Procedure to Calculate the Wind Pressures on a 30-Story Building


Prepare an Excel or MathCad spreadsheet that permits you to calculate the wind forces upon a 30-story high at each slab level. Assume a 60 foot square building (with 10-feet heights per floor), using ASCE-7. Show both MWFR and C&C.

Given:

  • 30 stories building height = 30 x 10 ft = 300 ft.
  • 60 ft x 60 ft square building plan area
  • Wind Velocity: assume 146 MPH for the downtown Miami area
  • Assume an exposure C
  • Nature of occupancy: assume category I

Step 1. :

Determine I, the importance factor: assume category I

Step  2. :

Select the basic wind speed V for the location the building from the 50-year mean recurrence interval map. In this case choose V= 146 MPH, mandatory in the Florida Building Code. We are not using load combinations specified in sections 2.3 and 2.4 therefore we are not going to use wind directional factor Kd.

Step 3. :

Determine an exposure category and velocity pressure coefficients Kz or Kh, as applicable must be determined for each wind direction. In this case we assume exposure C. From Table 6-5 (ASCE 7-98) for exposure C and height above ground level z = 300 feet we get Kh and Kz = 1.40

Step 4. :

Determine the ratio of height to least horizontal dimension H/W and the fundamental frequency f of the building. If H/W< 5 and f>1HZ, the building can be considered nonflexible, permitting simpler expressions for determining the gust factor G.

H/W= 300/60 = 5

We do not have information about the structural system for this building in order to determine f = fundamental frequency f of the building. We can assume that this building can be considered nonflexible. We can consider this building “rigid” as defined in ASCE 7-98 section 6.2

Therefore, only one value of gust response factor, G calculated at the building roof level is required for determining design loads on the main lateral system. The value will be 0.85.

Step 5.:

A topographic factor Kzt must be determined in accordance with section 6.5.7 (ASCE 7-98). Let’s assume that this building is located at a flat area, as usual in Miami area, therefore we do not include any topographic factor in these calculations and Kzt= 1.0

Step 6. :

For the purpose of determining internal pressure coefficients, an enclosure classification must be determined. We assume this is an enclosed building as defined in ASCE section 6.2. The Internal Pressure Coefficient GCpi will be ± 0.18

Step 7.:

Determine the external pressure coefficient Cp or GCpf or force coefficients Cf as applicable. We do not have information about roof (gable, hip, monoslope, etc). Let’s assume flat roof. We get Cp= 0.80 (windward) and  Cp = - 0.50 (leeward) for L/B= 1

Step 8. :

Determine velocity pressure Qz or Qh as applicable in accordance with section 6.5.11.2 or 6.5.11.3. Importance factor I for category I and hurricane prone regions with V> 100 MPH, I = 0.77

Velocity pressure calculated at height z  =

Qz = 0.00256Kz Kzt Kd V² I (lb/ft²) and Qh is the  velocity pressure calculated using the Qz at mean roof height h.

Kzt=1.0 (topographic factor)     Kd = 1.0 (directionally factor)

For exposure C cases 1 & 2:

Ft                  Kh and Kz

0-15              0.85

20                 0.90

25                 0.94

30                 0.98

40                 1.04

50                 1.09

60                 1.13

70                 1.17

80                 1.21

90                 1.24

100            1.26

120            1.31

140            1.36

160            1.39

180            1.43

200            1.46

250            1.53

300            1.59

Qz = (0.00256) ( Kz)  (0.77) (1.0) (1.0) (146)² =  42  Kz (lbs/ft²)

Step 9. :

Calculate Main Forces Resisting System. Design wind pressures for the main wind force resisting system of buildings of all heights shall be determined by the following equation:

P = Q G Cp – Qi ( G Cpi) (lb/ft²)

Where Q= Qz for windward walls evaluated at height z above the ground

G= gust response effect factor

Cp = external pressure coefficient

GCpi = internal pressure coefficient

Qi = Qz for positive internal evaluation in partially enclosed buildings.

In the following page we show the results for this particular case:

 

Windward      Leeward     Design Value   Floor by floor

Height   Windward    Leeward   Pressure psf   Suction psf        psf                 load kips

ft            Kz       Qz       Kh   Qh    Pz= Qz GCp   Ph= Qh G Cp

10            0.85    35.7                       24.27              15.17           39.44           23.66

20            0.90    37.8                       25.70              16.06           41.76           25.06

30            0.98   41.16                      27.99              17.49           45.48           27.29

40            1.04   43.68                      29.70              18.56           48.26           28.96

50            1.09   45.78                      31.13              19.46           50.59           30.35

60            1.13   47.46                      32.27              20.17           52.44           31.46

70            1.17   49.14                      33.41              20.88           54.29           32.58

80            1.21   50.82                      34.55              21.59           56.15           33.69

90            1.24   52.08                      35.41              22.13           57.54           34.52

100          1.26   52.92                      35.98              22.49           58.47           35.08

110          1.29   54.18                      36.84              23.02           59.86           35.92

120          1.31   55.02                      37.41              23.38           60.79           36.47

130          1.34   56.28                      38.27              23.91           62.18           37.31

140          1.36   57.12                      38.84              24.27           63.11           37.87

150          1.38   57.96                      39.41              24.63           64.04           38.42

160          1.39   58.38                      39.69              24.81           64.50           38.70

170          1.41   59.22                      40.27              25.17           65.44           39.26

180          1.43   60.06                      40.84              25.52           66.36           39.82

190          1.45   60.90                      41.41              25.88           67.29           40.37

200          1.46   61.32                      41.69              26.06           67.75           40.65

210          1.48   62.16                      42.26              26.41           68.67           41.21

220          1.50   63.00                      42.84              26.77           69.61           41.77

230          1.51   63.42                      43.12              26.95           70.07           42.04

240          1.52   63.84                      43.41              27.13           70.54           42.32

250          1.53   64.26                      43.69              27.31           71.00           42.60

260          1.55   65.10                      44.26              27.66           71.92           43.15

270          1.56   65.52                      44.55              27.84           72.39           43.43

280          1.57   65.94                      44.84              28.02           72.86           43.72

290          1.58   66.36                      45.12              28.20           73.32           44.00

300          1.59   66.78                      45.41              28.38           73.79           44.27

 

Notes: Kh= Kz and  Qh= Qz

G= 0.85

Cp= 0.80 (windward) and 0.50 (leeward)

Exposed area tributary at each level = 10 ft x 60 ft = 600 ft²

Reference: ASCE 7-98 Wind Loads, Chapter 6 (on the webpage).



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