## Example 221

A rectangular building of height H = 194 m is situated in a suburban terrain. The breadth B and width D of the building are 56 m and 32 m, respectively. The period of the building corresponding to the fundamental sway mode is 5.15 s. The values of the mode shape at various heights are given below:

The generalized mass and damping ratio corresponding to this mode are 18 x 106kg and 2%, respectively.

Assuming that the mean wind profile follows the power law with a power law coefficient a = 0.22, determine the maximum drift for a 50-year wind storm of 21 m/s at 10 m height, blowing normal to the breadth of the building. Given that the friction velocity is 2.96 m/s, the drag coefficient Cd is 1.3 and density of air p = 1.2 kg/m3.

Solution

The mean height of the building H = 97 m

/97\0'22 /97\0'22 U(97) = U(10) ^-J = 21 (^-J = 34.6 m/s

At mid-height, the reduced frequency nHU 97n f = "^r^r =-= 2.8n

From Equation 22.13, the spectrum of turbulent wind is given by

2:962 200 2:8 4906

4906 2

The admittance function, from Equation 22.28, becomes

0 0