Numerical study on buckling of steel web plates with openings

  • Serror, Mohammed H. (Department of Structural Engineering, Faculty of Engineering, Cairo University) ;
  • Hamed, Ahmed N. (Department of Structural Engineering, Faculty of Engineering, Cairo University) ;
  • Mourad, Sherif A. (Department of Structural Engineering, Faculty of Engineering, Cairo University)
  • Received : 2016.07.25
  • Accepted : 2016.12.01
  • Published : 2016.12.30


Cellular and castellated steel beams are used to obtain higher stiffness and bending capacity using the same weight of steel. In addition, the beam openings may be used as a pass for different mechanical fixtures such as ducts and pipes. The aim of this study is to investigate the effect of different parameters on both elastic and inelastic critical buckling stresses of steel web plates with openings. These parameters are plate aspect ratio; opening shape (circular or rectangular); end distance to the first opening; opening spacing; opening size; plate slenderness ratio; steel grade; and initial web imperfection. The web/flange interaction has been simplified by web edge restraints representing simply supported boundary conditions. A numerical parametric study has been performed through linear and nonlinear finite element (FE) models, where the FE results have been verified against both experimental and numerical results in the literature. The web plates are subject to in-plane linearly varying compression with different loading patterns, ranging from uniform compression to pure bending. A buckling stress modification factor (${\beta}$-factor) has been introduced as a ratio of buckling stress of web plate with openings to buckling stress of the corresponding solid web plate. The variation of ${\beta}$-factor against the aforementioned parameters has been reported. Furthermore, the critical plate slenderness ratio separating elastic buckling and yielding has been identified and discussed for two steel grades of DIN-17100, namely: ST-37/2 and ST-52/3. The FE results revealed that the minimum ${\beta}$-factor is 0.9 for web plates under uniform compression and 0.7 for those under both compression and tension.


numerical study;web plate with openings;elastic and inelastic buckling;buckling stress modification factor


  1. AASHTO LRFD (1994), Bridge Design Specifications, Washington, D.C., USA.
  2. Anghel, V., Sorohan, S., Constantin, N., Gavan, M. and Boritu, A. (2011), "Numerical study of the lateral buckling of thin walled open cross-section beams", SISOM 2011 and Session of Comission of Acoustics, pp. 3-7.
  3. AWS-D1.1 (2004), Structural Welding Code - Steel; American Welding Society, 550 N.W. Le Jeune Road, Miami, FL, USA.
  4. ANSYS (1998), Swanson analysis system; release 11.0. Houston, LA, USA.
  5. Bruneau, M., Uang, C.M. and Sabelli, S.E. (1998), "Ductile Design of Steel Structures", McGraw Hill, New York, NY, USA.
  6. Chung, K.F., Liu, T.C.H. and Ko, C.H. (2001), "Investigation on vierendeel mechanism in steel beams with circular web openings", J. Constr. Steel Res., 57(5), 467-490.
  7. Durif, S., Bouchair, A. and Vassart, O. (2014), "Experimental and numerical investigation on web-post specimen from cellular beams with sinusoidal openings", Eng. Struct., 59, 587-598.
  8. ECP-205 (ASD) (2011), Egyptian Code of Practice for Steel Construction and Bridges; Housing and Research Center, Giza, Egypt.
  9. Ellobody, E. (2012), "Nonlinear analysis of cellular steel beams under combined buckling modes", Thin-Wall. Struct., 52, 66-79.
  10. El-Sawy, K.M. and Nazmy, A.S. (2001), "Effect of aspect ratio on the elastic buckling of uniaxially loaded plates with eccentric holes", Thin-Wall. Struct., 39(12), 983-998.
  11. El-Sawy, K.M., Nazmy, A.S. and Martini, M.I. (2004), "Elasto-plastic buckling of perforated plates under uniaxial compression", Thin-Wall. Struct., 42(8), 1083-1101.
  12. El-Sawy, K.M., Sweedan, A.M.I. and Martini, M.I. (2009), "Major-axis elastic buckling of axially loaded castellated steel columns", Thin-Wall. Struct., 47(11), 1295-1304.
  13. Erdal, F., Doan, E. and Saka, M.P. (2011), "Optimum design of cellular beams using harmony search and particle swarm optimizers", J. Constr. Steel Res., 67(2), 237-247.
  14. Hamed, A.N., Serror, M.H. and Mourad, S.A. (2015), "Critical buckling stress of castellated web plates under linearly varying uniaxial compression", M.Sc. Thesis; Department of Structural Engineering, Faculty of Engineering, Cairo University, Cairo, Egypt.
  15. Kamble, S.R. (2012), "Analysis of stress distribution in castellated beam using finite element method and experimental techniques", Int. J. Mech. Eng. Appl. Res., 3(3), 190-197.
  16. Kang, J. (2014), "Exact solutions of stresses, strains, and displacements of a perforated rectangular plate by a central circular hole subjected to linearly varying in-plane normal stresses on two opposite edges", Int. J. Mech. Sci., 84, 18-24.
  17. Komur, M.A. and Sonmez, M. (2008), "Elastic buckling of rectangular plates under linearly varying inplane normal load with a circular cutout", Mech. Res. Commun., 35(6), 361-371.
  18. Maiorana, E., Pellegrino, C. and Modena, C. (2009), "Elastic stability of plates with circular and rectangular holes subjected to axial compression and bending moment", Thin-Wall. Struct., 47(3), 241-255.
  19. Moen, C.D. and Schafer, B.W. (2009), "Elastic buckling of thin plates with holes in compression or bending", Thin-Wall. Struct., 47(12), 1597-1607.
  20. Narayanan, R. and Chow, F.Y. (1984), "Ultimate capacity of uniaxially compressed perforated plates", Thin-Wall. Struct., 2(3), 241-264.
  21. Panedpojaman, P. and Rongram, T. (2014), "Design equations for vierendeel bending of steel beams with circular web openings", Proceedings of the World Congress on Engineering, London, UK, July.
  22. Redwood, R., Zaarour, W. and Megharief, J. (1996), "Web post buckling in castellated beams", Proceedings of International Conference on Advances in Steel Structures, Hong Kong, December, pp. 67-71.
  23. Serror, M.H. (2011), "Effect of web opening on buckling instability of simply supported steel I-beam", J. Civil Eng. Arch., 5(9), 809-818.
  24. Shanmugam, N.E., Thevendran, V. and Tan, Y.H. (1999), "Design formula for axially compressed perforated plates", Thin-Wall. Struct., 34(1), 1-20.
  25. Shanmugam, N.E., Lian, V.T. and Thevendran, V. (2002), "Finite element modelling of plate girders with web openings", Thin-Wall. Struct., 40(5), 443-464.
  26. Soltani, M.R., Bouchair, A. and Mimoune, M. (2012), "Nonlinear FE analysis of the ultimate behavior of steel castellated beams", J. Constr. Steel Res., 70, 101-114.
  27. Sonck, D., Impe, R.V., Belis, J. and Vandebroek, M. (2011), "Buckling failure of compressed cellular members", Proc. IABSE-IASS.
  28. Sonck, D., Impe, R.V. and Belis, J. (2014), "Experimental investigation of residual stresses in steel cellular and castellated members", Constr. Build. Mater., 54, 512-519.
  29. Sweedan, A.M.I. and El-Sawy, K.M. (2011), "Elastic local buckling of perforated webs of steel cellular beamcolumn elements", J. Constr. Steel Res., 67(7), 1115-1127.
  30. Thomas, P. (1996), "Plate buckling anaysis using linear and non-linear finite element methods", Youngstown State University, Youngstown, OH, USA.
  31. Timoshenko, S. and Gere, J. (1961), Theory of Elastic Stability, (2nd Ed.), New York, NY, USA.
  32. Tsavdaridis, K.D. and Mello, C.D. (2011), "Web buckling study of the behaviour and strength of perforated steel beams with different novel web opening shapes", J. Constr. Steel Res., 67(10), 1605-1620.
  33. Wakchaure, M.R., Sagade, A.V. and Auti, V.A. (2012), "Parametric study of castellated beam with varying depth of web opening", Int. J. Sci. Res. Publ., 2(8), 1-6.
  34. Wang, P., Ma, Q. and Wang, X. (2014), "Investigation on Vierendeel mechanism failure of castellated steel beams with fillet corner web openings", Eng. Struct., 74, 44-51.
  35. Yuan, W.B., Kim, B. and Li, L.Y. (2014), "Buckling of axially loaded castellated steel columns", J. Constr. Steel Res., 92, 40-45.