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Re: More questions about rigid plywood Diaphragms

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Dennis,

I don't believe that there is anything inherent in sloped diaphragms that 
makes them non-rigid.  I agree with Charles that the engineer should have a 
basis in structural mechanics for a judgment of rigid or flexible.  

A characteristic of a sloped diaphragm that needs to be included in its 
analysis is that it acts in its plane, so that neither the load that it 
carries nor its deflection are horizontal.  The top of the wall that it 
braces can only deflect horizontally -- provided the top doesn't lift off 
(I've seen evidence of lift-off of the top of a URM wall bolted to a 
steeply-sloped roof diaphragm after an earthquake: there was a horizontal 
crack and a horizontal offset at a level that I believe indicated the lower 
end of the anchor bolts).  In order for the building to deform under lateral 
loads without separation of the wall from the diaphragm, the diaphragm must 
warp in the vicinity of the diaphragm-wall intersection.  

Here are a couple more items that may be significant in analyzing sloped 
diaphragms:

1)  The non-horizontal plane of action will affect the apparent rigidity and 
capacity of the sloped diaphragm for horizontal forces.  It is the horizontal 
components of those vectors that we use. 

2)  If the intersection of two diaphragm planes is detailed to keep them from 
separating vertically (for example, for loads acting to the right, the 
diaphragm plane that rises to the right to the ridge will deflect up and to 
the right; the diaphragm plane that falls to the right from the ridge will 
deflect downward to the right, resulting in a vertical discontinuity at the 
ridge during diaphragm displacement) shear will be transferred across the 
ridge so that the ridge does not act as a chord, and the 
diaphragm-in-two-planes may be considered a single diaphragm.  The required 
detailing isn't much, and most roofs probably have the necessary 
interconnection of diaphragms by default  -- without design.  Since we don't 
want the building to split at the ridge, I believe it is worth a detailed 
analysis in the case of steeply-sloped diaphragms.  

I believe that it is unrealistic to assume that the ridge acts as a chord for 
the sloped diaphragms -- if it did, it would be acting in compression for one 
plane and in tension for the other plane -- at the same time.  The tension 
and compression cancel, shear is transferred across the ridge, and -- viola 
-- its all one diaphragm again.
 
I've toyed with this effect to my satisfaction for the analysis of some of my 
projects, but I've never seen anything analytical published on it.  I think 
it would make a good master's thesis topic.  In the past year or two, we've 
had some contributions to a couple of related threads on this List.

Nels Roselund
Structural Engineer