Wood Beam Stability Factor for Multi-Ply Beam 2

[MJC6125]

If a multi-ply wood beam is unbraced for lateral torsional buckling, how do y'all calculate the beam stability factor for this beam, like a (4) 1 3/4" x 16" LVL? Do you consider the entire built-up 'composite' beam, thus when you calculate Rb=sqrt((le*d/b^2)) per equation 3.3-5 of the NDS, b=4*1.75 = 7 in? Do you use the individual beam ply for calculating Rb, b = 1.75 in? Or do you try to do something in between (ForteWeb appears to use the following equation b,eff = b,single ply * (number of plys)^(1/3)). This is based on the weak-axis moment of interia, I, value of all the plys bending in the weak axis direction at the same time but sharing the load equally to each ply (not compositely).

I did find this previous post that discussed this question already:[URL unfurl="true"]https://www.eng-tips.com/viewthread.cfm?qid=433798[/url] There is some info in there that says "Research has shown that nailed and bolted beams have at most 30% composite action effect in terms of resisting torsional buckling, so. It is recommended to use single ply width unless adhesives are used to laminate the members together." I doubt I'll find any new answers this time, but I figured it's worth asking. And the ForteWeb approach is something that was not mentioned in that older post.

 

[DaveAtkins]

I assume the multi ply beam width is the width of the entire section, but it appears this is not supported by research.

In wood design, I find there are times when "what is normally done" is difficult to justify with calculations. I use my engineering judgment, and tend to be a lot more liberal with assumptions in wood design than in the design of concrete, masonry or steel.

DaveAtkins

 

[SE2607]

...and tend to be a lot more liberal with assumptions in wood design than in the design of concrete, masonry or steel

Why?

 

[XR250]

For me it is because wood is generally a lot stronger than we give it credit for, the dead load of the structures is generally low in relation to the design live load (which almost never occurs - except for snow) and there is many redundancies that we do not account for. And historically, they perform well without us pesky engineers getting involved.

 

[phamENG]

I wonder if it would be appropriate to apply a sort of K_f factor similar to built up wood columns. Now, nails for a column gives you 60% of the capacity rather than 30% (and bolts gives you 75%), so it may not be a 1-to-1...but it's accounting for the same thing: composite action in weak axis bending to resist instability.

 

[DaveAtkins]

SE2607,

I have designed a lot of multi story apartment buildings and one story wood buildings. I have found if you don't find creative ways to justify how these structures are built, you end up asking the contractor to do things which are not typically done.

I am not saying I let things go that are clearly wrong. I am saying in cases like this one, where research says you technically don't have a truly composite member, but these headers seem to work anyway, I accept the ambiguity.

DaveAtkins

 

[Eng16080]

This is one of those frustrating gray areas where there can be a huge difference in member capacity depending on which approach you use. Obviously, it's best to provide lateral bracing at a reasonable interval for all beams whenever possible. The typical window/door header, however, is a common scenario where there is often no lateral bracing along the beam length.

Running an analysis of a triple 2x12 header beam spanning 10' (using Woodworks), CL = 0.989 when the 3 plies are assumed to act as one single piece, and CL = 0.555 when each ply acts individually. The difference in beam capacity is nearly 50 percent.

Personally, I'm not sure how to make an engineering judgement decision on this. While under most circumstances it seems unlikely that a multi-ply beam would be connected sufficiently to act as a single piece, it also seems unlikely that the buckling resistance would be no greater than that of a single ply acting alone. I suppose the real answer is somewhere between. Perhaps if the multi-ply beam was connected as it would need to be to resist a bending force in the weak axis (with the connections adequate to transfer shear between the plies), that would justify using the full width.

With all that said, if, after careful contemplation, you were to use the most conservative approach here, an unfortunate downside on the business end is that you'll now need to explain to every builder why your competition calls for a triple 2x12 header beam but you require something more substantial.

A couple other thoughts (since I'm basically just rambling at this point):
[ol 1]
[li]I believe the Canadian code does require that only a single ply be considered in the analysis, or at least I recall reading that the Canadian version of Woodworks defaults to a single ply.[/li]
[li]If you were to use a single ply and were finding it difficult to get window/door headers to work, one alternative is to place the header at the top of the wall, where it can be considered as laterally braced by the floor framing above.[/li]
[/ol]

 

[phamENG]

In the absence of formal 'guidance' from leading wood industry groups, I think assuming a K_f=0.5 and applying it to C_L in the same way we apply it to C_pis reasonable.

Here's how I get there:

F_b'=F_b x C_L* x K_f (Where C_L* is C_L without this reduction factor).
M_a=F_b' x S

M_a >= w x l_max²/8

So...

F_b x C_L* x K_f >= w x l_max²/8 x S

From this we can tell that K_f is proportional to l_max².

Going back to the 'what is normally done'...look at the footnotes to the beam/header table in the IRC.

f.Spans are calculated assuming the top of the header or girder is laterally braced by perpendicular framing. Where the top of the header or girder is not laterally braced (for example, cripple studs bearing on the header), tabulated spans for headers consisting of 2 × 8, 2 × 10, or 2 × 12 sizes shall be multiplied by 0.70 or the header or girder shall be designed.

So if L has to be reduced by 0.7, that would be accomplished by reducing the beam stability factor by 0.49. This tracks pretty closely with Eng16080's figuring using wood works. It's more punitive, which is why they allow it to be 'designed'. I'd be interested to know how wood works calculates that.

 

[DaveAtkins]

I also sometimes do a mental exercise to imagine what might happen. Would the three plies really twist and slide independent of one another? Is there plywood or OSB on the outside face and GWB on the inside face which helps prevent twist?

There is usually a lot more going on than we consider.

DaveAtkins

 

[Eng16080]

I'd be interested to know how wood works calculates that.

Per NDS Section 3.3.3, in the calculation for RB, WoodWorks uses the value "b" equal to either the full width (4.5" per my example) or the width of a single ply (1.5" per my example) for the two options. There are no additional adjustments in the calculation for CL aside from that.

 

[SE2607]

I have designed a lot of multi story apartment buildings and one story wood buildings. I have found if you don't find creative ways to justify how these structures are built, you end up asking the contractor to do things which are not typically done.

I am not saying I let things go that are clearly wrong. I am saying in cases like this one, where research says you technically don't have a truly composite member, but these headers seem to work anyway, I accept the ambiguity.

As my 7th grade algebra teacher, Mr. Griswold often said: "Practice makes permanent."

 

[KootK]

We discussed this some back in 2017: Link

There, a member cited research indicating a very low level of composite action for torsional buckling.

Research has shown that nailed and bolted beams have at most 30% composite action effect in terms of resisting torsional buckling

Sadly, we never got our hands on the research so as to validate that but, if the sub 30% is accurate, that's getting pretty close to "why bother" territory.

Such a low value of composite action for torsional behavior wouldn't surprise me, however, as I suspect that it doesn't take much fastener shear slip to neuter a nice, St. Venant shear stress loop.

FWIW, I also echo Jayrod's preference for the detailing solution shown below when that is feasible.

 

[JoshPlumSE]

Such a low value of composite action for torsional behavior wouldn't surprise me, however, as I suspect that it doesn't take much fastener shear slip to neuter a nice, St. Venant shear stress loop.

I was going to say that how a treated a built up member like this would depend on how you connected them together. Nails, bolts, screws, glue?

If the this is just 4 LVL's sistered together, my thoughts would be:
1) Does one of the LVL's work for 1/4 of the load? If so, then we don't even need to have this discussion, you can connect them together anyway you like. But, they should still be connected together.

2) If the single LVL doesn't work with 1/4 of the load, then how overstressed is it. If it's less than 30%, then I would make sure that that I have enough nails in there to make me comfortable with the assumption that the sister joists can all work together.

3) Let's say the single LVL is more than 30% stressed under 1/4 the load. But, the built up section easily passes (no more than 75% of capacity). In that case, I would do everything I could to ensure that they act together. I wouldn't generally want them to be bolted. If they were, I might spec that they be glued together first. I don't think that glue should be that big of a cost riser. We use it a lot to prevent squeaky floors. Right?

4) If the only works when it's considered to be a single section of those built-up dimensions then I'd probably have to come up with another solution.

 

[skeletron]

CL 6.5.3.2.4 of CSA O86-19 states:
"For built-up beams consisting of 2 or more individual members of the same depth, the maximum ratio permitted in [the calculation for KL lateral stability factor] for laterally-unsupported members may be based on the total width of the beam, provided that the individual members are fastened together securely at intervals not exceeding 4x the depth. For other conditions, lateral support shall be provided at points of bearing to prevent lateral displacement and rotation and KL shall be determined in accordance with CL 7.5.6.4 [which requires calculation of a slenderness ratio, some sort of material stress ratio, and then a logic decision to determine the KL factor]"
No further explanation is provided in the commentary.

If you go through the exercise with 2x10, 2x12 material you'll see that 3 ply and above allow you to take the KL=1.0. The plys would need to be connected at abnormally large nailing intervals (37" and 45" o/c respectively), so I would usually just defer to something typical like 2-3 rows of nails @ 12", 16", or 24" o/c. The 2 ply beams can use KL=1.0 if the compressive edge is held in by decking or other provisions are provided (CL 6.5.3.2.3). Otherwise you get kicked over to the glulam clause (CL 7.5.6.4) for calculating the KL factor.

WoodWorks allows you to toggle between single-ply width or full member width in the design settings, but does not explicitly check the 2.5:1 ratio for you. However, if you use the single-ply width (conservative), I would expect the toggles from top edge and bottom edge bracing to also be representative of your situation. This will apply some reduction, but in most cases (joists @ 16" o/c on top or continuous decking) it would be 5-10% reduction in KL versus the prescriptive provisions to use KL=1.0.

The ultimate test would be to run through the span charts in Part 9 and back calculate the KL factor they use. I don't feel like doing that.

For LVLs, I approach this in a similar method to how @JoshPlumSE describes. However, I also use the prescriptive fastener installation patterns in TJ-9505 (page 16) and call it a day. I would bet that most site carpenters are nailing at 12" or 16" regardless because it's muscle memory. In many cases, I'll try to use a solid beam (PSL) rather than 3 or 4 ply, recognizing that the built-up LVL is easier to install but the PSL may take less labour and QA/QC.