This paper induces the reduction factor of the total input energy due to the damping in the elastic single-mass system on the basis of the equilibrium of the total input energy to the system. In the induction of , the paper defines the fundamental formula at the nonstationary response based on the theoretical reduction formula at the stationary response, and gives the coefficient of the formula by analytical response results. Finally, the paper indicates the conformity of the proposal of the evaluation formula of by comparing with analytical response results.
When the building responses by earthquakes, the additional overturning moment the gravity load of the building produces as horizontal displacement increases. This influence called P-Δ effect is generally remarkable when the base shear coefficient is small. The purpose of this paper is to investigate the P-Δ effect on the horizontal deformation of ordinary high-rise buildings by earthquake response analysis using three types of input seismic motions (sweep wave, earthquakes specified in the notification and recorded seismic waves), and to derive response evaluation formula considering the P-Δ effect. The induced evaluation formula induced theoretically showed excellent compatibility with analytical response results.
This paper presents the revised response reduction factor with higher accuracy, which is modified from the past proposal. In the modification, two phenomena are considered. One is the influence of the asymmetry of response of one cycle just before the maximum response on the calculation of the equivalent damping factor. The other is the influence of the change of the period due to the damping. The paper also proposes simplified formula for the response reduction factor. Finally, the consistency of the modified formula and the simplified formula with the time history analytical results is investigated, which proves the excellent compatibility.
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