Biaxial Bending in a Glulam Beam
Biaxial Bending in a Glulam Beam
(OP)
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 fbx/FbE in the second term.
Would the Fbe term be computed with E'y min or E'x min?
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 fbx/FbE 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
www.medeek.com






RE: Biaxial Bending in a Glulam Beam
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
www.medeek.com
RE: Biaxial Bending in a Glulam Beam
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?
RE: Biaxial Bending in a Glulam Beam
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
RE: Biaxial Bending in a Glulam Beam
A confused student is a good student.
Nathaniel P. Wilkerson, PE
www.medeek.com
RE: Biaxial Bending in a Glulam Beam
A confused student is a good student.
Nathaniel P. Wilkerson, PE
www.medeek.com
RE: Biaxial Bending in a Glulam Beam
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.
RE: Biaxial Bending in a Glulam Beam
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
www.medeek.com
RE: Biaxial Bending in a Glulam Beam
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.
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.
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.
RE: Biaxial Bending in a Glulam Beam
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
www.medeek.com
RE: Biaxial Bending in a Glulam Beam
RE: Biaxial Bending in a Glulam Beam
A confused student is a good student.
Nathaniel P. Wilkerson, PE
www.medeek.com
RE: Biaxial Bending in a Glulam Beam
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....
RE: Biaxial Bending in a Glulam Beam
A confused student is a good student.
Nathaniel P. Wilkerson, PE
www.medeek.com
RE: Biaxial Bending in a Glulam Beam
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.
RE: Biaxial Bending in a Glulam Beam
RE: Biaxial Bending in a Glulam Beam
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
www.medeek.com
RE: Biaxial Bending in a Glulam Beam
RE: Biaxial Bending in a Glulam Beam
A confused student is a good student.
Nathaniel P. Wilkerson, PE
www.medeek.com
RE: Biaxial Bending in a Glulam Beam
A confused student is a good student.
Nathaniel P. Wilkerson, PE
www.medeek.com
RE: Biaxial Bending in a Glulam Beam
by solving some of the problems from Structural Wood Design Solved Example Problems, AWC, 2005 Edition.
Problem #7 - Glulam Beam subjected to bi-axial bending: No axial load, torsion is ignored... Eqn. used is 3.9-3 with first term zero.
Problem #13 - Beam-Column, Sawn Lumber subjected to axial load + Major axis bending..... Eqn. used is 3.9-3 with third term zero.
Problem #14 - Continuation of Problem #13, Beam-Column subjected to eccentric loading in combination with other loads...
......... Eqn. used is 15.4.1 with all three terms non-zero. The calculations are exhaustive...
The code distinguishes between bending caused by eccenticity of axial load and bending caused by
loading acting on the sides of wood members......
For calculating CL about strong axis (X), use Emin about minor axis - Eymin.
Dropped-down header over garage opening needs to be designed for bi-axial bending when subjected to wind.......