Calculations

Wind Force:

Initial Parameters:
l = 7.19 ft
w = 3.54 ft
max α = 75º/45º
V = 150 mph
Cd = 1.4 (short flat plate)
Wp = 90 lb (weight per panel)
n = 1.2 (safety factor) 
Mf = force on each mount (4 mounts)
Fx = x component of pull force
Fy = y component of pull force

@75º

P = .00256*V^2 = .00256 * (150mph)^2 = 57.6 lb/ft^2


Aeff = l*w*sin(α) = 7.19 ft * 3.54 ft * sin(75º) = 24.59 ft^2


Fmax = Aeff*P*Cd = 24.59 ft^2 * 57.6 lb/ft^2 * 1.4 = 1,982.9 lb


Nmax = Fmax * sin(α) =  1983 lb * sin(75º) = 1,915.3 lb

Nsafety = Nmax * n = 1,915.3 lb * 1.2 = 2,298.4 lb


Nload(safety) = Nsafety / A = 2,298.4 lb / (7.19 ft * 3.54 ft) = 90.3 lb/ft^2


Mf = Nsafety / # of mounts = 2298.4 lb / 4 = 575 lb

Fx = Mf * cos(90º-α) = 5745 lb * cos(90º-75º) = 555 lb

Fy = Mf * sin(90º-α) = 575 lb * sin(90º-75º) = 149 lb


Hcenter(wind) = sin(α) * l / 2 = sin(75º) * 7.19 ft / 2 = 3.47 ft

Hcenter(Wp) =  cos(α) * l / 2 = cos(75º) * 7.19ft / 2 = 1.86 ft


Bending Moment (safety) = Hcenter(wind) * Nsafety + n * Wp * Hcenter(Wp)
                                       = 3.47 ft * 2,298.4 lb + 1.2 * 90 lb * 1.86 ft = 8,176 ft*lb 
                                       = 8,176 ft*lb * 12 in/ft = 98,112 in*lb

@45º

P = .00256*V^2 = .00256 * (150mph)^2 = 57.6 lb/ft^2

Aeff = l*w*sin(α) = 7.19 ft * 3.54 ft * sin(45º) = 18.00 ft^2

Fmax = Aeff*P*Cd = 18.00 ft^2 * 57.6 lb/ft^2 * 1.4 = 1,451.5 lb

Nmax = Fmax * sin(α) =  1,451.5 lb * sin(45º) = 1,026.4 lb

Nsafety = Nmax * n = 1,026.4 lb * 1.2 = 1,231.7 lb

Nload(safety) = Nsafety / A = 1,231.7 lb / (7.19 ft * 3.54 ft) = 48.4 lb/ft^2

Mf = Nsafety / # of mounts = 1,231.7 lb / 4 = 308 lb

Fx = Mf * cos(90º-α) = 308 lb * cos(90º-75º) = 198 lb

Fy = Mf * sin(90º-α) = 308 lb * sin(90º-75º) = 236 lb

Hcenter(wind) = sin(α) * l / 2 = sin(45º) * 7.19 ft / 2 = 2.54 ft

Hcenter(Wp) =  cos(α) * l / 2 = cos(45º) * 7.19ft / 2 = 2.54 ft

Bending Moment (safety) = Hcenter(wind) * Nsafety + n * Wp * Hcenter(Wp)

                                       = 2.54 ft * 1,231.7 lb + 1.2 * 90 lb * 2.54 ft = 3,402.8 ft*lb 

                                       =3,402.8 ft*lb * 12 in/ft = 40,834 in*lb

Snowfall Force:
Initial Parameters:

min α = 15º (flush with roof or min adjustment angle)

l = 7.19 ft

w = 3.54 ft
Hmax = 3.2 ft (max snowfall accumulation)

ρ = 12.49 lb/ft^3
r1 = .8 (low wind condition roof factor)
Wp = 90 lb (weight per panel)
n = 1.2 (dead load safety factor)

Mf = force on each mount (4 mounts)

Fx = x component of pull force

Fy = y component of pull force

V = l*w*H = 7.19 ft * 3.54 ft * 3.2 ft = 81.45 ft^3

Wground = V*ρ + Wp = 81.45 ft^3 * 12.49 lb/ft^3 + 90 lb= 1,107.3 lb

Wroof(max) = Wground * r1 = 1,107.3 lb * .8 = 885.8 lb


Nroof(max) = Wroof(max) * cos(α) = 885.8 lb * cos(15º) = 855.6 lb

Nload(max) = Nroof(max) / A = 855.6 lb / (7.19 ft * 3.54 ft) = 33.6 lb/ft^2

Nroof(safety) = Nroof(max) * n = 855.6 lb * 1.2 = 1,026.7 lb

Nload(safety) = Nload(max) * n = 33.9 lb/ft^2 = 40.7 lb/ft^2

Mf = Nsafety / # of mounts = 1,026.7 lb / 4 = 257 lb

Fx = Mf * cos(90º-α) = 257 lb * cos(90º-15º) = 66.5 lb

Fy = Mf * sin(90º-α) = 257 lb * sin(90º-15º) = 248 lb

Hcenter = sin(90º-α) * l / 2 = sin(90º-15º) * 7.19 ft / 2 = 3.47 ft

Bending Moment = Hcenter * Nroof(safety) = 3.47 ft * 1,026.7 lb = 3,563 ft*lb

*all calculations are per panel and assume a uniform load distribution