Recent progress in the plastic methods of structural analysis

Abstract The “plastic methods” are concerned with the conditions of failure of statically indeterminate structures of ductile metal, mild steel in particular. Continuous beams and frames of mild steel can carry loads considerably in excess of those which cause the elastic limit of the material to be first reached. A real physical failure occurs when the load has reached a certain fairly well-defined value, above which small load increases rapidly produce much larger permanent deformations than had occurred at lower load levels. The plastic methods attempt to base the design upon this realistic concept of failure, and hence attempt to eliminate some of the uncertainty necessarily involved in design methods which do not deal directly with real structural failure. This paper reviews recent developments in methods of plastic failure analysis based on certain simple hypotheses as to the carrying capacity of flexural members. The basic hypotheses are first defined and a simple example is given to illustrate their use. This serves also to explain the philosophy and advantages of the plastic methods in suitable applications. Some weaknesses of the basic hypotheses and limitations of the plastic methods are indicated. In treating general frames the need for a sufficient description of the manner of loading is pointed out. Two extreme types of loading termed “proportional loading” and “variable repeated loading” are defined; any actual loading program lies between these two extremes. The remainder of Part I is devoted to stating the mathematical theorems appropriate to the problem of porportional loading and to explaining techniques by means of which failure loads of this type may be readily computed for general continuous frames. A problem of a two-span portal frame is solved in order to illustrate the new techniques.