First‐Order Limit Analysis of Plane Frames

Abstract

An effective procedure for limit analysis of plane frames under proportional loading is developed, within the framework of simple plastic theory. The proposed method is sequential in the sense that a strength (static) analysis precedes deformation analysis. The static analysis starts from the independent mechanisms of the structure, which are generated in a systematic and efficient way. Then, through an energetic theorem, deformation analysis is cast as a linear programming (LP) problem, in which extensive use is made of the previous information from the static analysis. Passive hinges are detected by a posteriori check of moment and plastic deformations distributions, and additional analyses are performed until safety and parity conditions are satisfied. In comparison with other methods, the proposed one uses fewer variables and constraints. Two examples (one of them worked in detail) are included.