ON THE OPTIMUM ASEISMIC DESIGN DATA OF TALL BUILDING STRUCTURES BASED ON THE ELASTO-PLASTIC EARTHQUAKE RESPONSES

Abstract

For the purpose of obtaining the pertinent aseismic desigu data of tall elasto-plastic buildingstructures, the earthquake responses of a large number of bi-linear elasto-plastic, multi-story sheartype structural models having various distributions of stifihess and shear strength at the elasticlimit are analyzed systematically by using an analog computer.The distributions of stiffness and shear strength of standard model are expressed in theform, {~rd={fiJ={l -A(I- l/ss-l)~} in which ~l and s-' are variable structural parameterscorresponding to the distribution characteristics, I and a denote the number of mass ordered fromthe base to top and the number of the degree-of-freedom of the structural model, respectively.Also, to find the effect of the fluctuation of the strength distribution on the earthquake responses, the models having the irregular distribution of shear strength are considered in this study.On the other hand, the mass distribution is supposed to be uniform over the height. Asregards the damping characteristics, it is assumed that its distribution is identical to the stiffnessdistribution and that each structural model has 2 % critical damping with respect to the funda-mental harmonics. Also it is assumed that the rigidity ratio of the second to the first branch ofthe hi-linear hysteresis 1oop is uniformly 0.2 over the bight.As regards earthquake excitations, the five typical wave-shape functions of acceleration recordsof the past strong earthquakes are considered and the time-constant represented by the duration-time is yarned for giving various reference frequencies to the spectral characteristics of eachwave-shape function. On the other hand, the maximum amplitude of acceleration for each wave-shape function is adjusted so as to give the same level of the average value of the maximum ductilityratios of the multi-story structural model.Defining the optimum distribution of shear strength as that giving rise to the uniform distri-bution of the maximum ductility ratio over the height, the following remarks are obtained basedon this analysis:1) The distribution of the maximum ductility ratio is strongly dependent on the distributionof shear strength whereas the distribution of the maximum relative displacement depends uponthat of stiffness.2) The increment of the average value of the maximum ductility ratios over the height is almostinversely proportional to that of the average value of shear strengths of a multi-story structuralmodel for a given earthquake excitation.3) For practical purpose, the optimum distribution of shear strength is determined by averag-ing the distributions of the maximum shear force or those of the maxtmum equivalent shear force, which is defined as the maximum elastic shear force giving the same potential energy to the elasto-plastic energy corresponding to the maximum relative displacement, f'or various models havingdifferent distribution characteristics and for earthquake excitations having appropriate wave-shape functions and time-constants.4) The optimum distribution of shear strength is yarned depending upon the level of the averagevalue of the maximum ductility ratios as well as the range of the fundamental natural frequency ofstructures. Hence, in general, it has to be determined according to the allowable ductility ratioof structures and the relation between the natural frequencies of structures and the dominant fre-quencies of excitations.