Subject: Rigid vs Flexible Diaphragms - Some Comments
From: "Mark T. Swingle" <mswingle(--nospam--at)earthlink.net>
Date: Fri, 07 May 1999 01:58:26 -0700
Thank you Bill Cain for putting the actual UBC wording regarding
flexible vs rigid diaphragms (3 May 99, message #22 if in digest form).
Here are my comments on the evolution of this provision and its use
for buildings with wood diaphragms and wood shear walls.
1. FLEXIBLE vs RIGID
I was told by a reputable source that the cut-off point between
rigid and flexible (max diap deflection of TWO times the average
story drift) was a number pulled out of a hat. I was told this
during a SEAONC Code Committe meeting (approx 2 years ago) by
someone who claimed to have participated in the development of
this very definition. He claimed to be somewhat troubled by the
fact that there was no technical justification for it, it was
just a "gut feeling" (my words). He was trying to get someone
to do some basic analyses to either justify it or adjust it.
The idea was that a diaphragm stiffer than this is where the
effects of redistribution and rotation start to occur.
2. DIAPHRAGM FLEXIBLE AND RIGID AT SAME TIME?
Careful reading of this provision implies that if the building
has interior shear walls, then EACH diaphragm section (between
two adjacent walls) needs to be checked as to whether it is
rigid or flexible. What do you do if, in one direction, some
diaphragms are rigid and some are flexible! This can happen if
the widths vary a large amount. Check it out! Yes, structural
analysis can be made as difficult and complicated as your
3. DO THE EQUATIONS WORK? (IS A DIAPHRAGM ALWAYS A SIMPLE SPAN
AND IS A SHEAR WALL ALWAYS A CANTILEVER?)
In order to follow the code language and apply the test for a
wood diap and wood shear wall building, one must use the
deflection formulas in Volume 3 of the UBC. The only difference
between the shear wall and diaphragm equations is that the
diaphragm is assumed to be a simple span, and the shear wall is
assumed to be a cantilever (check the coefficients).
This would be fine for a one-story box with only perimeter shear
walls. However, if the building has interior walls, then the
diaphragm is a continuous beam, not a simple span. How does one
use the equation to calculate deflection in this case?
Furthermore, in a multi-story building, only the top floor shear
walls would truly act as a cantilever, and even then only if the
adjacent openings were full height! In actuality, if the shear
walls have windows adjacent to them, then the stiffness will be
significantly different due to the affect of the spandrels above
and below the window. What is the effective height of the wall
in this case? Ditto for the lower story walls which will be in
reverse curvature, not be cantilevered.
4. WHAT ABOUT UNBLOCKED DIAPHRAGMS?
The equation in the code for diaphragms is for BLOCKED diaps
only. What does the CODE say about the deflection of UNblocked
diaphragms? (Hint: nothing). How can a building official
require a determination of flexible vs rigid if there is no code
5. NON-LINEAR EQUATION LEADS TO ITERATION!?
In reference to the shear walls specifically, the deflection
equation is highly dependent on the load per nail, in addition
to other items, i.e. it is non-linear. Are we really expected
to iterate through several cycles, revising the shear wall
stiffnesses based on the previous assumption until it
converges? Are you kidding? By this logic, we also need to
distribute shears accordingly among the walls IN EACH LINE,
because in the new way, the forces do not distribute linearly
according to length IF THE LENGTHS VARY.
6. WHAT AND WHERE IS THE CHORD?
In reference to diaphragms specifically, the deflection equation
is dependent upon the axial stiffness of the chord member.
Typically, the double top plates are assumed to be the chord for
the purpose of this equation. However, would not the continuous
rim joist and the sole plate of the wall above contribute? They
certainly would in compression, and perhaps not in tension if
not properly spliced. (And where is the diaphragm chord in a
bulding with concrete walls?)
My point in bringing up all of this is to point out that, IMHO, the
idea of requiring this type of analysis is ridiculous, and cannot
really be enforced by the building official because the UBC, as
complex as it has become, still cannot address all of the possible
factors in wood frame buildings, and lacks the necessary tools to
accomplish it. Engineering judgement SHOULD still have a role in
design. And until some entity comes up with defintive research on the
subject, wood diaps are flexible, concrete diaps are rigid, and steel
decking is rigid (perhaps flexible with no concrete fill??!!).
What I have done in the past (on wood buildings with deep diaphragms)
is to analyze for both rigid and flexible diaphragms, and take the
worst case. However, my rigid analysis was crude, completely UNLIKE
the ideas expressed above. I simply assumed that the diaphragm was a
continuous beam of uniform EI and applied the loads. As you can
imagine, all that happened was that for the rigid case, the INTERIOR
walls received more load than they would for the flexible case.
I would be very interested in your comments regarding the above.
Mark Thomas Swingle, SE