definition of "b" in slenderness ratio

[bjb]

In the 2001 NDS, equation 3.3-5, if you have a multi-ply beam, is the value of "b" to be used only the width of an individual ply or the total width of the built-up beam?

It seems to me that if the plies are well connected that "b" should be the width of the builtup beam. On the other hand, when it comes to the column stability factor, you can use the total width of the builtup column, but then have to reduce the Cp factor by 0.6 or 0.75 depending on if you nail or bolt the plies together. I see nothing in the NDS that addresses builtup beams.

I think that with a beam, normally the bending moment is not constant, so the compression force in the unsupported compression edge is not constant, and therefore some portions of the beam have less tendency to buckle than other more highly stressed areas. In a typical wood column the compressive force is usually constant between points of lateral support. Maybe this is a way to rationalize using the full width of a builtup wood beam without a reduction factor.

 

[JAE]

b is the total width of the built-up beam, assuming the plies are nailed per the specification and assuming the built-up reduction factors are applied.

 

[bjb]

Thank you JAE.

Are you saying that if you nail the plies of a built-up beam together per 15.3.3 of the 2001 NDS you would then multiply Cl by 0.6, according to 15.3.2 of the 2001 NDS?

In the past I have handled built-up beams as individual plies and considered its strength as the sum of the parts to be conservative. I would base my slenderness ratio on an individual ply, and figure out the allowable stress for that ply. The strength of my beam would then be the the strength of the one ply multiplied by the number of plies.

 

[JAE]

That is a very conservative way to go. The sum of the parts, if nailed together properly, OR - if sheathing prevents lateral buckling of the individual plies - then the built-up shape works as one shape....with the nailing only, for columns, we use the reduction factor for built-up shapes. With sheathing, we just treat the built-up column as a single shape.

 

[bjb]

That makes sense. I am not clear though, do you use a reduction factor on built-up beams or only on unsheathed built-up columns?

I actually just received a call from someone at trus joist where they said that in the load tables in their catalog they take the approach of basing everything on a single ply and then summing the plies, but they said that in reality you could use the full width of the built-up shape. Their policy is to be very conservative with the values they publish in their catalog.

 

[JAE]

Well...for beams, if the pieces are each side by side (instead of on top of one another) and you have vertical bending, and you have no connection between the individual pieces, then yes, each "lamination" works side by side and the strength capacity is really the sum of the individual beams.

But if there is any connection at all, you can use the wider b which helps resist lateral buckling. Only minimal nailing is required here as the horizontal shear that is developed to resist the lateral movement of the "laminated" beam is small. And usually, you have floor or roof sheathing anyway, which ties them together and prevents lateral buckling.

If you have a beam going through air, with no sheathing, and its built-up - I would simply be more detailed in how its individual pieces are connected together and still use the full width "b". I don't think there is any reduction factor for beams like there is for columns.

 

[boo1]

A nice link for beam adjustment factors is:

http://jan.ucc.nau.edu/~dsl/egr437/class/woodbeams/adjust.html