ANALYTICAL STUDY ON SEISMIC RESPONSE OF REINFORCED CONCRETE BUILDINGS CONSIDERING P-Δ EFFECT

Abstract

 The P-Δ effect caused by additional moment due to gravity load produces when the building responses by earthquakes, and produces the influence on the earthquake resistance properties particularly for buildings with a small base shear coefficient. The purpose of this paper is to investigate the P-Δ effect on the deformation of ordinary high-rise buildings by earthquake response analysis using three types of input seismic motions (sweep wave giving stationary loop, earthquakes specified in the notification and actual seismic wave), and to derive response evaluation formula considering P-Δ effect.

 The analytical model of the structure is the modified fish-bone frame model of a 14-story reinforced concrete building expressing infinite even-span. The investigation and comparison were made by changing the value of the base shear coefficient in the range of about 0.05 to 0.4.

 The major findings obtained in this paper were as follows.

 1) For the sweep wave giving stationary loop, a clear reduction of the response due to the P-Δ effect was confirmed for all cases of the analytical models. The smaller the base shear coefficient was, the more significant this tendency was.

 2) For the earthquake ground motions for the notification and observed seismic waves, three were cases where the response displacement decreased or increased by considering P-Δ effect.

 3) The equivalent damping factor at the maximum response was calculated. Their values were greater when the P-Δ effect was considered because the potential energy of the equivalent linear model became smaller due to the decrease in the restoring shear force, although the energy dissipation was the same for both cases.

 4) The response deformations decreased for the sweep wave because the response reduction effect due to the increase in the equivalent damping constant was greater than the effect of decrease in strength due to the P-Δ effect. On the other hand, there were both cases in which the response displacement decreased or increased depending on the degree of increase in equivalent damping factor and decrease in restoring shear force, for non-stationary waves.

 5) The response evaluation formula considering P-Δ effect in the ordinary high-rise building was proposed. It can be said that the proposed evaluation formula gave appropriately evaluation of the response displacement considering P-Δ effect. However, P-Δ effect produced little difference in response deformation, in case of non-stationary response.