built up wood beam adequacy

huangyhg

built up wood beam adequacy ?
need confirmation from an expert.    i have built a deck at the back of my house using the following design.     the deck is 10'-0" wide by 36'-0" long.   there was an existing deck which i demolished and decided to use the existing concrete footings which are 8'-0" from the house wall and spaced at 12'-0" o/c.  on the footings are 4 x 4 posts approx 4'-6" in height supporting a built up wood beam of (2) 2 x 12 construction grade pressure treated lumber.  the wood beam was built up so that the splices are staggered and no further from each post than 3'-0" (1/4 span).  the beam is held together with 3" lg. screws, 3 in each row approx 3" o/c and the rows being approx 18" o/c. the beam is fixed to the sides of the posts with (2) 1/2" bolts at each post.   the 2 x 8 joists are fixed to the house wall at one end and rest on the built up beam at the other giving a 2'-0" cantilever and are spaced at 16" o/c.  posts are also diagonally braced back to the beam. i considered the live load on the joists as being the same as the living area of the house (40 psf) but am now wondering about 12'-0" span of the built up beam under a heavy snow load, possibly 60 psf.  should this beam need any further attention ?  advice greatly appreciated.  
hi, haggis.
can you just clarify a small (?) detail about your "splices".
am i correct in reading your spec to mean that at each splice you have two abutting ends of 2*12 adjacent to one continuous section, so that at the 'splice' there is just a single section of 2*12 effective ?
hi austim,
thanks for the quick response.  i think you are reading what i described, that 2 abbutting ends on the 2 x 12's have a continuous 2 x 12 behind them.   i was thinking that by virtue of the screws i had the strength of (2) 2 x 12's for the entire lenth of the beam.
by saying at the splice locations i just have one 2 x 12 effective, now you have me thinking that i am relying on the screws to do more than just hold the sections together and in fact i dont have a beam matching the properties of one single 4 x 12.   
maybe at the splice locations i could straddle the abutting ends with a metal plate say 1/8" thick with 2 bolts on each side of the splice and then i'm relying on the screws do no more than hold the sections together.  again, the splice locations are no more than 1/4 of the span between posts.
hope this is a little clearer.
hi austim,
apart from the method of building up the (2) 2 x 12 beam.  i thought i would let you know how i arrived at this section of lumber.
with the span between posts being 12'-0" and the deck width being 10'-0" and assuming the snow load is 60 psf, the snow load for this section of deck would be an evenly disributed 7200lbs.   with the deck having an overhang 2'-0" beyond the built up beam, i applied the following formula to arrive at the reactions at r1 and r2.  
r1 being at the built up beam.
r1 = 7200 x 5 / 8 = 4500lbs  r2= 7200 x 3 / 8 = 2700
now knowing that the 12'-0" span of the built up beam supports a load of 4500lbs, i applied the following formula to arrive at the beam deflection.
wl^3 / 48ei
e = 1,600,000  and i being 380in^4
the deflection theoretically would be 0.016" inches which is negligable.
would i be correct in my way of calculating this ?
thanks in advance.
hi again, haggis
a few points:
1.  no, your current details only provide the bending strength of one section of 2*12.  i suspect that you will find that is not quite sufficient to comply with your local standards.
2.  yes, a splice cover plate (either steel plate or a third thickness of 2*12 locally [i would make them at least 3 feet long]) should do the trick.
3.  no problem with your sequence of calculations in principle, but...
    4500 lbs ok;
    380in^4 presumably allows for the actual timber
    dimensions [the nominal 4*12 dimensions give i=576];
    review your calculated deflection - with your values i
    get midspan deflection = 0.46 inches - still ok in my
    opinion.
i hope that this helps.
hi austim,
thanks for all your help, it is greatly appreciated.  i noticed that i had used the wrong formula.   should have been:  5wl^3/384 ei for a uniform load on the beam.
think i'll stick to mechanical and leave the structural to the experts.
thanks again.
you should also check the stresses in the single ply section of the built up beam...this is what will determine whether the deck stays up.
however, if you look at bending moment diagrams for a continuous three span beam, the point of zero moment is almost always close to the quarter point of each span.in the "center span unloaded" load case, the moment is
0.05 wl^2.
assuming a deck load of 70 psf total ( i always use 60 psf for residential decks, after some spectacular deck collapses during parties at the jersey shore) the load on the beam is 428 plf. the moment at the splice is
37 in-k,the section modulus is (1.5*11.25^2)/6 or 31.6, and the bending stress in the single  2 x 12 is 1170 psi. the fb of southern pine (which most treated wood is), with a 1.15 duration factor is 1121 psi. this is pretty marginal, but i personally wouldn't bother reinforcing the splice unless there was a large knot or crack nearby. if the wood is #1 or select structural grade, you have a factor of safety.
if you check the maximum moment in the full beam, mmax= .1167wl^2, negative moment over the post under the "end span unloaded" load case and s=2 x 31.6, or 63.2; the max moment is therefore 86.3 in-k, resulting in a stress of 1365 psi. given the 1.15 duration factor, the basic lumber stress would have to be 1187 psi, which is just below the capacity of #1 grade southern pine.
you should check the grade stamps on the 2 x 12s to determine the grade used.
i would also be concerned about the capacity of the bolts used. a 1/2 inch diameter bolt in single shear perpendicular to grain in southern pine is good for about 600#; yet the two bolts are expected to hold up to 12 feet of beam, or 5100 pounds! this is a serious detail! i advise bolting additional 2x4 vertical supports to the posts snugged up under the edge of the 2x12s, that way you get the bolts acting parallel to grain.
thanks trussdoc,
i hadn't considered grain direction in the wood.  i understand what you are saying though.    done it at the weekend...(2) 2 x 4's one snugged under each 2 x 12 and bolted to the 4 x 4 posts.   even looks a lot better !
thanks again.