Built-Up Sawn Lumber 2-Span Continuous Beam

[ajk1]

Background:

I am checking a continuous 2-span built-up sawn lumber beam of a cottage that was constructed within the last year (I had nothing to do with its design or construction). The beam that I am checking is the main floor perimeter beam supporting the main floor, and the wood stud wall above which in turn supoorts a loft and the roof.

Preliminary checking indicates that this beam is over-spanned. The spacing of the supports (number of supports were reduced), and the size of the beam were both increased by the contractor, from the original system designed cottage, but no engineer sized the new setup.

Although certain simpifying shortcuts could be made when designing such a beam, I cannot take such shortcuts when checking because I may put the owner to needless expense strengthening the beam, where perhaps no strengthening is required if more accurate checking methodology is used.

Given:

The 2 spans are about 7 feet and 11 feet, and 2 of the plies of the 4 ply beam are butted at about the 2 foot locatiion from the centre support in one span, and about 3 foot from the centre support in the other span.

Questions:

1. Does Woodworks software account for the location of the joints?

2. When checking manually, how should the butted plies be dealt with? For example, is there a "development length" over which the ply picks up its share of load from the adjacent plies of the 4 ply beam? Are the nails generally adequate to make that tansfer of load?

3. Are "clear" spans rather than centre-to-centre spans entered into Woodworks?

4. Is there any worked example of design or checking of a built-up continuous wood beam with some of the plies butted within the spans?

 

[OldPaperMaker]

ajk1,
1. I assume that 2 of the 4 plys don't have the required capacity in the 11' span and you did not design the existing beam.
2. You noted in your first post that this beam is supporting a floor, a loft, the roof and two walls, so it is a key component of the support for the house.
3. As KootK noted it is damn tuff to design a moment connection is a wood beam.
4. I would throw in the towel and design a new beam that you know will support the design loads. You will sleep better at night time.

 

[ajk1]

That would be very expensive...have to temporarily support the cottage while pulling out the old beam. I would expose myself to liability because the contractor would sue me for not designing an economical fix that he would have to pay for. Then I would not sleep at night. If the cottage were not all built and completed, then I would agree with you. As a lawyer pointed out to me 30 years ago, when I first prepared to act as an expert witness, repair/remedial measures are not the same as new design. There is a professional and legal obligation to minimize the remedial costs, consistent of course with providing a safe design that can be shown to satisfy the intent of the Code. But thank you for urging me to sketch it up so everyone had a clearer understanding of the set-up. Much appreciated.

 

[KootK]

You're quite welcome AJK. It's an interesting question and I do owe you a few favors for your past efforts on my threads.

My interests are 80% technical / 20% project management. My wife's are the reverse. You can imagine where the bulk of the "power" resides in this couple.

The greatest trick that bond stress ever pulled was convincing the world it didn't exist.

 

[BAretired]

I think you are all being overly conservative. Don't know which code you are using, but the 2006 Alberta Building Code Part 9, Article 9.23.9.1.3) states:

Where a beam is continuous over more than one span, individual members are permitted to be butted together to form a joint at or within 150 mm of the end quarter points of the clear spans, provided the quarter points are not those closest to the ends of the beam.

I do not have a later issue of the ABC but this requirement has been unchanged for as long as I can remember. The Alberta Building Code, so far as I am aware, is consistent with the National Building Code of Canada but I cannot vouch for codes outside Canada.

BA

 

[KootK]

Nice find BA. I'll still need to understand the mechanism before I dive in however. I feel like a bad Canadian for not knowing about this provision. I'm pretty sure that I did this a few times as an EIT without even thinking about it.

The greatest trick that bond stress ever pulled was convincing the world it didn't exist.

 

[BAretired]

If the concern is insufficient nailing, a couple of bolts at each end of the cutoff plies should do the trick and costs very little. See attached link:



BA

 

[KootK]

Technically, you would need two additional sets of bolts on the other sides of the butt joints to get the shear back into those outer plies as you move towards the supports. Also, to the extent that there is moment at the butt splices, I still question the stiffness of a nailed/bolted moment connection in wood.

The greatest trick that bond stress ever pulled was convincing the world it didn't exist.

 

[BAretired]

You can add more bolts if you like, but I don't think it is necessary unless governed by shear. Plies 2 and 4 act as 7'-6" long simple spans and need bolts to transfer a reaction of 7.5w/4 to Plies 1 and 3 where w is the uniform load per foot on the 4 ply beam.

The moment at the splice point is close to zero because it is close to an inflection point, so the connection is not considered to be transferring any moment.

BA

 

[KootK]

We must be seeing this in quite different light BA. Are you considering the beam as two simple spans meeting at a common support? With only the two bolts that you've shown, you'd only have continuity in two of the plies over the center support, where one would expect the moment demand to be highest?

Also, was the ABC quote from Part 9?

The greatest trick that bond stress ever pulled was convincing the world it didn't exist.

 

[dhengr]

To add to KootK’s thoughts and observations list, 29AUG, 12:35....

2 cont.) We all know that when all else fails, ask the boss. So, that’s not lame, that’s just self preservation, and getting it straight from the horse’s mouth. Remember, when the boss is happy and involved, everyone else is happy too.

3,4,6 & 7) I essentially agree.

5 cont.) Your portal frame corner joint may have turner out to be a real educator, but it was probably also the worst (most difficult) possible case of trying to develop a moment in wood. You can induce quite a moment in that corner joint, with little effort, and you only have about a 6"x6" face area into which to place the locking nails or hardware; small moment lever arms btwn. fasteners and can’t get a enough nails in that area, edge dist. and splitting, etc. I think our problem here is slightly different since the individual members are aligned, and we have a much longer distance over which to place nails and start to develop a moment transfer/shear transfer. And still, the moment transfer is not exactly the same, and that’s where your ‘do they deflect together, if so they all carry load approx. equally’ comes into play. We aren’t really transferring moment at the butt splice, we are transferring load or shear all along the members to make them act in unison, and need to add some extra fasteners around the butt joints to try to control their differential movement at those joints.

At the neg. moment, you are not really providing moment continuity at the butt joint, and the moment is low there in any case. You are transferring load or shear through the joint, out at 2' or 3' (or less lever arm as you move to the post) and this causes the spliced members to participate in the neg. moment cap’y over the post (i.e. taking their 85 or 90% of one quarter share). And, there will likely be some curvature/deflection (irregularity/discontinuity) in the immediate area of the butt joints. Thus, my guess is the max. neg. moment is probably carried by about 3 or 3.5 - 2x’s, not all 4. I would pretty much assume all 4 -2x’s acting at mid-span, because you have a longer dist. to develop their continuity from both directions.

8) The factors of safety and material strength reductions are really quite high in the wood codes because of the non-homogeneous nature of the material and the possibility of sizeable discrete defects. And, you have the normal plywd. or LVL redistribution of weak spots which lead to a stronger member. So, in part, they are probably working into our FoS.

9) Loading on top vs. hung loading from one side... In the first case we have a floor framing system and then a sheathed stud wall which loads the beam from the top, probably all four members fairly uniformly. Then, the stud wall acts kinda like a deep beam, and I’ve actually seen them span long distances when the beam or found. wall failed. I would watch large jamb loads which tend to concentrate loads and may change max. moments or shears. In the second case, your fastening system is having to transfer the whole load (lbs./lin.ft.) through the first beam element/ply into the other three to make them act in unison. Two pretty different connection problems.

10) BA’s ABC find should sound about right to all of us, an approx. point of contraflexure. The moments will be fairly low in that span length region, and the shear stress will only be about half of the max. shear at the reaction points, and as mentioned above shear usually is not critical anyway.

I would pay some attention to the potential for unbalanced loading and see how that might move the shear diagrams and moment diagrams around at the butt splice points. In this regard it would be helpful if Ajk1 would provide those load, shear and moment diags. since he’s been doing the calcs. Then also the member calcs., stresses, etc., at mid-spans, over the middle post and the max. shears at reactions. I’m not going to do them. What does the bending stress vs. allowables look like at mid-span Bm. #2 and at the negative moment? What about horiz. shear at the worst reactions? And, what are the moments and shears at the butt splices, for comparison?

 

[BAretired]

We must be seeing this in quite different light BA. Are you considering the beam as two simple spans meeting at a common support? With only the two bolts that you've shown, you'd only have continuity in two of the plies over the center support, where one would expect the moment demand to be highest?

Also, was the ABC quote from Part 9?

I agree with what dhengr stated above. The beam is semi continuous. There may be an effective section of 3 or 3.5 plies resisting the negative moment at the central support.

If there were no nails between plies, each ply would deflect separately. Ply 2 and 4 would act like a simple span of about 8'. Their left reaction would produce a concentrated load on plies 1 and 3 which would deflect relative to plies 2A and 4A. So the 3' long cantilever of plies 2A and 4A would tend to hog the uniform load from plies 1 and 3, partially compensating for the concentrated load mentioned above.

There probably are nails between plies, so the above is a worst case scenario. A regular spacing of nails between plies will tend to improve the performance. Butt joints are not and should not be considered capable of carrying moment.

Finally, the ABC quote was indeed from Part 9.

BA

 

[KootK]

All summed up, I would say that we can all agree that the fastening of the plies is quite important to the assumption of load sharing. And to bring it back to AJK's original point, force transfer at the butt joint seems as though it would require consideration of localized nailing to transfer at least shear, if not moment. That's not what I see in the field however. And I'm not aware of any code guidance for ply fastening other than generic "two rows at __ o/c" kind of stuff. If designers are supposed to be giving it special attention, I don't see that either. I still see a problem here.

The greatest trick that bond stress ever pulled was convincing the world it didn't exist.

 

[BAretired]

I agree that fastening of the plies is important, particularly at the end of ply 2 and 4.

I just had a quick look at Wood Design Manual 2001 in the "Built-Up Beam Selection Tables". For No.1/No.2 SPF, a 4 ply 38x286 (2"x12") beam has a factored resistance of Mr = 24.2kn-m (17,860'#) and Vr = 28.7kN (6,460#). That does not seem adequate for the factored loads given, even if all plies were fully continuous over the two spans.



BA

 

[ajk1]

If all 4 plies are equally effective, and the beam +ve and -ve moments are determined based on continuity, and accounting for the preservative treatment incisions (Kt=0.75), Woodworks says that the beam is over-stressed in flexure by 33%. Woodworks puts pattern loading on. The maximum positive and negative moments are very nearly equal.

There is significant moment at the splice point, but this can be taken by 2 of the 4 plies, without over-stress. However, the moment that should be used for this check should perhaps be a little further out than the actual splice point.

I agree with much of what you both say. I have the Woodwporks output at the office but I will try to retrieve it here at home and send it soon.

I do not find in NBC 2010, the clause BAretired notes is in 9.23.9.1.3 of the Alberta Code. What is the title associated with clause 9.23.9 in the Alberta Code? I do recall reading something like that, somewhere, but as I live in Ontario, it would not have been in the Alberta Code. I will continue searching for it.

 

[KootK]

You got repetitive member in there too AJK? That might help make up a little ground.

The greatest trick that bond stress ever pulled was convincing the world it didn't exist.

 

[ajk1]

What do you mean by "repetitive member"?

 

[KootK]

If you have three or more of the same members sharing load, and they're not spaced too far apart, you get a nice little bump on you allowable stress. It applies to multi-ply beams. If your using wood works, you're probably taking advantage of this automatically.

The greatest trick that bond stress ever pulled was convincing the world it didn't exist.

 

[ajk1]

yes i believe so.

 

[OldPaperMaker]

ajk1,
Is there some reason that haven't mentioned adding a new footing and post either at mid span or under the spliced plys? This may reduce the stress enough so that two plys will definately handle the loads.

 

[BAretired]

ajk1,

I don't have the latest code, but I am attaching an excerpt from ABC 2006, Part 9 with the paragraph I quoted earlier.

An extra support suggested by OldPaperMaker might be the easiest solution.

BA