Journal of Constructional Steel Resear

a

ng

acc

icuforversteatid oes oValidation of the new approach is carried out through comparison of simplified 2D models with the results obtained from a recent experimentalinvestigation as well as from more complex 3D numerical simulations.c 2006 Elsevier Ltd. All rights reserved.Keywords: Effective width; Shear lag; Composite beams

1. Introduction

The enhanced stiffness, strength and ductility of compositesteelconcrete beams in comparison with RC and steelcounterparts, which result from the synergy between the twomaterials, have been recognised for many years [17,30]. Theconsideration of this type of member in the design process istreated in a similar manner to that of steel and RC members,i.e. through the application of traditional T-section analysis andemployment of simplified 2Dmodels for the structural analysis.This simplification however involves a number of assumptions,most notably regarding the definition of the portion of slabmobilised, referred to as the effective width. When a compositebeam deforms, shear strains develop in the slab and cause ashear lag effect. This consists of non-uniform distributions ofnormal stresses across the slab width and the non-planarity ofthe slab cross-section. The effective width allows considerationof this effect and it is typically used both for the structural

that considered mainly elastic behaviour. In recent years,several research studies (e.g. Amadio and Fragiacomo [9],Chiewanichakorn et al. [19]) have been performed whichrecognised that the effective width is not a constant parameterand changes with the development of inelasticity on thecomposite member. This work resulted in various suggestedmodifications for assessing the effective width.

In this paper, the behaviour of several composite beamsis assessed through detailed 3D numerical simulations whichprovide an insight into the key parameters influencing theeffective width. A new proposed methodology for evaluatingeffective widths is then described. The approach is moreconsistent with underlying behavioural principles and isalso easier to apply compared to other existing proceduresbut, at present, is limited to composite beams with fullinteraction. The method is applied in a parametric study toexamine the influence of the various parameters governingAssessment of effective slab

J.M. Castro, A.Y. Elgh

Department of Civil and Environmental E

Received 4 October 2006;

Abstract

This paper deals with the behaviour of composite beams with partstructural analysis and design. Current design codes propose valuesignoring in this way the influence of other important parameters. Seillustrate these parameters and accordingly a new methodology is suggeapply in comparison with other existing methods based on stress integrrepresentation of the actual beam state when simplified analysis is carrieis mostly related to the actual slab width and, in many cases, the valuanalysis and design stages.The effective widths prescribed by current design codes

were established many years ago and are based on research

Corresponding author.E-mail address: a.elghazouli@imperial.ac.uk (A.Y. Elghazouli).

0143-974X/$ - see front matter c 2006 Elsevier Ltd. All rights reserved.doi:10.1016/j.jcsr.2006.11.018ch 63 (2007) 13171327www.elsevier.com/locate/jcsr

widths in composite beams

zouli, B.A. Izzuddinineering, Imperial College, London, UK

epted 27 November 2006

lar focus on the effective slab width, which is required for simplifiedthe effective width which are mostly a function of the beam span

al 3D numerical simulations are conducted in this paper in order tod for evaluating the effective width. The proposed approach is easier toon, and provides effective width values which result in a more reliableut. The application of the new method indicates that the effective widthbtained can significantly differ from those proposed in design codes.the effective width and to illustrate that this parameter islargely related to the actual slab width. Finally, simplified 2Dnumerical simulations are conducted to predict the responseobtained from a recent experimental study on a simplysupported composite beam as well as from more complex3D analyses.

cti1318 J.M. Castro et al. / Journal of Constru

2. Previous studies on effective width

The study of shear lag effects in composite systems startedduring the sixties when several researchers extended existingwork on steel plates [31] and applied the concepts to compositebeams. Adekola [2] used the analytical solutions derived byAllen and Severn [7] and calculated effective widths forsimply supported beams considering the variation of geometricparameters. Several years later, Ansourian [10] applied thefinite element method to perform elastic analysis of fixedcomposite beams. From the results, it was concluded thataccurate slab stresses are obtained when the effective width istaken as one quarter of the span. On the other hand, to achieveadequate accuracy in obtaining steel beam stresses, the use ofan effective width equal to the actual slab width was suggested.

Heins and Fan [24] presented an analytical method forpredicting the ultimate load behaviour of simply supportedcomposite bridge decks. The method involved the applicationof the finite difference technique to solve a set of coupledpartial differential equations and elasto-plastic behaviour wasaccomplished by a step-by-step incremental load procedure.With the developed method, effective widths of slabs at ultimateload were evaluated.

Fahmy and Robinson [23] investigated ten compositecantilever beams incorporating ribbed metal deck andrepresentative of positive moment beam-to-column connectionsof an unbraced frame. Nonlinear material behaviour andshear interaction were considered in the analysis. Effectivewidths for strength and stiffness calculations were determined.This investigation proposed a direct relationship between theeffective width and the length-to-width ratio and the columnwidth-to-slab width ratio. Elkelish and Robinson [22] in asimilar study examined the influence of the type of loading onthe effective width. Results from this work have also indicatedhigher effective widths in the inelastic range compared to thosefor the elastic stage.

Brosnan and Uang [11] performed numerical studies usingANSYS of composite L-beams (edge beams) and concludedthat the effective widths of slab in these systems are differentfrom those proposed in the codes for internal compositebeams (T-beams). More recently, Amadio and Fragiacomo [9]conducted a series of parametric studies of simply supportedand cantilever composite beams using ABAQUS. Both elasticand nonlinear analyses were performed and different levelsof shear connection were considered. The results for elasticbehaviour showed that the connection deformability is a veryimportant parameter on the evaluation of the effective widthfor stress analysis. Proposed values were given for cross-sections along the beam span. On the other hand, the full widthwas proposed for stiffness calculations. The results from thenonlinear analyses showed the enlargement of the effectivewidths obtained for the elastic stage even reaching the full slabwidths in some situations. These conclusions were validatedwith results obtained from experimental tests performed on fourcomposite beams [8].From a review of the literature on effective width, thecomplexity and inconsistencies surrounding this issue becomeonal Steel Research 63 (2007) 13171327

apparent. Nevertheless, it is evident that the effective widthdepends on a number of parameters such as the span, beamspacing, boundary conditions, degree of shear connection, etc.Clearly, the effective width is not constant along the span ofa composite beam and changes during the loading processparticularly at the onset of plasticity.

3. Existing definitions and provisions

There is no standard definition for effective width that can begenerally acceptable for all conditions. Two main approachesfor the evaluation of this parameter are often referred to in theliterature. One is related to the stress state of the slab and asecond to the stiffness of the composite beam.

The first definition is based on the stress distributions in theslab, which is directly related to the shear lag phenomenon. Inthis case, the effective width (beff) is considered as the widthof slab that sustains a force equal to that in the actual slab,assuming the longitudinal stresses (x ) to be constant across theeffective slab width and equal to the peak stress over the steelbeam centreline, as shown in Fig. 1. In mathematical terms, thisis expressed as follows:

beff = 1[x ]y=0 + b2 b2

xdy. (1)

The level at which the stresses should be obtained is not clearlyestablished. It can be applied to the top surface stresses in theslab or at the mid-plane surface. Fahmy and Robinson [23] andElkelish and Robinson [22] employed a modified version of theoriginal definition as the effective width was evaluated from theratio of the total force developed in the slab to the integration ofstresses in the centreline of the beam through the slab thickness,such that

beff = + tslab2 tslab2

+ b2 b2

xdydz + tslab2 tslab2

[x ]y=0dz. (2)

Recently, Chiewanichakorn et al. [19] calculated effectivewidths based on results from 3D finite element analysis. Byrecognising that the stress pattern is not constant through theslab thickness, the effective width was established in such away that the total force developing in the slab and its point ofapplication is the same in both the 3D model and in a simplifiedT-section analysis.

The other approach, whereby the effective width is basedon stiffness calculations, involves the determination of thedeflection of a composite beam and then, from analyticalexpressions, derivation of the equivalent second moment ofarea that will cause the same deformation in the idealisedbeam. From the equivalent second moment of area, an averageeffective width is then estimated [3,11].

It is important to note that the effective widths derived fromthe two approaches can be substantially different, as shownby Brosnan and Uang [11]. Also, care must be taken when

dealing with an effective width based on stiffness in cases whereconsiderable shear connection deformation is expected.

nalJ.M. Castro et al. / Journal of Constructio

Fig. 1. Stress-based effective width.

Fig. 2. Equivalent spans (Le) proposed in Eurocode 4 [13].

In terms of the design guidance for effective width,codes normally provide simplified provisions. To discuss this,European, British and North American provisions are brieflysummarised below.

The effective width proposed in design codes is typicallya function of the beam span. For example, Eurocode 4 [13]recommends that the total effective width (beff) should bedetermined as the summation of the effective widths evaluatedon each side of the beam web (bei). The value of bei isequal to Le/8 but should not exceed the geometric width biwhich corresponds to half of the distance between adjacentbeams, where Le is the equivalent span corresponding to theapproximate distance between points of zero bending moment.For typical continuous composite beams in frames, Eurocode4 stipulates the equivalent spans illustrated in Fig. 2. It is alsoworth noting that Eurocode 4 allows the adoption of a constanteffective width over the whole of each span. These provisionsare similar to those prescribed in the British Standard 5950 [12].With regard to North American proposals for effectivewidth, the most recent AISC provisions [5] are relatively simpleSteel Research 63 (2007) 13171327 1319

when compared to their European counterparts. In AISC 360-05, no guidance is provided for continuous beams. However,in the commentary document of the code [6], a simplifiedapproach is suggested for evaluating stiffness of continuouscomposite beams which considers a weighted average ofsecond moments of area in the positive and negative bendingmoment regions of the beam.

The effective width recommendations available in mostcode provisions were derived on the basis of gravity loadingconditions. Therefore, different values of the effective widthwould be expected for composite beams under lateral loadingconditions such as those due to seismic actions [21,16].Eurocode 8 [14], specifically addresses this scenario byproposing different effective widths to those prescribed inEurocode 4. In addition, Eurocode 8 also distinguishes betweeneffective widths for use in analysis and for strength calculations.The values proposed are mostly a function of the span lengthbut are also dependent on column dimensions. Due to thesignificant differences between the effective widths proposed inEurocode 4 and those proposed in Eurocode 8, designers mayencounter some difficulties during the design process.

In addition to the effective width proposals provided forcomposite beams in building structures, similar recommenda-tions are available for composite bridges. A detailed summaryand comparison of these proposals can be found elsewhere [4,18]. It is worth mentioning that most provisions propose the ef-fective width as a function of the span length and limited by thedistance between adjacent beams. However, in the AASHTOspecifications [1], the effective width is also a function of theslab thickness. Another important observation is that most rec-ommendations for building and bridge structures do not dif-ferentiate between effective widths for use in analysis and forstrength evaluation.

4. Detailed numerical assessment

The behaviour of a simply supported composite beam underpositive bending moment is now investigated through a 3Ddetailed model of a six metre composite beam analysed inADAPTIC [25]. The main aspects of the behaviour are pointedout for both the elastic and inelastic stages. The beam consistsof a 120 mm thick concrete slab and a European IPE 300 steelsection. The total slab width is 2.5 m. Steel is assumed to have ayield strength of 275 N/mm2 whereas the uniaxial compressiveand tensile strengths of concrete are 30 N/mm2 and 2 N/mm2,respectively.

In terms of the numerical model, the steel section isrepresented with 3D cubic elasto-plastic beam elements (cbp3)[28] incorporating a fibre approach. On the other hand, theconcrete slab is modelled with a recently developed flatshell element (csl4) [29] which has been validated againstexperimental results [20]. This novel element is able toefficiently reproduce the behaviour of geometrically orthotropicslabs such as typical ribbed steel-decked composite floorsystems. Both beam and shell elements account for geometric

nonlinearities. Composite action is achieved through inclusionof special link elements (lnks) [26] with rigid axial and bending

uctio

orte

arise for the evaluation of effective widths based on stresscalculations. The nearly ufor both middle and topas visible as would be exto the low gradient of bthe beam is loaded withstress distribution at the bobserves its tensile peak aof the steel beam. This caarising from the presence

The influence of sdistribution in the slab idirectly related to the in-

ear stiffness. Two newch the slab widths areectively. The mid-spanre plotted in Fig. 5. Asevident for larger slab

ctly related to the in-thickness. For thickertherefore the presenceillustrated by observingniform stress distribution is also notedsurfaces. The shear lag effect is notpected. The reason for this is relatedending moment at the mid-span asa uniformly distributed pressure. Theottom surface is also of interest as itt the edges rather than at the centrelinen be attributed to the localised effectsof a rigid link.lab width on longitudinal stress

larger the slab width, the lower the shcomposite beams are analysed in whitaken equal to 1.5 m and 3.5 m, respstress distributions at the mid-surface aexpected, the shear lag effect is morewidths.

A second parameter which is direplane shear stiffness of the slab is itsslabs, the shear stiffness is higher andof shear lag is attenuated. This trend is1320 J.M. Castro et al. / Journal of Constr

Fig. 3. Simply supp

properties which connect the centroids of both the steel sectionand the slab. Note that full interaction is assumed, betweenthe steel beam and the slab, and that a layer of reinforcementrepresenting a ratio of 0.4% of the slab cross-section isprovided. A representation of the numerical model is shown inFig. 3.

With regard to the material models adopted, a typicalbilinear elasto-plastic model with strain hardening (stl1)is employed for steel whereas for concrete a biaxialmodel (con11), which accounts for the combined effects ofcompressive nonlinearity and tensile crack opening and closure,is adopted. In this model, compressive nonlinear response isdealt with according to plasticity theory in which a biaxialinteraction surface is employed. Account is taken of thehardening (before pre-crushing) and softening compressiveresponse. Tensile behaviour is considered through a smearedcrack approach assuming a fixed crack orientation. Softeningresponse in tension is incorporated to represent tensionstiffening effects. Further details of this model can be foundelsewhere [27,29].

In order to assess the parameters influencing the longitudinalstress distribution in the slab, various loading conditions aswell as different slab widths and thicknesses are considered anddiscussed below.

4.1. Elastic behaviour

Focusing on the elastic range, the longitudinal stressdistribution across the slab is firstly examined. The beam isloaded with a uniformly distributed pressure. In Fig. 4, the mid-span stress distributions at top, middle and bottom surfacesare depicted. It is clear from the figure that the stress patternis not constant across the slab thickness; hence difficultiess now examined. This parameter isplane shear stiffness of the slab. Thenal Steel Research 63 (2007) 13171327

d composite beam.

Fig. 4. Longitudinal stress distributions across slab width at different slabsurfaces.

Fig. 5. Influence of slab width (b) on stress distribution at mid-surface.the stress distributions plotted in Fig. 6. It is clear that whenthe slab thickness is smaller, the variation of the longitudinal

alJ.M. Castro et al. / Journal of Construction

Fig. 6. Influence of slab thickness (tslab) on stress distribution at mid-surface.

Fig. 7. Influence of load type on stress distribution at mid-surface.

stress is relatively more evident. However, the influence of thisparameter is not as significant as that observed for the slabwidth.

The last parameter investigated is the type of load. Theresults presented above were obtained from a beam loadedwith uniform pressure. Two new cases are now analysed. Inthe first one, a single point load is applied at the mid-span ofthe composite beam whereas in the second case a line loadis applied at the mid-span of the beam, transversely to thelongitudinal direction. The stress distributions at mid-surfaceare depicted in Fig. 7, which clearly demonstrate the influenceof the load type on the beam behaviour. When a single pointload is applied, the stress variation is very significant. Evidently,if effective widths are derived on the basis of stress calculations,the resulting values can be considerably different depending onthe load type.

4.2. Elasto-plastic behaviour

The inelastic behaviour of the composite beam is examinedin this section. In order to illustrate the change of stress patternin the slab for increasing levels of plasticity, a point load is

applied at mid-span to represent a case of significant shear lag.In Fig. 8, the longitudinal stress distribution in the top surfaceSteel Research 63 (2007) 13171327 1321

Fig. 8. Top surface longitudinal stress distributions across slab width at mid-span for increasing levels of deformation.

Fig. 9. Edge-to-centreline (edge/centre) stress ratio.

of the slab is plotted for different levels of deformation ().At 3.25 cm, the distribution corresponds to the point when thestress at the centreline attains the peak. Similarly, for a verticaldeformation of around 6 cm, the peak stress is reached at theslab edge.

Inspection of Fig. 8 reveals that compressive longitudinalstresses in the slab tend to become uniform for increasingdemand levels. When the peak stress is reached at thecentreline, these fibres enter a softening regime (incorporated inthe concrete constitutive model) and stress redistribution occursin the slab. At a certain stage, the stresses at the edge are highercompared to those at the centreline. The ratio between edge andcentreline stresses (edge/centre) is depicted in Fig. 9.

Examination of Fig. 9 provides useful information regardingthe nonlinear behaviour of the composite beam. It is of interestto point out that the stress ratio remains constant while thebeam response is fully elastic. However, a reduction in this ratiois observed from a vertical deformation of about 1 cm. Thiscorresponds to the occurrence of first yield in the bottom flangeof the steel beam. At around 2.5 cm, the ratio between edgeand centreline stresses starts increasing due to the initiation of

nonlinear concrete response. After 3.25 cm, the peak stress isattained at the centreline and the redistribution of stresses in the

1322

the composite beam. Asssive stresses develop inund the beam centreline.vided in this sectiontress state developing inear that shear lag effects

occur in the elastic range but, due to material nonlinearity, stressFig. 10. Variation of top surface concrete stresses at mid-span with verticaldeformation.

Fig. 11. Top surface transverse stress distribution along the centreline of thecomposite beam.

slab starts developing. This is reflected in a steep increase ofthe stress ratio. For a vertical deformation of about 6 cm, thepeak stress is reached at the slab edge and another change isobserved in the stress ratio curve.

With regard to stress magnitudes, the high values recordedfor the concrete peak stresses are noteworthy. As indicated inFig. 8, concrete stresses reach values well above 30 N/mm2,the uniaxial strength considered for concrete. In Fig. 10,top surface concrete stresses at mid-span are plotted againstvertical deformation. It becomes clear from the figure thatconcrete stresses at both centreline and slab edge reach valuesmarkedly higher compared to the uniaxial strength considered.This behaviour is intimately related to the confining effectsFig. 12. Curvature evaluationredistribution develops in the slab. The concept of a singleeffective width for use in both analysis and strength calculationsis therefore inaccurate and its use is not supported by eithernumerical or experimental observation.

5. Proposed approach

5.1. Description

A new approach is now presented to assess the effectivewidth of composite beams in the linear elastic range. Themethod can be applied to beams under positive and negativebending moment [15] but is currently limited to full-interactioncases.

Rather than evaluating the effective width based on thecomplex stress patterns developing in the slab, the approachconsists of finding equivalent second moment of areas fromresults obtained using a 3D finite element model. This modelis similar to those employed before in the investigation ofcomposite beam behaviour.

By analysing the 3D model subject to a set of loading andboundary conditions, the strain profiles () at the steel sectionsand the corresponding curvatures () can be readily obtained,as shown in Fig. 12.

Since the bending moment applied is also a knownparameter, the equivalent second moment of area (Ieq) of thecross-section can be easily derived by applying the expression

= ME Ieq

Ieq = ME . (3)

The effective width of the cross-section under consideration canthen be readily derived.

This approach has several advantages when comparedto those based on stress calculations. Firstly, it avoids thecomplexity of stress integration. It also provides more accuraterepresentation of the behaviour as it maintains the locationof the elastic neutral axis for a given bending moment. Thisis not however the case for stress-based methods in whichthe effective width is evaluated by controlling the level ofinternal forces in the slab whilst not ensuring that these are thenmobilised under the same bending moment in the simplifiedJ.M. Castro et al. / Journal of Constructional Steel Research 63 (2007) 13171327

developing at the mid-span region ofshown in Fig. 11, significant comprethe transverse direction at mid-span aro

The numerical observations prodemonstrate the complexity of the sthe slab of a composite beam. It is clin the proposed approach.

alJ.M. Castro et al. / Journal of Construction

analysis. An additional advantage of the new approach isthat it can be easily applied for obtaining effective widthdistributions along the length of composite beams. It shouldalso be noted that this approach can be used directly for bothsimply supported and continuous composite beams.

The suggested method may seem to imply that a Mbeffrelationship exists for a given composite beam. This is notnecessarily the case as curvatures in the 3D model are sensitiveto bending moment gradients. This observation is furtheremphasised by the different stress patterns obtained for variousloading conditions (Fig. 7).

As noted before, despite its advantages, this new approachdoes not currently incorporate beams with partial interaction.This extension could be an interesting topic for future research.It is also worth mentioning that the influence of the type ofshear connection is not considered in this approach. However,this aspect is deemed to be more relevant in beams withpartial interaction and is obviously of extreme importance whenductility and capacity issues are under investigation.

5.2. Illustrative examples

The applicability of the proposed approach is now examinedby applying it to some of the beams already investigated inthe detailed numerical study presented before in this paper.Note that, unless stated otherwise, the beams are loaded with auniformly distributed pressure. The influence of four geometricparameters is assessed by plotting the effective widths along thebeam.

The first parameter examined is the slab width (b). In Fig. 13effective widths are plotted for three composite beams with slabwidths of 1.5 m, 2.5 m and 3.5 m.

As expected, a higher percentage of slab is mobilised forthe 1.5 m case. This is consistent with the low shear lagpresent in this beam (Fig. 5) and confirms the higher in-planeshear stiffness associated with this case. On the other hand,for larger slab widths, the percentage of width mobilised issmaller; however an increase of effective widths is observed.The curves shown in Fig. 13(b) contradict the conventionalrecommendation of considering the effective width uniquely asa function of the span length. From the results, and focusing onthe effective width at mid-span rather than its variation over thespan, it is clear that the effective width is strongly dependenton the actual slab width. It should also be noted that, in thisexample, the value of L/4 proposed in most codes is only validfor the composite beam with 1.5 m of slab width.

The second parameter studied is the slab thickness.Two new variant beams are considered with 80 mm and150 mm slabs respectively. The effective width distributionsare depicted in Fig. 14. The results obtained show that thickerslabs are associated with higher in-plane shear stiffness andconsequently, with larger effective widths. Like the previousparameter, the effective width is more sensitive to variations inslab width rather than span length.

The influence of span length on the effective width

distribution is also examined. An additional composite beam of10 m length is analysed and the results are presented in Fig. 15.Steel Research 63 (2007) 13171327 1323

Fig. 13. Influence of slab width (b) on effective width distribution.

Visual inspection of the figure indicates the larger slab widthmobilised in the longer beam. The agreement with the estimateof Eurocode 4 for this beam is noteworthy, which is not thecase for the 6 m beam. However, a better correlation betweenthe effective width and the full slab width is again confirmed.

The proposed method for effective width evaluation is nowapplied to a cantilever beam loaded upwards at the tip. Thissystem is intended to represent a composite beam under lateralloading spanning to an external joint. The slab edge is assumedto be aligned with the column flange. Therefore, only anassumed length (bc) of 0.25 m is restraining the slab in-plane.The objective is to investigate whether the proposed approach isable to represent a reduced effective width in the contact regionwith the column. The effective widths obtained are representedin Fig. 16. The figure clearly shows a smaller effective widthin the contact region. The value obtained is around 2bc,i.e. 0.50 m. This corresponds to double the restrained lengthwhich appears to be realistic.

The analyses described above illustrate the applicability ofthe proposed method for effective width evaluation. Due toits simplicity and efficiency, it can be used for performingextensive parametric studies to quantitatively investigate theparameters affecting the effective width in the elastic range.It is important to note that the elastic effective widthsobtained at the mid-span of the beam are in the range of

cti1324 J.M. Castro et al. / Journal of Constru

Fig. 14. Influence of slab thickness (tslab) on effective width distribution.

80%100% of the actual slab width. This conclusion, coupledwith previous observations of stress redistribution in the slab inthe inelastic range, suggests that consideration of full widthsfor 2D frame analysis and strength evaluation appears to bean alternative approach to current code proposals. To assessthe validity of this suggestion, two comparative studies areundertaken and described in the following section.

6. Comparative studies

In order to assess the validity of adopting effective widths in2D analysis larger than that prescribed in codes, a comparison isperformed hereafter between the results obtained from a recentexperimental study conducted by Amadio et al. [8] on a simplysupported composite beam (B4 specimen) and those obtainedfrom simplified 2D beam analyses. It should be noted that thepurpose of this section is not to check the accuracy of theproposed approach described above but to investigate the globaland local response of composite beams, particularly when largeeffective widths are adopted.

As illustrated in Fig. 17, the test specimen consists of a3.8 m composite beam comprising a European HEB 180 sectionwhich supports a 120 mm thick and 1.6 m wide concrete slab.

Full shear connection was achieved by using 56 headed studswith 16 mm diameter and 100 mm height. The beamwas loadedonal Steel Research 63 (2007) 13171327

Fig. 15. Influence of beam span (L) on effective width distribution.

Fig. 16. Influence of external joint on effective width distribution.Fig. 17. Specimen B4 tested by Amadio et al. [8].

al

on

predicting the response obtained from the test. Shear interactionis considered using the smodel.

The global response ofboth the experiment andInspection of the figure indsimplified 2D model when80% of the actual slab widultimate capacity are almothe test and provide more ac

els are compared with thesults. In all the models,e strain gradients of thel section, and the resultslearly illustrate the betteradopting effective widthse. However it should beame approach adopted for the 2D

the composite beam obtained fromthe analyses is shown in Fig. 19.icates the accuracy provided by thethe effective width is considered asth. Both the initial stiffness and the

The results from the various 2D mod3D model due to absence of test rethe curvatures are obtained from thbeam element representing the steeare presented in Fig. 20. The curves cestimate provided by the 2D modelslarger than that proposed by the codJ.M. Castro et al. / Journal of Construction

Fig. 18. 2D idealisati

Table 1Steel properties of the B4 specimen

Material E (N/mm2) fy (N/mm2) (%)

Structural steel 210 000 317 1Reinforcing steel 210 000 554 2

Table 2Concrete properties of the B4 specimen

Property (N/mm2) Value

E 36 744fc 41.60ft 3.32

with two symmetric concentrated loads applied at 0.5 m fromthe mid-span. The mechanical properties of the materials forspecimen B4 are listed in Tables 1 and 2.

Like the 3D models employed before, the simplified 2Dmodels prepared in ADAPTIC consist of representing thecomposite beam by two parallel lines of cubic elasto-plasticbeam elements (cbp2) incorporating a fibre approach. Thelower line corresponds to the steel section whereas the upperline represents the concrete or composite slab. As shown inFig. 18, the two lines of beam elements are positioned at thecentroids of the two constituent parts and composite action isachieved through inclusion of links (lnk2) with rigid properties.Joint elements (jel2) are also incorporated at appropriatelocations within the links in order to model the interactioneffects as realistically as possible.

With regard to material modelling, a bilinear elasto-plasticmodel (stl1) is adopted for both structural and reinforcing steel.On the other hand, concrete nonlinear behaviour is accountedfor by adoption of a uniaxial constitutive model (con1)featuring both compressive and tensile softening. In terms ofshear interaction, trilinear behaviour curves are assigned to thejoint elements based on the properties provided by Amadioet al. [8].

An additional 3D model, similar to those described before inthis paper, is prepared in ADAPTIC to compare its accuracy inst coincident with those observed incurate representation in comparisonSteel Research 63 (2007) 13171327 1325

of a composite beam.

Fig. 19. Global response of the B4 specimen.

with the case when the code effective width (L/4) is employed.The excellent prediction provided by the 3D model is alsoworth noting, although this model is computationally muchmore demanding.

The local response is now examined by comparing themomentcurvature relationships evaluated at the central regionof the composite beam which is under pure bending conditions.mentioned that, for the same level of vertical deformation, largeeffective widths lead to an overestimation of curvatures.

cti1326 J.M. Castro et al. / Journal of Constru

Fig. 20. Momentcurvature relationships.

The comparisons established above were based on modelsincorporating shear interaction effects. However, it is of interestto check the accuracy of adopting large effective widths in a fullinteraction case. The same beam is now analysed assuming fullinteraction. The global responses obtained for both 2D and 3Dmodels are provided in Fig. 21 whereas the momentcurvaturerelationships are illustrated in Fig. 22.

Once again, the curves confirm the relative accuracyprovided by 2D models adopting effective widths approachingthe full slab width both in terms of initial stiffness andstrength. The initial stiffness ratios presented in Table 3 clearlydemonstrate that only a nearly full effective width can providea good estimate of the initial stiffness. With regard to the localresponse, it is worth noting the underestimation of maximumcurvature provided by the 2D models for the same levels ofvertical deformation of the beam.

From the above discussions it becomes clear thatconsideration of code effective widths led to an underestimationof the stiffness and capacity of a composite beam. This effectis more pronounced for small span beams. As the commoncode expression for effective width is a function of the beamspan, relatively low values are expected for such beams. Thisis reflected in smaller internal lever arms developing at thecross-section level with the consequent underestimation of thebeam capacity. However, for the case of beams associated withlarge slab widths, consideration of full effective widths leads torealistic estimates in terms of stiffness but, in some cases, thecapacity can be overestimated as compared to more detailed3D simulations, particularly when strain-hardening effects areconsidered in the 2D analyses. Nevertheless, it is relevant topoint out that only full effective widths can provide a realisticestimate of the moment capacity when plastic cross-sectionanalysis is performed.

7. Conclusions

In this paper, a new methodology for assessment of effectivewidth in composite beams is proposed. The method, which atpresent is limited to full-interaction cases, is easier to apply in

comparison with existing procedures based on stress integrationand provides more accurate estimates of the effective widthsonal Steel Research 63 (2007) 13171327

Fig. 21. Global responses for full interaction.

Fig. 22. Momentcurvature relationships for full interaction.

Table 3Initial stiffness ratios between 2D and 3D models

Effective width (beff) K2D/K3D

b 1.030.8b 0.97L/4 0.6b 0.89

to use in simplified 2D analysis. Illustrative examples showthat the effective width is mostly related to the full slab widthbut it also depends on a number of parameters such as theslab thickness, the beam span and on the boundary conditions.The effective widths obtained at the most stressed regions ofthe composite beams considered were always above 80% ofthe slab width. Additionally, detailed 3D numerical simulationsreveal that stress redistribution develops in the slab at the onsetof inelasticity. On this basis, comparisons with experimentalresults demonstrate that better predictions of the response areobtained when effective widths approaching the full slab widthare employed in 2D models.

References

[1] AASHTO. LRFD bridge design specifications. Washington (DC):

American Association of State Highway and Transportation Officials;1998.

J.M. Castro et al. / Journal of Constructional Steel Research 63 (2007) 13171327 1327

[2] Adekola AO. Effective width of composite beams of steel and concrete.The Structural Engineer 1968;46(9):2859.

[3] Adekola AO. The dependence of shear lag on partial interaction incomposite beams. International Journal of Solids and Structures 1974;10:389400.

[4] Ahn IS, Chiewanichakorn M, Chen SS, Aref AJ. Effective flange widthprovisions for composite steel bridges. Engineering Structures 2004;26(12):184351.

[5] AISC. AISC 360-05Specification for structural steel buildings. Chicago(IL): American Institute of Steel Construction; 2005.

[6] AISC. Commentary to the specification for structural steel buildings(AISC 360-05). Chicago (IL): American Institute of Steel Construction;2005.

[7] Allen DNdG, Severn RT. Composite action between beams and slabsunder transverse load. The Structural Engineer 1961;39(Part I):14954.

[8] Amadio C, Fedrigo C, Fragiacomo M, Macorini L. Experimentalevaluation of effective width in steelconcrete composite beams. Journalof Constructional Steel Research 2004;60(2):199220.

[9] Amadio C, Fragiacomo M. Effective width evaluation for steelconcretecomposite beams. Journal of Constructional Steel Research 2002;58(3):37388.

[10] Ansourian P. An application of the method of finite elements to theanalysis of composite floor systems. Proceedings of the Institution of CivilEngineers 1975;59:699726.

[11] Brosnan DP, Uang CM. Effective width of composite L-beams in

[17] Chapman JC. Composite construction in steel and concreteThebehaviour of composite beams. The Structural Engineer 1964;42(4):11525.

[18] Chiewanichakorn M. Intrinsic method of effective flange width evaluationfor steelconcrete composite bridges. Buffalo (NY): The State Universityof New York; 2005.

[19] Chiewanichakorn M, Aref AJ, Chen SS, Ahn IS. Effective flange widthdefinition for steelconcrete composite bridge girder. Journal of StructuralEngineering 2004;130(12):201631.

[20] Elghazouli AY, Izzuddin BA. Realistic modeling of composite andreinforced concrete floor slabs under extreme loading. II: Verification andapplication. Journal of Structural Engineering 2004;130(12):198596.

[21] Elghazouli AY, Migiakis CE. Effective size of composite beams forcapacity design. In: Int. conf. on steel structures, EuroSteel 99. 1999. p.58593.

[22] Elkelish S, Robinson H. Effective widths of composite beams with ribbedmetal deck. Canadian Journal of Civil Engineering 1986;13(5):57582.

[23] Fahmy EH, Robinson H. Analyses and tests to determine the effectivewidths of composite beams in unbraced multistory frames. CanadianJournal of Civil Engineering 1986;13(1):6675.

[24] Heins CP, Fan HM. Effective composite beam width at ultimate load.Journal of the Structural Division, ASCE 1976;102(ST11):216379.

[25] Izzuddin BA. Nonlinear dynamic analysis of framed structures. Universityof London; 1991.

[26] Izzuddin BA. Integration of beamcolumn and shell elements in large

buildings. Engineering Journal, AISC 1995;32(2):7380.

[12] BSI. BS 5950-3.1, Structural use of steelwork in buildingPart 3: Designin composite constructionSection 3.1 Code of practice for designof simple and continuous composite beams. London: British StandardsInstitution; 1990.

[13] CEN. EN 1994-1-1, Eurocode 4: Design of composite steel and concretestructuresPart 1.1: General rules and rules for buildings. Brussels:European Committee for Standardization; 2004.

[14] CEN. EN 1998-1, Eurocode 8: Design provisions for earthquakeresistance of structures, Part 1: General rules, seismic actions and rulesfor buildings. Brussels: European Committee for Standardization; 2005.

[15] Castro JM. Seismic behaviour of composite moment-resisting frames.Ph.D. thesis. University of London; 2006.

[16] Castro JM, Elghazouli AY. Behaviour of composite beams inmoment-resisting frames. In: 12th European conference on earthquakeengineering. Paper No. 521. 2002.displacement structural analysis. In: International symposium on newperspectives for shell and spatial structures (IASS-APCS). 2003.

[27] Izzuddin BA, Elghazouli AY. An advanced concrete model for R/C andcomposite floor slabs subject to extreme loading. In: 9th int. conf. on civiland structural engineering computing. 2003.

[28] Izzuddin BA, Elnashai AS. Adaptive space frame analysis. 2Adistributed plasticity approach. Proceedings of the Institution of CivilEngineersStructures and Buildings 1993;99(3):31726.

[29] Izzuddin BA, Tao XY, Elghazouli AY. Realistic modeling of compositeand reinforced concrete floor slabs under extreme loading. I: Analyticalmethod. Journal of Structural Engineering 2004;130(12):197284.

[30] Johnson RP. Research on steelconcrete composite beams. Journal of theStructural Division, ASCE 1970;96(3):44559.

[31] Miller AB. The effective width of a plate supported by a beam. Selectedengineering papers. The Institution of Civil Engineers; 1929. Paperno. 83.

Assessment of effective slab widths in composite beamsIntroductionPrevious studies on effective widthExisting definitions and provisionsDetailed numerical assessmentElastic behaviourElasto-plastic behaviour

Proposed approachDescriptionIllustrative examples

Comparative studiesConclusionsReferences