Structures Modeled as Single-Degree-of-Freedom Systems

Abstract

In general, the analysis and design of buildings and other structures to resist the effect produced by earthquakes requires conceptual idealizations and simplifying assumptions through which the physical system is represented by a new idealized system known as the mathematical model. In the mathematical model, the number of independent coordinates used to specify the position or configuration of the model at any time is referred to as the number of degrees of freedom. In principle, structures, being continuous systems, have an infinite number of degrees of freedom. However, the process of idealization or selection of an appropriate model permits the reduction of the number of degrees of freedom to a discrete number and in some cases, to just a single degree of freedom. Fig. 1.1 shows a one-story building which may be modeled with one degree of freedom.