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Re: Plywood rigid diaphragms

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Los Angeles has adopted a new voluntary ordinance called Division 93:
Voluntary Earthquake Hazard Reduction In Existing Wood Frame Residential
Buildings with Soft, Weak or Open Front Walls.   In this ordinance, you are
required to calculate shear wall deflections to show that the deflection is
less than .005H.   The shear wall deflection equation is from the UBC Volume
3.

Using this equation, the biggest part of the calculated shear wall deflection
is due to holdown slip (minimum 1/16" oversized hole in post for holdown
bolts, deflection of manufactured holdown base, shrinkage of lumber, crushing
of wood sill under vertical loads, etc).  Because of the holdown slip, the
plywood diaphragm will be rigid as compared to the the plywood shear walls.
The rigidity of the plywood diaphragm is going to primarily be based upon how
rigid the walls are.  In commercial buildings with masonry or concrete shear
walls, or steel braced frames, the deflection of the walls or braced frames
will be small compared to the plywood diaphragm, therefore the diaphragm will
behave flexibly.  

When you have wood shear walls, typically the architectural layout does not
allow for many walls because of all the openings for doors and windows.  In
residential construction (single family homes, apartments, small commercial,
etc), parallel shear walls may not be very far apart, say 30 or 40 feet, and
then the diaphragm length is 40 to 80 feet in the other direction.  When you
compare the deflection of  the most likely few shear walls along each edge of
the floor diaphragm with the deflection of the floor plywood diaphragm you
will probably see that the floor should be considered rigid.

Example:  For an 8 foot tall plywood shear wall (platform framing), the
allowable deflection is .005H = 8 x 12" x .005 = 0.48 inches under design
loads.  For an 8 foot tall masonry or concrete shear wall, wouldn't you expect
the deflection to be much less, say 0.05 inches.  With this type of shear wall
deflection, it may be easier to visualize how a plywood diaphragm is
considered to be rigid compared to the more flexible wood shear walls.

This becomes a nightmare when you try to distribute the load by rigidity
though, since you do not know the rigidity of the plywood shear walls,
primarily because of  the holdown slip and certain walls have more gravity
loads to resist overturning as opposed to other walls.  This then becomes an
iterative solution, since as you change the loading to a wall you change the
holdown size and therefore the holdown slip and deflection.  There are also
those codes which do not allow you to transfer forces by rotation when using a
wood diaphragm, sort of a catch 22, the plywood floor is rigid, but you can't
distribute the loads by rigidity. 

The holdown movement component for deflection (vertical displacement x (wall
height / wall length)) is the main component of the total shear wall
deflection.  On a 4x8 shear wall panel, the horizontal deflection due to just
the 1/16" oversized hole in the post is 0.125" (1/16 x (8/4) = 0.125") which
is 26% of the allowable for an 8 foot tall wall (0.125"/0.48"  = 26%).  When
you add in wood shrinkage and holdown deflection,  the deflection increases
furthur and you have not yet included the deflection from the rest of the
shear wall deflection equation ( wall bending, wall shear, nail slip).  The
situation becomes even worse when you calculate the deflection for the second
story shear walls, because of more deflection and slip of the holdown
assembly, now sitting on the wood floor instead of the concrete foundation.

Basically it seems the traditional holdowns do not work on short walls when
you try to limit the deflection to 0.005H, the wall has already exceed the
allowable deflection before the holdown sees any load.  In order to meet the
deflection criteria of 0.005H, the shear walls will have to probably be
longer, say 1:1 or 1:2 even for multistory buildings which won't go over very
well with architects.   The proprietary wood shear walls (Simpson Strong-Wall,
Shear Transfer Systems STS panel) appear to work well for one story
applications where wall aspect ratios are 2:1 or less since there design
values are based upon tests.  But, I personally would be cautious about using
them for a second floor shear wall, unless you reduce the allowable design
loads to account for the change in wood floor stiffness as compared to the
wall sitting on a concrete foundation.

I think the concerns are that if you design strictly by tributary area, you
may end up underdesigning certain walls.  In a simple box shaped building with
perimeter shear walls only, the short wall on one side is designed for 50
percent of the tributary area, the long wall on the other side is designed for
50% of the tributary area.  The short wall deflects (never sees the full 50%)
and the long wall now sees 70-100% of the load when it was actually just
designed for 50% of the load.  Now the question is how to come up with a
reasonable solution, which can be implemented within the design fee structure
that as engineers we typically get for designing wood structures. 

Any suggestions?

By the way, SEAOSC is planning a seminar on this topic for November.


Michael Cochran