Use of critical response spectrum for design of multi-story steel buildings under multi-component seismic excitation

During an earthquake, buildings are simultaneously excited by three-components of ground motion (two horizontal and one vertical) orientations of which are not known apriori. To take account for the uncertainty in the direction of incidence of earthquake waves, a structure is required to be designed such that it is safe for all directions of incidence. For this purpose, the combined effects of two horizontal components of motion are commonly determined using simplified methods such as the percentage rules (e.g. 100%+30%, 100%+40%), square root of the sum of squares (SRSS) and Complete Quadratic Combination (CQC-3) rules. The modern building codes recommend to estimate the orthogonal response quantities for the individual horizontal component of motion using response spectrum superposition methods with design spectrum in the principal direction of motion. In the present paper, a new method is proposed to evaluate the maximum response of multi-story buildings under the simultaneous action of two horizontal components of ground motion using the concept of critical response spectrum. The critical response spectrum is computed using the resultant response of a bidirectional single degree of freedom system at each time step under the simultaneous action of the two horizontal components of motion. For an illustration of the proposed method, steel building asymmetric in the plan is analysed using critical response spectra of the three different pairs of recorded ground motion and the results obtained are validated by comparison with the exact time-history solutions. The exact response is taken as the maximum of the responses estimated by applying the two horizontal time-histories of ground acceleration at different angles from 0 to 180 degree with respect to the structural x-axis. On the other hand, in the response spectrum method, two values of the desired response quantity are obtained by applying the critical response spectrum along the x- and y-directions of the structure and are combined using SRSS method. It has been found that the use of the critical spectrum provides a very convenient method for estimating the maximum response under multi-component excitation without the need for computation of critical incident angle of incidence.