Thermal Expansion Stress

[Seraph042]

I'm designing a system that will thermally cycle a stainless steel substrate up to 1200C from room temperature; right now my design consists of clamping the substrate onto a plate using a bolt head/washer with a nut on the other end of the screw, as shown on the attached figure.

I want to determine the minimum distance I can put the substrate away from the bolt so that buckling will not occur during thermal expansion. The substrate in question is 4"x1"x1/16" (the 1" is into the figure). The bolts I have selected have a 3mm nominal diameter and are made of Monel.

I calculated the critical compressive stress on the substrate to be 22.9 ksi, but I am having trouble incorporating the thermal expansion of both the sample and the bolt in order to determine the compressive stress on the sample. What steps should I take?

Here's some material info I got from matweb.com:

\alpha_{stainless steel}=15.1E-06 /degC, E_{stainless steel}=28.5E+06 psi, S_{y, stainless steel}=89.6E+03 psi

\alpha_{bolt}=13.9E-06 /degC, E_{bolt}=24.5E+06 psi

 

[minger]

When looking at thermal stresses, the typical approach is superposition. Assume that you have a beam fixed between two supports and heat it. You can think of there being two loads: one thermal, and one mechanically imposed by the support.

Typically one would allow a free end to move as if it were not being constrained. You would then calculate the load required to move it back into place.

I hope that gets you on the right track. If you need an example I'm sure someone can provide one.