relative rigidity of wood shear walls 1

[SLTA]

I am looking for some clarification on determining the relative rigidity of wood shear walls. For argument's sake let's assume that the walls are identical except for length, that they meet the code-required aspect ratios, and that the diaphragm is rigid.

I've seen several threads on here where folks say the relative rigidity is directly proportional to the inverse of the deflection, and thus linearly proportional to the the length of the wall. I can understand that from the deflection equations in Chapter 23 of the IBC. However, that isn't the result I find when looking at a simple model in Enercalc - it's more like proportional to L^3, which is suggested by the equations I found for a rigid diaphragm. (Also for argument's sake, ignoring torsion of the walls.)

Why are the expected and computed values so different? Are shear walls proportional to their length, or L^3?

 

[Lion06]

You are right, it is L^3. I would note, however, that this is true regardless of a rigid or flexible diaphragm. The type of diaphragm only determines the distribution of forces, it does not change the relative rigidities. That being said, the relative rigidities aren't that improtant with a flexible diaphragm.

 

[SLTA]

Thanks, that's a good reminder about the rigidities not changing. So where in the formula in the code do I get the L^3? I feel like I'm missing something basic...

IBC 2006, Eq. 23-2 in Section 2305.3.2

 

[JAE]

slta,

wood shearwalls are more proportional, generally, to length, not L^3. This due to generally longer length, shorter height walls.

A shearwall (of any type) will deflect D when subjected to a lateral load.

D is based upon two types of distortion.
1. Shear distortion within the plane of the sheathing.
2. Flexural distortion due to axial compression and tension in the studs.

The attached sketch offers some deflection formulae for these two types and shows that the total deflection, D, of a shearwall is the sum of Dv plus Df.

So the true answer is that wood shearwalls have rigidities that depend on something between L and L^3. For a short height, longer shear wall, the shear distortion would tend to govern the stiffness. For walls with tall heights, and short lengths, the flexural distortion would have more influence.

 

[SLTA]

Excellent description, JAE. I get it!