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Determine the external wind pressure on the roof of the rigid-gabled frame of a school building shown in Fig. P2.13. The structure is located in a suburb of Chicago, Illinois, where the terrain is representative of exposure B and the basic wind speed for risk category III buildings is 51 m/ s. Assume the wind direction is normal to the ridge as shown. Use K d = 0.85 for main wind-force resisting systems, and K e = 1. FIG. P2.13, P2.17

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Structural Analysis

6th Edition
KASSIMALI + 1 other
Publisher: Cengage,
ISBN: 9781337630931

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Chapter
Section
BuyFindarrow_forward

Structural Analysis

6th Edition
KASSIMALI + 1 other
Publisher: Cengage,
ISBN: 9781337630931
Chapter 2, Problem 13P
Textbook Problem
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Determine the external wind pressure on the roof of the rigid-gabled frame of a school building shown in Fig. P2.13. The structure is located in a suburb of Chicago, Illinois, where the terrain is representative of exposure B and the basic wind speed for risk category III buildings is 51 m/ s. Assume the wind direction is normal to the ridge as shown. Use Kd = 0.85 for main wind-force resisting systems, and Ke = 1.

Chapter 2, Problem 13P, Determine the external wind pressure on the roof of the rigid-gabled frame of a school building

FIG. P2.13, P2.17

To determine

Find the external wind pressure acting on the windward and leeward side of the roof of the building.

Explanation of Solution

Given information:

The terrain of the city belongs to Exposure B.

The building belongs to risk category III.

The basic wind speed is V=51m/s.

The direction of the wind is normal to the ridge.

Calculation:

Show the plan and elevation of the building as shown in Figure 1.

Refer Figure 1.

Calculate the angle of slope (θ) of the roof using the relation:

tanθ=5m6mθ=tan1(0.833)θ=39.8°

Calculate the mean roof height (h) as follows:

h=12m+5m2=14.5m

Calculate the value of (hL) as follows:

Substitute 14.5m for h and 12m for L.

hL=14.512=1.20831.21

Refer the Table 2.4 “Exposure Categories for Buildings for Wind Loads” in the textbook.

For exposure B.

The values of gradient height is zg=365.76m.

The value of power law coefficient is α=7.

Show the expression for the velocity pressure coefficient (Kh) as follows:

Kh=2.01(hzg)2α (1)

Substitute 14.5m for h, 365.76m for zg, and 7 for α in Equation (1).

Kh=2.01(14.5365.76)27=2.01×0.39762=0.79920.8

The value of the topographic factor (Kzt) as 1 for main wind force resisting system.

The value of the wind directionality factor (Kd) is 0.85 for main wind force resisting system.

The value of the ground elevation factor (Ke) is 1 for ground elevation at sea level.

Show the expression for the velocity pressure (qh) at height h as follows:

qh=0.613KhKztKdKeV2 (2)

Here, qh is in N/m2.

Substitute 0.8 for Kh, 1 for Kzt, 0.85 for Kd, 1 for Ke, and 51m/s for V in Equation (2).

qh=0.613×0.8×1×0.85×1×512=1084.2N/m2

Take the value of the gust effect factor (G) as 0.85 for rigid structures.

Consider windward Side of the roof.

Refer Figure 2

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