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# Rigid vs Flexible diaphragm discussion

• To: seaint(--nospam--at)seaint.org
• Subject: Rigid vs Flexible diaphragm discussion
• From: "Martin W. Johnson" <MWJ(--nospam--at)eqe.com>
• Date: Tue, 10 Aug 1999 08:52:36 -0700

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missing the real issue of how we are designing diaphragms versus how they
in fact behave.  Analysis approaches such as used for flexible and rigid
diaphragms are only basic approximations of what goes on.  We also do many
things that don't fit into either approach, such as allowing short walls to
"rock" and clustering a series of adjacent short walls on either side of a
corridor together as a group (which, by the way, assumes that the short
width of diaphragm between them is "rigid", a word many of you abhor).  But
the main thing that is not being recognized is that we are designing using
"imaginary" forces.

Consider the following situation.  A wood diaphragm has plywood shearwalls
on each side.  On the right side, two 4-foot long shear walls are provided.
On the left, a single 12-foot long shear wall is provided.  We design the
diaphragm and walls using the diaphragm Vpx forces in the code, and
determine the required nailing using the WSD tables in the UBC.  But both
the forces we are using and the defined strengths of the components are
"imaginary" WSD values.  The real strength of the plywood diaphragm and
walls is around 2.5 to 3 times larger than the "allowable" shears.  Hence
the structure will ACTUALLY tend to transmit interia forces at the REAL
strength of the structure, which, in Blue Book Terms, would have a base
shear of around Ro x V.

But here is the problem.  The short 4-foot long shear walls on the right
side of the diaphragm have got foundation systems that were only designed
using a factor of safety of 1.5 against overturning.  In other words, the
"real" strength of the short shear walls will never be attained, because
the walls are going to rock.  So only half of the expected inertia force
will be resisted on the right side.  Where does the rest of the inertia go?
IF the diaphragm is wide enough and flexible enough, the inertia will only
go into unexpectidly large lateral displacements along that end of the
diaphragm, and the wall on the left side won't notice much.  But if the
diapragm is not wide, but perhaps as wide as being square, the "left over"
inertia force is going to be transferred to the wall on the left side.
That wall is longer and will not rock.  So after the earthquake we will
look at the structure and see that the short walls do not have much
structural damage, but perhaps considerable nonstructural damage, while the
long wall has visible structural damage - bent nails, etc.  And we will
say, "Aha! Rigid diaphraghm behavior!".

I guess the point of this is that, first, there seems (to me) to be some
merit in "considering" the effects of rigid diaphragm behavior in
structures, "second," that thinking of the code in a manner that it is a
"recipe" which must be followed step-by-step causes us to overlook all of
the judgemental design assuptions we make, and third, that both of the
analysis approaches we are discussing - rigid and flexible- are ficticious.
The only "real" way to consider the behavior of structures is at the
"strength" level, considering the plastic behavior of the structures.  And
I do not advocate that, except for important structures where the fees are
better.  My recommendation is to "consider" the effects of rigid diapragm
behavior on structures, but have a mechanism to neglect it in instances
where it becomes obsessive, such as very wide diapragm spans or very small
(i.e., residential) structures.

Oh, and by the way, what about all of the plywood floor diapragms that have
got lightweight concrete topping on them?  Isn't that pretty rigid, even
though we ignore the strength contributed by the concrete???

Best regards to you all, Martin.

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