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## Summary:

- Is it possible to calculate critical temperature for a plate?

Hi,

in the Timoshenko’s book "Theory of elastic stability" one can find a case of simply supported rectangular plate uniformly compressed in one direction (compressive load is applied to shorter edges). The formula for critical load is: $$N_{cr}=\frac{\pi^{2} D}{b^{2}} \left( \frac{b}{a} + \frac{a}{b} \right)^{2} $$ where: D - flexural rigidity, b - length of shorter edge, a - length of longer edge.

Here’s a scheme of this plate:

Now what if we heat up the whole plate and replace the compressive load with supports blocking translation of these edges in the normal direction? Is it possible to calculate the critical temperature knowing the thermal expansion coefficient?

in the Timoshenko’s book "Theory of elastic stability" one can find a case of simply supported rectangular plate uniformly compressed in one direction (compressive load is applied to shorter edges). The formula for critical load is: $$N_{cr}=\frac{\pi^{2} D}{b^{2}} \left( \frac{b}{a} + \frac{a}{b} \right)^{2} $$ where: D - flexural rigidity, b - length of shorter edge, a - length of longer edge.

Here’s a scheme of this plate:

Now what if we heat up the whole plate and replace the compressive load with supports blocking translation of these edges in the normal direction? Is it possible to calculate the critical temperature knowing the thermal expansion coefficient?