APPROXIMATE SPECTRAL MULTIPLE SUPPORT SEISMIC ANALYSIS: TRAVELLING WAVE APPROACH.

It is now recognized that spatial variations in the earthquake ground motion under the supports should be considered in the seismic response analysis of bridges and other structures of large dimensions. These variations lead to differential displacements of adjacent bridge piers, which, in turn, result in a response which may differ appreciably from that of standard analysis where all bridge supports are assumed to move equally and in phase. In this paper, the response spectrum technique has been extended to multiple support excitation problems of relatively long structures under the travelling wave assumption. In this technique, the spectral displacement due to the multiple support motions is evaluated on the assumption that the modal displacement time history plot near its peak, (i.e. Near the spectral value), can be approximated by means of a sine curve. It is further assumed that the effects of the resulting reduced spectral displacements, evaluated by factoring through the dynamic displacement response ratio, can then be combined with the quasistatic effects based on the differential displacements, as computed from the maximum ground velocity during the earthquake, by means of the square root of the sum of squares formula. It has been shown by means of two simple examples that the proposed approach can lead to very satisfactory agreement with multiple support time history results, the determination of which is quite time-consuming. However, the limitations of the sine curve approximation for the response curve near the peak should not be overlooked.