Thermal Stress and Spring Systems

AI Thread Summary
The discussion focuses on calculating the force in a rod made of A-36 steel when subjected to thermal stress and spring compression. Given the rod's dimensions and spring constant, the thermal deformation is determined using the formula for thermal expansion. The temperature change from 40°F to 160°F leads to a specific deformation that, when combined with the spring's compression, allows for the calculation of the force using F=kx. The correct answer is confirmed to be 163 lbs, emphasizing the importance of following through with the calculations to understand the underlying principles. The conversation highlights the need for clarity in applying thermal stress equations to solve for forces in spring systems.
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The rod is made of A-36 steel and has a diameter of 0.25 in and a length of 4 ft. Attached to each end of the rod is a spring which is fixed to a wall. If the springs are compressed 0.5 in. when the temperature of the rod is T=40 F, determine the force in the rod when its temperature is T=160 F. It is given that k=10,000 lb/in.

Equations: F=kx, Thermal Deformation=alpha*change in temp*length

Attempted Solution: Find the thermal deformation in the rod at T=160 F, then use this in F=kx to solve for F.

I know the correct answer is 163 lbs, but I don't understand why.
 
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