ABSTRACT
In a modal framework, Chen & Kareem (2001) derived equivalent static wind loads that produce, with static analyses, the same extreme structural responses as those obtained with formal dynamic analyses. Such static loadings are defined as weighted combinations of inertial loads. An inertial load statically applied to the structure produces a deflection affine to the corresponding mode shape. A 76-story, 306 m tall building is analysed under wind actions (a one-dimensional Gaussian velocity turbulence field). This structure is a numerical example used in (Xu, Samali, & Kwok 1992) to study the mitigation of the alongwind response of structures using a tuned liquid column damper (TLCD) instead of a more traditional tuned mass damper (TMD). These damping devices are source of non-proportional damping and consequently, the modal damping matrix and the modal transfer matrix are no longer diagonal and full matrix inversions is required. A way to avoid this matrix inversion is to recourse to an asymptotic expansion of the modal transfer matrix, as proposed by Denoël & Degée (2009) in a deterministic framework and then extended to a stochastic context (Canor, Blaise, & Denoël 2012). This paper further extends the formulation of the asymptotic expansion to the weighting coefficients necessary to derive equivalent static wind loads for such structures. The proposed method is formulated with the by-products resulting from the application of the asymptotic expansion of the modal transfer matrix.
