Reconstruction of the envelope of non-Gaussian structural responses with principal static wind loads

Abstract

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.

Assessment of extreme value overestimations with equivalent static wind loads

“…Among others, the conditional expected static wind load (CESWL) is a new kind of equivalent static wind load that was specifically designed for non-Gaussian wind pressures and responses (Blaise et al, 2016). This static wind load corresponds to the LRC method in a Gaussian framework.…”

“…The Conditional Expected Static Wind Load (CESWL), defined as the average of the wind load patterns given the occurrence of the design value, generalizes this features of the LRC method to non-Gaussian pressures and responses fields (Blaise et al, 2016).…”

“…When a large number of responses are of interest, the envelope reconstruction problem arises (Blaise et al, 2016), which consists in finding a set of static loadings (minimum in number and satisfying some accuracy criteria) whose own envelope somehow covers the actual envelope of structural responses. Several advanced techniques (Repetto and Solari, 2004;Katsumura et al, 2007;Chen and Zhou, 2007;Li et al, 2009;Zhou et al, 2011;Blaise and Deno€ el, 2013;Lou et al, 2015;Patruno et al, 2017) are available to solve the envelope reconstruction problem, for instance multi-objective equivalent static wind load that targets the reconstruction of several envelope values at a time.…”

“…These techniques rely on all sorts of approximations and overestimations of some envelope responses are unavoidable. Significant overestimations of the reconstructed envelope are typically undesired since they lead to uneconomical designs and one should make sure that the overestimation remains controlled (Blaise et al, 2016).…”

“…This paper exclusively focuses on using equivalent static wind loads to reconstruct the envelope. In particular, an interesting feature of the LRC method is that it does not provide any overestimation of the envelope and the LRC based reconstructed envelope is, therefore, the actual one as long as a Gaussian context is used (Blaise et al, 2016). The merit and advantage in this approach is that the structural engineer does not have to address overestimations and is ensured to do an economical design.…”