Coupled wind-induced responses and equivalent static wind loads on long-span roof structures with the consistent load–response–correlation method

Abstract

Long-span roof structures with multiple vibration modes may undergo coupled motions when exposed to spatiotemporally varying dynamic wind loads. This article presents a framework for the analysis of coupled wind-induced responses and equivalent static wind loads on long-span roof structures. This framework takes into account the inter-modal coupling of modal response components and cross correlation between the background and resonance. The load–response–correlation method is widely used for the background equivalent static wind loads of rigid structures. Also, the concept of load–response–correlation was extended for the correct estimation of equivalent static wind loads by considering the correlation between the load and exact total responses. However, there is no detailed study for the correct estimation of equivalent static wind loads on the component of background, resonance, and their cross response using load–response–correlation method. In this article, a consistent load–response–correlation method for equivalent static wind loads is presented in a unified framework which contains the background, resonance, and modal coupling. First, the accuracy of wind-induced responses is ensured by considering the modal coupling. Meanwhile, the efficiency is improved by decomposing the covariance matrix of the generalized resuming forces. Second, several effects of the wind-induced responses are discussed in detail, such as the effect of the modal coupling, the effect of the modal participations to resonant responses, and the effect of the cross correlation between the background and resonance. Finally, the proposed equivalent static wind loads are represented by the composition of the external wind loads and inertial forces, which are both the most probable load distributions. Accordingly, the equivalent static wind load distribution and the responses by equivalent static wind loads are reasonable.