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Journal of Constructional Steel Research 63 (2007) 505521www.elsevier.com/locate/jcsr

Finite element modelling of composite beams with full and partial shearconnection

F.D. Queiroza,, P.C.G.S. Vellascob, D.A. Nethercot a

aDepartment of Civil and Environmental Engineering, Imperial College London, SW7 2AZ, United Kingdomb Structural Engineering Department, State University of Rio de Janeiro, RJ, Brazil

Received 25 January 2006; accepted 8 June 2006

Abstract

The present investigation focuses on the evaluation of full and partial shear connection in composite beams using the commercial finite element

(FE) software ANSYS. The proposed three-dimensional FE model is able to simulate the overall flexural behaviour of simply supported composite

beams subjected to either concentrated or uniformly distributed loads. This covers: load deflection behaviour, longitudinal slip at the steelconcrete

interface, distribution of stud shear force and failure modes. The reliability of the model is demonstrated by comparisons with experiments and

with alternative numerical analyses. This is followed by an extensive parametric study using the calibrated FE model. The paper also discusses in

detail several numerical modelling issues related to potential convergence problems, loading strategies and computer efficiency. The accuracy and

simplicity of the proposed model make it suitable to predict and/or complement experimental investigations.

c 2006 Elsevier Ltd. All rights reserved.

Keywords:Composite beams; Finite element method; Material nonlinearity; Shear connection; Parametric analysis; ANSYS

1. Introduction

Composite steelconcrete construction, particularly for

multi-storey steel frames, has achieved a high market share in

several European countries, the USA, Canada and Australia.

This is mainly due to a reduction in construction depth, to

savings in steel weight and to rapid construction programmes.

Composite action enhances structural efficiency by combin-

ing the structural elements to create a single composite sec-

tion. Composite beam designs provide a significant economy

through reduced material, more slender floor depths and faster

construction. Moreover, this system is well recognised in termsof the stiffness and strength improvements that can be achieved

when compared with non-composite solutions.

A fundamental point for the structural behaviour and design

of composite beams is the level of connection and interaction

between the steel section and the concrete slab. The term full

shear connection relates to the case in which the connection

between the components is able to fully resist the forces applied

Corresponding author. Tel.: +44 (0) 20 7594 6097.E-mail addresses:[email protected](F.D. Queiroz),

[email protected](D.A. Nethercot).

to it. This is possibly the most common situation; however, over

the last two decades the use of beams in building construction

has led to many instances when the interconnection cannot

resist all the forces applied (partial shear connection). In this

case, the connection may fail in shear before either of the other

components reaches its own failure state.

In the case of the serviceability limit state of composite

beams, the condition when the connection between the

components is considered as infinitely stiff is said to comprise

full interaction. Whilst this is often assumed in design, it

is theoretically impossible and cases where the connection

has more limited stiffness (partial interaction) often need

to be considered. In this case, the connection itself may

deform, resulting in relative movement along the steelconcrete

interface and the effect of increased shear deformation in the

beam as a whole. Therefore, partial interaction occurs to some

extent in all beams whether fully connected or not [1]. However,

studies [1,2] have shown that any flexibility in the connection

may be ignored for beams designed for full connection.

The use of partial connection provides the opportunity to

achieve a better match of applied and resisting moment and

some economy in the provision of connectors. Generally, the

effects of partial interaction, which are increased by the use

0143-974X/$ - see front matter c 2006 Elsevier Ltd. All rights reserved.doi:10.1016/j.jcsr.2006.06.003

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506 F.D. Queiroz et al. / Journal of Constructional Steel Research 63 (2007) 505521

of partial shear connection, will result in reduced strength

and stiffness, and potentially enhanced ductility of the overall

structural system [2].

It is widely known that laboratory tests require a great

amount of time, are very expensive and, in some cases, can

even be impractical. On the other hand, the finite element

method has become, in recent years, a powerful and useful

tool for the analysis of a wide range of engineering problems.

According to Abdollahi [3], a comprehensive finite element

model permits a considerable reduction in the number of

experiments. Nevertheless, in a complete investigation of any

structural system, the experimental phase is essential. Taking

into account that numerical models should be based on reliable

test results, experimental and numerical/theoretical analyses

complement each other in the investigation of a particular

structural phenomenon [4].

Previous numerical studies have been conducted to

investigate the behaviour of composite beams. Nevertheless,

most of them are based on two-dimensional analytical models

(e.g., Gattesco [5] and Pi et al. [6]), and are thus not

able to simulate more complex aspects of behaviour, which

are intrinsic for three-dimensional studies; for instance: full

distribution of stresses and strains over the entire section

of the structural components (steel beam and concrete slab),

evolution of cracks and local deformations in the concrete slab.

In addition, in the particular case of the model developed by

Pi et al. [6], it was assumed that the shear connectors were

uniformly distributed along the length of a composite member.

A three-dimensional finite element model has been developed

by El-Lobody and Lam [7] using the package ABAQUS [8],

in which the mode of failure of the beams is detected by

a manual check of the compressive concrete stress and stud

forces for each load step. Nevertheless, just two beams were

used to validate the proposed model for composite beams with

solid slabs. All these studies [57] were focused just on the

presentation and validation of their corresponding models, but

these models were not used to investigate in more detail either

the effect of particular structural parameters or other aspects

of the system behaviour. It is only very recently that papers

on finite element analyses of composite systems have started

to contain parametric studies (e.g., investigations related to the

behaviour of individual shear connectors [9,10]).In order to obtain reliable results up to failure, finite element

models must properly represent the constituent parts, adopt

adequate elements and use appropriate solution techniques.

As the behaviour of composite beams presents significant

nonlinear effects, it is fundamental that the interaction of all

different components should be properly modelled, as well as

the interface behaviour. Once suitably validated, the model can

be utilised to investigate aspects of behaviour in far more detail

than is possible in laboratory work. For instance, it permits

the study of the sensitivity of response to variability of key

component characteristics, including material properties and

shear stud layout. Consequently, different spacing in distinct

parts of the beam can be adopted, allowing the investigation ofpartial interaction effects.

The present investigation focuses on the modelling of

composite beams with full and partial shear connection using

the software ANSYS [11]. A three-dimensional model is

proposed, in which all the main structural parameters andassociated nonlinearities are included (concrete slab, steel beam

and shear connectors). Test and numerical data available in

the literature are used to validate the model, which is able to

deal with simply supported systems with I-beams and solid flat

slabs. Other features such as steel profiled sheeting, different

types of slab (e.g., precast slabs) and distinct end-connectivities

are not included in the present study.

Based on the validated model, an extensive parametric

analysis of composite beams is performed, specifically aimed

at:

studying the effect of the continuation of shear connection

beyond the supports of simply supported composite beams; investigating the overall structural system behaviour when

different concrete compressive strengths are used in the slab

and in the associated push-out tests. This situation has often

been observed in reported laboratory studies but has not

previously received any systematic study, being important,

for instance, for the definition of the loadslip curves used

for the shear connectors;

analysing the influence of small variations in key input

parameters (i.e., concrete and steel material properties) on

the structural behaviour of uniformly loaded composite

beams. This sensitivity study can be used to identify the

variables (e.g., web and flange yield stresses, concrete

strength, etc.) which are more important in terms ofdefinition of the overall response of the system and therefore

can be helpful in terms of establishing possible differences

between numerical and test results;

assessing the influence of the effects of partial shear

connection and partial interaction not only on the overall

flexural behaviour of composite beams (represented by the

loaddeflection curve), but also on the associated failure

modes for either slab crushing or stud failure, and on the

distribution of stud shear forces along the beam length.

This paper also discusses several numerical modelling issues

related to convergence problems that arise when the concrete

material is considered, loading strategies for the simulation of

distributed loads and a comparison between the load controland the displacement control methods in terms of computer

efficiency.

2. Finite element model

2.1. Software, element types and mesh construction

Advances in computational features and software have

brought the finite element method within reach of both

academic research and engineers in practice by means of

general-purpose nonlinear finite element analysis packages,

with one of the most used nowadays being ANSYS. The

program offers a wide range of options regarding element types,material behaviour and numerical solution controls, as well as

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F.D. Queiroz et al. / Journal of Constructional Steel Research 63 (2007) 505521 507

Fig. 1. Typical composite beam FE mesh.

graphic user interfaces (known as GUIs), auto-meshers, andsophisticated postprocessors and graphics to speed the analyses.

In this paper, the structural system modelling is based on the use

of this commercial software.

The finite element types considered in the model are as

follows: elastic-plastic shell (SHELL43) and solid (SOLID65)

elements for the steel section and the concrete slab,

respectively, and nonlinear springs (COMBIN39) to represent

the shear connectors. Both longitudinal and transverse

reinforcing bars are modelled as smeared throughout the solid

finite elements.

The element SHELL43 is defined by four nodes having

six degrees of freedom at each node. The deformation shapes

are linear in both in-plane directions. The element allows forplasticity, creep, stress stiffening, large deflections, and large

strain capabilities [11]. The element SOLID65 is used for three-

dimensional modelling of solids with or without reinforcing

bars (rebar capability). The element has eight nodes and three

degrees of freedom (translations) at each node. The concrete is

capable of cracking (in three orthogonal directions), crushing,

plastic deformation, and creep [11]. The rebars are capable of

sustaining tension and compression forces, but not shear, being

also capable of plastic deformation and creep.

The element COMBIN39 is defined by two node points

and a generalized forcedeflection curve and has longitudinal

or torsional capability. The longitudinal option is a uniaxial

tensioncompression element with up to three degrees offreedom (translations) at each node.

Symmetry of the composite beams is taken into account by

modelling only one half of the beam span. A typical FE mesh

for a composite beam is shown inFig. 1.

2.2. Material modelling

The von Mises yield criterion with isotropic hardening rule

(multilinear work-hardening material) is used to represent the

steel beam (flanges and web) behaviour. The stressstrain

relationship is linear elastic up to yielding, perfectly plastic

between the elastic limit (y ) and the beginning of strainhardening and follows the constitutive law used by Gattesco [5]

for the strain-hardening branch:

= fy+ E

h(

h)1 E

h

h

4(fu fy) (1)

where fy and fu are the yield and ultimate tensile stresses of

the steel component, respectively; Eh and h are the strain-

hardening modulus (i.e., 3500 N/mm2) and the strain at strain

hardening of the steel component, respectively.

The von Mises yield criterion with isotropic hardening rule

is also used for the reinforcing steel. An elastic-linear-work-

hardening material is considered, with tangent modulus being

equal to 1/10 000 of the elastic modulus, in order to avoid

numerical problems. The values measured in the experimental

tests for the material properties of the steel components (steel

beam and reinforcing bars) are used in the finite element

analyses.The concrete slab behaviour is modelled by a multilinear

isotropic hardening relationship, using the von Mises yield

criterion coupled with an isotropic work hardening assumption.

The uniaxial behaviour is described by a piece-wise linear

total stresstotal strain curve, starting at the origin, with

positive stress and strain values, considering the concrete

compressive strength (fc) corresponding to a compressive

strain of 0.2%. The stressstrain curve also assumes a total

increase of 0.05 N/mm2 in the compressive strength up to

the concrete strain of 0.35% to avoid numerical problems due

to an unrestricted yielding flow. The concrete element shear

transfer coefficients considered are: 0.2 (open crack) and 0.6

(closed crack). Typical values range from 0 to 1, where 0represents a smooth crack (complete loss of shear transfer) and

1 a rough crack (no loss of shear transfer). The default value

of 0.6 is used as the stress relaxation coefficient (a device that

helps accelerate convergence when cracking is imminent). The

crushing capability of the concrete element is also disabled to

improve convergence.

The concrete slab compressive strength is taken as the actual

cylinder strength test value. The concrete tensile strength and

the Poissons ratio are assumed as 1/10 of its compressive

strength and 0.2, respectively. The concrete elastic modulus is

evaluated according to Eurocode 4 [12], i.e.:

Ec = 9500(fc + 8)1/3c24

1/2 (2)

where:c is equal to 24 kN/m3.

The model allows for any pattern of stud distribution to be

considered, for instance: the conventional uniform arrangement

and a triangular spacing scheme where the stud distribution

follows the nominal elastic shear diagram [13]. In all analyses,

the number/spacing of studs adopted in the experimental

programmes is utilised. As far as the shear connector behaviour

is concerned, the loadslip curves for the studs are used

(obtained from available push-out tests) by defining a table

of force values and relative displacements (slip) as input data

for the nonlinear springs. These springs are modelled at thesteelconcrete interface, as shown inFig. 2.

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Fig. 2. Modelling of shear connectors (longitudinal view). (a) Shear studs in a typical composite beam. (b) Shear studs in a typical composite beam finite element

mesh. (c) Representation of the shear stud model.

2.3. Application of load and numerical control

Regarding application of load, concentrated loads are

incrementally applied to the model by means of an

equivalent displacement to overcome convergence problems

(displacement control). For the convergence criterion, the L2-

norm (square root sum of the squares) of displacements is

considered. Uniformly distributed loads are represented bymeans of point loads applied at all mid-section concrete

nodes. These concentrated loads are also applied to the model

incrementally using the load control strategy and the L2-

norm. The tolerance associated with this convergence criterion

(CNVTOL command of ANSYS) and the load step increment

are varied in order to solve potential numerical problems.

Whenever the solution does not converge for the set of

parameters considered, as far as load step size and converge

criterion are concerned, the RESTART command is used in

conjunction with the CNVTOL option. ANSYS allows two

different types of restart: the single-frame restart and the multi-

frame restart, which can be used for static or full transient

structural analyses. The single-frame restart only allows theuser to resume a job at the point it stopped. The multi-frame

restart can resume a job at any point in the analysis for

which information is saved. This capability enables multiple

model analyses, presenting more options for data retrieval

after an undesired aborted solution. The second approach

is used throughout the present analyses and the associated

error is controlled by comparisons between applied forces and

reactions (balance of forces) for each load step.

The load control strategy is adopted due to the fact that,in structural problems in which significant nonlinear effects

occur, it is difficult to derive a relationship between loads

and associated displacements for the case of distributed loads,

mainly for the plastic range of behaviour. For the case in

which only one point load is applied to the system, there is

a direct relationship between force and displacement, making

the displacement control method easier to be utilised. The load

control method is, however, less efficient than the displacement

control method in nonlinear analyses. This fact is observed

especially when the applied load approaches the ultimate load

of the system, as an incremental increase in the load leads

to a significant increase in the corresponding displacements,

causing difficulties in terms of numerical convergence. Forthe type and size of the finite element problem investigated,

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the load control method demanded, on average, 40% more

disk space and took 140% longer to be processed than similar

displacement control solutions.

Preliminary attempts to overcome the convergence problemsarising from the use of the load control method included the

specification of different types of equation solvers. The best

approach in terms of numerical performance was the option

in which the software ANSYS selects a solver based on the

physics of the problem. The arc-length method was also tested

but proved not to be the best option for this particular type of

analysis.

2.4. Failure criterion

Two limits are established to define the ultimate load for

each finite element investigation: a lower and an upper bound,

corresponding to concrete compressive strains of 0.2%, and0.35%, respectively. These two limits define an interval in

which the composite beam collapse load is located. A third

limit condition, hereinafter referred to as the stud failure point,

can also be reached when the composite beams most heavily

loaded stud reaches its ultimate load, as defined from the

appropriate push-out tests.

If the stud failure point is located before the lower bound

of concrete (i.e., the corresponding load of the stud failure

point is smaller than the lower bound load) then the mode

of failure of the composite beam is considered as being stud

failure. Conversely, if the stud failure point is located after the

upper bound of concrete, the mode of failure is assumed as

being concrete crushing. For the intermediate case, where thestud failure point lies between the lower and upper bounds of

concrete, than the mode of failure could be either of them.

Therefore, the proposed finite element model is able to

predict the failure modes associated with either slab crushing

or stud failure.

3. Validation of the model

The present model is validated by comparisons against

Chapman and Balakrishnan tests [13], as well as against

alternative numerical studies (Gattesco [5], Pi et al. [6] and El-

Lobody and Lam [7]).

3.1. Chapman and Balakrishnan tests

The tests performed by Chapman and Balakrishnan

successfully illustrate the behaviour of the composite system

which is being investigated. The beams spanned 5490 mm

with an I-shaped steel member 305 mm deep (12 6

44 lb/ft BSB) and a concrete slab 152 mm thick1220 mm

wide. The number and type of studs, as well as the steel and

concrete strengths, varied according to the tested composite

beam. The slab was longitudinally reinforced with four top

and four bottom 8 mm bars. The transverse reinforcement

incorporated top and bottom bars of 12.7 mm @ 152 mm

centres and 12.7 mm @ 305 mm centres, respectively. Thetensile strength, the Youngs modulus and the Poissons ratio

Fig. 3. Simply supported beam layout (dimensions in mm).

Fig. 4. Load (kN) vs. midspan deflection (mm) beams A2 and A3.

of the reinforcing steel bars were 320 N/mm2, 205000 N/mm2

and 0.3, respectively. A list of material properties for all beams

is given in [1316] and a full description of these beams is

presented inFig. 3andTable 1.Based on the composite section strength of the concrete

slab, steel components and shear connectors, the level of

shear connection could be determined. This value is defined

as the ratio between the shear connection capacity and the

weakest element capacity (concrete slab or steel beam).Table 2summarises the level of shear connection for all the composite

beams, considering two different approaches. The first one uses

the nominal values presented by [13] for the stud strength and

steel yield stress. In the second one, the material properties

are taken as the actual measured values [13]. Considerable

differences among the levels of shear connection according to

these two approaches are noticed, leading to the conclusion that,

in order to calculate the level of shear connection of composite

systems, the actual material properties of the components

(measured values), related to each experimental programme,

should be used.For all composite beams shown in Table 1, loadmidspan

deflection curves are compared to the test results. Figs. 48(beams A2 to E1) and Figs. 911 (beams U1 to U4)

depict comparisons between the FE model results and the

experimental data for the midspan concentrated and uniformly

distributed loaded composite beams, respectively. The limit

points for the concrete are represented by a full triangle (lower

bound) and by a full square (upper bound), and the stud failure

point is represented by a full circle (item 2.4). Good agreement

was obtained between test and numerical results.In order to illustrate finite element data for local results,

the numerical and test values regarding the slip at the

steelconcrete interface along the beam axis for the cases E1

and U4 are plotted inFigs. 12and13, respectively. The graphs

show that the proposed model can predict the slip distributionwith good precision. From these figures, it can be noticed that

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Table 1

Details of composite beams tested by [13]

Beam A2 A3 A4 A5 A6 B1 C1 D1 E1 U1 U3 U4

Stud diam. (mm) 19

12.7

Stud overall length (mm) 102

76

50

Number of studs 100

76

68

56

44

32

Spacing in pairs (mm) 121 a

159 a

178 a216 a

274 a

378 a

Mode of failure Slab crushing

Stud failure

Load type Midspan concentrated Uniformly

distributed

a Triangular spacing.

Table 2

Level of shear connection of the composite beams (%)


Nominal values 238 213 175 138 101 138 138 313 313 175 175 101

Measured values 231 186 137 123 95 116 114 136 148 155 177 90

Fig. 5. Load (kN) vs. midspan deflection (mm) beams A4 and A5.

Fig. 6. Load (kN) vs. midspan deflection (mm) beams A6 and B1.

Fig. 7. Load (kN) vs. midspan deflection (mm) beams C1 and D1.

Fig. 8. Load (kN) vs. midspan deflection (mm) beam E1.

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Fig. 9. Load (kN/m) vs. midspan deflection (mm) beam U1.



the slip is not uniform along the beam length, even where the

externally applied shear force is uniform (midspan concentrated

load case). The maximum slip value tends to occur when X/L

equals 0.4 (point load case) and X/L equals 0.3 (uniformly

distributed load case UDL). According to [13], the large slip

which occurs near midspan is due to the high interface shear inthe plastic region.

Table 3 presents the ultimate load for each of the studied

composite beams. This load is expressed in terms of the test

results and both lower and upper bound limits (FE analysis).

This table also presents the ratio between the numerical and

test results for each limit point and their associated dispersion

values. It can be noticed that the proposed model was able to

predict the experimental ultimate load very accurately, as well

as the associated mode of failure (slab crushing or stud failure).

3.2. Comparisons with previous numerical studies

Gattesco [5] presented an analytical procedure for theinvestigation of composite beams, in which the nonlinear

Fig. 12. Slip distribution along span beam E1.

Fig. 13. Slip distribution along span beam U4.

behaviour of all materials was considered. The parametric

analysis demonstrated that the numerical program was able to

model full and partial shear connection. El-Lobody and Lam [7]

used the ABAQUS FE software to undertake a numericalanalysis of composite girders with solid and precast hollow

core slabs. Both models included the material nonlinearities,

as well as the stud nonlinear loadslip characteristics. Partial

interaction between the steel and concrete components was

also incorporated in the total Lagrangian finite element

model formulated by Pi et al. [6]. The model was validated

by comparisons against simply supported and continuous

composite beams tests.

In Figs. 14 and 15 the loadmidspan deflection curves

obtained from these previous numerical models are compared

with the present study results for the composite beams E1 and

U4. Good agreement between the curves was obtained.

3.3. Effect of the overhang region (region beyond supports)

As it can be seen in Fig. 3, the experiments conducted

by Chapman and Balakrishnan concerned composite beams in

which a number of shear connectors were used in the overhang

regions. According to [13], a more rational test procedure

would have been to limit the slab length to the distance between

supports. Nevertheless, it was also stated by [13] that, in

practice, the concrete slabs do not always necessarily terminate

at the reactions. In this section, the effect of the overhang

regions (i.e., the regions beyond supports) will be assessed in

terms of both overall and local behaviour. None of the already-

mentioned previous studies on the Chapman and Balakrishnantests [57] investigated this aspect.

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Table 3

Ultimate load results for the experimental and numerical analyses

Beam Pexp PLB(0.2%) PUB(0.35%) 1 = PLB/Pexp 2 = PUB/Pexp % = (2 1) 100

A2 448 429 469 0.96 1.05 9

A3 449 425 447 0.95 0.99 4

A4a 523 444 470 0.85 0.90 5

A5 468 462 479 0.99 1.02 3

A6 430b 449b 1.04

B1 486 459 468 (466b ) 0.94 0.96 (0.95b ) 2

C1 448 445 474 0.99 1.06 7

D1 481 457 475 0.95 0.99 4

E1 513 520 548 1.01 1.07 6

U1 191 171 178 0.90 0.93 3

U3 185 166 182 0.90 0.98 8

U4 176b 179b 1.02

Pexp, PLBand PUBare the test ultimate load, lower and upper bound loads, respectively (midspan load [kN]; uniformly distributed load [kN/m]).a The strength of the concrete used in the push-out test was much less than the concrete strength of the composite beam;b

Stud failure, so bounds not applicable.

Fig. 14. Load vs. midspan deflection Other similar studies (beam E1).

Fig. 15. Load vs. midspan deflection Other similar studies (beam U4).

In the following (Figs. 1625), the analyses in which theseregions are included in the model will be hereinafter referred to

as the extended case (results presented in item 3.1), and the

ones in which only the regions between supports are modelled

will be referred to as the standard case.

The loaddeflection curves for the composite beams A4, D1,

E1 (midspan concentrated load) and U4 (UDL) are shown in

Figs. 1619, respectively. It can be observed that an increase

in the system stiffness was present for the extended case when

compared with the standard one. The connectors placed beyond

the supports have an anchorage effect on the beam, leading to

an improvement in the composite effect of the system.

This behaviour is in accordance with the observations by

Goodman and Popov [17], who investigated the behaviour oflayered wood beam systems with interlayer slip. Results of

Fig. 16. Load (kN) vs. midspan deflection (mm) beam A4.

Fig. 17. Load (kN) vs. midspan deflection (mm) beam D1.

Fig. 18. Load (kN) vs. midspan deflection (mm) beam E1.

experiments with layered beams connected with nails, withand without glued ends, showed that there was a decrease

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Fig. 20. Ratio of stud forces vs. relative position of the stud beam A4.

Fig. 21. Ratio of stud forces vs. relative position of the stud beam D1.

Fig. 22. Ratio of stud forces vs. relative position of the stud beam E1.

in the beam deflection values for the former case (i.e.,

the structural system was stiffer). Although the conclusions

presented were illustrated for the case of layered systems of

wood, any mechanically-connected layered beam system (e.g.,

steelconcrete beams connected by means of shear studs) canbe analysed in the same manner. The effect of the use of

Fig. 23. Ratio of stud forces vs. relative position of the stud beam U4.

Fig. 24. Slip distribution along span beam E1.

Fig. 25. Slip distribution along span beam U4.

connectors beyond the beam supports could be linked to the

situation of glued beam ends described above.

For the case of beams subjected to uniformly distributedload (as exemplified by Fig. 19 for beam U4), the increase

in the stiffness of the system is more significant than for the

case of beams subjected to midspan point loads (Figs. 1618).

Considering the distribution of flexural moments in the regions

next to the supports, the moments for a beam subjected to a

UDL present proportionally higher values than the moments for

a beam subjected to a midspan concentrated load, making the

shear connectors in this region more important than the ones

towards the midspan. In the point load case, the studs work in

a more uniform manner along the beam. The overhang regions

lead to a more rapid development of the effective breadth of

the concrete slab (it is known that, for the standard case, the

effective breadth is theoretically zero at the support), resultingin a more accentuated increase in the stiffness.

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Table 4

Level of shear connection (%) extended vs. standard beams


Extended 231 186 137 123 95 116 114 136 148 155 177 90

Standard 207 164 127 112 83 106 104 125 136 144 164 79

Table 5

Ultimate load results for the experimental and numerical analyses standard case

Beam Pexp PLB(0.2%) PUB(0.35%) 1 = PLB/Pexp 2 = PUB/Pexp % = (2 1) 100

A2 448 431 468 0.96 1.04 8

A3 449 426 445 0.95 0.99 4

A4a 523 444 469 0.85 0.90 5

A5 468 448 467c 0.96 1.00 4

A6 430b 444b 1.03

B1 486 444 (440b ) 452 0.91 (0.91b ) 0.93 2

C1 448 446 469 1.00 1.05 5

D1 481 462 472 0.96 0.98 2

E1 513 518 540 1.01 1.05 4

U1 191 162 171 0.85 0.90 5

U3 185 154 169 0.83 0.91 8

U4 176b 166b 0.94

Pexp, PLBand PUBare the test ultimate load, lower and upper bound loads, respectively (midspan load [kN]; uniformly distributed load [kN/m]).a The strength of the concrete used in the push-out test was much less than the concrete strength of the composite beam;b Stud failure, so bounds not applicable;c ANSYS analysis terminated.

In addition, it is worth pointing out that the shear connectors

in the overhang regions should be taken into account when

calculating the level of shear connection, as they have an

influence on the system behaviour. Therefore, if only the region

between supports is considered, the connection level decreases,as shown inTable 4.

In order to illustrate the results in terms of stud force

distribution, tests A4, D1, E1 and U4 are considered. In

Figs. 2023, stud force distribution graphs are plotted relating

force ratio to stud position. It can be seen that, for the standard

cases, there is a disturbance in the stud force distribution in

the region near the supports, caused by the reduction of the

effective breadth of the slab in this region. For the extended

cases, this effect is not so significant, as the effective breadth

of the slab is almost completely developed in the support

region (it can be noticed that the tendency of the curve is

maintained along the beam). In the region between the supports

and midspan, only the steel and concrete deformation patternsdefine the behaviour.

The slip at the steelconcrete interface along the beam

axis for the cases E1 and U4 is plotted in Figs. 24 and

25, respectively, for both extended and standard cases. It is

evident from these graphs that the overhang regions also have

a considerable effect on the slip values, mainly in the regions

next to the supports. The disturbance of the slip distribution

near the supports caused by the effective breadth of the slab

can be noticed in Fig. 24, as well. In addition, it can be

observed in Fig. 24 that the curve corresponding to the extended

case is above the experimental curve. This fact may be due

to a difference between the loadslip behaviour of the shear

connectors in the tested composite beam and the loadslipbehaviour of the push-out test (used in the FE analysis).

Moreover, the curves related to the standard case are also above

the ones for the extended situation. Nevertheless, the sum of the

stud forces is the same, provided that the connectors beyond the

supports are considered.

Table 5 presents the ultimate loads for all analysesconsidering the standard case (beams between supports). It can

be observed that the values predicted by this model are very

close to the ones obtained for the extended composite beam

case (Table 3).

The complete results for all standard beams are presented

and discussed in Queiroz et al. [14,15], including a detailed

study in terms of the absolute force carried by the shear studs

for three different stud overall lengths (for a fixed diameter and

spacing), and the absolute force carried by the shear studs for

five different connector spacing values (for a fixed diameter and

length).

Based on this investigation, it can be seen that the

continuation of the shear connection beyond the beam supportscan affect not only the overall response (e.g., shape of the

loaddeflection curve), but also local results (e.g., slip and

stud force distributions along the beam). Nevertheless, for

the composite beams considered, the ultimate load was not

significantly influenced.

3.4. Effects of concrete slab strength and concrete strength for

push-out specimens

This section describes a comprehensive parametric analysis

of the overall structural behaviour of steelconcrete composite

beams when different concrete compressive strengths are

present in the slab and in the associated push-out tests. Itwill always be the case, for example, for composite beams

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Table 6

Influence of the slab concrete strength

Beam Diameter

(mm)

Overall length

(mm)

Spacing in pairs

(mm)

Cylinder strength of the concrete (N/mm2)

Push-out (used in the shear connector

springs)

Slab (used in the slab finite elements)

25.0

26.9

A2 19 102 159 30.7 28.8

30.7

32.6

23.1

24.8

A5 19 102 274 28.0 26.4

28.0

29.6

Table 7

Influence of the concrete strength used in the push-out tests

Beam Diameter

(mm)

Overall length

(mm)

Spacing in pairs

(mm)

Cylinder strength of the concrete (N/mm2)

Slab (used in the slab finite

elements)

Push-out (used in the shear connector springs)

19.7 (A4)

A2 19 102 159 26.9 28.0 (A5)

30.7

19.7

A4 19 102 216 20.1 28.0 (A5)

30.7 (A2)

19.7 (A4)

A5 19 102 274 24.8 28.030.7 (A2)

with precast slabs, for which results from push-out tests with

solid concrete slabs are usually used. Two different effects

are considered, utilising the standard model discussed in item

3.3: one for which the slab concrete strength is fixed and

the concrete strength for the associated push-out specimens

is varied and another assuming the opposite situation. Results

relating to the distribution of stud forces along the beam

length and to the moment capacity of the composite system

are discussed. The cases used for the parametric study are

summarised inTables 6and7.

Table 6 presents the scope of the analysis adopted toinvestigate the effect of the slab strength on the beam structural

response. For each beam (A2 and A5) five different slab

strengths are considered. The relative differences between two

consecutive slab concrete strengths are approximately the same.

For both beams, the diameter and overall length of the studs

are also equal. The concrete strength of the associated push-out

test carried out by [13] is fixed for each beam. Nevertheless, the

shear connector spacing of each beam is distinct.Table 7 presents the range of values adopted in order

to assess the influence of the concrete strength used in the

associated push-out tests. For each beam (A2, A4 and A5)

three different push-out strengths are assumed, i.e.: the concrete

strength of the beams A2, A4 and A5. For all beams, thediameter and overall stud length are also equal. The slab

concrete strength and the shear connector spacing are fixed and

distinct for each beam.

3.4.1. Influence of the slab concrete strength on the composite

beam response

The main focus of discussion is centred on: load versus

midspan deflection curves, distribution of stud forces along the

beam lengths and absolute forces carried by the shear studs for

different slab strengths, with the same concrete strength being

used in the associated push-out specimen.

Figs. 2628andFigs. 2931present the FE model resultsfor the beams A2 and A5, respectively. By analysing the

loaddeflection curves (Figs. 26 and 29), it is possible to

observe that an increase in the slab concrete strength resulted in

a stiffer system and in an increase in the moment capacity of the

beam, represented by the ultimate bound points. Nevertheless,

the former effect seems to be less significant than the latter

one.

According to Fig. 27 (absolute force carried by the shear

studs for different slab strengths), an increase in the stud

forces is observed as the slab concrete strength increases, most

noticeably for the two beams with the highest slab concrete

strengths (30.7 N/mm2 and 32.6 N/mm2). Based onFig. 30, a

similar conclusion may be drawn for beam A5, i.e.: an increasein the stud forces occurs as the slab concrete strength increases.

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Fig. 26. Load (kN) vs. midspan deflection (mm) for different slab concrete

strengths beam A2.

Fig. 27. Stud force vs. slab concrete strength beam A2 (lower and upper

bounds).


The mode of collapse for the beams with the highest slab

concrete strengths (28.0 N/mm2 and 29.6 N/mm2) was related

to stud failure. The composite beam with slab concrete strength

of 29.6 N/mm2 presented a lower bound closer to the stud

failure point than did the composite beam with a 28.0 N/mm2-

slab concrete strength (Fig. 29).

Two concrete strengths are chosen for each beam (A2 and

A5) to illustrate the distribution of stud forces along the beam

lengths (Figs. 28 and 31, respectively). It can be noticed that, for

the beam A2, the stud forces decrease towards the beam ends.

This was not the case for the beam A5, where the stud forces

did not vary significantly along the beam length.Fig. 30showsthat the variation in the stud forces for the beam A5 is smaller

Fig. 29. Load (kN) vs. midspan deflection (mm) for different slab concrete

strengths beam A5.

Fig. 30. Stud force vs. slab concrete strength beam A5 (lower and upper

bounds).


than the variation for the beam A2 (Fig. 27), therefore resultingin a more uniform distribution of forces along the beam.

The analysis shows that, therefore, an increase in the slab

concrete strength can have an influence not only on general

aspects of behaviour (e.g., overall stiffness of the system and

ultimate moment capacity) but also on local results (e.g., stud

forces).

3.4.2. Effect of the push-out concrete strength on the composite

beam response

The main focus of discussion is centred on varying the push-

out test concrete strengths (by means of adopting different

loadslip curves for the shear connector representation)

maintaining the same slab concrete strength. Figs. 3234,3537,3840present the FE model results for the beams A2,

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Fig. 32. Load (kN) vs.midspandeflection (mm) fordifferent concrete strengths

beam A2.

Fig. 33. Stud force vs.concrete strength beam A2 (lowerand upper bounds).


A4 and A5, respectively. Two concrete strengths are chosen foreach beam to illustrate the distribution of stud forces along the

beam lengths (Figs. 34,37and40).

The concrete strength used in the push-out test appears to

have a small influence on both the overall behaviour of the

composite beam and the stud force distribution, as can be

seen in the graphs of applied load versus midspan deflection

and absolute force carried by the shear studs versus concrete

strengths used in the push-out tests (beam A2:Figs. 32and33;

beam A4:Figs. 35and36; beam A5:Figs. 38and39).

4. Sensitivity study

In this section, an investigation is performed aimed atassessing the sensitivity of the overall response of composite


beam A4.




beam A5.

beams (represented by loaddeflection curves and ultimate

moment capacity) to likely variations in material strengths.

Beams U1, U3 and U4 described in item 3 are used forthis analysis, as well as the standard model discussed in item

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3.3. The numerical modelling of composite beams subjected

to uniformly distributed loads is not a straightforward process,

particularly due to their highly nonlinear behaviour. Hence, by

identifying the key structural variables which can affect thesystem response, possible differences between numerical and

tests results could be further comprehended.The range of steel and concrete strengths is assumed based

on observed variations for nominally identical samples. The

material properties studied are: (a) steel: web and flanges yield

stresses and ratios between the strain at strain hardening and the

yield strain; (b) concrete: compressive strength.The main results are as follows (a comprehensive description

of the material properties adopted and the case studies

considered can be found in Queiroz et al. [16]).

4.1. Influence of the slab concrete strength

It was noticed that, increasing the concrete strength, for afixed combination of yield stresses for the flanges and web:

the lower and upper bounds increase in terms of both the

ultimate load and the associated deflection. In some cases,

the failure mode of the composite beam can change from

slab crushing to stud failure; the corresponding loaddeflection curve becomes stiffer, but

this effect is not very significant when compared with the

effect previously mentioned.

These results confirm the outcomes discussed in item3.4.1.

4.2. Influence of the yield stress of the flanges and web

It could be observed that, for a fixed slab concrete strengthand increasing either the flanges or the web yield stresses:

the lower and upper bounds increase in terms of the ultimate

load;

the corresponding loaddeflection curve becomes stiffer. For

the range of material properties considered in the parametricanalysis, the change in the loaddeflection curve was more

significant for the cases in which the web yield stress was

modified.

4.3. Influence of the ratio of strains at strain hardening and at

yield

For the range of values considered, the steel ratio between

the strain at strain hardening and the yield strain did not

significantly affect the overall response of the composite beam.

Based on the outcomes of the sensitivity analysis, it can

be concluded that the web yield stress is the key structural

parameter in the definition of the overall shape of the

loaddeflection curve of the composite beams analysed. An

increase in this property makes the curve become stiffer. In

addition, the failure mode of the composite beams can be

influenced by the concrete strength.

5. Effect of partial shear connection

In this section, the proposed finite element model is used

to assess the influence of the effects of partial shear connection

and partial interaction not only on the overall flexural behaviour

of the structural system (represented by the loaddeflection

curve), but also on the associated failure modes for either slabcrushing or stud failure, and on the distribution of stud shear

forces along the beam length. In order to isolate the effect of

the level of shear connection, the material properties (steel,

concrete and shear connectors) and dimensions of the beam

E1 tested by [13] are used for all analyses. Two load cases

are considered: midspan point load and uniformly distributed

load. The levels of shear connection are calculated using the

actual material properties measured during the experimental

procedure. In the present study, levels ranging from 47% to

136% (by means of varying the number of shear connectors)

are analysed using the standard finite element model

(item 3.3).

As the present model of composite beams adopts a solidelement to represent the concrete material and a nonlinear

spring to model the shear connectors, the interaction between

the slab and the studs cannot be investigated explicitly. A

more refined model which adopts three-dimensional solid

elements for the shear connectors would be the ideal option

in order to capture this effect. Nevertheless, such an approach

would certainly lead to complications as far as the total size

of the finite element mesh (which can lead to a significant

increase in running times) and numerical convergence problems

are concerned, especially if the crushing capability of the

concrete material is not disabled. Based on comparisons with

experimental tests, the use of springs to model the studs has

proved to be, in spite of its simplicity, very efficient in terms offinite element analyses.

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Fig. 41. Load-deflection curve Midspan concentrated load.

Fig. 42. Load-deflection curve Midspan concentrated load Initial

stiffness.

5.1. Midspan point load case

The loadmidspan deflection curves for all cases (each one

having a different level of shear connection) are shown inFig. 41.Fig. 42presents these curves just for the initial branch,

in order to better illustrate the differences between the curves

in terms of initial stiffness. It can be observed that, as expected,

on decreasing the level of shear connection the system became

more flexible, with reduced strength and stiffness. However, the

decrease in stiffness did not seem to be as significant as the

decrease in the ultimate load.

The three higher levels (118%, 130% and 136%) resulted

in very similar curves, in terms of both stiffness and ultimate

load, represented by the lower and upper bound values, with

the mode of failure being slab crushing at the midspan of

the beam (location of maximum bending moment). Regarding

level 100%, its mode of failure could be either slab crushingor stud failure, as a stud failure point was obtained between

the lower and upper bounds. As the three lower levels (47%,

71% and 89%) resulted in stud failure, the level 100% was an

intermediate level between the two possible modes of failure.

The ratio between the ultimate load and the load at the end

of the elastic behaviour was not much affected by the distinct

levels of shear connection, being in the range from 1.5 to 2

for all cases, which is a common value as far as steelconcrete

composite beams are concerned.

The stud force distribution related to the composite beam

ultimate load is plotted relating force ratio to stud position in

Fig. 43. It can be seen that the variation of the stud force ratio

of all curves is approximately 10%. Moreover, if the 136% levelis not considered, this variation is only 5%. This means that, at

Fig. 43. Ratio of stud forces vs. relative position of the stud.

Fig. 44. Load-deflection curve UDL.

Fig. 45. Load-deflection curve UDL Initial stiffness.

ultimate load and regardless of the level of shear connection, the

connectors were able to redistribute the load almost uniformly

among them.

The results demonstrate that, therefore, the effects of partial

interaction, which are increased by the use of partial shearconnection, can be neglected for levels of shear connection

above 100%, as no significant improvement in terms of either

strength or stiffness of the beam was observed.

5.2. Uniformly distributed load case

The loadmidspan deflection curves for all cases are shown

inFig. 44. It can be observed that, as occurred for the midspan

load case, decreasing the level of shear connection makes

the system become more flexible, with reduced strength and

stiffness. Once more, the decrease in stiffness did not seem to

be as significant as the decrease in the ultimate load (Fig. 45).

The two higher levels (130% and 136%) resulted in verysimilar curves, in terms of both stiffness and ultimate load,

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Fig. 46. Ratio of stud forces vs. relative position of the stud.

represented by the lower and upper bound values, with the

mode of failure being slab crushing at the midspan of the

beam (location of maximum bending moment). Regarding level

118%, its mode of failure could be either slab crushing or studfailure, as a stud failure point was obtained between the lower

and upper bounds. As the other four levels (47%, 71%, 89%

and 100%) resulted in stud failure, the level 118% was an

intermediate level between the two possible modes of failure.

The ratio between the ultimate load and the load at the end

of the elastic behaviour was similar to the one observed for the

midspan point load case (from 1.5 to 2 for all cases).

The stud force distribution graph (Fig. 46) is plotted relating

force ratio to stud position. It can be noticed that the connectors

were able to plastify and redistribute the load almost uniformly

among them for a length of approximately 30% of the span

from each of the supports (0 X/L 0.3). In the central

region of the beam (0.3 X/L 0.5), the studs were lessheavily loaded. This behaviour occurred for all levels of shear

connection, except the two highest ones (130% and 136%), for

which the length of the central region increased by 10%.

The results show that, for the UDL case, the effects of

partial shear connection can be important for levels of shear

connection above 100%. It was observed that the connectors

were not loaded uniformly along the beam length (Fig. 46), with

the stud forces decreasing towards the midspan of the beam.

In addition, this behaviour is augmented by local deformations

of the concrete slab. Consequently, more shear connectors

are needed in order to obtain a total interaction level, for

which the effects of partial interaction may be neglected.

In spite of the fact that current design codes assume thesame strength for all shear connectors, as well as a uniform

distribution of load among them for the ultimate limit state,

an 18% difference between the total-interaction levels for the

concentrated load (100%) and UDL (118%) cases was obtained.

Nevertheless, this difference is not sufficiently significant to

propose modifications to well accepted design methods.

6. Conclusions

A three-dimensional finite element model of composite

beams is proposed based on the use of the commercial

software ANSYS. It has proved to be effective in terms of

predicting the loaddeflection response for beams subjected to

concentrated or uniformly distributed loads, longitudinal slipat the steelconcrete interface, shear force carried by the studs

and the mode of failure (stud failure or concrete crushing). It is

also able to investigate beams with either full or partial shear

connection. Comparisons against experimental results and

against alternative numerical analyses indicate that the presentmodel can be used to perform extensive parametric studies.

Based on the use of this model, it was shown that

the continuation of the shear connection beyond the beam

supports of simply supported beams can affect not only the

overall system response, but also the slip and the stud force

distributions along the beam.

Results from a parametric analysis, designed to investigate

the overall structural behaviour of composite beams when

different concrete compressive strengths are used in the slab

and in the associated push-out tests, revealed that the slab

concrete strength (for a fixed concrete strength for the push-out

specimen) can have an influence not only on the overall stiffness

of the system and on its ultimate moment capacity, but also onthe stud forces. In addition, for a fixed slab concrete strength,

it was observed that the concrete strength of push-out tests

appears to have a small influence on both the overall behaviour

of the composite beam and the stud force distribution.A sensitivity study was also undertaken, focused on the

assessment of the influence of small variations in key input

parameters (i.e., concrete and steel material properties) on the

overall structural behaviour of composite beams. For the range

of material properties considered, it was noticed that the web

yield stress was the main structural parameter influencing the

definition of the overall shape of the loaddeflection curve of

the composite beams analysed. In addition, it could be observed

that the slab concrete strength can affect the mode of failure ofthe composite beam, confirming the outcomes obtained in the

previous parametric study.Finally, a study was carried out on the effects of partial

shear connection/partial interaction. It was demonstrated that,

by decreasing the level of shear connection, the composite sys-

tem becomes more flexible, with reduced strength and stiffness,

mainly for beams with less than 100%, for which the partial in-

teraction effects are significant and must be taken into account.The proposed three-dimensional model provides the

opportunity to develop insights that would be virtually

impossible using experimental tests, due to costs and,

especially, the dispersion of material properties that inevitably

occurs in laboratory work. For instance, in the investigation

of the influence of the level of shear connection, the concrete

strength effect could be easily disregarded by the consideration

of a fixed value for this property. Despite the fact that the

proposed three-dimensional model is able to accurately provide

a wide range of results, including the detection of local

aspects of behaviour (e.g., local deformations of the concrete

slab), a two-dimensional model could be the solution for

more complex structural systems (e.g., beams with different

degrees of continuity), due to numerical convergence aspects

and processing times.

Acknowledgment

The authors would like to acknowledge the support providedby the Brazilian Foundation CAPES.

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