18.12 : Temperature Dependent Deformation

In a nonhomogeneous rod made up of steel and brass, restrained at both ends and subjected to a temperature change, several steps are involved in calculating the stress and compressive load. Due to the problem's static indeterminacy, one end support is disconnected, allowing the rod to experience the temperature change freely. Next, an unknown force is applied at the free end, triggering deformations in the rod's steel and brass portions. These deformations are then calculated and added together to determine the total deformation of the rod.

Given the constraints imposed on the rod, it is asserted that this total deformation must be zero. This assertion aids in identifying the unknown force, which has an equal and opposite reaction at the fixed end of the rod. The forces in the rod's steel and brass portions are considered equal, which helps determine the corresponding stress values in each portion. It is important to note that although the total deformation of the rod is zero, the individual deformations in the steel and brass sections are not. Lastly, the strains in the steel and brass portions are calculated. The respective deformations in each portion are then expressed, confirming that while their sum equals zero, neither deformation is zero individually.