Response Spectrum Analysis of Structures Subjected to Seismic Actions

Response spectrum analysis (RSA) is a method widely used for the design of buildings. Conceptually the method is a simplification of modal analysis, i.e., response history (or time history) analysis (RHA) using modal decomposition, that benefits from the properties of the response spectrum concept. The purpose of the method is to provide quick estimates of the peak response without the need to carry out response history analysis. This is very important because response spectrum analysis (RSA) is based on a series of quick and simple calculations, while time history analysis requires the solution of the differential equation of motion over time. Despite its approximate nature, the method is very useful since it allows the use of response spectrum, a very convenient way to describe seismic hazard. RSA is very appealing to practicing engineers because seismic loading is defined by means of a response spectrum. All design codes worldwide define seismic input (or hazard) by means of a code-compliant, typically smooth, response spectrum that can be easily adjusted according to the site seismic hazard. Such spectra are able to implicitly take into consideration the fact that structures are designed to resist seismic actions by deforming inelastically. Two variations of RSA are offered in almost every seismic design code. Following the notation of Eurocode 8 (EC8 2004), these variations are the “lateral force method” and the “modal response spectrum analysis.” This entry discusses the underlying concepts of both methods in a comprehensive manner. The interested reader is also advised to consult the classic textbooks of Chopra (2000) and Clough and Penzien (1975).