab and steel deck

The contact behavior between concrete slab and steel deck isalso considered and is modeled with the pair of CONTA173/TARGE170 elements as described before. In this case, the two facesare constrained such that they are not able to penetrate into eachother; however they are free to slip and/or become separated. Thecontact surfaces are assumed friction-free and ‘‘no-penetration’’ isthe only constrain (see Fig. 19).

3.9. Modeling connectivity with screws

All short screws are assumed to create a no-slip conditionbetween the two connecting steel faces. The effect of bending inlong screws is accounted for by modeling beam elements betweenthe furring channel and the steel joist. Additionally, screws areassumed to have adequate strength to maintain connectivitybetween steel parts until the end of analysis.

CONTA178 element is used to model the connectivity betweenany two faces attached with a short screw [30]. This connectivity is

Fig. 22. Load–deformation graphs for models A1p and A1b compared with experimental data.

Fig. 23. Load–deformation graphs for models A2p and A2b compared with experimental data.

Y. Majdi et al. / Engineering Structures 77 (2014) 65–83 75

assumed to be over multiple pairs of nodes rather than one singlepair of node on the contacting faces. CONTA178 is a node-to-nodecontact element. The element has two nodes with three degrees offreedom at each node: translations in the X, Y, and Z directions.Each node of the element is attached to one of the two connectingfaces; such that the two nodes will have coincident coordinates inthe space. The contact behavior between each node pair isassumed perfectly bonded in all directions. The average of forces

transmitted between the two sides of the contact can be inter-preted as forces in the screw connecting the two faces.

BEAM188 element is used to model the connectivity of longscrews between furring channel and the steel joist [30]. Once againthe connectivity is assumed to be over multiple pairs of nodesrather than one single pair of node. BEAM188 is a two node lineelement with 6 (or 7) degrees of freedom at each node. Theseinclude translations in the x, y, and z directions and rotations about

Fig. 24. Load–deformation graphs for models A3p and A3b compared with experimental data.

Fig. 25. Model A1b: distribution of shear force in short fasteners (connecting steeldeck to the joists) over half-span length.

Fig. 26. Model A1b: distribution of shear force in long fasteners (connecting furringchannel to the joists) over half-span length.

Fig. 27. Model A1b: deflection of the system at ultimate load.

Fig. 28. Model A1b: distribution of flexural stress in the concrete slab at ultimateload (steel parts not shown for clarity).

76 Y. Majdi et al. / Engineering Structures 77 (2014) 65–83

the x, y, and z directions (a seventh degree of freedom which iswarping magnitude is optional for the element and is not used inthe present modeling). One node of the element is attached tothe bottom face of furring channel while the other node is attachedto the top face of steel joist. The average of shear forces and bend-ing moments in all beam elements can be interpreted as the shearforce and bending moment in the attaching long screw. Values ofaxial and flexural stiffness for the beam elements group is adjustedto match the actual stiffness of the connecting screw.

Refer to Fig. 20 for finite element modeling of fasteners.

Table 1List of finite element models with their specifications.

Model name Steel joist sectiona Concrete slab’s heightb,in (cm)

Concrete slab’swidth, ft (m)

Span length,ft (m)

f 0c , ksi (MPa) Fyc, ksi (MPa) Shear connector

typeBond slipbehavior applied?

A1p 600S200-68 3.5 (8.89) 3 (0.914) 12 (3.66) 3.2 (22.06) 41 (282.68) Regular NOA1b 600S200-68 3.5 (8.89) 3 (0.914) 12 (3.66) 3.2 (22.06) 41 (282.68) Regular YESA2p 600S200-68 3.5 (8.89) 3 (0.914) 12 (3.66) 3.2 (22.06) 41 (282.68) With cut & bent NOA2b 600S200-68 3.5 (8.89) 3 (0.914) 12 (3.66) 3.2 (22.06) 41 (282.68) With cut & bent YESA3p 600S200-54 3 (7.62) 3 (0.914) 12 (3.66) 2.3 (15.86) 37 (255.11) With cut & bent NOA3b 600S200-54 3 (7.62) 3 (0.914) 12 (3.66) 2.3 (15.86) 37 (255.11) With cut & bent YESB1p 600S200-68 3.5 (8.89) 3 (0.914) 8 (2.44) 3.2 (22.06) 41 (282.68) Regular NOB1b 600S200-68 3.5 (8.89) 3 (0.914) 8 (2.44) 3.2 (22.06) 41 (282.68) Regular YESB2p 600S200-68 3.5 (8.89) 3 (0.914) 10 (3.05) 3.2 (22.06) 41 (282.68) Regular NOB2b 600S200-68 3.5 (8.89) 3 (0.914) 10 (3.05) 3.2 (22.06) 41 (282.68) Regular YESB3p 600S200-68 3.5 (8.89) 3 (0.914) 12 (3.66) 3.2 (22.06) 41 (282.68) Regular NOB3b 600S200-68 3.5 (8.89) 3 (0.914) 12 (3.66) 3.2 (22.06) 41 (282.68) Regular YESB4p 600S200-68 3.5 (8.89) 3 (0.914) 16 (4.88) 3.2 (22.06) 41 (282.68) Regular NOB4b 600S200-68 3.5 (8.89) 3 (0.914) 16 3.2 (22.06) 41 (282.68) Regular YESC1p 600S200-97 3.5 (8.89) 3 (0.914) 12 (3.66) 3.2 (22.06) 41 (282.68) Regular NOC1b 600S200-97 3.5 (8.89) 3 (0.914) 12 (3.66) 3.2 (22.06) 41 (282.68) Regular YESC2p 600S200-68 3.5 (8.89) 3 (0.914) 12 (3.66) 3.2 (22.06) 41 (282.68) Regular NOC2b 600S200-68 3.5 (8.89) 3 (0.914) 12 (3.66) 3.2 (22.06) 41 (282.68) Regular YESC3p 600S200-68 3 (7.62) 3 (0.914) 12 (3.66) 3.2 (22.06) 41 (282.68) Regular NOC3b 600S200-68 3 (7.62) 3 (0.914) 12 (3.66) 3.2 (22.06) 41 (282.68) Regular YESC4p 600S200-54 3 (7.62) 3 (0.914) 12 (3.66) 3.2 (22.06) 41 (282.68) Regular NOC4b 600S200-54 3 (7.62) 3 (0.914) 12 (3.66) 3.2 (22.06) 41 (282.68) Regular YES

a Designation as adopted by AISI standard [36], e.g., 600S200-68 means cold-formed C section with total height of 6 in., flange width of 2 in. and nominal thickness of0.068 in. (for SI, 1 in. = 2.54 cm).

b Measure from top of lower steel deck’s rib.c Proof stress of cold-formed steel, obtained from 0.2% offset method.

1 For interpretation of color in Figs. 27 through 31, the reader is referred to the webversion of this article.

Y. Majdi et al. / Engineering Structures 77 (2014) 65–83 77

3.10. Furring channel with cut and bent ribs

As a modification to the regular set-up, some cuts are madeon the shear connector’s lips at longitudinal distances of every1 foot (30.48 cm) to study their effect on the system’s structuralbehavior. The cut edges are then bent up to form some ribswhich will interlock into the concrete and provide betterintegrity [2]. Finite element modeling of these bent ribs is shownin Fig. 21. Surfaces of the ribs are in contact with the concrete.Additionally, a hinge connection has been considered at thebottom of bent ribs.

4. Analysis assumptions

Nonlinear analysis is performed on each model using theNewton–Raphson method. All models are loaded gradually inmultiple steps and in a displacement based control procedure.

The amount of loading is increased until the maximum princi-pal compressive strain in concrete elements on the top attainsthe value of 0.003 which is the amount of ultimate strain for con-crete proposed by the ACI code [29]. The analysis will stop thenand the total amount of the applied load in the last step will berecorded as the ultimate strength (ultimate load) of the system.Post crushing and post peak behaviors of the composite floor sys-tem are not taken into account.

It is observed that solution convergence is extremely difficult toachieve as a result of a high level of nonlinearity in the system(material nonlinearity, large deformation and contact behavior).In order to overcome the convergence issues, the following tech-niques are introduced and used:

1. All models are loaded in a displacement based control proce-dure rather than a load based control procedure.

2. If rebar are not designed in the concrete slab in certain direc-tions, a very small value of reinforcement (arbitrarily chosenas 0.1% of the concrete volume) smeared in concrete elementsis used as fictitious reinforcement to prevent numerical

instabilities caused by an extensive concrete cracking at largedeformation. Note this fictitious reinforcement does not resultin a significant error as the stress observed in cracked concreteis very close to zero (see Fig. 28).1

3. In each analysis, initially a large value of convergence tolerancewas allowed for the solution. This value is then reduced step bystep as the analysis results are monitored. The reduction in theconvergence tolerance is continued until further decreasewould have no considerable effect on the analysis results. Inall the analyses, convergence tolerance is based on both dis-placement and force criteria.

4. In places of concentrated loads, local concrete stiffener blocksare modeled inside the C-channels, similar to the actual condi-tions in experimental tests. This prevents extensive local yield-ing and cracking which could prematurely terminate theanalysis.

5. In all models, loading is applied in multiple steps such that themaximum increase in deflections of the system is limited to0.01 inch in a loading step.

5. Results of finite element analyses

5.1. Designation of models

Each model is designated by a capital letter ‘‘A’’, ‘‘B’’, ‘‘C’’followed by a number and ending with either letter ‘‘p’’ or‘‘b’’.

The first capital letter specifies the category of the model.Models of category ‘‘A’’ have regular or with cut & bent ribs furringchannel and their results will be compared with the existing exper-imental data by Punurai [8]. Category ‘‘B’’ models are created tostudy the effect of shear connector’s slip in concrete on the sys-tem’s behavior for different span lengths. Category ‘‘C’’ modelsare created to study the effect of shear connector’s slip in concrete

Fig. 29. Model A1b: distribution of flexural stress in steel parts at ultimate load(concrete slab not shown for clarity).

Fig. 30. Model A1b: distribution of furring channel’s slip from the end support tothe mid-span at ultimate load.

Fig. 31. Model A1b: distribution of furring channel’s bond stress from the endsupport to the mid-span at ultimate load (bond stress shown is the summation offront and back faces).

78 Y. Majdi et al. / Engineering Structures 77 (2014) 65–83

on the system’s behavior for different values of section’s momentof inertia.

Letter ‘‘p’’ in the end of a model’s name shows that the shearconnector in that model is perfectly bonded with the surroundingconcrete while letter ‘‘b’’ shows that the shear connector in thatmodel has a bond-slip behavior inside the concrete following thebi-linear model proposed by Majdi et al. [31].

A list of the models together with their specifications is given inTable 1. In all models, height of concrete is measured from thelower steel deck’s rib to the top of concrete and Fy represents proofstress of cold-formed steel.

5.2. Results for category ‘‘A’’ models

In Figs. 22–24, load–deformation graphs for category ‘‘A’’models are illustrated and compared with experimental data.

Contour result at ultimate load for deflection of the compositebeam A1b is shown in Fig. 27.1 Also, flexural stress in concrete,flexural stress in steel, shear connector’s slip distribution and shearconnector’s bond stress distribution are depicted in Figs. 28–31,respectively at mid-span of model A1b. Note Fig. 28 impliesthat Inelastic Neutral Axis at ultimate load lies at the boarderof yellow and brown. Also, since flexural stress is close to zeroin the brown zone, that zone can be assumed as the crackedconcrete.

Further, Figs. 25 and 26 depict distribution of shear force ineach fastener for model A1b at ultimate load.

Based on studying the results of category ‘‘A’’ models, thefollowing conclusions can be drawn:

– Results of finite element modeling for the proposed compositefloor system are in acceptable agreement with the experimentaldata.

– The finite element analyses presented here lead to more conser-vative results as compared to the experiments. This can beattributed to several reasons such as: 1 – Self-weight is modeledin two concentrated points rather than uniformly along thebeam. 2 – Post cracking tensile strength of concrete is neglected.3 – Materials under bending can be stronger than what they arein pure tension, especially in large deformations. 4 – Thesmooth stress/strain curve of materials is approximated witha multi-linear pattern. 5 – Theoretical assumptions regardingmaterial plasticity and large deformation are conservative. 6 –Systematic and random errors always exist in experiments.

– Cut and bent ribs of the shear connector do not significantlyimprove the ultimate strength and the general structural behav-ior of the system based on the present finite element modelingand the test results by Punurai [8].

– Referring to Figs. 28–31, it is observed that the new proposedshear connector (the furring channel) is successfully capableof developing a composite action in the system. As seen inFig. 30, slip of the furring channel inside concrete slab is withinreasonable range. Also, Fig. 31 shows distribution of the bondstress on surface of the furring channel agrees with shear dia-gram of the composite beam which proves the shear transferhas been successfully provided by the furring channel up tothe ultimate load.

5.3. Results for category ‘‘B’’ and ‘‘C’’ models

Load–deformation graphs for category ‘‘B’’ models are shown inFig. 32. It is observed that as the span length increases, the effect ofbond-slip on structural response of the system reduces.

All category ‘‘C’’ models have the same span lengths of 12 feet(3.66 m) and the same material properties and concrete slabwidth. However, different values of section’s moments of inertia

are used in the finite element modeling by changing the joistthickness and the height of concrete slab. The load–deformationgraphs for these models are shown in Fig. 33. It is observed that

Fig. 32. Load–deformation graphs for category ‘‘B’’ models.

Fig. 33. Load–deformation graphs for category ‘‘C’’ models.

Y. Majdi et al. / Engineering Structures 77 (2014) 65–83 79

as the section’s moment of inertia decreases, the effect of bond-slip on structural response of the system reduces. The momentof inertia calculated for category ‘‘C’’ models are based on non-slip condition and no crack in concrete, to provide the easiest cal-culations for users.

Eventually, it is concluded that for each one of models in cate-gory ‘‘B’’ and ‘‘C’’, the value of moment of inertia over span lengthcan be chosen as a parameter to represent the effectiveness ofbond-slip behavior in structural response of the system.

Values of ultimate loads and initial slopes of load–deformationgraphs (initial stiffness) are compared versus moment of inertiaover span length as depicted in Tables 2 and 3, respectively. Theamounts of percentage reduction in ultimate loads and initialslopes are plotted versus the parameter of moment of inertia overspan length as shown in Figs. 34 and 35, respectively.

In order to quantify the effect of bond-slip behavior on ultimateload and stiffness of the proposed composite floor system, thefollowing equations are derived by curve fitting:

Table 2Comparison of ultimate loads for different values of moments of inertia over span lengths.

Model M.I./span, in3 (cm3) Ultimate total load, kips (kN) % Reduction due to bond-slip

Perfect bond condition Bond-slip applied

B1p & B1b 0.5450 26.455 (117.68) 22.961 (102.14) 13.207(8.9309)

B2p & B2b 0.4360 19.643 (87.38) 18.836 (83.79) 4.108(7.1448)

B3p & B3b 0.3634 17.964 (79.91) 17.644 (78.48) 1.781(5.9551)

B4p & B4b 0.2725 13.264 (59.00) 13.223 (58.82) 0.309(4.4655)

C1p & C1b 0.4672 23.043 (102.50) 21.412 (95.25) 7.078(7.6560)

C2p & C2b 0.3634 17.964 (79.91) 17.644 (78.48) 1.781(5.9551)

C3p & C3b 0.3073 15.429 (68.63) 15.31 (68.10) 0.771(5.0357)

C4p & C4b 0.2587 12.911 (57.43) 12.88 (57.29) 0.240(4.2393)

Table 3Comparison of initial slopes of load–deformation graphs (stiffness) for different values of moments of inertia over span lengths.

Model M.I./span, in3 (cm3) Initial slope of the graph, kips/in (kN/cm) % Reduction due to bond-slip

Perfect bond condition Bond-slip applied

B1p & B1b 0.5450 74.282 (130.088) 62.791 (109.964) 15.469(8.9309)

B2p & B2b 0.4360 38.5 (67.424) 33.875 (59.324) 12.013(7.1448)

B3p & B3b 0.3634 23.041 (40.351) 20.774 (36.381) 9.839(5.9551)

B4p & B4b 0.2725 10.358 (18.140) 9.555 (16.733) 7.752(4.4655)

C1p & C1b 0.4672 30.518 (53.445) 26.667 (46.701) 12.619(7.6560)

C2p & C2b 0.3634 23.041 (40.351) 20.774 (36.381) 9.839(5.9551)

C3p & C3b 0.3073 19.445 (34.053) 17.776 (31.131) 8.583(5.0357)

C4p & C4b 0.2587 16.142 (28.269) 14.943 (26.169) 7.428(4.2393)

Fig. 34. Percentage reduction in ultimate total load due to bond-slip behavior plotted versus moment of inertia over span length.

80 Y. Majdi et al. / Engineering Structures 77 (2014) 65–83

Fig. 35. Percentage reduction in initial slope of load–deformation graph (stiffness) due to bond-slip behavior plotted versus moment of inertia over span length.

Y. Majdi et al. / Engineering Structures 77 (2014) 65–83 81

PRU ¼ 394:16IL

� �5:42

ð10Þ

PRS ¼ 27:78IL

� �ð11Þ

where PRU is the Percentage reduction in ultimate load due tobond-slip behavior (shear connector’s slip) [%]; PRS the Percentagereduction in stiffness (initial slope of load–deformation graph)due to bond-slip behavior (shear connector’s slip) [%]; I the Momentof inertia of the composite section [in4] and L the Span length of thecomposite beam [in]. For calculation of moment of inertia (I), con-crete should be converted to an equivalent steel and no crackingshould be assumed in concrete. Further, effects of steel deck andconcrete slab ribs should be neglected [35].

In SI units, the equations will take the following form:

PRU ¼ 0:0004IL

� �5:42

PRS ¼ 1:691IL

� �

where IL has unit of cm3.

Fig. 36. Section analysis of the proposed composite floo

6. Simplified section analysis

Basic principles of mechanics of materials can be employed toperform section analysis on the proposed composite floor systemto determine ultimate moment capacity, elastic deformation, andaverage shear flow between steel joists and concrete slab. Majdiand Hsu [35] have published a technical report which completelycovers the procedure and details for analysis and design of the pro-posed composite floor system based on section analysis and coderequirements.

The key assumptions in section analysis of this floor system are:1 – There is perfect bond condition between steel joist and con-crete slab; However, corrections on system’s ultimate strengthand deflection can be applied using Eqs. (10) and (11) to accountfor the effect of shear connector’s slip. 2 – Proof stress of cold-formed steel is used as the yield stress. 3 – Participation of steeldeck in strength and stiffness of the system is negligible. This isproven by both finite element analysis [32] and analysis of thecross section [35]. 4 – Effect of concrete slab ribs should beneglected [3].

Fig. 36 illustrate inelastic section analysis to determine ultimatemoment capacity of the system.

r system assuming inelastic behavior of materials.

Table 4Comparison of ultimate loads obtained from F.E. modeling, section analysis andexperiments.

Model Ultimate total load, kips (kN)

From F.E. modeling From section analysis From experiment

A1p 17.964 (79.908) 17.289 (76.905) 19.733 (87.777)A1b 17.644 (78.484)A2p 17.966 (79.917) 17.289 (76.905) 19.981 (88.880)A2b 17.874 (79.507)A3p 11.05 (49.153) 11.459 (50.972) 12.041 (53.561)A3b 10.987 (48.873)

Table 5Comparison of average shear flow at ultimate load obtained from F.E. modeling andsection analysis.

Model Average shear flow on top of joist at ultimate load, kips/in (kN/cm)

From F.E. modeling From section analysis

A1b 0.857 (1.501) 0.914 (1.601)A2b 0.881 (1.543) 0.914 (1.601)A3b 0.605 (1.060) 0.654 (1.145)

82 Y. Majdi et al. / Engineering Structures 77 (2014) 65–83

Results of system’s ultimate load for category ‘‘A’’ models fromfinite element analyses, experiment data and section analyses arecompared in Table 4. Further, average shear flow for category ‘‘A’’models obtained from finite element analyses (shown in Figs. 25and 26) are compared in Table 5 with the results from section anal-yses. As concluded from those tables, there is quite acceptableagreement between results from the three methods. Note thatthe present finite element modeling and section analysis haveachieved more conservative results in comparison to experiments.

7. Conclusions

The following conclusions can be drawn from this study:

– Use of multi-linear material nonlinearity with von Mises yieldcriteria, associative flow rule and isotropic (work) hardeningcombined with large-deformation geometrical nonlinearityand nonlinear contact behavior between steel and concrete pro-duced reasonable results in finite element analysis of the dis-cussed floor system and results are in good agreement withthe experimental data. The analysis by ANSYS terminates incomputation as soon as the compressive principal strain onthe top of the concrete reaches the value of 0.003 as suggestedin the ACI code and the corresponding load is considered as theultimate total load on the system. Post-crushing and post-peakbehaviors of the composite floor system are not taken intoaccount in this study.

– To overcome the convergence issues of the highly nonlinearsystem of this study, several techniques are used. For instance,if rebar are not designed in the concrete slab in certain direc-tions, a very small value of reinforcement smeared in concreteelements is used as fictitious stiffness to prevent numericalinstabilities.

– The proposed furring channel is capable of effectively providingthe necessary shear transfer between steel and concrete toachieve a composite action. Bond-slip behavior of the furringchannel inside concrete has been accounted for in the models.

– Applying bond-slip behavior between steel and concrete in themodels will decrease the ultimate strength and the initial stiff-ness of the system as compared to the perfect bond condition.This decrease is more significant for systems with higher value

of moment of inertia over span length. Empirical equations arederived and presented to determine the percentage decrease inthe ultimate strength and stiffness.

– The ultimate loads obtained from finite element analyses,experimental data and section analyses have been found to bein quite acceptable agreements. Results from the finite elementmodeling and section analysis are generally more conservativecompared to experiments. Further, results of the average shearflow between steel joist and concrete from the finite elementanalysis and section analysis have been found to be acceptablyclose.

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