a b s t r a c tIn current wind design practice, static wind loads are usually defined to obtain, by simple static analyses, the extreme values of any structural response that would be formally obtained with a strict dynamic buffeting analysis. The minimum and maximum values that may reach any response define the envelope. Equivalent static wind loads (ESWLs) allow to recover extreme responses in the envelope. As a first objective, this paper formalizes a general method to determine ESWL, in a nodal basis, by extending the concept of load-response correlation, which is only valid in the background range. The general method, the displacement-response correlation (DRC) method, covers the background and resonant contributions of the considered response. As a second objective, the paper addresses the problem of building a set of static wind loads that adequately reconstructs the envelopes of responses. The concept of principal static wind loads (PSWL) is introduced to form a reduced basis of representative loads well-suited for envelope reconstruction. Its optimality is demonstrated both analytically and with a detailed illustrative example.

a b s t r a c tIn current practice, structural engineers commonly focus on the wind-resistant design by means of static wind loads. In the case of non-Gaussianities, there is room for improvement to properly derive these static loads. First, this paper extends in a non-Gaussian context the concept of the load-response correlation (LRC) method establishing equivalent static wind loads (ESWLs). This is done by a proper recourse to the new concept of conditional expected static wind load and a proposed bicubic model for the joint and conditional distribution functions. Second, this paper investigates the envelope reconstruction problem targeting the efficient reconstruction of the envelope values of a set of non-Gaussian structural responses by means of principal static wind loads (PSWLs). They have been introduced in a Gaussian context and are obtained by a singular value decomposition of ESWLs. This paper addresses the extension of PSWLs to non-Gaussian structural responses, as well. The developments apply to structures with a linear behavior and subjected to an aerodynamic pressure field exhibiting mildly to strongly nonGaussian features. In this context, the well-known load-response correlation and conditional sampling methods are used for comparisons. This study is undertaken for quasi-static analysis of structures and is illustrated on a low-rise building.

In current practice, wind structural design is often carried out using the concept of equivalent static wind loads. The main characteristic of such loadings is to reproduce, with static analyses, the same extreme structural responses as those resulting from a formal buffeting analysis. This paper proposes a method for the computation of equivalent static wind loads for structures with slight non-proportional damping in a modal framework. Because of the smallness of the out-of diagonal terms, this method is based on recent developments related to asymptotic expansion of the modal transfer matrix of such structures. As a main benefit, the static loading is described as a perturbation of the equivalent loading that would be obtained for the uncoupled system. The main contribution of this paper is to formalize the expression of the correction terms resulting from the non-proportionality of damping. The method is presented with a detailed illustrative example.

a b s t r a c tThe use of normal modes of vibration in the analysis of structures with non-proportional damping reduces the size of the resulting set of governing equations, but does not decouple them. A common practice consists in decoupling the equations by disregarding the off-diagonal elements in the modal damping matrix. Recently, an approximation based on an asymptotic expansion of the modal transfer matrix has been proposed in a deterministic framework to partially account for off-diagonal terms, but still with a set of uncoupled equations. This paper aims at extending this method in a stochastic context. First the mathematical background is introduced and the method is illustrated with a simple example. Then its relevance is demonstrated within the context of the structural analysis of a large and realistic structure.

The wind-resistant design using equivalent static wind loads is convenient for structural engineers. This paper studies the reliability of such an approach in the case of non-Gaussianities in both aerodynamic pressures and responses. These non-Gaussianities are responsible for overestimations of envelope values and may result in uneconomical designs, if not appropriately understood, assessed and addressed. In this study, it is shown that the equivalent static wind loads defined with the Conditional Expected Load method, which extends the physical meaning of the Load-Response Correlation approach in a non-Gaussian framework, improves the issue of overestimations of envelope values. Several envelopes of structural responses are considered: the mean of extremes and the 86% quantiles of extremes, together with two reference periods (10 min and 1 h). Extensive wind tunnel measurements have been collected, which correspond to 371 h full scale. This study is undertaken for quasi-static analysis of structures and is illustrated with a low-rise building.