Indeterminate Structure

An indeterminate structure is a type of structure in which the number of equilibrium equations is not enough to compute the reactions. This means that there are more unknown forces or moments in the structure than there are equilibrium equations available to solve for them. As a result, additional equations or conditions are required to determine all the unknowns.

Reasons for Indeterminacy

There are several reasons why a structure can be indeterminate:

1. Redundant Members: In some cases, a structure may contain more members than are necessary for stability. These extra members are called redundant members and can cause the structure to be indeterminate. Redundant members can be removed without affecting the stability of the structure, but they introduce additional unknown forces or moments.

2. Support Conditions: The support conditions of a structure can also contribute to its indeterminacy. If the supports are not fully fixed or if their reactions are not fully known, it can result in an indeterminate structure. For example, if a beam is supported by a hinge instead of a fixed support, the reaction at the hinge cannot be determined solely by equilibrium equations.

3. Internal Hinges or Sliding Joints: Structures that contain internal hinges or sliding joints can also be indeterminate. These types of connections allow for relative movement between members, introducing additional unknowns into the system.

Solving Indeterminate Structures

To solve an indeterminate structure, additional equations or conditions must be applied. These can be obtained through the use of compatibility equations, force or moment equilibrium equations for specific sections or joints, or by assuming certain distribution of forces or moments. The number of additional equations needed depends on the degree of indeterminacy of the structure.

Advantages of Indeterminate Structures

While indeterminate structures require additional analysis and calculations, they offer certain advantages over determinate structures. Indeterminate structures can be designed to be more efficient and economical, as they can distribute forces and moments more evenly and minimize material usage. They also provide better resistance to external loads and can have greater overall stability.

Conclusion

In summary, an indeterminate structure is a type of structure in which the number of equilibrium equations is not enough to compute the reactions. It can be caused by redundant members, support conditions, or the presence of internal hinges or sliding joints. Additional equations or conditions are needed to solve the unknown forces or moments in an indeterminate structure. Despite the additional complexity, indeterminate structures offer advantages in terms of efficiency and stability.