## Structural Response by Equivalent Lateral Force Procedure

As discussed in Chapters 10 and 11, the seismic response analysis of a structure may be carried out effectively and accurately by either the response spectrum method or a step-by-step integration procedure. Notwithstanding their availability and adequacy, these two methods still have a shortcoming because both require knowing the mass and stiffness matrices of the system being analyzed before they can be applied. This means that their application requires the results from a preliminary design since a system’s stiffness and mass matrices depends on the dimensions and characteristics of its structural members, and these dimensions and characteristics depend, in turn, on the results from the seismic response analysis. It is convenient, thus, to count with a simplifi ed approximate method by means of which such preliminary analyses can be performed simply and expeditiously. Such a simplifi ed method may also be convenient for the design of simple structures for which the time and expense of a response spectrum or step-by-step method cannot be justifi ed. The equivalent lateral force procedure described in this chapter is such a method. This procedure is based on the consideration of earthquake effects by means of a series of lateral forces applied statically, and the use of these lateral forces to determine the displacements and internal forces in the system. In turn, the magnitude of such lateral forces is based on an estimate of the fundamental natural period of the structure and some simple formulas. Its simplicity lies on the fact that a dynamic analysis is avoided and thus there is no need to determine the natural frequencies and mode shapes of the system, or to carry out a time-history analysis. This chapter presents in detail the derivation of the procedure and lays out the assumptions on which it is based. The limitations of the method are also discussed in some detail. The procedure is derived specifi cally for buildings although, in principle, it is possible to extend its application to other structures.