Shakedown of Grids under Combined Bending and Torsion

Abstract

The shakedown analysis of plane elastoplastic grillage structures for which plasticity is affected by the combined action of bending moment and torsion is formulated using the static or lower bound Bleich‐Melan theorem. Discretization of the structure into finite elements and the nonlinear yield surface into a piecewise linear one, converts the formulation into a linear programming problem that can be solved efficiently using standard packages. How the necessary requirements of equilibrium and yield conformity are satisfied, and how the elastic locus is calculated are also mentioned. A method of identifying whether incremental collapse or alternating plasticity is the governing mode of failure is given. Based on the formulation presented, a FORTRAN computer program named SGRID was written to carry out the shakedown analysis of general planar grillages. Finally, several examples of typical bridge grillages are presented primarily to demonstrate the effect of including torsion in the analyses and also to indicate how easy it is to perform such analyses for practical engineering applications.