# Statically Indeterminate Problem Solving

JoVE Core
Mechanical Engineering
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JoVE Core Mechanical Engineering
Statically Indeterminate Problem Solving

### Próximo Vídeo18.11: Thermal Strain

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.

## Statically Indeterminate Problem Solving

Statically indeterminate problems are those where statics alone can not determine the internal forces or reactions. Consider a structure comprising two cylindrical rods made of steel and brass. These rods are joined at point B and restrained by rigid supports at points A and C. Now, the reactions at points A and C and the deflection at point B are to be determined. This rod structure is classified as statically indeterminate as the structure has more supports than are necessary for maintaining equilibrium, leading to a surplus of unknown reactions over the available equilibrium equations.

The statical indeterminacy is resolved by considering the reaction at point C as redundant and releasing it from its support. This redundant reaction is treated as an additional load. The superposition method is then deployed to determine the deformation in each section of the rod structure. By combining these individual deformations, the total deformation expression for the entire structure is derived. Considering the expressions, the total deformation of the rod structure equals zero, and the summation of all the loads equals zero, the unknown reaction forces are determined. Finally, the deflection at point B is calculated by summing the deformations in the rod structure sections preceding point B.