The current method of assessment is based on FE models which still lack computational efficiency and are restricted by a number of limitations. Therefore, this work aims at the feasibility of developing FE models which are applicable to deformation and strength prediction of full scale perforated steel beams. The main area of interest is the stability of the web-post under the combined effect of shear and compression, especially at the edge of the web openings, where the stabilizing effect of tension field action is less than that at the centre of the web-post

D'Mello, C.

Tsavdaridis, K. D.

English

Tsavdaridis, KD

D Mello, C

White Rose Research Online

This is a repository copy of Finite element investigation on web-post buckling of perforatedsteel beams with various web opening shapes subjected under different shear-moment interaction.White Rose Research Online URL for this paper:http://eprints.whiterose.ac.uk/80993/Version: Accepted VersionProceedings Paper:Tsavdaridis, KD and D Mello, C (2011) Finite element investigation on web-post buckling ofperforated steel beams with various web opening shapes subjected under different shear-moment interaction. In: 6th European Conference on Steel and Composite Structures. 6th European Conference on Steel and Composite Structures, 31 August - 2 September 2011, Budapest University of Technology and Economics, Hungary. EUROSTEEL 2011 , 1851 - 1856. eprints@whiterose.ac.ukhttps://eprints.whiterose.ac.uk/Reuse Unless indicated otherwise, fulltext items are protected by copyright with all rights reserved. The copyright exception in section 29 of the Copyright, Designs and Patents Act 1988 allows the making of a single copy solely for the purpose of non-commercial research or private study within the limits of fair dealing. The publisher or other rights-holder may allow further reproduction and re-use of this version - refer to the White Rose Research Online record for this item. Where records identify the publisher as the copyright holder, users can verify any specific terms of use on the publisher’s website. Takedown If you consider content in White Rose Research Online to be in breach of UK law, please notify us by emailing eprints@whiterose.ac.uk including the URL of the record and the reason for the withdrawal request. FE MODELLING TECHNIQUES FORWEB-POST BUCKLING RESPONSEPerforated Steel Beams with Closely Spaced Web Openings of Various ShapesKonstantinos Daniel Tsavdaridisaand Cedric D’MellobaCity University, London, School of Engineering and Mathematical Science, UKINTRODUCTIONThe current method of assessment is based on FE models which still lack computational efficiencyand are restricted by a number of limitations. Therefore, this work aims at the feasibility ofdeveloping FE models which are applicable to deformation and strength prediction of full scaleperforated steel beams. The main area of interest is the stability of the web-post under the combinedeffect of shear and compression, especially at the edge of the web openings, where the stabilizingeffect of tension field action is less than that at the centre of the web-post.1 WEB-POST BUCKLING1.1 Structural behaviourWeb-post buckling is one of the major and more complex failure mechanisms for perforated beamswith closely spaced web openings (i.e. those usually manufactured with the profile cuttingprocedure). Slender web-posts in combination with deep I-sections induce instability into suchstructural forms. The result is a very complex failure mechanism where the axial force due to globalmoment, the shear force due to the global shear force and the local Vierendeel moments due to thetransfer of shear force across the web opening length, act simultaneously and in combination withthe local actions of the two adjacent web openings. The mechanism depends on a number ofparameters, including the spacing between openings. Additional vertical deflections as well as out-of-plane displacements due to the presence of multiple web openings are considered.1.2 Method of studyFE analyses can be used as a tool to analyse buckling phenomenon. Linear buckling is a useful firststep which gives an idea of buckling mode shapes. However, the buckling loads found throughlinear buckling analyses are highly non-conservative and should therefore be used with caution. TheFE analyses presented here makes use of ANSYS v11.0, which includes material non-linearity (i.e.plastic behaviour) and geometrical non-linearity (buckling). An extensive parametric FE local studyis included in which a number of geometric parameters are varied. Further relevant work can befound in [1], in which experimental tests are presented and compared with FE analyses. Also, non-standard innovative web opening shapes have been included as they have a number of advantages,including the structural behaviour, the economic design and the ease of fabrication [2].In applying any non-linear FE analysis, it is essential to validate generic results preferably bycomparison with tests, or alternatively by comparing them with the results of similar analyses withknown closed form solutions. However, there are not any closed form solutions for the design ofperforated steel beams and particularly for web-post buckling. The movement of the stressconcentration (i.e. plastic hinges) in the vicinity of the web openings is still under question.Consequently, an analytical comparison between the experimental tests conducted in the literature[1,3] is carried out to validate the FE method. Finally, a parametric FE study with four differentweb opening shapes is conducted to demonstrate the divergence of the results.1.3 Non-linear buckling as a design toolThe inherent difficulty in solving non-linear FE buckling problems is due to the fact that in solvingthese types of problems in a static framework, at the point of geometric instability the stiffnessmatrix may be singular and so prevent a solution from being obtained.1.4 Eigen-value buckling analysisSimilar to dynamic analyses, a linear analysis should always be performed in advance of solving thenon-linear problem. Eigen-value buckling is part of a typical solution for a non-linear bucklingproblem. The eigen-value buckling analysis predicts the theoretical buckling strength of an idealelastic structure. It computes the structural eigen-values for the given system loading andconstraints taking into consideration the secondary effects (i.e. geometric non-linearity). This isknown as “classical Euler buckling analysis”. Any buckling mode from a linear buckling analysiscan be used to generate ‘imperfections’ on the model for use in a non-linear buckling analysis(material and geometric non-linearity).1.5 Non-linear static buckling analysisTo determine the critical load (but not the post-buckling response), a typical non-linear staticsolution can be run. A non-linear buckling analysis is more accurate than an eigen-value bucklinganalysis because it employs non-linear, large-deflection static analysis to predict buckling loads.The true non-linear nature of this analysis permits the modelling of geometric imperfections, loadperturbations, material non-linearities and gaps.For this type of analysis, small eccentric loads or imperfections are needed to initiate the desiredbuckling mode on a ‘perfect’ FE model. The common method is to create a small imperfection inthe mesh for use in non-linear buckling analyses. Similar techniques involve application of smallpoint loads on certain areas transverse to the web, inducing buckling. The post-buckling behaviouris not of interest in this paper.2 MODELLING THE EXPERIMENTAL WORK2.1 Beam modelsThe two perforated beams shown in Fig. 1 have been modelled. One is a non-composite castellatedbeam with mid-depth hexagonal web openings and the other a mid-range perforated beam with oneweb-post at each size and circular web openings. Experimental details can be found in [1,2,3]. Inthe experimental work it was ensured that the load was transferred via a bearing plate, as aneccentric load could cause local buckling at the edges of the web openings close to the point load.Table 1 below summarises the experimental and FE results.Fig. 1. Testing arrangements, section properties and material properties2.2 Eigen bucklingA point load is applied at the mid-span and four eigen-modes are extracted based on the ‘BlockLanczos’ method to verify whether or not there is a possibility of multiple buckling mode shapesbeing triggered (two of them are shown in Fig. 2) following the linear static analysis.MNMXMNMXMNMX=199.848MNMX=187.808Fig. 2. Four Buckling Modes Extracted by the ‘Block Lanczos’ MethodFrom other work carried out by the authors, the best representation of the real structural behaviouris obtained by using the first eigen-mode and a scaled factor equal to tw/200. However, while thefailure mode and the web-post profile is similar to the tested specimen’s, Fig. 3 and Fig. 4 showthat the amplitude of the out-of-plane displacements in the FE analysis is lower than that from thetest. This difference in overall stiffness is due to the existence of manufacturing imperfections andexperimental uncertainties, as well as the lack of information on the material properties of the steel.Fig. 3. Tested cellular beam compared with FE model (Von-Mises stresses)The predicted mode of buckling includes some flange rotation, which is also observed in the testbeam. In most of the FE analyses, an early out-of-plane web movement is observed due to theapplied lateral force. The latter can be a trigger load, an imperfection or the eigen-vectors. As theload is increased the web starts to return to its original position. At higher load levels the web startsbecoming unstable which is the onset of buckling. Increasing the load results in the web deformingplastically (buckling), while in some cases a jump in the opposite direction is observed (Fig. 5a). Inthe current study, the ‘critical buckling load’ is assumed to be the onset of buckling. This is realisticalthough somewhat conservative approach.Eigen-mode 1Frequency: 1.332Eigen-mode 2Frequency: 6.524Eigen-mode 1Frequency: 1.524Eigen-mode 2Frequency: 1.583Fig. 4. Out-of-plane displ. vs Web depth (a) castellated and (b) cellular beam [Eigen buckling]Fig. 5. Out-of-plane displ. at web-post 1 (a) castellated (b) cellular beam [Eigen buckling]Fig. 6. Out-of-plane displ. vs Web depth (a) castellated and (b) cellular beam [Non-linear buckling]Fig. 7. Out-of-plane displ. at web-post 1 (a) castellated and (b) cellular beam [Non-linear buckling]2.3 Non-linear bucklingTwo load steps were used in this analysis. Load-step 1 was used to load the beam up to 154kN andthen load-step 2 to gradually increase the load from 154kN to 350kN, past the expected bucklingload. A small out-of-plane load transverse to web was also applied during load-step 1. Following aninvestigation into the optimum position and the magnitude of the trigger load, a 2- point load of just0.1N was applied at the middle of the top half of the web-post 1 (Fig. 7a).2.4 Comparisons and resultsTable 1. Test loads and predicted strengthsModelPy(test)(kN)Pcr(test)(kN)Pult(test)(kN)Py(FEM)(kN)Pcr(FEM)(kN)Pult(FEM)(kN)Pcr(FEM)Pcr(test/theory)Pult(FEM)Pult(test)CastellatedTheoretical:75.62Theoretical:68.9573.841: 70.00 1: 77.90 1: 87.40 1: 1.129 1: 1.1842: 70.00 2: 84.00 2: 91.04 2: 1.218 2: 1.233Cellular 185.5 219.24 255.861: 195.5 1: 265.5 1: 315.0 1: 1.211 1: 1.2312: 193.2 2: 252.0 2: 330.0 2: 1.149 2: 1.2891: Eigen-mode is used to initiate buckling2: Trigger load is applied to initiate bucklingThe results show higher loads from the FE analysis. This overestimation of the FE model is due tothe limited number of the nodes on each element (i.e. only four nodes), as well as the ‘reducedintegration points’ function which is used to avoid numerical problems such as shear locking onshell elements.3 PARAMETRIC FE STUDY3.1 FE modelsAn eigen buckling analysis (based on the scaled frequency of mode 1) is used to predict the criticalloads in the following parametric FE study. The main objective is to revise the existing designmodel for circular web openings for this complex failure mode and establish new models for otherstandard and non-standard web opening shapes [1,2,5]. The web opening diameter (i.e. depth) is the70% of the beam’s overall depth, whereas in the case of using inclined elliptical web openings (Fig.8), the web opening depth is decreased to 60.4% of the beam depth. Various web opening spacingratios are reported in this paper while the minimum web-post width is always kept to 63mm, whichcorresponds to a spacing of 1.2do for the standard circular web opening. In addition, three webthicknesses are examined giving do/tw ratios which vary from 25.6 to 68.5.Fig. 8. Testing specimens and material propertiesTable 2. Predicted strengths from the parametric FE studyWebopeningarea(mm2)S/doPcr(FEM) (kN) Pult(FEM) (kN)Onset of Buckling Bucklingtw (mm)tw (mm) tw (mm)4.6 7.6 10.6 4.6 7.6 10.6 4.6 7.6 10.6Specimen 1 76615.9 1.2 140 218 379 155 261 386 159 290 450Specimen 2 99225 1.2 55 84 111 144 261 324 233 347 396Specimen 3 58733.6 1.2 189 327 394 202 377 444 214 462 522Specimen 4 54552 0.9 177 294 428 185 320 473 195 328 541Specimen 5a 54552 1.23 164 318 497 196 347 517 289 367 531Specimen 5b 54552 1.23 168 378 475 180 387 524 204 401 5384 SUMMARYFEA is a good solution choice when traditional buckling theory is difficult and there are no closedformed solutions. More importantly, all the factors affecting beam stability can be incorporated intoa FE model and neither the effective length nor the uniform moment equivalent factor is needed.The contribution of FEA to prediction of the web-post buckling response has been clearlydemonstrated by the eigen-value tracking method and perturbation by force imperfectionstransverse to the web. The FEA solutions were non-trivial, requiring non-linear geometric andmaterial consideration. The FE models were correlated with benchmarked tests. Having adjusted themodelling technique to match the previously established benchmarks, solutions for new webopening shapes are generated. Further development of perforated steel beams can lead to economicdesign, using light members with high capacities. An established work is to be published by theauthors where details of the FE techniques and a comprehensive parametric study, is carried out.REFERENCES[1] Tsavdaridis, KD, Structural Performance of Steel Perforated Beams with Various Shapes and Sizes ofWeb Openings and with Partial Concrete Encasement, PhD Thesis, School of Engineering andMathematical Sciences, City University, London, 2010.[2] Tsavdaridis, KD, D’Mello, C, “Web buckling study of the behaviour and strength of perforated steelbeams with various novel web opening shapes”, Journal of Constructional Steel Research,doi:10.1016/j.jcsr.2011.04.004, 2010.[3] Zaarour, W, Redwood, R, “Web buckling in thin webbed castellated beams”, Journal of StructuralEngineering, Vol. 122, no. 8, pp. 860-866, 1996.[4] Demirdjian, S, Stability of castellated beam webs, MEng Thesis, Department of Civil Engineering andApplied Mechanics, McGill University, Montreal, 1999.[5] Tsavdaridis, KD, D’Mello, C. “FE investigation of perforated sections with standard and non-standardweb opening configurations and sizes”, 6thInternational Conference on Advances is Steel Structures,Vol. 1, pp. 213-220, Hong Kong, China, 2009.

Finite element investigation on web-post buckling of perforated steel beams with various web opening shapes subjected under different shear-moment interaction

City Research Online

Tsavdaridis, K. D. & D'Mello, C. (2011). Finite Element Investigation on Web-Post Buckling of Perforated Steel Beams with Various Web Opening Shapes subjected under different shear-moment interaction. Paper presented at the 6th European Conference on Steel and Composite Structures, 31-08-2011 - 02-09-2011, Budapest, Hungary.City Research OnlineOriginal citation: Tsavdaridis, K. D. & D'Mello, C. (2011). Finite Element Investigation on Web-Post Buckling of Perforated Steel Beams with Various Web Opening Shapes subjected under different shear-moment interaction. Paper presented at the 6th European Conference on Steel and Composite Structures, 31-08-2011 - 02-09-2011, Budapest, Hungary.Permanent City Research Online URL: http://openaccess.city.ac.uk/1043/ Copyright & reuseCity  University  London has developed City  Research Online  so that  its  users  may access the research outputs of City University London's staff. Copyright © and Moral Rights for this paper are retained by the individual author(s) and/ or other copyright holders. Users may download and/ or print one  copy  of  any  article(s)  in  City  Research  Online  to  facilitate  their  private  study  or  for  non-commercial research. Users may not engage in further distribution of the material or use it for any profit-making activities or any commercial gain. All material in City Research Online is checked for eligibility for copyright before being made available in the live archive. URLs from City Research Online may be freely distributed and linked to from other web pages. Versions of researchThe version in City Research Online may differ from the final published version. Users are advised to check the Permanent City Research Online URL above for the status of the paper.EnquiriesIf you have any enquiries about any aspect of City Research Online, or if you wish to make contact  with the author(s) of this paper, please email the team at publications@city.ac.uk. FE MODELLING TECHNIQUES FOR WEB-POST BUCKLING RESPONSE Perforated Steel Beams with Closely Spaced Web Openings of Various Shapes Konstantinos Daniel Tsavdaridisa and Cedric D’Mellob a City University, London, School of Engineering and Mathematical Science, UK INTRODUCTION The current method of assessment is based on FE models which still lack computational efficiency and are restricted by a number of limitations. Therefore, this work aims at the feasibility of developing FE models which are applicable to deformation and strength prediction of full scale perforated steel beams. The main area of interest is the stability of the web-post under the combined effect of shear and compression, especially at the edge of the web openings, where the stabilizing effect of tension field action is less than that at the centre of the web-post. 1 WEB-POST BUCKLING 1.1 Structural behaviour Web-post buckling is one of the major and more complex failure mechanisms for perforated beams with closely spaced web openings (i.e. those usually manufactured with the profile cutting procedure). Slender web-posts in combination with deep I-sections induce instability into such structural forms. The result is a very complex failure mechanism where the axial force due to global moment, the shear force due to the global shear force and the local Vierendeel moments due to the transfer of shear force across the web opening length, act simultaneously and in combination with the local actions of the two adjacent web openings. The mechanism depends on a number of parameters, including the spacing between openings. Additional vertical deflections as well as out-of-plane displacements due to the presence of multiple web openings are considered.  1.2 Method of study FE analyses can be used as a tool to analyse buckling phenomenon. Linear buckling is a useful first step which gives an idea of buckling mode shapes. However, the buckling loads found through linear buckling analyses are highly non-conservative and should therefore be used with caution. The FE analyses presented here makes use of ANSYS v11.0, which includes material non-linearity (i.e. plastic behaviour) and geometrical non-linearity (buckling). An extensive parametric FE local study is included in which a number of geometric parameters are varied. Further relevant work can be found in [1], in which experimental tests are presented and compared with FE analyses. Also, non-standard innovative web opening shapes have been included as they have a number of advantages, including the structural behaviour, the economic design and the ease of fabrication [2]. In applying any non-linear FE analysis, it is essential to validate generic results preferably by comparison with tests, or alternatively by comparing them with the results of similar analyses with known closed form solutions. However, there are not any closed form solutions for the design of perforated steel beams and particularly for web-post buckling. The movement of the stress concentration (i.e. plastic hinges) in the vicinity of the web openings is still under question. Consequently, an analytical comparison between the experimental tests conducted in the literature [1,3] is carried out to validate the FE method. Finally, a parametric FE study with four different web opening shapes is conducted to demonstrate the divergence of the results.    1.3 Non-linear buckling as a design tool The inherent difficulty in solving non-linear FE buckling problems is due to the fact that in solving these types of problems in a static framework, at the point of geometric instability the stiffness matrix may be singular and so prevent a solution from being obtained. 1.4 Eigen-value buckling analysis Similar to dynamic analyses, a linear analysis should always be performed in advance of solving the non-linear problem. Eigen-value buckling is part of a typical solution for a non-linear buckling problem. The eigen-value buckling analysis predicts the theoretical buckling strength of an ideal elastic structure. It computes the structural eigen-values for the given system loading and constraints taking into consideration the secondary effects (i.e. geometric non-linearity). This is known as “classical Euler buckling analysis”.  Any buckling mode from a linear buckling analysis can be used to generate ‘imperfections’ on the model for use in a non-linear buckling analysis (material and geometric non-linearity). 1.5 Non-linear static buckling analysis  To determine the critical load (but not the post-buckling response), a typical non-linear static solution can be run. A non-linear buckling analysis is more accurate than an eigen-value buckling analysis because it employs non-linear, large-deflection static analysis to predict buckling loads. The true non-linear nature of this analysis permits the modelling of geometric imperfections, load perturbations, material non-linearities and gaps.  For this type of analysis, small eccentric loads or imperfections are needed to initiate the desired buckling mode on a ‘perfect’ FE model. The common method is to create a small imperfection in the mesh for use in non-linear buckling analyses. Similar techniques involve application of small point loads on certain areas transverse to the web, inducing buckling. The post-buckling behaviour is not of interest in this paper. 2 MODELLING THE EXPERIMENTAL WORK 2.1 Beam models The two perforated beams shown in Fig. 1 have been modelled. One is a non-composite castellated beam with mid-depth hexagonal web openings and the other a mid-range perforated beam with one web-post at each size and circular web openings. Experimental details can be found in [1,2,3]. In the experimental work it was ensured that the load was transferred via a bearing plate, as an eccentric load could cause local buckling at the edges of the web openings close to the point load. Table 1 below summarises the experimental and FE results.  Fig. 1.  Testing arrangements, section properties and material properties    2.2 Eigen buckling  A point load is applied at the mid-span and four eigen-modes are extracted based on the ‘Block Lanczos’ method to verify whether or not there is a possibility of multiple buckling mode shapes being triggered (two of them are shown in Fig. 2) following the linear static analysis.    MNMXMNMX   MNMX199.848     MNMX187.808      Fig. 2.  Four Buckling Modes Extracted by ‘Block Lanczos’ Method  From other work carried out by the authors, the best representation of the real structural behaviour is obtained by using the first eigen-mode and a scaled factor equal to tw/200. However, while the failure mode and the web-post profile is similar to the tested specimen’s, Fig. 3 and Fig. 4 show that the amplitude of the out-of-plane displacements in the FE analysis is lower than that from the test. This difference in overall stiffness is due to the existence of manufacturing imperfections and experimental uncertainties, as well as the lack of information on the material properties of the steel.   Fig. 3.  Tested cellular beam compared with FE model (Von-Mises stresses) The predicted mode of buckling includes some flange rotation, which is also observed in the test beam. In most of the FE analyses, an early out-of-plane web movement is observed due to the applied lateral force. The latter can be a trigger load, an imperfection or the eigen-vectors. As the load is increased the web starts to return to its original position. At higher load levels the web starts becoming unstable which is the onset of buckling. Increasing the load results in the web deforming plastically (buckling), while in some cases a jump in the opposite direction is observed (Fig. 5a). In the current study, the ‘critical buckling load’ is assumed to be the onset of buckling. This is realistic although somewhat conservative approach. Eigen mode 1 Frequency: 1.332 Eigen mode 2 Frequency: 6.524 Eigen mode 1 Frequency: 1.524 Eigen mode 2 Frequency: 1.583      Fig. 4.  Out-of-plane displ. vs Web depth (a) castellated and (b) cellular beam [Eigen buckling]        Fig. 5.  Out-of-plane displ. at web-post 1 (a) castellated (b) cellular beam [Eigen buckling]      Fig. 6. Out-of-plane displ. vs Web depth (a) castellated and (b) cellular beam [Non-linear buckling]     Fig. 7.  Out-of-plane displ. at web-post 1 (a) castellated and (b) cellular beam [Non-linear buckling] 2.3 Non-linear buckling Two load steps were used in this analysis. Load-step 1 was used to load the beam up to 154kN and then load-step 2 to gradually increase the load from 154kN to 350kN, past the expected buckling load. A small out-of-plane load transverse to web was also applied during load-step 1. Following an investigation into the optimum position and the magnitude of the trigger load, a 2- point load of just 0.1N was applied at the middle of the top half of the web-post 1 (Fig. 7a).  2.4 Comparisons and results Table 1. Test loads and predicted strengths Model Py(test) (kN) Pcr(test) (kN) Pult(test)(kN) Py(FEM)(kN) Pcr(FEM)(kN) Pult(FEM)(kN) Pcr(FEM)  Pcr(test/theory) Pult(FEM)Pult(test) Castellated Theoretical: 75.62 Theoretical:68.95 73.84 1: 70.00 1: 77.90 1: 87.40 1: 1.129 1: 1.184  2: 70.00 2: 84.00 2: 91.04 2: 1.218 2: 1.233 Cellular 185.5 219.24 255.861: 195.5 1: 265.5 1: 315.0 1: 1.211 1: 1.231 2: 193.2 2: 252.0 2: 330.0 2: 1.149 2: 1.289 1: Eigen-mode is used to initiate buckling 2: Trigger load is applied to initiate buckling  The results show higher loads from the FE analysis. This overestimation of the FE model is due to the limited number of the nodes on each element (i.e. only four nodes), as well as the ‘reduced integration points’ function which is used to avoid numerical problems such as shear locking on shell elements. 3 PARAMETRIC FE STUDY 3.1 FE models An eigen buckling analysis (based on the scaled frequency of mode 1) is used to predict the critical loads in the following parametric FE study. The main objective is to revise the existing design model for circular web openings for this complex failure mode and establish new models for other standard and non-standard web opening shapes [1,2,5]. The web opening diameter (i.e. depth) is the 70% of the beam’s overall depth, whereas in the case of using inclined elliptical web openings (Fig. 8), the web opening depth is decreased to 60.4% of the beam depth. Various web opening spacing ratios are reported in this paper while the minimum web-post width is always kept to 63mm, which corresponds to a spacing of 1.2do for the standard circular web opening. In addition, three web thicknesses are examined giving do/tw ratios which vary from 25.6 to 68.5.      Fig. 8. Testing specimens and material properties      Table 2. Predicted strengths from the parametric FE study  Web opening area (mm2) S/do Pcr(FEM) (kN) Pult(FEM) (kN) Onset of Buckling Buckling tw (mm) tw (mm) tw (mm) 4.6 7.6 10.6 4.6 7.6 10.6 4.6 7.6 10.6Specimen 1 76615.9 1.2 140 218 379 155 261 386 159 290 450 Specimen 2 99225 1.2 55 84 111 144 261 324 233 347 396 Specimen 3 58733.6 1.2 189 327 394 202 377 444 214 462 522 Specimen 4 54552 0.9 177 294 428 185 320 473 195 328 541 Specimen 5a 54552 1.23 164 318 497 196 347 517 289 367 531 Specimen 5b 54552 1.23 168 378 475 180 387 524 204 401 538 4 SUMMARY  FEA is a good solution choice when traditional buckling theory is difficult and there are no closed formed solutions. More importantly, all the factors affecting beam stability can be incorporated into a FE model and neither the effective length nor the uniform moment equivalent factor is needed. The contribution of FEA to prediction of the web-post buckling response has been clearly demonstrated by the eigen-value tracking method and perturbation by force imperfections transverse to the web. The FEA solutions were non-trivial, requiring non-linear geometric and material consideration. The FE models were correlated with benchmarked tests. Having adjusted the modelling technique to match the previously established benchmarks, solutions for new web opening shapes are generated. Further development of perforated steel beams can lead to economic design, using light members with high capacities. An established work is to be published by the authors where details of the FE techniques and a comprehensive parametric study, is carried out.       REFERENCES [1] Tsavdaridis, KD, Structural Performance of Steel Perforated Beams with Various Shapes and Sizes of Web Openings and with Partial Concrete Encasement, PhD Thesis, School of Engineering and Mathematical Sciences, City University, London, 2010. [2] Tsavdaridis, KD, D’Mello, C, “Web buckling study of the behaviour and strength of perforated steel beams with various novel web opening shapes”, Journal of Constructional Steel Research, doi:10.1016/j.jcsr.2011.04.004, 2010.   [3] Zaarour, W, Redwood, R, “Web buckling in thin webbed castellated beams”, Journal of Structural Engineering, Vol. 122, no. 8, pp. 860-866, 1996. [4] Demirdjian, S, Stability of castellated beam webs, MEng Thesis, Department of Civil Engineering and Applied Mechanics, McGill University, Montreal, 1999. [5] Tsavdaridis, KD, D’Mello, C. “FE investigation of perforated sections with standard and non-standard web opening configurations and sizes”, 6th International Conference on Advances is Steel Structures, Vol. 1, pp. 213-220, Hong Kong, China, 2009.  

Finite Element Investigation on Web-Post Buckling of Perforated Steel Beams with Various Web Opening Shapes subjected under different shear-moment interaction

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Finite Element Investigation on Web-Post Buckling of Perforated Steel Beams with Various Web Opening Shapes subjected under different shear-moment interaction

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