# Info Using Fig 1.19, read the peak factor gp corresponding to v= 0.119

Calculate the required gust response factor Cg from the formula With the known gust effect factor Cg peak dynamic forces are determined by multiplying mean wind pressures by Cg.

### 1.4.3.4. Wind-Induced Building Motion

Although the maximum lateral deflection is generally in a direction parallel to wind (along-wind direction), the maximum acceleration leading to possible human perception of motion or even discomfort may occur in a direction perpendicular to the wind (across-wind direction). Across-wind accelerations are likely to exceed along-wind accelerations if Figure 1.19. Peak factor gp as a function of average fluctuation rate. (From NBCC 1995.)

the building is slender about both axes, with the aspect ratio ^ WD/H less than one-third, where W and D are the across-wind and along-wind plan dimensions and H is the height of the building.

Based on wind tunnel studies, NBC gives two expressions for determining the across-and along-wind accelerations.

The across-wind acceleration aw is given by aw = nW gpJWD r— r bW b W ,

The along-wind acceleration aD is given by

Observe that A, the maximum wind-induced lateral displacement in the along-wind direction is typically obtained from a computer analysis. Substitution of this value in Eq. (1.20) yields the best estimation of aD. However, as a rough guess for: preliminary evaluations, A can be assumed equal to H/450, the drift index normally used in winddesign of tall buildings.

Using a linear modal representation for the building motion, the maximum deflection, A can be related to the fundamental frequency of the building. The resulting expression is shown in Eq. (1.60) for the ratio aD /g.

where aD = acceleration in the along-wind direction g = acceleration due to gravity = 9.81 m/sec2

gP = a statistical peak factor for the loading effect K = a factor related to surface roughness coefficient of terrain = 0.08 for exposure A = 0.10 for exposure B = 0.14 for exposure C 5 = size reduction factor, from Fig. 1.17 F = gust energy ratio, from Fig 1.18 Ce = exposure factor

¡5d = critical damping ratio, in the along-wind direction a = power coefficient related to Ce = 0.28 for exposure A = 0.50 for exposure B = 0.72 for exposure C q = reference wind pressure, kpa

= 650 x 10-6 x V2, (V in meters per second) D = building depth parallel to wind, meters pB = mass density of building, kg/m3

Design Example. A representative calculation for aw and aD using Eq. (1.58) and (1.59) will be made for the sample problem worked earlier to illustrate the calculation of a gust factor. Given.

Building frequency nw = nD = 0.125 Hz

Building density pB = 195 kg/m3 (12.2 pcf)

All other data as given for the previous illustrative problem.

Required. Building accelerations in both across-wind along-wind directions. Solution. Step 1. Calculate ar 