I am building a deck onto my house. The area in question has a 15'
x 34.375' dimension. I would like to use (2)2" x 10" x 34.375' as the
beam but not sure if it will hold the weight of the deck plus
furniture and possible a hot tub. The beam would run parallel to the
house and will be support by (5) 4 x 4 post equally spaced, 15' from
the house. There would be 2" x 10" x 15' floor joist lumber spaced on
16" centers spanning 34.375',the joist will be covered by 3/4" plywood
and hardy backer board with tile.
Will the(2)2"x10"x34.375' hold the weight? if not what size of beam do
I need to use for this layout? Thank you

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Request for Question Clarification by redhoss-ga on 28 Apr 2006 06:01 PDT

You don't say what the height is of the deck above ground level. I
would not think that supporting a hot tub with your deck frame would
be a good idea. Depending on the size a hot tub (with water) will
weigh several thousand pounds. Most decks are built around hot tubs
that rest on a concrete slab. I can check your deck design without the
hot tub.

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Clarification of Question by tbiffath-ga on 28 Apr 2006 18:44 PDT

The will be about 6' above the ground

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Clarification of Question by tbiffath-ga on 28 Apr 2006 18:50 PDT

The Deck will be about 8' above the ground. And I need the deck info
ASAP. I could add posts under the hot tub if needed.

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:

http://www.architectureweek.com/2000/1018/building_1-1.html

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:

http://www.awc.org/calculators/span/calc/timbercalcstyle.asp

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

I really thank you for your time and your answer, I feel a lot better
with your analyses. you really are a professional. thanks