Equivalent static wind loads for structures with non-proportional damping

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.