I am trying to understand stresses that are induced by thermal gradients. Now, I can think of a hundred different questions to ask, but I want to take baby steps to get there. Let's just talk about a simple cantilever beam in the x-y plane where the x-axis is the beam's longitudinal axis and the y-axis is parallel to its height. Z points 'into the page' along its thickness.(adsbygoogle = window.adsbygoogle || []).push({});

Let's say that there is a temperature gradient in the x-direction. The beam will want to elongate due to thermal expansion, but the gradient will cause it to want to elongate by different amounts. I am assuming that this will only induce an axial stress/strain.

What if I want to do a simple back-of-envelope calculation to approximate the equivalent axial load required to induce this stress? I was assuming that I can just take the worst ΔT and use:

ΔL/L = ε = αΔT

σ = P/A = εE

so that:

P/(AE) = αΔT

∴ P = AEαΔT

Any thoughts or issues with this approach?

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# Stress Due to Thermal Gradient

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