Hello everyone(adsbygoogle = window.adsbygoogle || []).push({});

First off, a very happy new year to all my PF friends. I need some help with a mathematical analysis of the following situation:

One end of a metallic rod of length [itex]L_{1}[/itex] measured at temperature [itex]T_{1}[/itex] is fixed to a rigid wall and the other end is connected to a spring with force constant [itex]k[/itex] (the other end of the spring is anchored to a parallel rigid wall). The coefficient of linear expansion of the rod is [itex]\alpha[/itex]. We have to find the compression of the spring when the temperature is raised to [itex]T_{2}[/itex].

I've worked out the details...

If we add the strains algebraically,

[tex]\epsilon = \epsilon_{thermal} + \epsilon_{spring}[/tex]

with [itex]\epsilon_{thermal} = \alpha\Delta T[/itex], [itex]\epsilon_{spring} = -\frac{k\Delta L}{YA}[/itex] and [itex]\epsilon = \frac{\Delta L}{L_{1}}[/itex], we do get an expression for [itex]\Delta L[/itex] under the combined action of these forces. This does yield the correct answer but I want to be sure about it. Is it correct?

Thanks and cheers

Vivek

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# Homework Help: Thermal + Compressive Stress in a Rod + Spring system

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