Introduction toStiffness Matrix Method of Structural AnalysisByProf. Dr. Wail Nourildean Al-Rifaie

In the stiffness matrix method for the analysis of framed structures, the structure is replaced by unlimited number of unknowns by a mathematical model which has a limited of unknowns at certain chosen discrete points. In stiffness matrix method, a structure is discretized and idealized by using a mathematical model which is an assembly of subdivision or discrete elements are assumed to be interconnected only at the joints, called nodes. The external loading is transformed into equivalent forces applied at the nodes.

The behaviour of each element independently and later as an assembly of these elements is obtained by releating their response to that of the nodes in such a way that the following basic conditions are satisfied at each node:

1. The equations of equilibrium.2. The compatibility of displacements.3. The material constitutive relationship.

Example:

Overall Stiffness matrix