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Deformation of block of wood when one surface is heated

See the attached diagram.

A block of wood that is 3 inches wide x 6 inches long x .380 inches thick is fixed/anchored to a structure.

The top surface of the wood block is heated to 300 degrees C. The bottom surface is cooled to an undetermined temperature.

The differential in temperature causes the top surface to expand/elongate while the bottom wood surface contracts. The difference in the expansion and contraction causes the end of wood block to deflect/deform by 1.25 inches.

The wood properties as well as a thermal conductivity are given.

1) Determine the cold temperature on the bottom surface of the wood that would cause enough temp differential between the hot & cold to cause the end of the wood to deflect as shown.

2) Based on the deflection of 1.25 inches, we are also asked to determine the vertical force, horizontal force, and actual force that caused the deformation.

If this were a traditional structural mechanics problem, I could reasonably determine that the vertical load (P) that could cause a deflection of 1.25 inches is approx. 144 lbs.

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Solution Summary

The deformation of blocks of wood when one surface is heated is determined.