A Modal Conditional Mean Spectrum for Nonlinear Structural Response Time-History Analysis of Tall Buildings to Consider Higher Mode Effects

Selection and scaling of an appropriate suite of earthquake ground motion records for consistency with a target spectrum are associated with nonlinear structural response time-history analysis. The commonly used target spectrum could be a uniform hazard spectrum (UHS), conditional (mean) spectrum (CMS or CS). The CMS (CS) overcomes the limitations of the “overly conservative” and “unrealistic spectral shape” of UHS and has been accepted as a more reasonable target spectrum recently. However, the CMS only selects a single conditional period (usually the first period T 1 of the structure) ignoring the influence of the high-order vibration mode (other periods) on the structure. To address this, this paper proposes a modal conditional mean spectrum (MCMS) considering the influence of higher-order modes by weighted (measured using the modal participation mass ratio) averaging the CMS under each period of the structure. The MCMS matches CMS( T 1 ) at a period T " ( T "< T 1 ). The spectrum values of MCMS are significantly higher than those of CMS( T 1 ) for periods shorter than T " and slightly lower than those of CMS( T 1 ) for periods longer than T ". Then, two typical high-rise case structures (symmetric and asymmetric structures) with different elevations are designed, and the MCMS, CMS( T 1 ) and UHS are used as target spectra for nonlinear structural response time-history analysis for comparison. Based on the analysis of four engineering demand parameters, namely peak floor acceleration (PFA), peak floor velocity (PFV), peak floor displacement (PFD), and maximum interstory drift ratio (IDR), it was found that the results of the UHS were consistently higher than those of the CMS( T 1 ) and the MCMS. However, it was also observed that the PFA results of MCMS were higher than those of CMS( T 1 ), whereas the PFD, PFV, and IDR results of MCMS were lower than those of CMS( T 1 ). It should be noted that MCMS is a target spectrum that takes into account the influence of higher-order mode effects in CMS.