Quasi-static combination of wind loads: a copula-based approach

The combination of wind loads or wind effects in high- and middle-rise buildings is an extremely important and complicated issue. The complete description of the wind action would require the knowledge of some joint probability density functions (JPDFs) of the load components and in particular of their extreme values. In order to estimate these JPDFs from the marginal distributions of the variables a copula-based approach is introduced. Copula is a mathematical tool already quite common in some engineering branches but practically unexplored in wind engineering. This approach is extremely useful to estimate the JPDFs of extreme values also when experimental load time histories are available, as generally they are not long enough to do it. Similarly, if a Monte Carlo approach is followed, the estimate based on the copula allows to reduce significantly the number of simulations to be performed. In this paper the copula-based approach is applied to experimental data measured in the wind tunnel for a rigid tall building, in order to determine the wind load combination coefficients focusing on a generic effect given by the linear combination of two load components. The influence of the resonant part of the structural response is neglected. The method is validated against the extreme values determined directly on the linear combination of the time histories. Two examples are discussed, considering almost uncorrelated and fairly correlated wind loads, and two different copulas are employed.