Deformations of Plastic Frames Considering Axial Forces

In the framework of a first-order theory and for the general case of the incomplete collapse mechanism the analysis reduces to solving a pair of dual quadratic programming problems which always have global optimum solutions. The primal problem has the stress field components as variables and consists of minimizing the complementary energy of the structure, subject to satisfaction of the equilibrium and yield constraints. The dual problem has the characteristic displacements of the auxiliary frame as variables and consists of minimizing a modified expression of the potential energy of the frame, subject to satisfaction of the compatibility and flow rule constraints. Solutions to the primal and dual problems are obtained simultaneously by an existing computer program, which enables the determination of the complete stress distribution and deformed shape of the frame.