د رېږدلې انجنيري

Member stiffness relations

A typical member stiffness relation has the following general form:

$\mathbf {Q} ^{m}=\mathbf {k} ^{m}\mathbf {q} ^{m}+\mathbf {Q} ^{om}\qquad \qquad \qquad \mathrm {(1)}$

where

m = member number m.

$\mathbf {Q} ^{m}$ = vector of member's characteristic forces, which are unknown internal forces.

$\mathbf {k} ^{m}$ = member stiffness matrix which characterises the member's resistance against deformations.

$\mathbf {q} ^{m}$ = vector of member's characteristic displacements or deformations.

$\mathbf {Q} ^{om}$ = vector of member's characteristic forces caused by external effects (such as known forces and temperature changes) applied to the member while $\mathbf {q} ^{m}=0$).

If $\mathbf {q} ^{m}$ are member deformations rather than absolute displacements, then $\mathbf {Q} ^{m}$ 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.