Chapter 6 - Limit Analysis by Linear Programming

Abstract

Plastic limit analysis is concerned with the problem of finding how “strong” a given structure is. It estimates the factor by which the live load component needs to be amplified so that a structural crisis, which takes the form of plastic collapse, occurs. Plastic collapse takes place when the structure is converted into a mechanism by the development of a suitable number and disposition of plastic hinges. Plastic collapse factor represents one of the most important outcomes of a plastic structural analysis, as it is useful for the reliable and economical safety assessment and design of ductile structures. This chapter aims to fill the gap between the mathematical programming methods and the classical and often tedious techniques involving, for instance, upper bound approximations to the collapse load using an approach based on identification and combination of basic mechanisms. It begins with brief statements concerning the dual pair of bound theorems of limit analysis that clearly suggest associated formulations as constrained optimization problems. It focuses on the application of static theorem. Following this, it introduces the solutions of some simple examples through application of the LP capability of the popular Microsoft Excel spreadsheet software. Furthermore, it provides a general description of the discrete plane frame problem with a view to its eventual computer implementation as a MATLAB script. It concludes with a note on the optimal plastic design problems.