Very often in practice a structure is subjected to loads consisting of several components, whose respective maximum and minimum values are known, but whose order and instantaneous magnitudes cannot be specified in advance. For example, an airplane wing might be subjected to dead loads, maneuvering loads, gust loads, etc., whose maximum and minimum values can be estimated closely, but which are applied independently in a manner which is not predictable. Again, a machine part might be subjected to unspecified combinations of bending and torsional loads, whose respective greatest and least values only are known. The present paper deals with the analysis of structures of this kind, when plastic deformation in parts of the structure is permitted in order to obtain the most economical design consistent with safety. Emphasis is placed upon the use of a geometrical representation of the instantaneous state of stress in an appropriate “stress space.” For simplicity the present discussion is based upon a pin-jointed plane truss as a typical structure. With appropriate changes of language the concepts developed here may be extended to more general structures and to problems of continua.

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