A new and simpler proof is given for a theorem due to Melan concerning the conditions under which an elastic-plastic body will “shake down” i.e., reach a residual stress state on which only elastic stresses are superimposed for all further variations of the surface loading stresses within limits prescribed at surface points. The theorem is applied to discuss the case of a circular bar subjected to an axial force and a torsional moment which vary independently between given limits. Relations to previous work on trusses and rigid frames are discussed briefly.

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