Okay tbiffath, I think we can proceed. You don't say what wood you are
using, but we will use conservative numbers. A good conservative value
for deck live load plus dead load appears to be 60 PSF:
Most codes require a deck to support an estimated live load of 40
pounds per square foot (psf) combined with a 10 psf dead load for a
total of 50 psf. However some require a structure sized for 60 psf.
Check with the applicable local codes for the locale of the project.
Here are numbers requred to do the calculations:
2x10 section modulus = 21.39 in^3
2x10 moment of inertia = 101.6 in^4
Allowable bending stress (s) = 1,000 psi (could be higher depending on wood used)
Modulus of elasticity (E) = 1,000,000 psi
Alowable deflection (D) = L/360 = 8.5 ft x 12 inches per ft/360 = 0.28 in
w (total loading per foot) = 7.5 ft x 60 PSF = 450 lb/ft
The formula for maximum bending moment is:
M = wl^2/8 = (450 x 8.5^2)/8 = 4,064 ft-lb = 48,769 in-lb
Solving for required section mudulus:
S = M/s = 48,769/1,000 psi = 48.8 in^3
With your doubled 2x10's we have an S = 2 x 21.39 = 42.78 in^3
Since we have used conservative numbers, this is very close and will
be okay. You should select as good a grade of lumber for your beams
and floor joists as you can anyway.
Now to check for deflection.
The formula for deflection is:
D = 5wl^4/384EI
Solving for I we have:
I = 5wl^4/384ED = (5 x 450 x 8.5^4)/(384 x 1,000,000 x 0.28)
NOTE: To get answer in proper units we must multiply by 1728.
I = 188 in^4
With your doubled 2x10's we have an I = 2 x 101.6 = 203.2 in^4
This is more than adequate.
You either made a very well educated guess at the beam requirements or
received some very good advice. Just make sure that whatever you may
decide to do with your hot tub plans, do not add any loading to the
deck. The hot tub weight would over stress your beams and floor
joists. I did a quick check on your floor joists here:
Your design looks very good.
If there is any of this that you don't understand, please ask for a clarification.
Good luck with your deck, Redhoss