© 1951 by Oxford University Press
THE BEHAVIOUR OF FRAMED STRUCTURES UNDER REPEATED LOADING
( Engineering Laboratory, University of Cambridge )
When a structure is subjected to several loads, each of which may vary independently of the other loads between certain limits, it becomes necessary to consider the possibility that failure may occur by the establishment of a cycle of plastic deformation, even though no possible combination of the loads could cause collapse. If, for example, a flexural member was bent repeatedly first in one sense and then in the other sense, so that yield occurred at each reversal of stress, fracture would be expected to occur after a comparatively short time. Alternatively, the permanent deformations might continue to increase each time a particular sequence of loads was repeated, so that large deformations would be developed after a few repetitions of the loads. In such cases the structure must be designed so that after a few applications of the various possible peak load combinations, a state of residual stress is reached which enables all further variations of the loads to be supported elastically. When this happens the structure is said to have shaken down.
In this paper the behaviour of framed structures under variable loads is discussed, and a theorem is established which enables framed structures to be examined with a view to determining whether shake-down will occur under a given set of loads which may alternate between prescribed limits.