Unequal settlements in Statically Determinate Structures

Unequal settlements in the supports of a statically determinate structure do not develop any reactions from supports, member forces, or forces in limited members. This is because statically determinate structures are designed to have a fixed number of unknowns, which can be solved using equilibrium equations.

Explanation:

Statically determinate structures are those structures where the number of unknown reactions and member forces can be determined using equilibrium equations. These structures are designed to have a fixed number of unknowns, which can be solved using the principles of statics.

When a statically determinate structure experiences unequal settlements in its supports, the structure may deform, but the number of unknowns remains the same. The deformation of the structure due to unequal settlements does not affect the equilibrium of the structure. Therefore, the reactions from supports, member forces, or forces in limited members do not change.

In other words, the unequal settlements do not create any new unknowns that need to be solved. The original set of equilibrium equations still holds, and the unknowns can still be determined.

In contrast, statically indeterminate structures are those structures where the number of unknown reactions and member forces cannot be determined using equilibrium equations alone. These structures have more unknowns than equations, and therefore, the deformation of the structure due to unequal settlements can create new unknowns that need to be solved.

Conclusion:

In conclusion, unequal settlements in the supports of a statically determinate structure do not develop any reactions from supports, member forces, or forces in limited members. This is because the number of unknowns in a statically determinate structure remains the same, regardless of the deformation caused by unequal settlements.