Static Determinacy

When all the forces in a structure can be determined directly from equilibrium equations, the structure is considered statically determinate. In contrast, when all the forces in a structure cannot be determined directly from equilibrium equations, the structure is considered statically indeterminate. In the latter case, there are more unknown forces than available equilibrium equations, and we would need additional compatibility equations along with equilibrium equations to find all the forces.

The Degree of Static Indeterminacy (DOSI) is the difference of the number of unknown forces and the number of equilibrium equations.

Therefore:

• DOSI = 0; structure is statically determinate.
• DOSI > 0; structure is statically indeterminate.
• DOSI < 0; structure is unstable.

For frames (and beams):

For trusses:

• r = number of reaction components
• n_frame = number of frame members
• n_strut = number of strut members
• n_truss = number of truss members
• j = number of joints
• e_c = number of equations of condition

The term e_c applies when there is an internal roller or hinge. The following table summarizes how to find e_c for each support type. Note that n is the number of members connected to the support.

Example 1

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Example 2

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Example 3

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Cover Photo Source: Francisco Diez (Flickr)