General equations for the computation of stress rates in solid and hollow cylinders subjected to transient temperature distributions are developed, based on the assumptions of an elastic, perfectly plastic material obeying the Tresca yield condition with Poisson ratio of one half. For most temperature distributions, it appears that these equations can be integrated only by numerical means. However, for one particular temperature distribution, equivalent to a phase transformation which occurs at a fixed temperature, it is found possible to integrate them analytically, and expressions for the transient and residual stresses are obtained in closed form. The latter results are compared with experiment and qualitative agreement noted.

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