Incremental Collapse of Structures with Constant Plus Cyclically Varying Loads

Abstract

Energy methods previously developed for the shakedown analyses of framed structures are extended to include structures subjected to cyclically varying loads in the presence of constant, or bias, loads. This approach is based on the hypothesis that, if the total hysteresis energy absorbed by a structure during an indefinitely prolonged repetitive loading program is unbounded, then the structure must ultimately fail. This hypothesis leads to results that are entirely consistent with the classical shakedown theorems. Several illustrative examples demonstrate that the incremental collapse envelopes of framed structures subjected to cyclically varying patterns of loading can be drastically reduced when constant loads are present. These results are essentially due to inelastic interactions between the cyclic and constant loads that magnify the effects of hysteresis. In fact, the reduction in the safe loading ranges (as defined by the incremental collapse envelope) can be a sensitive function of the constant, or bias, load components.