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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

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