Wood Framing 2

[wslainc]

I Have 2x10s @ 16" o.c. spanning 12' w/ 3/4" ply as sheathing and slate 24x24 tile on top. is this exterior deck prone to damage due to deflection if I have a party and 20 people are on it???
Please let me know your thoughts.

 

[DaveVikingPE]

Loads: 3/4" plywood = 2.25 psf
Slate tile (1/4"?) = 10 psf

Source of this info: one of my books.

DL = 2.25 + 10 = 12.25 psf X 16/12 = 16.33 PLF

Live loads - how about... 40 psf x 16/12 = 53.33 PLF + 20 people on their tip-toes standing on each other's shoulders (assume you have *really* high ceilings) @ 200 # each (assume they're well-fed and/or light-heavyweight bodybuilders) = 4000 #

DL + LL (scratch loads, no load factors applied) = 16.33 + 53.33 = 69.67 PLF, with a 4000 # concentrated load in the middle of the beam (worst case).

Shear force = wl/2 + P/2 = 69.67 X 12/2 + 4000/2 = 2418 # - your connections must be rated for this load or better; and worry about the girder to which they are attached (if that's the way the deck is built)
Moment = wl^2/8 + Pl/4 = 13254.1 ft-#

2-2x10's, southern pine #1 (assumed); A = 28.5 si, S = 45.13 in^3, I = 214.34 in^4; Fb = 1050 psi, Fv = 70 psi, E = 1,300,000 psi

Shear stress = fv = 1.5V/A = 1.5 X 2418/28.5 = 127 NG
Bending stress = fb = M/S = 13254.1 X 12/45.13 = 3524.25 NG
Deflection = 5wl^4/384EI + Pl^3/48EI = 5 X 69.67/12 X (12 X 12)^4/384 X1300000 X 214.34 + 4000 X (12 X 12)^3/48 X 1300000 X 214.34 = .12 + .89 = 1.01" Check deflection limit l/240 = 144"/240 = .6" NG

From the above, I would say that the deck might start to fail in shear, bending and that deflection of 1" will probably start some of the tiles to crack.

You may want to try different loads, like: 20 people back-to-back lining up on the beam, changing the line load and decreasing the concentrated load.

Question: how's the deck act when it rains? If it's got plywood and tile on it, I would be concerned about ponding loads, assuming the party is "rain or shine."

Is it a Halloween party? If so, add an additional ten pounds or so per persons for costumes.

 

[RockEngineer]

Now DaveViking you are getting sarcastic and the person may not even know it. Use Dave's method but use either the 40 psf live load or the 20 people not both.

His other concerns are valid.

Happy Halloween.

 

[boo1]

For my deck designs we use 60 psf LL. Dave omitted the beams weight in the DL, and assumed no snow load. Most decks in my area are build with SYP #2 pressure treated (lower the allowable stresses). For tile decks we limit deflection to L/360. To limit the deflection to minimize cracking. The tiles or slate can crack.

Typically Iuse 2x12s at 12" oc with 3/4" pt plywood then a water shield membrane toped with a tie backer board or a light weight air intrained cement topping then apply the tile with a flexable thin set.

 

[DaveVikingPE]

Sarcastic? Moi?

Maybe: but he did ask about 20 people on the deck, right? I was really adding a bit of humor to the example...

I agree with boo1 on the 60 psf live load, as well as the upped deflection limit regarding tile. It may well snow on 31 October, too - if it's a Halloween party. I think the weight of the beams is important from a deflection standpoint, too.

I do, however, hate outdoor tile decks. I think they're ugly, unless combined with tasteful landscaping.

 

[boo1]

Tiles on wood decking, outdoors asks for trouble! The outside (wet conditions) also lower the allowable yield stresses.

Good pumkining