Analysis And Design Of Composite Beams With Web Openings
T. M. Cameira Neto / Instituto Superior Técnico (2014)Analysis and Design of Composite Beams with Web OpeningsTiago Miguel Cameira Netotiago.c.neto@ist.utl.ptDepartment of Civil Engineering, Arquitecture and Georesources, Instituto Superior Técnico, Lisbon University,Av. Rovisco Pais, 1049-001 Lisbon – PortugalJuly 2014AbstractThis paper provides guidance on determining the design resistance of composite beams with largeweb openings.A numerical model has been developed, in order to evaluate the structural behaviour of perforatedbeams as well as the influence of web openings in the load carry capacity. The non-linear behaviour ofthe concrete and steel has been taken into account. Thus, the concrete has been modelled withconcrete damaged plasticity, CDP, included in the finite element software. The model’s calibration andvalidation based in experimental tests and numerical models published, guaranteed that the modelledmaterials and simplifications made in the model would provide to the desirable results.The behaviour of beams with large web openings is described and a design model is presented.Expressions are given for the design resistances of the Tee sections above and below openings, allgenerally following the principles and terminology of Eurocodes 2, 3 and 4.Finally, the last part of the research consists in the demonstration and discusses of the parametricstudy results made from a numerical model.Keywords: Composite beam; Perforated section; Web opening; Vierendeel mechanism; Shearmoment interaction curves; Concrete damaged plasticity;1. IntroductionComposite beams comprise steel I-sectionsor H-sections attached by shear connectors to aconcrete or composite slab, so that the bendingresistance and flexural stiffness of the beamsare considerably higher than those of steelsection alone. A common method ofincorporating services within the floor-ceilingzone buildings using this form of construction isto create large openings in the webs of Isections or H-sections beams. The openings aremost likely to be rectangular or circular, and maybe in the form of discrete openings or a series ofopenings along the beam. Two examples areshown in Figs. 1 and 2.The presence of web openings may have asevere penalty on the load carrying capacities ofbeams, depending on the shapes, the sizes andthe locations of the web openings. Due to thepresence of web openings, three differentmodes of failure may take place at theperforated sections as follows:i) Shear failure;ii) Flexural failure;iii) Vierendeel mechanism.A large number of tests has been carried outon composite beams with discrete rectangularopenings, notably those at the University ofKansas, USA [1,2], and also in Canada [3] andat the University of Kaiserslautern, Germany [4].
T. M. Cameira Neto / Instituto Superior Técnico (2014)Fig. 1 Cellular beam with a series of circular openings.2Fig. 2 Rectangular web openings in composite beams.2. Behaviour of composite beams with web openingsThe forces acting around a rectangularopening in the web of a composite beam areshown in Fig. 3. The global bending action isresisted by tensile force in the lower Teesection, and by compression force in theconcrete slab, which is controlled by thelongitudinal shear forces developed in theshear connectors is limited, and thereforecompression force is also developed in theupper Tee section (as in partial shearconnection).Fig. 3 Forces around an opening in a composite beam.In general, the shear force at an opening ismainly resisted by the web of the upper Teesection, because the lower Tee section is oftenhighly stressed in tension. The concrete slabalso participates in resisting this shear force[5,6].Local Vierendeel bending action occurs dueto the rate of change of bending moment,hence the shear force, across an opening. Thisincrease in bending moment is resisted by thelocal bending resistances of the upper andlower Tee sections. At the higher moment sideof the opening, composite action occursbetween the upper web-flange section and theconcrete slab. The magnitude of this tensioncompression couple depends on the number ofshear connectors provided directly above theopening. In general, this local composite actiondramatically improves the resistance of thecomposite beam against the Vierendeelbending, and therefore longer openings can beused in composite beams than in steel beams[7].The bending resistance of a compositebeam subject to these forces is illustrated inFig. 4. For structural adequacy, the totalVierendeel bending resistance of the Teesections incorporating local composite actionat an opening, should exceed the design shearforce times the effective length of the opening,.The optimum positions for web openings inthe span of the beam depend on the relativeproportion of bending moment and shearforces. In general, the openings have a greatereffect on the shear resistance of the beam thanthe bending resistance [7]. Thus, the optimumpositions for large openings tends to beroughly at the quarter span points of auniformly loaded beam, where the shear forceis 50%, and the bending moment is 75% oftheir maximum values.Fig. 4 Global and local bending resistance due tocomposite action.
3T. M. Cameira Neto / Instituto Superior Técnico (2014)3. Analytical design approach for beams with single web openingsAn overall review on the designrecommendations [6–9] shows that in general,there are two design approaches in assessingthe structural behaviour of beams withrectangular web openings.3.1. Tee section approachIn this approach the structural adequacy ofa bema with web openings depends on thesection resistances of the tee sections aboveand below the web openings under co-existingaxial forces, shear forcesand localmoments, as shown in Fig. 5. All of theselocal forces and moments are due to globalbending action. The accuracy of the designmethods depends on the accuracy of a numberof design rules against respective failuremodes. Moreover, there are a number ofdifferent ways in allowing for the effects of coexisting axial and shear forces in assessing themoment resistances of tee sections. Thecalculation procedures are usually complicatedand they differ significantly among each other,depending on the design methodologyadopted, and also the calculation effortsinvolved. It should be noted that the designmethods are often very general, and applicablein principle for beams with web openings ofvarious shapes and sizes. However, due to thecomplexity of the problems, approximatedesign rules are often presented for practicaldesign to reduce calculation effort, leading toconservative results.resistances of the perforated sections underco-existing global shear force,, andbending moment,. In general, the designprocedures for both the shear and the momentresistances of perforated sections are relativelysimple and similar among different methods.However, the Vierendeel moment resistancesof the perforated sections are evaluatedimplicitly based on various assumptions on theeffects of co-existing shear forces andmoments. Simplifications are usually made tothose design rules derived from the Teesection approach, and thus, empirical globalshear-moment ( - ) interaction curves areoften provided to engineers for practicaldesign. However, it is the simplification or theover-development on the design rules thatreduces the scope of applicability of the designrules.3.2. Perforated section approachIn this approach, the perforated crosssections are the critical sections to beconsidered in design. The structural adequacyof the beams depends on the sectionFig. 5 Global and local actions at perforated section of acomposite beam.
T. M. Cameira Neto / Instituto Superior Técnico (2014)44. Finite element modelingIn order to verify the structural behaviour ofcomposite beams with large web openings, afiniteelementmodelisestablished.Comparison on the predicted ultimate loads offour composite beams from the finite elementmodels and the test data acquired ispresented.The general purpose finite elementpackage ABAQUS was adopted for thenumerical simulation of composite beams withlarge web openings. Despite the principalmode of failure involves only in-planedeformation, a three-dimensional finite elementmodel is adopted with the following features: Iso-parametriceight-nodewithreduced integration elements (C3D8R)are used to model both the concreteslab and the steel beam. A bi-linear stress-strain curve isadopted in the material model of steelas shown in Fig. 6. The concretemodelling is based in concretedamaged plasticity implemented inABAQUS. The concrete damageplasticity model uses the concept ofisotropicdamagedelasticity,incombination with isotropic tensile andcompressive plasticity, to represent theinelastic behaviour of concrete. Theconstitutive relationship of concrete ispresented in Figs. 7 and 8, assuggested by EN1992-1-1 [10]. Itshould be noted that for concreteunder compression, the response islinear until the value of the proportionallimit stress,, is reached, which isassumed to be equal to 0,4 times thecompressive strength, . Withgeometricnon-linearityincorporated into the finite elementmodel, large deformation in theperforated section after yielding ispredicted accurately to allow for loadre-distribution within the perforatedsection.Fig. 6 Constitutive relationship of steel.Fig. 7 Constitutive relationship of concrete incompression.Fig. 8 Constitutive relationship of concrete intension.
5T. M. Cameira Neto / Instituto Superior Técnico (2014)5. Calibration against experimental tests and numerical analysesThe finite element model was calibratedagainst data from three tests and a numericalanalysis. The first comparison was establishedto show the response of composite beammaterials, concrete and steel. Therefore, thefirst model developed is a conventionalcomposite beam, as shown in Fig. 9.Fig. 9 Details of test specimen [13]Prakash et al. 2011, modelled theinteraction between concrete and steel withshear connectors distributed through the beamspan. However, in this case the tie function isadopted to simulate the connector’s action.The main difference associated to the tieconnection consists in the union of sharednodes of the different materials. The secondtest was a composite beam with a webopening which was conducted by Clawson andDarwin 1980, namely Test CD4. The generaltest set-ups and the dimensions of the testspecimen are shown in Fig. 10.Moreover, the predicted load deflectioncurves of the composite beams are plotted inFig. 11.It is shown that both the deformationcharacteristics and the ultimate loads obtainedfrom the finite element models and theexperiments agree well with one another.The third and fourth test presented twospan [11] and three-span [12] continuouscomposite beams respectively. In thesestudies, the concrete will be both incompression and tension. The aim of thesemodels was to show that the concrete intension presented over the support, does notinfluence the resistance of the beam nor therotation capacity.From the results presented in the Fig. 12and 13, it can be concluded that in case of totalconnection, it is good to simulate theinteraction between the materials based on thetie function. It should be noted that in thesemodels the reinforcements in the concrete slabwere not modelled, since the tension capacityof concrete was considered. In both Figures,deflexion measurements were taken atmidspan. The deflexion history of thecontinuous two and three span beam is shownin Fig. 12 and 13 respectively.In general, the predicted load deflectioncurves derived from the numerical studiescompare very well with the experimental data.It should be noted that in Fig. 12 the loaddeflection curve of the left spam is presentedon the left and the right spam behaviour on theright.Fig. 10 Details of test specimen [9].Fig. 11 Load-deflection curves, Prakash et al. 2011 to the left; Clawson and Darwin 1980, to the right
T. M. Cameira Neto / Instituto Superior Técnico (2014)Fig. 12 Load deflection curves of the two span beam.6Fig. 13 Load factor-deflexion curves for centre span.6. Parametric studyThe developed model has a HEA800 or aIPE500 beam and a 250 mm thickness slab ofconcrete under uniformly distributed load. Thewidth of the concrete flanges in the compositebeams is taken as either the actual width or theeffective width of the test beams, whichever issmaller. The effective width of the concreteflange in a composite beam is equal to aquarter of the beam span according toestablished design practice.The analysis used in ABAQUS was theStatic Riks, as it does iterations to obtain theultimate load. In order to represent better thereality, the supports were modelled in a smallarea instead of a line with the restrictionsrequired.The parametric study was carried out todemonstrate the structural behaviour ofcomposite beams with web openings. In thisstudy was analyzed the influence of: The opening depth;The geometric configuration of the webopening;The location of the opening;The span length;The concrete slab thickness;Multiple spans.6.1. Opening depthIt is intended that the model covers a widerange of opening depth, thus a total of threedifferent values of opening depth areconsidered as follows: 0.25 h; 0.50 h;0.75 h, where h is the section height ofsteel beam.In order to understand the effect of the webopenings size to the structural performance ofperforated sections, it is important to relate theglobal shear force and bending moment actingon the perforated sections to the local forcesand moment acting on the tee-sections aboveand below the web openings. It should benoted that any increase in the opening depthalways reduces both the shear and themoment resistances of the perforated sectionswhile it has no effect on the applied forces, i.e.the global shear force and bending moment atthe perforated sections. Thus, both shear andflexural failures of the perforated sections areprimarily controlled by the value of the openingdepth.However, while the opening length has noeffect on local shear and moment resistancesof the tee-sections above and below the webopenings, any increase in the opening lengthwill increase the local Vierendeel momentacting at the tee-sections significantly. Thus,the Vierendeel mechanism of the perforatedsections is essentially controlled by theopening length. In practice, both the openingdepth and the opening length are geometricallyrelated, and thus any increase in sizes in webopenings will reduce not only both the globalshear and the global moment resistances ofthe perforated sections, but also the local axial,shear and moment resistances of the tee-
7T. M. Cameira Neto / Instituto Superior Técnico (2014)sections- Furthermore, the Vierendeel momentis also increased at the same time.6.2. Opening shapesA total of four web openings of differentshapes are considered in the present study asfollows: Circular;Rectangular;Square;Elongated circular opening.The key dimensional parameter in all theseopening shapes is the opening length, which isthe length of the tee-sections above and belowthe openings. The length of the opening hasmajor effect on the local applied moment ontee-sections.For ease of comparison and discussion theresults presented in this section are related toa simply supported beam IPE500 with a span(a)(c)of 4 m under uniformly distributed loads. It waschosen the 4 m span because the Vierendeelmechanism has a major influence in shortbeams. The load-deflection curves of thebeams with web openings of various shapes atdifferent locations are plotted in Fig. 14. Itshould be noted that for web openings ofvarious shapes but of same opening depthsand lengths, their structural performanceshould be similar. However, in Fig. 14 the loadcapacity of the beam with the square openingis not similar to the circular opening since thecorners of the square opening were notrounded. It is possible to conclude that theshape is a major parameter in the structuralresponse of the beam, however it is notpossible to define a optimum shape because itdepends on the opening location along thebeam length. Only in Fig. 14 (a) the loaddeflection curves are significantly different dueto the Vierendeel mechanism.(b)(d)Fig. 14 Load deflection curves of IPE500 S355 with perforated section. Openings location: (a) 0.5 m from the support; (b) 1.0 mfrom the support; (c) 1.5 m from the support; (d) midspan.
8T. M. Cameira Neto / Instituto Superior Técnico (2014)6.3. Location of the openingIn order to demonstrate how the location ofthe web openings can influence the loadingcapacity, an analysis was developed.On another hand, when Vierendeelmechanism does not represent a main role inthe structural behaviour, flexural failure takesplace, thus the worst location for the webopenings is at midspan where the bendingmoment is at his maximum value.This study considers four values for thelocation of the web openings measured fromthe support to the center line of the opening: 6.4. The span lengthOne eighth;One fourth;Three eighths;One half.A total of four span lengths are consideredin the present study as follows: Since the Vierendeel mechanism occurswhen the openings are relatively close to thesupport, due to the high shear force, it isexpected to obtain a lower load capacity whenthe Vierendeel mechanism overlaps theflexural failure. It is noticeable in Fig.14 howthe location influences the structural behaviourand as it was previously mentioned theoptimum locations is roughly at the quarterspan.4.0 m;6.0 m;10.0 m.Through this analysis it was found that withthe increase of the span length, the Vierendeelmechanism becomes less relevant. In Fig. 15the three spans analysed are represented, andit is possible to see that for bigger span, thereis less load capacity loss due to the webopenings, regardless of its position.(b)(a)(c)Fig. 15 Load deflection curves of HEA800 S355 with circular web opening, diameter 0.40 m. Span length: (a) 4 m; (b) 6 m;(c) 10 m.
9T. M. Cameira Neto / Instituto Superior Técnico (2014)6.5. Concrete slab thicknessThis section is intended to demonstrate thecontribution of the concrete slab in shearresistance, more specifically in resistance tobending moment of Vierendeel. The webopenings reduce the shear strength capacity ofthe perforated section, making it susceptible toVierendeel mechanism. In Fig. 16 and 17 ispresented the Von Mises tensions in a steelbeam and a composite beam with a circularopening with a diameter of 0.3 m, respectively.The concrete slab has 250 mm thickness. Itshould be noted that the collapse of thecomposite beam is a mix of Vierendeel andflexural failure, unlike the steel beam whereinfailure is Vierendeel. Thus, it is possible toconclude that concrete contributes to the shearresistance of the perforated section.6.6. Multiple spansThis study analyzes the influence of webopenings in continuous beams, in other wordsorder to determine if the existence of anopening in a span will affect the behavior of theadjacent spans.In Fig.18, it is possible to verify that thestructural behaviour of the span without theopening remains the same. It should be notedthat in Figure 18 b) the load deflexion curvewhich has lower load capacity refers to amodel in which both the spans have anopening.It can be concluded that the existence ofweb openings in a certain span does notinfluence the load capacity of the adjacentspans.Fig. 16 Von Mises tensions in the steel beam.Fig. 17 Von Mises tensions in the composite beam.Fig. 18 Load deflection curves of IPE500 with rectangular opening. (a) Span with the opening; (b) Span without opening.
T. M. Cameira Neto / Instituto Superior Técnico (2014)7. ConclusionsThe concrete damaged plasticity failurecriterions implemented in ABAQUS revealadequate simulation of the non-linearbehaviour of concrete.The presence of openings in compositebeams reduces the load capacity of these. Theinfluence of the openings is related to thefailure mode of the beams, i.e if the beam has
used in composite beams than in steel beams [7]. The bending resistance of a composite beam subject to these forces is illustrated in Fig. 4. For structural adequacy, the total Vierendeel bending resistance of the Tee sections incorporating local composite action at an opening, should exceed the design shear
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