Structural Engineering and Mechanics

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On the use of the Lagrange Multiplier Technique for the unilateral local buckling of point-restrained plates, with application to side-plated concrete beams in structural retrofit

  • Hedayati, P. (Department of Civil Engineering, Isfahan University of Technology) ;
  • Azhari, M. (Department of Civil Engineering, Isfahan University of Technology) ;
  • Shahidi, A.R. (Department of Civil Engineering, Isfahan University of Technology) ;
  • Bradford, M.A. (Centre for Infrastructure Engineering and Safety, School of Civil and Environmental Engineering, The University of New South Wales)
  • Received : 2004.06.30
  • Accepted : 2007.05.17
  • Published : 2007.08.20
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Abstract

Reinforced concrete beams can be strengthened in a structural retrofit process by attaching steel plates to their sides by bolting. Whilst bolting produces a confident degree of shear connection under conditions of either static or seismic overload, the plates are susceptible to local buckling. The aim of this paper is to investigate the local buckling of unilaterally-restrained plates with point supports in a generic fashion, but with particular emphasis on the provision of the restraints by bolts, and on the geometric configuration of these bolts on the buckling loads. A numerical procedure, which is based on the Rayleigh-Ritz method in conjunction with the technique of Lagrange multipliers, is developed to study the unilateral local buckling of rectangular plates bolted to the concrete with various arrangements of the pattern of bolting. A sufficient number of separable polynomials are used to define the flexural buckling displacements, while the restraint condition is modelled as a tensionless foundation using a penalty function approach to this form of mathematical contact problem. The additional constraint provided by the bolts is also modelled using Lagrange multipliers, providing an efficacious method of numerical analysis. Local buckling coefficients are determined for a range of bolting configurations, and these are compared with those developed elsewhere with simplifying assumptions. The interaction of the actions in bolted plates during buckling is also considered.

Keywords

References

  1. Allen, H.B. and Bulson, P.S. (1980), Background to Buckling, McGraw-Hill, London
  2. Azhari, M. and Bradford, M.A. (1993), 'Inelastic local buckling of plates with and without residual stresses', Eng. Struct., 15(1), 31-39 https://doi.org/10.1016/0141-0296(93)90014-U
  3. Baniotopoulos, C.C., Abdalla, K.M. and Panagiotopoulos, P.D. (1994), 'A variational inequality and duadratic programming approach to the separation problem of steel bolted bracket', Comput. Struct., 53(4), 983-991 https://doi.org/10.1016/0045-7949(94)90384-0
  4. Bradford, M.A. (1998), 'Service-load deformations of concrete-filled RHS columns', Eighth Int. Symposium on Tubular Structures, Singapore (Y.S. Choo et al. eds.), Balkema, 425-423
  5. Bradford, M.A., Smith, S.T. and Oehlers, D.J. (2000), 'Semi-compact steel plates with unilateral restraint subjected to bending, compression and shear', J. Constr. Steel Res., 56(1),47-67 https://doi.org/10.1016/S0143-974X(99)00073-5
  6. Chand, R., Huang, E.J. and Rimm, K. (1976), 'Analysis of unbonded contact problems by means of quadratic programming', J. Optimiz. Theory App., 20, 171-189 https://doi.org/10.1007/BF01767450
  7. Conry, T.F. (1970), 'The use of mathematical programming in design of uniform distribution in nonlinear elastic system', PhD Thesis, The University of Wisconsin, WI, USA
  8. Conry, T.F and Seireg, A. (1971), 'A mathematical programming method for design of elastic bodies in contact', J. Appl. Mech., 2, 387-392
  9. Fischer, U. and Melosh, R.J. (1987), 'Solving discretized contact problems using linear programming', Comput. Struct., 25, 661-664 https://doi.org/10.1016/0045-7949(87)90158-1
  10. Hedayati, P. (2001), Unilateral Local Buckling of Steel Bolted Plates, MSc Thesis, Department of Civil Engineering, Isfahan University of Technology, Isfahan, Iran
  11. Khathlan, A.A. (1994), 'Large deformation analysis of plates on unilateral elastic foundation', J. Eng. Mech., Am. Soc. Civil Eng., 120(8), 1820-1827 https://doi.org/10.1061/(ASCE)0733-9399(1994)120:8(1820)
  12. Liew, K.M. and Wang, C.M. (1995), 'Elastic buckling of regular polygonal plates', Thin Wall. Struct., 21, 163-173 https://doi.org/10.1016/0263-8231(94)00031-T
  13. Nguyen, N.T., Oehlers, D.J. and Bradford, M.A. (2001), 'An analytical model for reinforced concrete beams with bolted side plates accounting for longitudinal and transverse partial interaction', Int. J Solids Struct., 38(38-39), 6997-7015 https://doi.org/10.1016/S0020-7683(01)00005-1
  14. Oehlers, D.J. (1990), 'Strengthening reinforced concrete beams by bonding steel plates to their soffits', Struct. Eng. Conf., Adelaide, I.E. Australia, 346-350
  15. Oehlers, D.J., Wright, H.D. and Burnet, M.J. (1994), 'Flexural strength of profiled beams', J. Struct. Eng., Am. Soc. Civil Eng., 120(2), 378-393
  16. Ohtake, K., Oden, J.T. and Kikuchi, N. (1980a), 'Analysis of certain unilateral problems in von Karman plate theory by a penalty method. Part 1: A variational principle with penalty', Comput. Meth. Appl. Mech. Eng., 24, 187-213 https://doi.org/10.1016/0045-7825(80)90045-6
  17. Ohtake, K., Oden, J.T. and Kikuchi, N. (1980b), 'Analysis of certain unilateral problems in von Karman plate theory by a penalty method. Part 2: Approximation and numerical analysis', Comput. Meth. Appl. Mech. Eng., 24, 317-337 https://doi.org/10.1016/0045-7825(80)90068-7
  18. Shahwan, K.W. and Wass, A.M. (1994), 'A mechanical model for the buckling of unilaterally constrained rectangular plates', Int. J. Solids Struct., 31(1), 75-78 https://doi.org/10.1016/0020-7683(94)90176-7
  19. Shahwan, K.W. and Wass, A.M. (1998), 'Buckling of unilaterally constrained infinite plates', J. Eng. Mech., Am. Soc. Civil Eng., 124(2), 127-136 https://doi.org/10.1061/(ASCE)0733-9399(1998)124:2(127)
  20. Shen, H. and Williams, F.W. (1997), 'Biaxial buckling and post-buckling of composite laminated plates on two-parameter elastic foundations', Comput. Struct., 63(6), 1177-1185 https://doi.org/10.1016/S0045-7949(96)00398-7
  21. Smith, S.T., Bradford, M.A. and Oehlers, D.J. (1999a), 'Elastic buckling of unilaterally constrained plates in pure shear', Eng. Struct., 21, 443-453 https://doi.org/10.1016/S0141-0296(97)00218-6
  22. Smith, S.T., Bradford, M.A. and Oehlers, D.J. (1999b), 'Local buckling of side-plated reinforced concrete beams. II: Experimental study', J. Struct. Eng., Am. Soc. Civil Eng., 125(6), 635-643
  23. Smith, S. T., Oehlers, D.J. and Bradford, M.A. (1999c), 'Local buckling of side-plated reinforced concrete beams. I: Theoretical study', J. Struct. Eng., Am. Soc. Civil Eng., 125(6), 622-634
  24. Smith, S.T., Bradford, M.A. and Oehlers, D.J. (1999d), 'Numerical convergence of simple and orthogonal polynomials for the unilateral plate buckling problem using the Rayleigh-Ritz method', Int. J. Numer. Meth. Eng., 44, 1685-1707 https://doi.org/10.1002/(SICI)1097-0207(19990420)44:11<1685::AID-NME562>3.0.CO;2-9
  25. Swartz, S.E. and O'Neill, R.J. (1995), 'Linear elastic buckling of plates subjected to combined loads', Thin Wall. Struct., 21, 1-15 https://doi.org/10.1016/0263-8231(94)P4389-R
  26. Timoshenko, S.P. and Gere, J.M. (1961), Theory of Elastic Stability, McGraw-Hill, New York
  27. Uy, B. (2001), 'Local and post local buckling of fabricated steel and composite cross-sections', J. Struct. Eng., Am. Soc. Civil Eng., 127(6), 666-677 https://doi.org/10.1061/(ASCE)0733-9372(2001)127:7(666)
  28. Wang, C.M. and Liew, K.M. (1994), 'Buckling of triangular plates under uniform compression', Eng. Struct., 16(1), 43-50 https://doi.org/10.1016/0141-0296(94)90103-1
  29. Wright, H.D. (1995), 'Local stability of filled and encased steel sections', J. Struct. Eng., Am. Soc. Civil Eng., 121(10), 1382-1388

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