Biaxial Bending in a Glulam Beam 1

[medeek]

Let's assume I've got a larger garage door header (16' span) that is dropped down from the ceiling about 5', on the gable end of the garage. It's going to pick up certain amount of dead load and snow load from the roof, not much but some. If one were to simply look at the vertical loads the header size could be quite small, maybe a 4x12 DF No. 2 would be typical.

Now if I add in a C&C wind load that is perpendicular to the wall and assign some of the load to this header via the pony wall above it I have a beam that is loaded in biaxial bending.

I typically use Forte for a lot of my quick beam and header calcs but it does not let one apply a out-of-plane load to a glulam header. I am wondering if anyone has any suggestions for a different app/program that can calculate biaxial bending in glulam beams and headers. I contacted Woodworks and their sizer program also does not do biaxial bending or loads.

On that same note I was thinking about writing my own spreadsheet/program that will do the calculations but then it occurred to me that I don't actually know what equation to use for pure biaxial bending (no compression or tension axial loads combined). Do I use equation 3.9-3 with the first term disappearing or would it be more appropriate to use equation C3.9.2-1 with its first term disappearing? Notice the slightly different result since the first option would include f_bx/F_bE in the second term.

Would the Fbe term be computed with E'_{y min} or E'_{x min}?



A confused student is a good student.
Nathaniel P. Wilkerson, PE

http://www.medeek.com

 

[medeek]

My current beam calculator only checks gravity loads. I run the following checks:

1.) Bearing/Reactions
2.) Shear
3.) Bending
4.) Deflection LL/TL

For biaxial I would run these same checks and also:

5.) Lateral Reactions
6.) Lateral Shear
7.) Lateral Bending
8.) Lateral Deflection (this will typically be a lateral wind load so 42% of the lateral wind load can be used per IBC table 1604.3 footnote f).
9.) Combined Bi-Axial Bending

A confused student is a good student.
Nathaniel P. Wilkerson, PE

http://www.medeek.com

 

[XR250]

The most I ever heck on these is vertical deflection and bending stress and out-of-plane deflection.
These things just seem to work. Typically on large residential spans, deflection is going to control most designs anyway.
Has anyone ever seen a failure?

 

[dik]

Try to eliminate any biaxial condition if possible is the easy solution.

Can you increase the connection of your header connection to the glulam column to accommodate any moment to eliminate/minimise any eccentricity for flexure about the weak axis and biaxial condition? Is the glulam column laterally supported by any wall sheathing?

A biaxial condition with an isotropic condition is pretty tricky, and I'm not sure how an orthotropic material like wood would behave.

Dik

 

[medeek]

Does anyone check the biaxial condition on headers like I do? Maybe I'm overthinking this?

A confused student is a good student.
Nathaniel P. Wilkerson, PE

http://www.medeek.com

 

[medeek]

I'm also thinking equation 3.9-3 would be the more appropriate equation to use since it includes the buckling effect.

A confused student is a good student.
Nathaniel P. Wilkerson, PE

http://www.medeek.com

 

[KootK]

Does anyone check the biaxial condition on headers like I do?

Not that I've seen. I do it a couple of times each year when sanity starts to get dull. Sometimes, if you get creative, you can pull some proverbial rabbits from some proverbial hats. Here, try this:

1) Vertically, don't worry about any load other than dead load. Even sheathed with butter cup petals, your gable will probably be stiff and strong enough to span on its own. Even the dead load is questionable when you consider the 5' chuck of wall acting as essentially a box beam.

2) Use 2.5' as your wind trib width. Garage doors span horizontally.

3) Add in the stiffening / strengthening of couple of continuous 2x6 Plates.




I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[medeek]

@KootK

The gable end truss sheathed out probably is quite stiff with all of its vertical members, your right it can probably support its own weight. I guess I could just run a bending check on the header with only the wind loads, essentially loading the beam in plank orientation.

Technically the trib width is 2.5' however I like to use at least 5' (the full pony wall height) since I don't like to rely upon the ceiling diaphragm to provide any lateral support, this is probably conservative in some cases. However, if there is no drywall (ie. detached garage) and the proper angled bracing has not been installed per my gable end bracing detail (more likely than not) then I don't feel that this is conservative but probably the opposite. Then some of the trib width of the gable truss area will also be felt by the header as well as the full pony wall height.

The double top plate does add to the lateral strength, especially when the headers are 4x members. However if you figure that a splice will probably occur somewhere in the center region of the header span this additional strength/stiffness will be compromised. Out of curiosity I would be interested to know what the moment capacity of a typical 48" double top chord splice is given the number of 16d nails on each side of the splice. My diaphragm spreadsheet checks the tension in the splice connection but not the moment capacity since this is typically not a factor in the design (ie. roof for floor diaphragm is proving the moment capacity). This would be one of those group of fasteners things and would depend on some of the geometry, a 2x6 splice would be a bit more stiff than a 2x4 splice would be my guess.

A confused student is a good student.
Nathaniel P. Wilkerson, PE

http://www.medeek.com

 

[KootK]

That's the thing though: if you make a bunch of compounding conservative choices along the way, things that do work out in the wild appear not to on paper. So your choices become:

1) Dig deep, trust your builder, and express your assumptions and requirements in the construction documents.

2) Play the over thinking card and stick your head in the sand.

I do #2 sometimes when I have to but vastly prefer #1.

However, if there is no drywall (ie. detached garage) and the proper angled bracing has not been installed per my gable end bracing detail (more likely than not) then I don't feel that this is conservative but probably the opposite. Then some of the trib width of the gable truss area will also be felt by the header as well as the full pony wall height.

The much more substantial wind load on the garage door ultimately goes out to the king studs and up to that same gable truss / top plate joint. If there's no bracing at that joint, you're screwed as far as any kind of quantitative justification goes. So I say plan for the bracing and maximize your use of it.

However if you figure that a splice will probably occur somewhere in the center region of the header span this additional strength/stiffness will be compromised.

Strength will be compromised but stiffness, which will be more critical, probably will not. For lateral effects, most any nailing patter in the plates will result in their going along for the ride and thus stiffening things up. Perhaps ask for there to be no plate splices in the middle 8'/12'/whatever you can get away with.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[medeek]

I just see a lot of wimpy headers. If I've got a 16' garage door a 4x12 header is undersized, especially when you start putting a pony wall above it, that is my gut feeling. If you apply lateral loading to these headers on their weak axis you end up failing in bending and deflections are often unacceptable. The numbers work fine if you just look at the vertical loads since there is virtually nothing on the gable ends typically.

Your absolutely right on the gable bracing though, if its not there the wind loading on the gable wall and truss pretty much trash any of my quantitative logic expressed thus far. So I guess you need to assume it is there which means the trib width to the header is only half the pony wall height and that makes things more manageable.

A confused student is a good student.
Nathaniel P. Wilkerson, PE

http://www.medeek.com

 

[rn14]

My experience is that most don't look at the biaxial condition. Many don't even look at the out of plane load actually (I do because I'm a nervous Nelly). By the time you use load duration factors, flat use factor, etc, it seams to not usually be an issue except in special cases.

 

[medeek]

In most cases the header is usually quite close or against the bottom of the trusses and inline with the ceiling diaphragm so your right it is usually not an issue. However, most of the residences I look at are in Ocean Shores with a 155 mph (ultimate) windspeed so the the out of plane loading on walls and large spanning members is something I never want to ignore.

A confused student is a good student.
Nathaniel P. Wilkerson, PE

http://www.medeek.com

 

[Triangled]

1. I'd definitely check biaxial bending
2. the equation you indicated seems correct to me. Essentially the 2 bending stresses are additive in the lower leeward corner, as I understand it. But maybe I'm missing something?
3. The trick is, if you use glulam, getting the specification right. In the weak direction, of course, there are multiple lams of varying strengths all loaded individually in their strong directions. I am pretty sure the load tables show all of this, i'd just work through it carefully.
4. If my stresses were close to the allowables, I'd take into consideration all of the above construction realities as to whether I should retain my design or beef it up.
5. If you use glulam, APA-EWS is a fine resource. They even have a help desk to answer technical questions, at least they used to....

 

[medeek]

The AWC supplement gives bending values for glulams F_bx and F_by for both axis. One can quickly notice that the F_by value (about the weak axis) is typically lower. Is there something beyond these values from table 5A that I should be using?

A confused student is a good student.
Nathaniel P. Wilkerson, PE

http://www.medeek.com

 

[Triangled]

i don't have tables in front of me, but, if you have Fb x and y, you should be good to go.
Just a philosophical thought... there is a thread of logic that might induce a tendency to conservatism in this kind of calc, as follows:
as i recall ( and i don't have me books in front of me) weak axis, plank-wise, bending is generally allowed (all things being equal) higher extreme fiber bending stresses than strong axis extreme fiber bending stresses, i suppose because there are a lot more of them, and, wood being wood, the more the better hence repetitive stress increases etc. To put it the other way, the fewer the fibers in tension, the lesser the allowable. In biaxial bending, we have pretty much just one fiber in that case.

 

[Triangled]

Your glulam Fby's for typical combinations are probably lower due to the multiple variations of wood strengths in the various laminations, strongest laminations defining FBx being reserved for the outer lamination(s). For Fby, they'd have to do some kinda weird statistical thingamajig accounting for laminations with strengths varying from high to low. I have little doubt that there exists a glulam specification that is designed to accommodate significant weak axis bending.... here is a cool visual of what's going on with glulam combinations

http://www.americanlaminators.com/layup.html

 

[medeek]

If you look at the combined stress state of biaxial bending you end up with one corner of the beam that has a higher stress (tension and compression) that the rest of the beam fibers. The stresses are additive as you stated. Perhaps this graphic I created in SketchUp illustrates this point:

The neutral axis for a biaxially loaded beam is skewed or inclined at some angle as shown.



A confused student is a good student.
Nathaniel P. Wilkerson, PE

http://www.medeek.com

 

[Triangled]

Cool illustrations

 

[medeek]

If the stress magnitude is equal for both axis then the neutral axis will extend from corner to corner along the beams diagonal. Not that any of this really matters but it is some interesting observations.

A confused student is a good student.
Nathaniel P. Wilkerson, PE

http://www.medeek.com

 

[medeek]

Combining an axial load with the biaxial bending yields a stress distribution(s) like the following:

A confused student is a good student.
Nathaniel P. Wilkerson, PE

http://www.medeek.com