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Re: Plwd: Rigid Diaphragm Analysis - Opinions Wanted

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Dennis:

For the last 10 years our firm has done a large number of Assisted Living
and Skilled Nursing Facilities in many different states, including
California.  Most of these structures are L-shaped, C-shaped, X-shaped or
some other combination that includes a central core (kitchen, dining,
offices) and projecting wings (residential).  These structures are one, two
and three story but in recent years mostly two story.  Initially these
buildings were all wood frame but in the last three years a number of them
have light light gage steel walls, with light gage steel floor and roof
trusses and concrete decks.  The concrete decks threw us into the rigid
diaphragm mode even though the rest of the structure was basically light
frame construction.  Our procedure for handling the concrete diaphragms has
evolved into one which we will also be using for plywood diaphragms.

- Projecting wings are analysed separately.  Even in a "rigid diaphragm"
condition there is a limited effect that one wing can have on another.  

- There is usually a connecting section where the wings come together.  This
area often has limited wind exposure compared to the wings because of the
roof geometry, different shear wall layout and different shape.  This area
is also analyzed separately.

- The individual areas are analyzed separately using a rigid diaphragm
analysis.  Preliminary designs of the shear walls have to be made so that
stiffnesses can be determined.

- Here I add a step.  The projecting wings look like a beam, they are
supported like a beam, they have a calculatable (is that a word?) stiffness
like a beam and I think that they will transfer loads to the shear walls
like a beam.  I check the wing diaphragms as an "equivalent beam" with an EI
based on the stiffness of the diaphragm.  The supports are modeled as
springs based on the wall stiffnesses.  

- If the equivalent beam yields a larger value than the rigid diaphragm
analysis I go with the equivalent beam values.  If the equivalent beam gives
lower values I use every fudge factor and allowable stress increase at my
disposal to try to lower the design load and stay within the code.

-  At the boundaries between the analyzed diaphragms the loads are combined.
This is a very critical area because of reentrant corner effects.  Per the
code we do not take 1/3 increase for drag and collector members in these
areas.  We also aren't bashful about adding strength in these areas.

This method which was used for concrete rigid diaphragms now will have to be
used for wood "rigid diaphragms" as well. 

I often been uncomfortable with the results that come out of a "rigid
diaphragm" because our diaphragms are never completely rigid.  We need to
apply judgement when choosing our methods of analysis.  When diaphragms have
a length to depth ratio of even 1.5:1 they start to look like beams to me.
The code requires that "The model shall also include the stiffness and
strength of elements, which are significant to the distribution of forces,
and shall represent the spatial distribution of the mass and stiffness of
the structure."(1630.1.2) and "The design story shear... shall be
distributed to the various elements of the vertical lateral-force resisting
system in proportion to their rigidities, considering the rigidity of the
diaphragm."(1630.6)

If we consider the diaphragm as a beam with a calculated stiffness we are
considering the rigidity of the diaphragm and therefore complying with the
code.  I haven't yet considered it wise to omit the rigid diaphragm values
completely so I do them both.  For me the time consuming part of this
analysis is determining the stiffnesses of the individual resisting elements
before you know the final loads and possibly having to iterate a few times
to get the real answer.  We have to do this regardless of what method we use. 

If your work is primarily residential identifying individual diaphragms with
individual chords and stiffnesses is tedious business. 

Just another thought for the discussion

Dave Morris P.E.
Corvallis, Oregon