Displacement method of analysis
Ramez B. Gayed, Amin Ghali · 2021
Mathematical formulations of the displacement and force methods are similar, but one or the other is preferable. The displacement method is more useful in the analysis of statically indeterminate structures, particularly when the degree of statical indeterminacy is high. The procedure is suitable for computer solutions. The stiffness and flexibility matrices – used, respectively, in the displacement and force methods – are related by the fact that one is the inverse of the other, provided that the same coordinate system of forces and displacements is used in their formation. However, since the coordinate systems chosen in the displacement and force methods of analysis are not the same, the relation is not valid between the stiffness and flexibility matrices involved in the analyses. The computer generates the stiffness matrices for a prismatic member in a three- or two-dimensional frame with respect to the member local coordinates. Then, the computer assembles the stiffness matrices of all members in a stiffness matrix of the structure with respect to its global coordinates. Solution of simultaneous equations of equilibrium gives the nodal displacements in global directions. Transformation of global displacements to local coordinates of an individual member, and multiplication by its stiffness matrix, gives the forces at member ends.