Deformation Analysis of Structures Near Collapse Load

The primary function of any structure is to provide adequate strength to resist the loads acting on it without undergoing excessive deformations which, in turn, might render the structure of no further use. For every structure, therefore, deformations under working loads must be within certain definite limits. If the loads are increased beyond their working values, the material at the critical sections is expected to yield. This brings about a sharp increase in the deformations. These increased deformations may cause several forms of premature local buckling in structures composed of mild steel, while in reinforced concrete structures, local fracture of concrete, with resulting failure of the section, is likely to occur due to the brittle nature of the concrete material. These effects may lead to local collapse of structures at loads lower than those otherwise expected to produce failure. It is imperative, therefore, to develop methods for estimating hinge rotations and other deformations at ultimate loads which are simple and economically feasible to put into practice by an average practicing engineer. Various methods to accomplish this have been proposed for steel as well as reinforced concrete structures. They are primarily based on either slope deflection equations or energy methods. The slope deflection equations used for estimating deformations of any structure at ultimate loads, if extended as shown later in this paper, lend themselves to the introduction of the principle of elastic moment distribution. The method presented herein makes use of this principle.