The nonlinear dynamic response of shear systems representative of buildings with excess stiffness and strength at all stories above the first one is studied. Variables covered were number of stories, fundamental period, along-height form of variation of story stiffness, ratio of post-yield to initial stiffness, in addition to the variable of primary interest: the factor r, expressing the ratio of the average value of the safety factor for lateral shear at the upper stories to that at the bottom story. The lateral strength at the latter was taken as equal to the nominal value of the corresponding story shear computed by conventional modal dynamic analysis for the design spectrum specified by Mexico City seismic design regulations of 1987 for a seismic behavior (ductility) reduction coefficient of 4.0. The excitation was in some cases the EW component of the accelerogram recorded at the parking lot of the Ministry of Communications and Transport in the same city during the destructive earthquake of September 19, 1985, and in some other cases an ensemble of artificial accelerograms with similar statistical properties. It is concluded that the nonlinear seismic response of shear buildings whose upper stories have lateral strengths and stiffnesses which correspond to safety factors larger than those applied to the first story is very sensitive to the relation between the average of the over-strength factors at the upper stories and that at the first one, as well as to the ratio of post-yield to initial stiffnesses. The nature and magnitude of the influence of r on the maximum ductility demands at the first story depend on the low-strain fundamental natural period of the system. The ductility demands computed for elastoplastic systems may in some cases be extremely large. Accounting for P-delta effects leads to an enhancement of the sensitivity of the response with respect to r.

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