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Plywood Diaphragm Deflection Derivation NDS

Plywood Diaphragm Deflection Derivation NDS

Plywood Diaphragm Deflection Derivation NDS

(OP)
I am trying to model a wood diaphragm as a semi-rigid diaphragm. To do this I need to convert the G_a apparent shear stiffness from NDS to a material shear stiffness G. I have done this with metal decks, but am running into a problem with plywood.

Variables defined in NDS:
v = force per unit length on the diaphragm as a simply supported beam
L = length of said diaphragm-as-beam

To determine shear deflection of a simply supported diaphragm (as NDS assumes) I integrate shear strain over half the length and get vL^2/(8GA) (I am assuming stress is distributed evenly based on seismic loads originating in the field of the diaphragm.)
Neglecting kip to pound conversions for the time being, the middle term of the NDS equation is vL/(4G_a)

Set the 2 equal, vL/(4G_a) = vL^2/(8GA) → G_a = 2GA/L = 2Gt(W/L)
Since thickness is accounted for in the NDS tables, G_a is related to G by a factor of 2 times the diaphragm aspect ratio.

Does the NDS really assume an aspect ratio L:W = 2:1 for deflection calcs? Seems odd, especially considering the limit for blocked diaphragms is 4:1.

Am I missing something, mistaken in my calcs, or does this seem correct?

RE: Plywood Diaphragm Deflection Derivation NDS

(OP)
Anyone have an opinion on this?

RE: Plywood Diaphragm Deflection Derivation NDS

From ATC 7 A.1.3:

Δs = [F w L2] / [16 G t b]

F = a form factor: 2 for uniform shear distribution
b = depth of the diaphragm
w = 2 v b / L

Substituting and cancelling:

Δs = [v L] / [4 G t]

However, why wouldn't you use the apparent shear stiffness factor Ga directly to account for both web shear and nail slip deflections?

RE: Plywood Diaphragm Deflection Derivation NDS

(OP)
"w = 2 v b / L"

I am not familiar with what ATC is.
What are "w" and "v" in your equation?

Looks like depth of diaphragm is accounted for in that equation unlike the NDS equation I posted above?

RE: Plywood Diaphragm Deflection Derivation NDS

Link. The other terms are conventional so didn’t think to define them. w is the uniform line load acting on the diaphragm. v is the max unit shear in the diaphragm. The equation for w above is the typical v=V/Depth equation solved for w. Yes, the derivation for the NDS equation in my post above shows that it applies to any simple span diaphragm regardless of span to depth ratio. Out of curiousity, how will you account for nail slip in your model if using G rather than Ga?

RE: Plywood Diaphragm Deflection Derivation NDS

(OP)
Ah perhaps that was where I got confused. I have never heard this "v" term. The NDS defines it as "induced unit shear in diaphragm" and no explanation even in the commentary. I assumed it was the shear per unit length as a beam, not max shear per unit depth. Hence I was equating a term with v being unit shear per length (the same equation as your equation) with an equation using v to mean shear per unit depth.

One would think the code would define terms unambiguously. I originally was trying to derive it BECAUSE it was unclear. I wonder how many people read that definition and pick the wrong meaning. Shear per depth vs length.

Edit to add:
G_a already accounts for nail slip. Therefore when converting from G_a to a shear stiffness G input into a model, that also accounts for nail slip. Look up G_a, apply conversion (turns out to be G=G_a/t), input the equivalent G into software.

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