Math CentralQuandaries & Queries


Question from roger:

Knowing that the coefficient of thermal expansion of steel is 6.5E-06
in/in/deg F. How do you calculate the loads applied as a result of the expansion?

I don't think that you can, at least from that datum; it depends upon how much the steel resists efforts to compress it below its equilibrium dimension.

This in turn can be given by any of several values. In the unlikely situation that the sample is contained in an undeformable collar, or in the more plausible case of a wide plate, loaded in the thin dimension, the number needed would represent bulk compressibility. For a slug with free sides and small changes of temperature, unable to expand in one dimension only, elastic deformation would presumably rule. Thermally buckled struts, and samples expanding beyond the limits of elastic deformation would work differently again. Most of these would depend critically on the shape, in many cases requiring finite-element modelling.

Good Hunting!

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