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# RE: Rigid vs Flexible diaphragm discussion

• To: "'seaint(--nospam--at)seaint.org'" <seaint(--nospam--at)seaint.org>
• Subject: RE: Rigid vs Flexible diaphragm discussion
• From: "Swingle, Mark" <Mark.Swingle(--nospam--at)dgs.ca.gov>
• Date: Wed, 11 Aug 1999 14:49:49 -0700

```Martin,

further discussion.  I have tried to convey some of the concepts that you
outlined, but my explanations are not always so clear.  Many others have

I and many others have pointed out that in many situations the lateral
system behaves such that the force distribution is somewhere BETWEEN "rigid"
and "flexible".  This is exactly the situation you described.  In your
example, the short walls will see LESS force than the tributary load case
("flexible" diaphragm), but MORE force than an infinitely rigid diaphragm.
Conversely, the long walls will see MORE force than the tributary, but LESS
than the completely rigid case.

I previously stated that one must "accurately model the stiffness of the
diaphragm" or something to that effect.  I never stated the degree of
precision that was intended, but this was a poor choice of words.  I was
only trying to point out that one should not go to the other extreme if one
judges or calculates that the diaphragm is not "flexible".  I meant that one
should at least model it in his mind if not by equations.  This is the
"considering" that Charles Greenlaw has so eloquently clarified for us all.

Several problems exist in the code itself, and several problems exist due to
many engineers' MIS-understanding of the code.  The ones that misunderstand
the code may be your plan checker or an expert witness for the plaintiff
(you being the defendant).

One problem in the code is the definition of "flexible" diaphragm and its
implications as to whether actual and accidental eccentricity must be
accounted for (not just "considered").  In your example, the reason that the
diaphragm will redistribute forces (from the short walls to the long walls)
has more to do with the DIFFERENCE in stiffness between the adjacent shear
walls than it does with the deflection of the diaphragm vs the "average
story drift" of the shear walls.

If one has an infinitely stiff diaphragm, then the concept of torsional
eccentricity is well-defined.  However, if the diaphragm redistributes
forces to a degree less than infinitely stiff (such as in your example),
what do we do about torsion?  Suppose your calculations (or those by the
expert witness 9 years from now) show that the diaphragm is NOT flexible per
the code definition.  In this case, there are an infinite number of ways
that the mass can be "displaced from the calculated center of mass...a
distance equal to 5 percent...".  In other words, the concept of moving the
mass for accidental torsion is not mathematically rigorous when the forces
are PARTIALLY determined by tributary loads.  It would be easy for an expert
witness to show that you did not account for accidental eccentricity
according to HIS/HER interpretation of the code language.

Some better way needs to be defined IN THE CODE as to how to account for
torsion when the diaphragm is BETWEEN "rigid" and "flexible".

One other problem in the code is that the formula for shear wall deflection
is in the body of the code, although it does not come with CODE LANGUAGE to
clarify that it is only valid (?!) for isolated, full-height, cantilevered
shear walls.  Only one-story commercial warehouses or perhaps some one-story
residential garages fit this case.  This formula is next to useless for
multi-story bldgs and walls with adjacent spandrels that modify the
stiffness.  This formula is also useless absent load-deflection curves for
the various holdown devices.

So, if you were to use OTHER researched, tested, or well-reasoned
methodologies to come up with shear wall stiffnesses (and thus shear
distributions), you could be shown to have violated the language of the
code.  Or, if you had made an engineering judgement as to how the forces
would distribute, as in your example, then you could be shown to have
violated the code, because you did not use the deflection formula in the
code.

These formulas need to be removed from the body of the code (or referenced
standards), or they need to be clarified as to their proper application, so
that other methodologies would become valid based upon some assumed
"rationality" due mechanics or laboratory results.

I know some of you are weary of this discussion, but hopefully if you are
one of those, you haven't read this far and have long since deleted this
message.  These are real issues to those that design residential buildings.

Mark Swingle, SE
Oakland, CA

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Martin W. Johnson wrote: