Wood shear wall deflection / stiffness analysis

[jeffandmike]

It is my understanding that with a flexible (horizontal) wood diaphragm and wood framed shearwalls (assume we're using segmented shearwall design), forces are distributed to each shearwall in a wall line based on tributary area. My question is, what if each wall in the same wall line has a different calculated (theoretical) deflection?

Won't the force try to redistribute to the stiffest wall (one with the least deflection), assuming the tops of all walls in the line are tied together with a double top plate and correctly constructed splices (as is typically the case)? If that's correct, then shouldn't the forces be redistributed based on stiffness?

My second question is, assuming we don't redistribute based on stiffness, what is the total deflection of the wall line? Is it reasonable to take the average of all of the deflections?

Thanks in advance for any help / explanation you are able to provide.

 

[JAE]

Could you clarify your terms for me? Do you mean by "wall line" a line of walls in the same plane, with the lateral force in that same plane?

If so, and all the walls tied together by a collector, their deflection would be similar and the force in each wall distributed relative to their individual stiffnesses. (must follow Hooke's Law).

The tributary distribution for flexible diaphragms is utiiized for the distribution of lateral forces for various shearwalls across the diaphragm (i.e. not in the same plane but oriented in the same direction such as two walls - one at each end of a diaprhagm).

 

[jeffandmike]

Yes, by "wall line", I am referring to a line of walls in the same plane, with the lateral force in that same plane.

I am curious if it is common practice among engineering firms to distribute based on relative stiffness for wood framed shearwalls (within the same wall line or plane) and flexible wood diaphragms?

I know the equations for calculating deflection can be complex and then a few iterations are required to correctly design the shearwalls. This method may also require utilizing different shearwall detailing throughout the wall line (i.e. edge nailing, sheathing thickness, etc.) A majority of engineers in our firm (at this point) have opted to distribute based on tributary area (again, talking about walls in the same wall line).

It is my understanding that this is the most common method for distributing the lateral forces (in this instance). I have the book entitled "Design of Wood Structures, 3rd Ed." (Breyer) and on page 511, he goes through an example similar to the one we are looking at. He doesn't calculate deflections (stiffnesses) and it appears that he is distributing based on tributary area (again within the same wall line or plane).

In addition, APA puts out a publication called "Diaphragms and Shearwalls" (L350G.pdf, can be found at

http://www.apawood.org/level_c.cfm?content=pub_searchresults&pK=diaphragm&pT=Yes&pD=Yes&pF=Yes)

where they go through some sample designs (starting on page 18). They appear to distribute based on tributary area as well. They do calculate deflections but never go back and redistribute based on stiffnesses.

Any thoughts?

 

[JAE]

I would say that the stiffness of a wood sheathed shearwall may be complex, but it probably, generally, follows linearly with the length of the shearwall (assuming the same height throughout).

If this is true, then if the walls have a common, consistent collector, the lateral deflection of the tops of the walls are about the same. If they are about the same, then the force required to deflect each wall is proportional to its length. For longer walls, the force would be higher.

That said, wood structures are quite flexible and forgiving and the distribution of forces through a diaphragm probably do not behave as a rigid diaphragm.

One thought, and I add this because most designs aren't sensitive to a moderate amount of overdesign, would be to look at it both ways to get a feel for the sensitivity of your assumption - tributary distribution vs. stiffness/length distribution.

Your collectors, shearwalls, and subsequent foundations all would have a range of values that would give you a feel for how much effect this question really creates.

It may be a lot of time over a minimal amount of variance.

 

[jeffandmike]

Sounds reasonable to me. Thanks for your help.

 

[rope]

There is an ICBO publication titled SEISMIC DESIGN MANUAL, VOLUME 2". The book has detailed examples on plywood shear walls using flex dist of shear and shear by relative rigidity of wall element. The book is available on the ICBO website.