Temperature Dependent Deformation

Consider a non-homogenous rod made of steel and brass, restrained at both ends and subjected to a temperature change.

The stress and load on the rod are determined by disconnecting one supported end and allowing the rod to undergo a temperature change.

Applying an unknown force at the free end determines the deformations for both the steel and brass portions in terms of the unknown force. The resulting deformations are summed up to arrive at the total deformation.

Asserting that the total deformation must be zero due to constraints helps find the unknown force, which has an equal and opposite reaction at the fixed end.

Equal forces in steel and brass portions of the rod are considered in determining the corresponding stress values of the portions.

Finally, the strain in the steel and brass portions is calculated, and respective deformations are expressed.

The total deformation of the steel and brass sections is zero, and individual deformations in the steel and brass sections are non-zero.