Theory

The degree of static indeterminacy (DSI) of a structure is a measure of how many unknown internal forces and reactions exist within the structure over and above the minimum necessary to ensure stability and equilibrium. These are beyond those that can be determined through the application of the equations of static equilibrium. In other words, DSI measures the number of additional equations that must be solved (based on conditions of compatibility) to fully determine the internal forces and reactions within the structure.

There are various formula used to determine the static indeterminacy of various type of structure:

- DSI for Beams ------------- (R - C + 3)

• DSI for Truss ------------ (M + R) - 2J
• DSI for Rigid frames ------------ (3M + R) - 3J
  
  

where J is the number of joints (or points of connection) within the structure, M is number of elements (members), C is conditions of construction and R is the number of reaction components (i.e., vertical , horizontal , and moment )at each support.

A statically determinate structure has zero degree of static indeterminacy, meaning that all internal forces and reactions can be determined solely through the application of static equilibrium equations. A statically indeterminate structure, on the other hand, has a degree of static indeterminacy equal to or greater than one. It requires additional equations beyond the equations of static equilibrium to fully determine internal forces and reactions. Force method can be used to determine the additional compatibility equations needed to solve for internal forces and reactions in a statically indeterminate structure. The force method involves the use of compatibility equations, which describe the relationship between deformations and rotations at different points within the structure, and equilibrium equations, which describe the balance of forces and moments within the structure.

In summary, the degree of static indeterminacy is a crucial factor in determining the internal forces and reactions within a structure, and its calculation is an important step in the analysis of statically indeterminate structures.