3D Wind-Excited Response of Slender Structures: Closed-Form Solution

Abstract

Along-wind, crosswind, and torsional vibrations of structures are different aspects of the same physical phenomenon. Despite this fact, each aspect has been the object of numerous studies involving lines of research that have frequently been independent of each other. These independent lines of research have often been characterized by notable inconsistencies and clashes. This paper proposes a single coherent formulation that provides compact expressions for estimating the along-wind, crosswind, and torsional response based on a generalized gust factor approach. It presents the wind-loading model and uses a generalized equivalent spectrum technique to derive closed-form solutions of the 3D wind-excited response of slender structures and structural elements. This extends a solution previously obtained for along-wind vibrations to the crosswind and torsional response. Numerical examples are provided that illustrate the simplicity and precision of this method. Because of this simplicity and precision, the method is suitable for use in design offices as a means of providing rapid estimates of the dynamic response of slender structures to gust buffeting actions. In particular, the estimates of the crosswind and torsional response will allow the designers to make more informed decisions on when to conduct physical model studies in boundary-layer wind tunnels.