Abstract :
[en] Static wind loads are being used for the design of large civil structures such as high-rise buildings, large roofs and long-span bridges. Once static wind loads are known, they are used through the iterative design process without repeating cumbersome dynamical analyses. In this framework, structural engineers can effectively focus on the structural sizing since static analyses are straightforward. No codified wind loads, however, exist for those large structures with unique shapes and there is no consensual view on how to formally derived them. For each new major project, the challenge consists therefore in deriving a relevant set of static wind loads. Obviously, these loads must provide the actual envelope values of structural responses of interest. This states the objective of the envelope reconstruction problem and constitutes the core of this thesis. The proposed developments to solve this problem are relevant for structures responding with a linear dynamic behavior to the buffeting action of synoptic winds in a stationary framework.
The pioneering concept of Equivalent Static Wind Load is normally considered for the design. An extensive review points out two main limitations of the current formulations. They have been originally established in a Gaussian context, are associated with either a nodal or nodal-modal basis and do not have a formal definition. The proposed Conditional Expected Load method overcomes the three drawbacks by defining a Conditional Expected Static Wind Load. This novel approach presents a general rigorous formulation for linear structural behavior, irrespective of the basis used for the analysis and relevant in a non-Gaussian context. The method is particularized for a certain class of non-Gaussian processes through a bicubic translation model. This model covers a large range of non-Gaussianity in the random processes and therefore paves the way for the formal establishment of “non-Gaussian” static wind loads with a physical interpretation.
Other kinds of static loads such as the covariance proper transformation loading modes and the modal inertial loads are additionally studied. Unfortunately, both sets of loads are simply relevant for two limit structural behaviors, quasi-static and resonant, respectively. Moreover, they do not adapt to the set of structural responses of interest. From both points of view, one key result from our study is the innovative concept of Principal Static Wind Load as a sound solution for the envelope reconstruction problem. The concept relies upon a robust mathematical foundation. These loads are determined by the singular value decomposition of a large set of equivalent static wind loads. This decomposition can be seen as a way to rank the most relevant load patterns for the envelope reconstruction problem. The principal static wind loads have also the added distinctive advantage to be flexible. They are, indeed, able to naturally adapt to the set of structural responses of interest.
Finally, a complete methodology to solve the envelope reconstruction problem irrespective of the structure, its load-bearing system and its susceptibility to vibrations in a Gaussian or non-Gaussian context is rigorously conceptualized. The intrinsic controllability of a set of pertinent parameters provides a smart balance between over and underestimation of the actual envelope. Moreover, combinations of static wind loads are computed to speed-up the reconstruction of the envelope values. The problem of determining these combination coefficients is formulated as a constrained nonlinear optimization. Equivalent and principal static wind loads, covariance proper transformation loading modes and modal inertial loads are implemented within the proposed methodology. Three examples: a four-span bridge, a real-life large stadium roof and a low-rise building demonstrate that the envelope reconstruction accuracy is considerably improved with principal static wind loads and with combinations thereof.
