Approximate Seismic Analysis of Multi-story Buildings with Mass and Stiffness Irregularities

Abstract

An approximate analysis is presented for multi-story setback buildings subjected to strong ground motions. Setback buildings with mass and stiffness discontinuities are common in modern architecture and quite often they are asymmetric in plan. Such buildings are classified by Eurocode 8 (EC8-2004) and codes from other countries as irregular structures, which specify a full 3-dimensional dynamic analysis. There are no recommendations of how the practicing engineer can assess the fundamental frequency by a simple formula or methodology and there are no provisions which allow the structural detailing by a pseudo-static design against an equivalent lateral load. Therefore, an approximate analysis which provides basic dynamic data (frequencies and peak values of base resultant forces) of setback buildings and furthermore an overview of their response during a ground excitation is a useful tool at the preliminary stage of a practical design. This methodology is based on Southwell's formula and the concept of the equivalent single story system. This has been introduced by the authors in earlier papers for assessing the response of uniform along the height of buildings. At present, the accuracy of this procedure is examined in asymmetric tall buildings with a mass or stiffness irregularity. As basic data of the dynamic response of elastic multi-story building systems can be derived by analyzing simple (equivalent) single story systems, a structural layout of minimum elastic torsional response can easily be constructed. The behavior of such structural configurations, which is basically translational in the elastic phase, is also examined in the post elastic phase when the strength assignment of the various bents is stiffness proportional.