SIMPLEST IDEALIZATION OF MULTISTORY

SIMPLEST IDEALIZATION OF MULTISTORY BUILDINGS

It is desirable to begin the study of dynamics of multistory buildings with their simplest possible idealization, as shown in Fig. 22. In this idealization, we assume that the columns supporting and interconnecting the floor systems are massless and the entire mass of the structure is concentrated at the floor levels; the floor systems and beams are rigid whereas the col• umns are flexible to lateral deformation but rigid in the vertical direction. The structure is assumed to be supported on rigid ground. This so-called shear building model is useful in develop• ing the basic concepts of multistory building dynamics. However, refined idealizations are usually necessary to accurate• ly determine the dynamic response of buildings. Such idealiza• tions are briefly discussed later.
The masses concentrated at the floor levels are denoted by mi, m2, ••• mN where m, = mass at the jth floor. The stiffness properties of the linear structure arc characterized by the lateral stiffness kl' k2, ••• kN of individual stories, where k, = lateral stiffness of the jth story, i.e. the story shear force required to cause unit deformation in the story (Fig. 22).
It will be convenient to first develop the equations of motion fur systems with no damping; the damping terms will subse• quently be included.