Assignment Assignment No.2 (Wind load analysis By ASCE 7-02) Data on Design Problem (Wind load analysis) My Serial No = 33 Nature of Building: Typical Office Building Stories: 30 + 33 = 63 Stories First floor height: 17ft Typical storey height: 13 ft Building height, h: 17 + (62x13) = 823 ft. Location: Toronto, Ontario Wind speed V: 110 mph Terrain: Flat, open country with scattered obstructions obstructions having the size of single -family
dwellings, height generally less than 30 ft Plan dimensions: 98.5 ft (B) x 164 ft (L)
Building lateral-load-resisting system: moment frame with shear walls. Fundamental period T= 3.12 sec.
The building is regular and it does not have unusual geometric irregularities. It does not have response characteristics that would subject the building to across-wind loading, vortex shedding, or instability due to galloping or flutter. The building does not have a site location for which channelling effects or buffeting in the wake of upwind obstructions warrant special consideration. The building is sited on the upper half of a 2 -D ridge and has the following topographic conditions: LH = 100 ft, H = 100 ft x = 50 ft (See Fig. 1.11) Damping factor: 1.5% of critical; the building is for typical office occupancy Air density = 0.0024 slugs/ft
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Mode exponent ϕ = 1, KZT = 1 Coefficient Cfs = 1.3; Building density = 0.287 slugs/ft
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Requirements: 1. Determine the wind pressure on the windward and leeward sides as well as total wind pressure on the building. 2. Total load/ft at each floor level and the Total base shear. 3. Overturning moment (OTM) at each floor level and total OTM. 4. Calculate maximum along wind deflection and acceleration. 5. Comment whether the building is safe based on drift index and comfort based acceleration under dynamic wind gust effect. 6.
30-Story Building on flat ground (computer program solution)
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DESIGN Step 1: Building Classification The building is for office occupancy with certain areas designated designated for the congregation of more than 300 people. From Tables 1.7 and 1.7a, the classification of the building for wind loading: Category: III Importance factor for wind I w = 1.15.
Step 2: Building Exposure: Exposure category is B
Step 3. Basic Wind Speed V: Basic wind speed V = 110 mph, as given in the statement of the problem. Step 4. Determination of Gust Response Factor (G or G f ) Definitions according to which building may consider flexible The building's height-to-least horizontal dimension is 823/98.5 = 8.4, greater than 4, So the building is not flexible. It is rigid. nd But according to the 2 definition natural frequency (1/T) = 1/3.12 = 0.32 less than 1Hz so, it is flexible.
Therefore, gust effect factor G must be determined. Determination of Gust Response Factor
V = wind speed in ft/sec = Vmph x =
= 161.33 ft/sec = 0.6 x 823 = 493.8ft greater than zmin = 30ft (from Table 1.9) OK
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C =0.3 (Table 1.9)
l = 320 (Table 1.9) and
(Table 1.9)
Q = the background response
=
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n1 = natural frequency = (1/T) = 0.321 Hz
=
=
4
=
x
( 0.53 + 0.47
√ √
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G = 0.8378 Determination of along wind displacement displacement
= 0.501
3.909
Maximum along Wind displacement: displacement:
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Air density = 0.0024 slugs/ft ; Mode exponent ϕ = 1, KZT = 1; Coefficient Cfs = 1.3; Building density = 0.287 slugs/ft
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Mass of the Building per unit height (Ʋz) = 0.467 x 98.5 x 164 = 7543.92 slugs / ft
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m1 = Ʋz x (h/3) = 7543.92 x (823/3) = 2069548.72 slugs
Xmax(z) is also commonly referred to as lateral drift, ∆. Tall buildings are usually designed for a
drift index
. In our case,
, indicating that the building is
quite stiff.
=
Determination of along wind acceleration
= 3.909 x
2
= 0.655 ft/s
= 0.655 x 31.11 = 20.38 milli-g
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Step 5. Directionality Factor K d
Kd = 0.85 (Table 1.8) Step 6: Combined Velocity Pressure, Exposure Coefficient K z(windward) and Leeward (K h) Using Table 1.6 and formulas (vary with height)
Calculated in the table of calculations Step 7: Determination of topographic factor, K zt
The building is located on a 2-D ridge, may experience higher winds than buildings situated on level ground and topographic effects should be considered. For the given values of Lh, H, and x the multipliers K1, K2, and K3 are obtained from Fig. 1.11 LH = 100 ft, H = 100 ft x = 50 ft (See Fig. 1.11)
and substituting 2H for Lh for evaluating K2 and K3.
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Upwind of crest (Ʋ) = 1.5 ; Ƴ = 3 Evaluating K2 and K3
( )
Calculated in the table of calculations
Calculated in the table of calculations Step 8: Velocity Pressure qz (windward) or q h(leeward )
Step 9: External pressure coefficients, Cp (windward and leeward)
Complete calculations are given in the table
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