GQ Q2 gRR2

1 + 1.7 x 0.134V3.42 x 0.634 + 3.789-2 x 1.665 1 + 1.7 x 3.4 x 0.134

L = building breadth parallel to wind = 100 ft, given

ß = damping ratio = 0.015, given ln means logarithm to base e = 2.71.

G is the gust factor. gQ = gV = 3.4 (defined in the equation for G).

Calculations for Design Wind Pressures: Graphical Procedure.

Given. A concrete building located in a hurricane prone region with the following characteristics:

• Building plan dimensions = 185 x 125 ft (56.396 x 38.10 m)

• The building is sited on the upper half of a 2-D ridge and has the following topographic parameters:

(See Fig. 1.11 for definitions.)

• It is anticipated that design will be performed by using basic load combinations specified in Sections 2.3.2 and 2.4.1 of ASCE 7-02. Observe that load factors associated with wind load combinations do not account for the directionality factor Kd. Therefore, the values of qz that account for Kd = 0.85, as shown in Fig. 1.2, may be used directly in the ASCE 7-02 load combinations.

• The building is for typical office occupancy. However, it does have designated areas where more than 300 people congregate in one area.

Required. Using the graph given in Fig. 1.12, determine wind pressure for the main wind-force-resisting system (MWFRS) of the building. Use case 1 given in ASCE 7-02, Section 6.5.12.3. It should be noted that ASCE 7-02 specifies four distinct wind load cases. These include: 1) torsional effects caused by nonuniform pressure; 2) wind loads acting diagonally to the building; 3) torsion due to eccentricity between the elastic shear center and the center of mass at each level of the structure; and 4) wind distribution to capture possible across-wind response. In this example, we will calculate the wind loads in the x-direction for case 1, which consists of full design pressure acting on the projected area perpendicular to each principal axis of the building, considered separately along each principle axis. The designer is directed to Fig. 6.9 of ASCE 7-02 for a full description of the load cases.

Solution.

• The building is for office occupancy with certain areas designated for the congregation of more than 300 people. From Tables 1.1 and 6.1 of ASCE 7-02 (Tables 1.7 and 1.7a of this text), the classification of the building for wind load is category III, and importance factor for wind Iw = 1.15.

• Exposure category is C and basic wind speed V = 110 mph, as given in the statement of the problem. We select the curve designated as C110 in Fig. 1.12 to read the positive and negative pressures up the building height.

• The building's height-to-least-horizontal dimension is 450/125 = 3.6, less than 4.

Therefore, the building may be considered rigid from the first definition given in ASCE 7-02, Section C6.2. The second definition refers to the fundamental period T of the building. Using the formula

T = Cthn3'4, determine T

where

T = fundamental period of the building, in secs hn = height of the building, in feet

CT = coefficient equal to 0.030 for concrete moment frame buildings T = 0.030 x 4503/4 = 2.93 sec (say, 3 sec)

The natural frequency, n, which is the reciprocal of the period, is equal to 1/T = 1/3 = 0.33 Hz. This is less than 1 Hz, the limiting frequency that delineates a rigid structure from a flexible structure. Therefore gust effect factor Gf must be determined using the procedure given in ASCE 7-02, Section 6.5.8.2. However, to emphasize the graphical procedure, for now we will assume Gf = 0.910, a value that will be determined shortly. Observe that if the building is considered rigid Gf = G, would have been 0.85.

• Because the building is located on a 2-D ridge, it may experience higher winds than buildings situated on level ground. Therefore, consider topographic effects in the determination of design wind pressures.

For the given values of Lh, H, and x, the multipliers K1, K2, and K3 are obtained from Fig. 1.11. Observe that for H/Lh > 0.5, Note 2 for Fig. 1.11 alerts us to assume H/Lh = 0.5 for evaluating K1 and to substitute 2 H for Lh for evaluating K2 and K3. Therefore, for H/Lh = 200/200 = 1.0, which is greater than 0.5, from Fig. 1.11, for exposure C, for a 2-D ridge, K1 = 0.725.

Substituting 2 H for H, x/H = x/2H = 50/400 = 0.125, and from Fig. 1.11, K2 = 0.92. Instead of the values tabulated in Fig. 1.11, we may also use the formulas in Fig. 1.11a to calculate K2 and K3. Thus,

The parameter K3 varies as the ratio x/Lh. It may be obtained by using either the tabulated values in Fig. 1.11 or the formula given in Fig. 1.11a.

Again, substiuting 2 H for Lh, and y= 3,

We use the preceding formula to calculate K3 for the selected z/Lh values shown.

Note that y= 3 for 2-D ridges, which is the topography for our building.

z(ft) 450 350 250 150 100 50 30 15

z/Lh 2.25 1.75 1.25 0.75 0.50 '0.25 0.15 0.08 K3 0.001 0.005 0.023 0.106 0.224 0.473 0.638 0.78

Wind Parallel to X-Axis. From the building's plan dimensions, L/B = 125/180 = 0.694 < 1.0. Therefore, from Fig. 1.9, Cp for the windward face = 0.8, and Cp for the leeward face = -0.5. From Fig. 1.12, select the curve identified as C110. C stands for exposure C, and 110 stands for V = 110 mph. Use the graph to read the values of qz at various heights. For example, at h = 150 ft, qz = 36.3 psf.

However, since the qz and qh values in Fig. 1.12 are normalized for Kzt = 1.0, Kd = 0.85, and Iw = 1.0, we multiply these values by the Kzt and Iw values of the example problem before recording the corresponding values in columns (7) and (8) of Table 1.10. For example, qz = 36.3 psf at z = 150 ft, obtained from the graph is multiplied by Kzt = 1.145 and Iw = 1.15 to get a value of qz = 47.79 psf, shown in column (7).

Observe that Kzt varies up the height. Similarly, values of qz for different heights are recorded in column (7) of Table 1.10 after multiplication by Kzt and Iw. The suction qh in column (8) is the value from the graph at z = h = 450 ft multiplied by Kzt = 1.002 and Iw = 1.15. Observe that the suction qh referenced at roof height remains constant for the entire height of leeward wall. Column (9) gives the total design wind pressure throughout the building height. It is the summation of 0.8qz, the positive pressure on the windward wall, plus 0.5qh, the suction on the leeward wall, multiplied by the gust effect factor Gf = 0.91.

TABLE 1.10 Design Wind Pressures, Graphical Procedure; ASCE 7-02 Procedure

Design pressure qz (psf) Design pressure (psf) without

(From Fig 1.12) P = (0.8gz + 0.5qh) topographic factors,

TABLE 1.10 Design Wind Pressures, Graphical Procedure; ASCE 7-02 Procedure

Design pressure qz (psf) Design pressure (psf) without

(From Fig 1.12) P = (0.8gz + 0.5qh) topographic factors,

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