Wood Top Plate Capacity 5

[KootK]

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

 

[haynewp]

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. Remember for wood, use fv=1.5V/A to compare with Fv due to it's shear failure mode. I think your bending is probably in bad shape as well. Is this sheathed on both sides or just one?

 

[jheidt2543]

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!

 

[Ron]

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)

 

[LPPE]

Did you look at your top plate as spanning continuous over multiple supports (studs)? Just a thought.

 

[KootK]

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

 

[ishvaaag]

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.

 

[Structuralist]

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&quot 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 member will have reached its maximum.

Although I never calculated the advantages, there are other redundant issues that will assist the plate:
1. Solid blocking between the trusses,
2. The nailing of the vertical sheathing, siding, stucco etc will add some support.
3. The fact that you may not realize the live load on the roof depending on your geographic location.
4. The truss reaction is an approximation. The closes accurate loads will be the dead loads applied since these are fairly easy to determine - but the issuance of a 20-psf (for no-snow areas and flat roof) live load may never happen. This does not mean that you should not consider it, but that if the numbers calculate, the addition of a short duration live load should not cause all that many problems on the home unless there are other deficiencies present.

The only time I am concerned with the trusses aligning with studs is:
1. When designing light gauge metal stud walls and
2. When placing a girder truss in which case I make sure to specify a post or double stud at below each end of the girder trusses.

The important thing her is to follow your instinct as an engineer and run the numbers taking load duration factors into account as well (I am in the desert and rarely do I contend with roof live loads). The Structuralist Website:

http://www.structuralist.net

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[jheidt2543]

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.

 

[BuddyShowalter]

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 members C_r = 1.1 per ASTM D6555.

3) American Lumber Standard Committee which provides base design values for the NDS Supplement has increased shear values by a factor of 1.95. With the increase in shear, the shear stress factor, C_H, has been removed as an applicable adjustment for shear. These changes can be found in the 2001 NDS Supplement which is available this spring.

4) Depending on the location of splices, the applied moments will differ and should be considered on a case by case situation. For bending it is conservative to assume a simply supported span between the studs. For shear resistance, a simply supported assumption may not be conservative.

AF&PA's Wood Frame Construction Manual (WFCM) for One- and Two-Family Dwellings prescriptively limits rafter and floor spans because of this issue. You can learn more about the WFCM and its availability at

http://www.awc.org.

Hope this helps.

 

[KootK]

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 members, both effective in bending (though not laminated to provide composite Ix). The concern I have is with a splice showinging up in the lower of the two plates. If the splice is there, and the lower plate is free to separate in tension at that location, does that not mean that I really only have a single 2x6 resisting bending moments there??

Thanks Again

Adam P

 

[Structuralist]

Adam,
I mentioned this in my last post and I think Buddy will agree - a beam acting in bending will consider the neutral axis as free to slide (most conservatively).
Consider heavy timber beams which have a tendency to split parallel to grain along the neutral axis but we don't consider them to be of any lower strength in bending.
You also can't ignore the code required nailing of the plate splice, but this seems academic. Consider the plate to be similar to a bar joist or a plywood web joist, if you will. Upper chord in compression and lower chord in tension. One of the things that will help you make this work is to consider solid blocking which will increase the strength of the compression chord, and at the same time, help move the neutral axis higher.

Still, I think you need to consider this practically. As Buddy implied, treating the plate as simply supported is overly conservative - design it as a continuous beam can calculate locations of greatest moment to verifiy the capacity of the plate in bending. I think that when you consider three or four supports with equal spacing of trusses, you will find that the combination of materials, including the blocking will help to reduce the stress on the plate and adjacent loads placed closer to supports will help reduce bending in the worst case - mid span.

Dennis The Structuralist Website:

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[Ingenuity]

Structuralist,

When you state "...a beam acting in bending will consider the neutral axis as free to slide (most conservatively)..." you still have to consider the horizontal interface shear and if you have no horizontal shear capacity the two members will behave as independent elements (assuming we discount friction and nominal connections etc) - which is what Buddy is saying when he states "...the two members are not equivalent to a three inch deep member when considering bending strength" .If the NA is free to slide then we have no interface shear capacity.

Also, for heavy timber beams where there is a tendency to split parallel to grain along the neutral axis it is NOT often that the split occurs for the entire length of the member, and in cases that the split is long and problematic, often epoxy resin injection is used to "repair" the split and reinstate the horizontal shear capacity.

 

[Structuralist]

Ingenuity
What you say has merit, but why would you discount the connectors - 16d nails which probably have more value in shear based on splice requirements in the code, than the boundary nailing of most residential plywood diaphragms will develope over the entire lenth of the wall.

My point is that there is a connection, the two 2x member are acting togther. Furthrmore, there is additional contribution on the compression side by the nature of bending in the plate and the compression in the continuous blocking. There is also support added to the plates by the rigidity of the sheathing at least on one side of the wall and the nailing of the lower of the two plates to the end of the studs (if not toenailed). You don't have a simple beam senerio here - you have a system. If you wish to be exact, don't isolate out the plates and try and figure how they will perform sans connection, sheathing, and other elements of the system - test them as a system.

There has to be a practicality of design - without it we can overdesign outselves out of the business. I believe that if he can prove that a 3x member will handle the bending as a continuous beam over multiple supports, he should be safe. He can also go for a safer solution without worrying about the the analysis by installing a solid block between studs where the trusses do not beam concentric with the studes. He can secure the blocks to the studs or if possible, add trimmer studs to support the blocking. This will protect the plate and transfer the load to be studs - a simple and cost effective solution if he is concerned.

I apologize if I sound short-tempered on this issue - I don't mean to, but we engineers are constantly attempting to find perfection or to seek answers that generally lead to designs so contradictory to what has been done for more than 180 years of conventional construction that we don't help to bridge the gap between prescriptive building and full-code-compliance issues. Buddy knows me pretty well and for quite a few years. I'm not without experience, but I believe we need to start approaching problems with more practicality that we are attempting to do in code development - and if we can't, then we should be attempting to raise the minimum level of compliance for prescriptive or non-engineered design to be the minimum solution we can engineer. This is not what is happening.

So, when we get to an example of an engineers concern for how a double plate will act under a 3 kip load from the reaction of a roof truss, why shouldn't we seek a practical solution or one that is conservative, but not overly conservative.

I hope this explain my position on the issue and I apologize if I have offended anyone by it. The Structuralist Website:

http://www.structuralist.net

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[Ingenuity]

Structuralist,

I do NOT think you should disregard the nails, connectors, blocking or anything else that contributes to the "system" capacity...but your first two paragraphs of your previous post did not mention nails, blocking or other so i thought you were implying that with just 2No x 2x6 members without nails, blocking or any other assistance, that because at midspan where the shear was ZERO that you did not have to be concerned about horizontal shear - you analogy to a heavy beam with a parallel-to-grain split at the NA also reinforced my thoughts.

I am certainly not offended my your comments, and i tend to concur with your statements about code compliance and bridging gaps from how things have been/are being built to what is designed/engineered.

I think it was TYLin that stated "...seek to apply the laws of nature NOT blindly follow the codes of practice..."

 

[lshort]

Truss loads at roof joist.
Interesting question and I have looked at it several times myself. I have reached conclusions which sometimes cannot be concluded with proper Engineering calculations. My conclusions are based on a combination of calculations and personal observations on inspections of many structures over the years. There are a lot of redundancies within the systems that make things work. We as Engineers oversimplify in order to reach quick answers and sometimes that is necessary and other times it will lead to very conservative answers.
1. I live in a region where the snow load design is 60psf. Loads on double top plates are not considered a problem if the wall has sheathing attached and nailed properly.If the sheathing is nailed to the top plates I consider it stiff enough (Engineering judgement) to transfer the loads to the studs. The sheathing itself carries the load as a stiffened panel in compression and shear. If the sheathing was a material other then plywood or board then I would be concerned and a proper analysis should be done. Gyproc on the inside will also provide a stiffness to the top plate but is limited.
2. Watch out for girder trusses as they will require extra studs.
3. If you are designing multistory apartment buildings (3- 4 stories) with long span floor trusses and stud support walls then it is necessary to install extra studs to line up the loads since they are getting heavier from each
storey.
4. A roof will not fail because of one truss. Generally somewheres in close proximity will be a truss which aligns or is in midspan between studs which increases the shear load capacity. Plwwood sheathing, strapping, roof sheathing, ect with do a lot of load redistribution.
5. I think the code should address this problem and give some values to guide Engineers. A FEM analysis is probably very appropiate to get some realistic values.

 

[EIT2]

I realize that I am a year-and-a-half late in my reply, but, if this helps your future projects, for the past five years, for this mid-Wisconsin region of 40 psf ground snow, for roof truss spans of 50'+, I have been specifying triple SPF #2 top plates (engineered as a solid, continuous beam) with no negative feedback from the contractors.

Just a thought ...