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Strength of Materials: Thermal Stress

What is Thermal Stress

It is known that an object will contract or expand when the temperature changes. This contraction and expansion process can cause a thermal stress on an object if there is interference from contacting another part, or if the part is made out of different types of materials.

All translational direction (x, y, and z) can be effected by thermal stress during the expansion or contraction process. For this case I am only going to talk about one direction where the resulting forces are normal to the central axis, resulting in axial loads.

To solve a problem like this, first you must realize that all axial loaded problems caused by thermal expansion are statically indeterminate. The best method to solve this problem would be to take in consideration the expansion that would happen due to the change in temperature. Refer to equation 1 to calculate thermal expansion or contraction. This equation can only be used if the temperature change accross the length is constant, otherwise equation 2 would have to be used.

Thermal Expansion Equation (1)

General Thermal Expansion Equation (2)

Once the deflection caused by the temperature change is known, superposition method can be used to find the resulting forces.

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