![]() That is no different to joining two rods of different materials end to end, or two rods of the same material but different areas.įor the right half, the strain is αΔT 2 and the displacement in the right half will be The discontinuity in strain doesn't matter. In other words the beam "grows" in a linear manner from the fixed end. Assuming the end at 2L is free, the strain in the left half is αΔT 1 and the axial displacement at a distance x along the left half of the beam is u = αΔT 1x. I think you are confusing strain with displacement. I know this all assumes constant α's and E's, but as a 1st order approximation, I would think this could give me a worst-case equivalent load if I let T 2 be the highest temp from the actual distribution and let T 1 be the lowest temp from the actual distribution. So the net strain could be used to find an equivalent load using the logic from the OP. This would be the net expansion of the beam. The left half tries to keep up, but it can't and falls behind by Δx=Δx 2-Δx 1. So the right half wants to grow more than the left half. Immediately to the left at x=L - the beam wants to expand by Δx 1 and immediately to the right at x=L + it wants to expand by Δx 2. We know that the first half of the beam wants to expand by Δx 1=LαΔT 1 and the second by LαΔT 2. But to simplify things, let's just say that the beam is length 2L and the resulting temperature field is such that the first half of the beam (0≤xT 1. In the real world, if thermal BCs are applied, it is likely that the beam will end up with a continuous temperature distribution. Let's assume now that a cantilevered beam starts at T ref. Something to let me sanity check some ANSYS results. ![]() So what I am looking to do is to find a way to hand-calculate this to just get a rough number.
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