Gust loading factors for design applications

Wind loads on structures under the buffeting action of wind gusts have been treated traditionally by the “gust loading factor” (GLF) method in most major codes and standards around the world. The equivalent static wind loading used for design is equal to the mean wind force multiplied by the GLF. Although the traditional GLF method can ensure an accurate estimation of the displacement response, it fails to provide a reliable estimate of some other response components. In order to overcome this shortcoming, a more realistic procedure for design loads is proposed in this paper. The procedure developed herein employs a base moment GLF rather than the traditional displacement based GLF. The expected extreme base moment is computed by multiplying the mean base moment by the proposed GLF. The extreme base moment is then distributed to each floor in terms of the floor load in a format very similar to the one used to distribute the base shear in the current design practice for earthquakes. Numerical examples show the convenience in use and the accuracy of the proposed procedure over the traditional approach. and mean displacement responses in the first mode are included in the derivation, the gust factor is constant for a given structure. When the constant gust factor is used to the peak equivalent wind load, an equivalent wind load whose distribution is the same as that of the mean wind load is obtained. Obviously, this is in disagreement with the common understanding of the equivalent wind load on tall, long and flexible structures. For this kind of structures, the resonant response is dominant and the distribution of the equivalent wind load is, therefore, a function of the mass distribution and the mode shape. In this light, it is quite reasonable to examine the equivalent wind load by the traditional GLF method to ensure that the maximum load effects established are truly representative of the actual values. Secondly, as others have noted that the GLF method is not valid if either the mean wind force or the mean response is zero. An example of this kind is a suspended bridge or a cantilever bridge with asymmetrical first mode shape. Therefore, the mean displacement response in the first mode is equal to zero whether or not the mean wind load is zero. Zhou et al. (1998b) examined the along-wind loading on tall buildings utilizing the GLF in the light of various wind-induced response components. They have reported that the GLF method provides an accurate assessment of the structural displacement, but results in less accurate estimation of other response quantities, for example, the base shear force. This observation is based on the fact the GLF is formulated using the displacement response; therefore, it fails to provide accurate prediction of other response components. In light of the above, this paper aims at developing a more realistic procedure for design. The proposed procedure employs a base moment gustloading factor, referred to as MGLF in the remaining discussion. The MGLF is formulated for tall structures. The expected extreme base moment is computed from the mean base moment multiplied by the MGLF. The extreme base moment is then distributed to other floors in a manner very similar to the one used in the current design practice for earthquake action. Furthermore, simple relationship between the proposed MGLF and traditional displacement GLF (DGLF) is determined, which makes it possible to use the proposed approach while still utilizing the existing database. A numerical example is given to demonstrate the convenience and the accuracy of the proposed procedure in comparison with the traditional approach. 2 TRADITIONAL DISPLACEMENT GUST FACTOR METHOD The DGLF is defined based on the displacement response (Davenport 1967) ) ( / ) ( ˆ z Y z Y GY = (1) where Y G = the displacement GLF or DGLF; ) ( ˆ z Y = peak displacement response, when assuming a stationary Gaussian process Y Y g z Y z Y σ + = ) ( ) ( ˆ (2) in which Y g = displacement peak factor; Y σ = RMS displacement; ) (z Y = mean displacement response. Accordingly, the DGLF is ) ( / ) ( 1 z Y z g G Y Y Y σ + = (3) which is dependent on Y g Y Y , ,σ . These quantities are separately derived in the following. By invoking the quasi-steady and strip theories, the wind force is given by 2 )) , ( ) ( ( 2 / 1 ) , ( t z u z U W C t z P D + = ρ (4) where W = the width of the building normal to the oncoming wind; D C = drag coefficient. By neglecting the contribution of the quadratic term (this effect has been considered elsewhere, e.g., Kareem et al. 1998, Zhou et al. 1999), one can obtain the mean wind load and the fluctuating wind load on the structure, respectively, as α α ρ 2 2 2 ) / ( ) / ( 2 / 1 ) ( H z P H z U W C z P H H D = = (5) α ρ ) / )( , ( ) , ( H z t z u U W C t z p H D = (6) in which α = the exponent of mean wind velocity profile. The mean structural displacement can be well approximated by the first mode mean displacement response