Volume Effect Factor

[Triangled]

I have a double cantilevered glulam girder with 9' left cantilever and 9' right cantilever and 35.5' between columns for a total length of 53.5'
The moment diagrams for 3 cases (no snow) is attached, case 1 - TL everywhere, case 2 - TL at span (between columns) and DL only at cantilever (and roof supported by cantilever), case 3 - TL at cantilevers and DL only between columns.
My question is, what is proper length to use for Volume Effect Factor C[sub]V[/sub]?

 

[JAE]

Not sure how to interpret "distance between points of zero moment".

The NDS commentary (2015 Edition) for section 5.3.6 refers to ASTM D3737 as the source of the equation so you might have to start there.



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[Shotzie]

If this is analogous to the KZbg (size factor) from the CSA O86-14 wood code then the notes for L are as follows:

The length "L" to be used in the size factor equation is the length of the beam segment from point of zero moment to point of zero moment. This defines the length of the tension zone. For simple span beams, "L" is equal to the beam length. For beams with one or more points of inflection (typically multi-span and cantilever beams) there exists more than one beam segment. In these cases "L" is less than the overall beam length. The moment resistance, as modified by KZbg, must be calculated for each beam segment and compared to the maximum factored moment within that segment. The size factor, KZbg, is not to be applied cumulatively with the lateral stability factor KL. The size factor is associated with stresses on the tension side of the beam, whereas the lateral stability factor is associated with stresses on the compression side of the beam.

 

[Triangled]

JAE, that is exactly the question.

Shotzie, that is exactly the interpretation I thought.

So, please consider this interesting situation. In my case, the L for C[sub]V[/sub] should be the full beam length tip to tip including both cantilevers and column to column span, 53.5', which, in my case yields C[sub]V[/sub] = 0.806. If, however, I added a large enough point load midspan between the columns, sufficient to make the positive moment just a bit larger than zero, then the L for CV would by (say) half the full beam length, say 26.75', and would yield in my case CV = 0.864. My beam, by adding weight, becomes capable of carrying more weight. Or maybe I had too much to drink last night :-/

 

[kissymoose]

How about having a different volume factor for each load combination?
Though, even if you do, that cantilever TL/span DL combo looks like it controls no matter what. I'd be probably use the full 49.5ft length to find C_V as the moment doesn't get close to 0 at mid-span.
I tried a couple scenarios in mathcad, guessing the sizes, and it looks like it's less than a 3.5% difference between using L=full span and L=half span.

 

[kissymoose]

Just saw your response after I submitted mine. I'll say your example makes sense to me. Put a point load in the middle, take the tension out of the bottom laminates, and you've got a slight increase in their ability to support load.
Intuitively it seems like a parabolic moment is easier on the beam than a constant moment, like the Cb factor of steel design, even if the decreasing moment never reaches 0, but code-wise, it states "between points of zero moment." I'd prefer to just take L as full span instead taking the time, and money for the ASTM standard, to get a 5% increase.