(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A barrel of diameter D at 20 degrees Celsius is to be enclosed by an iron band. The circular band has an inside diameter of d at 20 degrees Celsius. It is w wide and t thick. (a) To what temperature must the band be heated so that it will fit over the barrel? (b) What will be the tension in the band when it cools to 20 degrees Celsius?

2. Relevant equations

For (a) I will need the equations to calculate the volume of the band and the change in volume of the band when heated. For (b), I will need the equation for determining thermal stress.

3. The attempt at a solution

For (a), is it safe to assume that the wideness of the band remains the same while the thickness of the band expands linearly? If so, then I can calculate the the desired volume after heating and use the volume expansion formula to determine the change in temp.

For (b), the equation for thermal stress has area as one of its variables. The area is some cross-section of the material. In the case of the band, will the cross-section used be t x w?

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# Homework Help: Heating a Band to Fit a Barrel

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