Direct Stiffness Method - Member Stiffness Relations

Member Stiffness Relations

A typical member stiffness relation has the following general form:

where

m = member number m.
= vector of member's characteristic forces, which are unknown internal forces.
= member stiffness matrix which characterises the member's resistance against deformations.
= vector of member's characteristic displacements or deformations.
= vector of member's characteristic forces caused by external effects (such as known forces and temperature changes) applied to the member while ).

If are member deformations rather than absolute displacements, then are independent member forces, and in such case (1) can be inverted to yield the so-called member flexibility matrix, which is used in the flexibility method.

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