Applying the ASME Codes: Plant Piping & Pressure Vessels (Mister Mech Mentor, Vol. 2)
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Some stress analysis problems involve superposition of stresses from different types of loading, or combination of stresses in different planes using Mohr's circle, or simply the calculation of transient stresses that arise from physically restraining a body while its temperature changes. This is especially true when fatigue life analysis is required.
Now I am fully aware that the really cool way to analyze such things is to use finite element analysis. However, you may not have the time or budget for that, but still need a good answer. Whatever the case, good approximations can be made by hand calculation, and the thermal restraint part is not all that difficult.
As you recall from school, the basic idea is to calculate the thermal growth an unrestrained body would undergo, in changing from one temperature to another. Next, determine the limiting effect of full or partial constraint of that expansion by some rigid or elastic structure. The stresses, which we visualize as being created by the imaginary process of forcing the thermal strains to reverse, by the full or a selected partial amount, are then calculated by normal means (the usual equations from strength of materials.)