Structural analysis by matrix methods for forces not at the coordinates

Abstract

The analysis of structures with forces not at the coordinates is developed and demonstrated for both the flexibility and stiffness methods. In the flexibility method a “free coordinate state” is defined in a superposition of element forces. The free coordinate state element displacements δ i 0 are computed from Betti's Law using the displacement configurations associated with the columns of the element flexibility matrices. In the stiffness method a “fixed coordinate state” is defined in a superposition of element displacements. The fixed coordinate state element forces P i 0 are computed from Betti's Law using the displacement configurations associated with the columns of the element stiffness matrices. It is shown that the problems of “thermal expansion” and “lack of fit” are treated by the same procedure as that used for forces not at the coordinates.