This paper presents the results of computations for determining transient thermal stresses in slabs and circular pressure vessels. The process of solution adopted is to substitute transient-temperature formulas into the already available stress expressions. The expressions for thermal shock are transformed by means of a simple integral theorem into a form appropriate for analyzing the thermal processes commonly used to relieve thermal shock. A new dimensionless stress parameter is defined and applied to the determination of optimum heating or cooling times of massive pressure vessels.

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