Discussion of “Cross Correlations of Modal Responses of Tall Buildings in Wind-Induced Lateral-Torsional Motion” by M. F. Huang, C. M. Chan, K. C. S. Kwok, and P. A. Hitchcock

摘要

The paper presented a slightly enhanced closed-form expressionnfor estimating the modal correlation coefficients of wind-excitednstructures needed for complete quadratic combination u0001CQCu0002 ofnresponse in various modes by extending the expression proposednin Chen and Kareem u00012005u0002. The modal correlation coefficientnbetween two adjacent modes, needed for the implementation ofnthe CQC scheme, is often estimated using the closed-form formu-nlation given in Der Kiureghian u00011980u0002 for the analysis of windnload effects on buildings and other structures, e.g., Xie et al.nu00012003u0002. Chen and Kareem u00012005u0002 emphasized that this formula-ntion is valid only when the generalized forces are fully correlated,nfor example, in the case of buildings with an earthquake inputnexcitation. The modal correlation coefficient depends not only onnthe modal frequencies and damping ratios but also on thencorrelation/coherence of the generalized forces. A utilization ofnthe formulation in Der Kiureghian u00011980u0002, primarily intended fornearthquake load effects, will overestimate the modal correlationnassociated with multiple excitations of partially correlated loads,ne.g., wind loads. Following the derivation given in Chen and Ka-nreem u00012005u0002, in which the cospectrum, i.e., the real part of thencross power spectral density u0001XPSDu0002 function, of the generalizednwind forces has been included, the authors have proposed includ-ning the quad-spectrum, i.e., the imaginary part, in an effort tonfurther improve the estimate of modal response correlation.