Statically Indeterminate Problem Solving

Consider two cylindrical rods, one of steel and another of brass, joined at point B and restrained by rigid supports at points A and C.

Determine the reactions at points A and C. Also, determine the deflection at point B.

Here, the rod structure is considered statically indeterminate as it has more supports than necessary for the condition of equilibrium, leading to an excess of unknown reactions over equilibrium equations.

So, the reaction at point C is considered redundant and released from the support. It is treated as an additional load.

Then, using the superposition method, the deformation in each section of the rod structure is determined and combined to determine the total deformation.

 Considering the total deformation expression, the total deformation of the rod structure equaling zero, and the summation of all the loads equaling zero, the unknown reaction forces are determined.

The deflection at point B is calculated by summing the deformations in the sections before point B in the rod structure.