Flexibility Method

# Flexibility method

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Description:
In structural engineering, the flexibility method is the classical consistent deformation method for computing member forces and displacements in structural systems. Its modern version formulated in terms of the members' flexibility matrices also has the name the matrix force method due to its use of member forces as the primary unknowns.

## Member flexibility

Flexibility is the inverse of stiffness. For example, consider a spring that has Q and q as, respectively, its force and deformation:
• The spring stiffness relation is Q = k q where k is the spring stiffness.
• Its flexibility relation is q = f Q, where f is the spring flexibility.
• Hence, f = 1/k.

A typical member flexibility relation has the following general form:

where
m = member number m.
[itex]mathbf^m [/itex] = vector of member's characteristic deformations.
[itex]mathbf^m [/itex] = member flexibility matrix which characterises the member's susceptibility to deform under forces.
[itex]mathbf^m [/itex] = vector of member's independent characteristic forces, which are unknown internal forces. These independent forces give rise to all member-end forces by member equilibrium.
[itex]mathbf^ [/itex] = vector of member's characteristic deformations caused by external effects (such as known forces and temperature changes) applied to the isolated, disconnected member (i.e.......
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