It has been noted in the preceding discussions that a complete elastoplastic analysis is generally quite complicated. The complexities arise mainly from the necessity of carrying out an analysis in an iterative and incremental manner. The development of efficient alternative methods that can be used to obtain the collapse load of a structural problem in a simple and more direct manner without recourse to an iterative and incremental analysis is, therefore, of great value to practicing engineers, despite the fact that the information so obtained is just a part of the total solution. Limit analysis is concerned with the development and applications of such methods that can furnish the engineer with an estimate of the collapse load of a structure in a direct manner. The estimation of the collapse load is of great value, not only as a simple check for a more refined analysis, but also as a basis for engineering design.
Figure 8.1a shows a simply supported rectangular beam subjected to a uniformly distributed load q. The beam is made of an elastic-perfectly plastic material. As the applied load q is gradually increased starting from zero, the beam is stressed first in a purely elastic manner until the elastic limit load q = q c is reached, at which the stresses at the upper and lower edges of the center section...
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