Appendix B
Detailed Calculations of Damage Classification
one surface (i.e., the top of the roof). Because the overhangs are extensive (3 feet), the uplift on the tee was considered to be in 2 segments—the flat portion and the overhangs. The effective wind area for the overhangs is 10 sf; the effective wind area for the main roof area is 113 sf. The GCp for the overhangs is -2.8 and the GCp for the flat roof is -1.1.
The total uplift pressure of 90 psf is the sum of the uplift on the flat roof and the uplift on the overhangs. P1 is the overhang pressure and P2 is the flat roof pressure. A partially enclosed building is considered appropriate in this case because wind did get inside the building through broken windows and other building envelope penetrations.
P1 = q(-2.8-0.55) = -3.35q
P2 = q(-1.1-0.55)=-1.65q
90 psf = [P1(20sf) + P2(113)]/133 sf= [3.35q(20) + 1.65q(113)]/133
Solving for q =47 psf
Calculating the wind speed from the equation q = 0.00256* I*Kd*Kz*Kz*V²
V = 147 mph
JOHN DEERE BUILDING PEMB:
The failure mode studied in this building was buckling of the steel roof purlins, which are 'Z' shaped. The thickness was 1/16 inch or 0.0625 inch. The 'Z' shaped channel was 8 inches deep, 16 feet long, and had 3-inch wide flanges that formed the 'Z'. The moment of inertia about the axis that buckled (y axis) was calculated to be 0.281 in
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(determined by bt³/12 x 2 flanges; the thickness of the flange that constituted the y axis was so small to be negligible). The load required to buckle the purlin is given by
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where E for steel = 29x106 psi. Using I = .281 and L- 16 ft x 12 in/ft, P
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= 2181 lbs. The tributary area is the 16-foot length x 5-foot purlin spacing. The distributed load required to result in a P
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= 2181 lbs is 2181 lbs/(16 feet x 5 feet) 27.3 psf.
Calculating the wind speed from the equation q = 0.00256* I*Kd*Kz*Kzt*V² and p = q(GCp — Gcpi). Again the MWFRS is used to determine GCp. The gust factor G is 0.85; Cp = -0.7 is the coefficient for uplift on the roof when the slope is about 15°; GCpi is 0.55.
p = q(-1.14) and q = 27.3/1.14 = 24 psf. Calculating wind speed from q yields V-122 mph.
If the Components and Cladding coefficients were more appropriate, in the field of the roof for an 80 sf effective wind area, GCp = -0.8, which would result in p = q(-1.35) and q=20.2 psf. Wind speed required for this pressure V = 96 mph.
