ABSTRACT
Figure 1.1 (a) shows an ideal one story structure model. It has a rigid girder with lumped mass m which is supported on two massless columns with a combined lateral stiffness equal to k. The energy loss is modeled by a viscous damper, also shown in the figure. This structure has only one degree of freedom, the lateral displacement of the girder. Under the action of the earthquake ground motion, u g, the structure deforms, Figure 1.1(b). The relative displacement of the girder with respect to the ground is u. The total displacement of the girder is u−(−u g) = u + u g. Figure 1.1(c) shows the free body diagram of the girder, in which f 1 denotes the inertia force, fs the spring (or the column) force and fD denotes the damping force. The equilibrium equation for the girder is simply
