wood top plate capacity

huangyhg

wood top plate capacity
last friday, i got a call from a wood truss supplier.  apparently, when they pre-fabbed the walls (2' o.c studs), they were built such that the studs did not line up with the trusses above (also 2' o.c.).  thus the trusses have the potential to land on the top plates as point loads (2000 lb approx) at midspan between studs.  the truss guys wanted me to evaluate wheather or not this condition was acceptable.
i would like to solicit comments and recommendations on the method of analysis for the capacity of stud wall top plates.
here are my thoughts and concerns:
1. for bending stress, i think that the top plate should be analyzed as two separate members with no consideration given to the lamination between them.  thus, the bending capacity would be twice the capacity of a single 2x6 used flat.
2. i wonder if i should even use both of the plates for capacity.  since it is possible for one of the plates to be spliced between any two studs, perhaps i should only count on the bending resistance of one plate.
3. for shear check, i do not believe that the lack of lamination between the plates reduces the capacity.  i assume the the shear capacity of two stacked 2x6 would be the same as one piece 3.0" x 5.25" (using the allowable stress values corresponding to the 2x6's of course).
4. is it valid to use both top plates for shear capacity even though there may be a splice break in one of them?  
when i checked the shear in this way, i found that the capicity is pretty damn small.  sample calc:
-double 2x6 plate
-ch = 2.0 (not very conservative)
-fv = 70 psi (#1/#2 spf)
-duration factor (1.15)
vr = 1.15 x 0.667 x 3.0 x 5.25 x 70 psi = 1690 lb
at 50 psf total roof loading and 2' truss spacing, that amounts to the reaction from only a 34' simply supported truss.  i commonly encounter trusses that span more than 34'.  what is especially disconcerting to me is that since this limit is based on the shear caused by a single point load, it doesn't really help the situation to reduce the spacing of the studs.
is there something that i am missing here?  is there some analytical way to account for the help that the top plates may get from the sheathing?  any advice that anyone has for me on this topic would be greatly appreciated.  thanks in advance for your efforts.
adam
unless you go out and verify for yourself,i wouldn't use ch=2 and i would assume there is a splice at your point of max shear. re  
adamp:
if the stud spacing is 2'o.c. and the truss spacing 2' o.c. but they don't line up, the most they could be off is 12".  why not shift the trusses to line up with the studs and then add one truss.  the cost of adding one truss is certainly less than the cost of all the engineeing you are trying to do or any fix you might come up with.  there could be some added framing at dormers etc., but still this seems to be the easy solution.
just a thought!
adamp...don't forget to consider that strapping at the trusses provides a part of the continuous tensile tie to the foundation for uplift.  if the trusses are offset, this tie has to be restored by most codes (certainly so by standard building code (us)).
if solid sheathing is used, additional fastening between sheathing and top plate will help the shear capacity (and bending...but shear is likely more critical in your case)
did you look at your top plate as spanning continuous over multiple supports (studs)?  just a thought.
thanks for the input guys.  some additional info:
1. the problem occurs at hip conditions in the roof.  thus, it's not really possible to shift the trusses since they must go in certain locations to achieve correct geometry.
2. the walls were prefabbed as well.  contractor doesn't want to rip the sheathing off to move the studs either.
3. the main problem, in terms of my analysis, seems to be shear.  continuity, while certainly applicable, would not change my situation very much in terms of design shear load.
i'm all for accounting for the help that the plates get from the sheathing.  does anybody have any suggestions on how to do that?
thanks again,
adam
you can do it in fem. as long in any situation -and normally the sheating will also be being accounted for lateral strength- the nails or glue are safely able to pass the forces one to the other, assuming continuity there is feasible. the fem can do in whatever way...otherwise you might adscribe some distributed spring support etc but relying more on engineering judgement...i think easier to make the fem model. in fem even discrete support at nails can be assumed.
adamp
i commonly have conditions in wood framing where the studs are at 16" on center and the roof trusses are at 24" o/c. ideally, only every third truss aligns with a stud that would cause the plates to be in bending. here are some thoughts:
1. treat the double plate as a 3x member - remember that in bending, the neutral axis is at the splice between the members and the shear at mid-span for a simply supported member becomes zero. what is important is the area close to the extreme fiber (leading to the importance of the depth of thee "beam") in bending. therefore, if you neglect one of the plates you are not accounting properly for bending.
2. there is no hinge at each stud - the top plate is continuous and should be analyzed as a continuous beam rather than simply supported - it will help in the long run.
3. i have a similar condition in my own home which i designed and constructed 9 years ago. it is a sante fe style home (flat roof with minimum slope for drainage). i have 10-foot plate heights and have added a lighting soffit 2' below the ceiling that extends out 24" from the wall around two walls in the room. above, the soffited area is used to display plants, pottery etc. because of the location of the mountains and the desire to block out my neighbors roof, i placed casement windows just below the plate line. because of the height resitriction (30" wide x 18" windows at about 8' apart) i had no room to install a header. since i am the engineer who designed the home, i performed the analysis at the worst location for the reaction of two trusses occuring between the 30" wide window which is actually cutting out one stud. simply supported, the plates deflected too much, but if i considered the plate as continouous i found that it calc'd out fine. the rationale is that you have a 48" plate splice that is nailed properly with 16d nails and that this becomes a built-up member. while it induces a moment over the studs, the location of the truss reaction also helps to reduce the deflection in the adjacent mid-spans and over the full length of the wall (as long as the reaction is low enough), the numbers should be accurate.
after 9 years, there has been no problem with the windows due to deflection of the double 2x6 df plate. after this length of time, any creep that would be affected by the   
adamp:
here is another thought.  how about doing what the steel stud guys sometimes do to reinforce their top track, add a rolled section steel angle?  a 3-1/2" x 2-1/2" x 1/4" angle with the 3-1/2" leg horizontal and the 2-1/2" leg down would certainly be more than you need.  it is more expensive than wood but, it is a lot faster than trying to justify a lot of engineering calcs.  you should also still have room to put rafter hangers/straps in too.
here are some items which should be considered when determining the strength and shear properties for double top plates
1) both of the plates will resist the applied loads. moment of inertia for this case will be the sum of the upper and lower top plate.  while some friction exists between the two plates, it is conservative to ignore any contributions due to friction or nailing of plates together.  the two members are not equivalent to a three inch deep member when considering bending strength.
2) for bending, applicable adjustments include (c_f, c_r, c_d, c_fu) note: for two   
thanks buddy,
can you tell me roughly what those wfcm limitations are?  since i used ch=2.0, my shear evalution still limits me to a 34' truss for any spacing of wall stud.  also, several people have recommended that i treat the top plate as two 1.5 x 5.5