FG Baustatik, Stahlbau, FEM
In case of cyclic loading, strain may accumulate due to a ratcheting mechanism until the state of shakedown is possibly achieved. Design Codes frequently require strain limits to be satisfied at the end of the specified lifetime of the structure. However, this requirement is sometimes tied to misleading prerequisites, and little guidance is provided on how the strains accumulated in the state of shakedown can be calculated. Incremental elastic-plastic analyses which require to go step-by-step through many cycles of a given load histogram are rather costly in terms of engineering time and numerical effort. As an alternative, the Simplified Theory of Plastic Zones (STPZ) is used in the present paper. Being a direct method, effects from load history are disregarded. The theory is described shortly and exemplarily applied to a simplification of a pipe bend and a straight pipe, both subjected to combinations of several loads which vary independently from each other so that a multidimensional load domain is represented. It is shown that the Simplified Theory of Plastic Zones is well suited to provide reasonable estimates of strains accumulated in the state of elastic shakedown at the cost of few linear elastic analyses.
The Simplified Theory of Plastic Zones (STPZ) may be used to determine post-shakedown quantities such as strain ranges and accumulated strains at plastic or elastic shakedown. The principles of the method are summarized. Its practical applicability is shown by the example of a pipe bend subjected to constant internal pressure along with cyclic inplane bending or/and cyclic radial temperature gradient. The results are compared with incremental analyses performed step-by-step throughout the entire load history until the state of plastic shakedown is achieved.