Extension of Theory to Buildings

Abstract

The 2-DOF analysis of the simple linear model developed in Chap. 3 can be applied to the case of a multistoried building. Let us represent the structural system of this building by mass matrix, M, damping matrix, C, and stiffness matrix, K. For a conventionally based structure, the relative displacement, u, of each degree of freedom with respect to the ground is given by

$$ {\rm M\ddot u + C\dot u + Ku = - Mr}\mathop {\ddot u}\nolimits_g $$

(4.1)

where r is a vector that couples each degree of freedom to the ground motion.