TABLE OF CONTENTS So far our analysis of the behaviour of structures has assumed that whether the structures are statically determinate or indeterminate the loads on them cause stresses which lie within the elastic limit. Design, based on this elastic behaviour, ensures that the greatest stress in a structure does not exceed the yield stress divided by an appropriate factor of safety.
An alternative approach is based on plastic analysis in which the loads required to cause the structure to collapse are calculated. The reasoning behind this method is that, in most steel structures, particularly redundant ones, the loads required to cause the structure to collapse are somewhat larger than the ones which cause yielding. Design, based on this method, calculates the loading required to cause complete collapse and then ensures that this load is greater than the applied loading; the ratio of collapse load to the maximum applied load is called the load factor. Generally, plastic,or ultimate load design, results in more economical structures.
In this chapter we shall investigate the mechanisms of plastic collapse and determine collapse loads for a variety of beams and frames.
Plastic analysis is governed by three fundamental theorems which are valid for elasto- plastic structures in which the displacements are small such that the geometry of the displaced structure does not affect the applied loading system.
The following conditions must be satisfied simultaneously by a structure in its collapsed state:
The equilibrium...
