Report - PEER - University of California, Berkeley

EFFECTIVE PERIODS OF HIGHLY NONLINEAR STRUCTURESHiroshi AKIYAMA 1ABSTRACTThe total energy input into a structure exerted by an earthquake is mainly governed by the totalmass and the effective period of the structure. The effective periods of elastic structures aretheir fundamental natural periods. When the structure is plastified, the structure is softened andthus the effective period of structure is elongated by the plastification of structure. Theinfluence of the plastification on the effective period is specified by the type of the restoringforce characteristics of the plastified element, the extent of plastification and the pattern ofdistribution of plastification. In this paper, effective periods are dealt with generally by usingvarious types of restoring force characteristics. Obtained formulae are verified theirapplicability by direct response analyses.Keywords: Effective period; Total energy input; Nonlinearity; Plastification.1. INTRODUCTIONEarthquake resistant design method based on the balance of energy between the totalenergy input exerted by an earthquake and the energy absorbed by a structureprovides a simplest design formulation and most consistent understanding onbehavior of a structure up to its collapse state. The most important point is that thetotal energy input due to an earthquake is a very stable amount governed only by thetotal mass of the structure and its fundamental natural period and is scarcelyinfluenced by the other structural parameters such as mass distribution, stiffnessdistribution, and strength distribution. The seismic energy input is absorbed mainly ina form of cumulative plastic strain energy developed in the structural elements. Thecumulative plastic strain energy can be called structural damage. Therefore, theseismic design of structures is recognized to be a technique to control the damagedistribution in a structure within an allowable limit. The energy spectrum (therelationship between the total energy input and the fundamental natural period ofstructure) is influenced only by the extent of the nonlinearity of structure. The purelyelastic system is characterized by the single natural period and receives the energyonly from the single wave component which has the same frequency as that of thestructure. On the other hand the nonlinear system is characterized by a set of1 Nihon University, Tokyo, Japan385