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# RE: Rigid vs. Flexible Diaphragm

• To: <seaint(--nospam--at)seaint.org>
• Subject: RE: Rigid vs. Flexible Diaphragm
• From: "Bill Allen" <T.W.Allen(--nospam--at)cox.net>
• Date: Wed, 5 May 2004 23:15:16 -0700

```Guatam -

First of all, I'm very familiar with the four term equation used in
determination the deflection of a shearwall built of wood structural panels
(WSP), but it's good to know were are looking at the problem from the same
perspective.

I agree that nail slip is a significant term, but, when the goal of
enveloping RDA and FDA is to determine the outer bounds of possible loads a
shear wall might see, distribution based on capacity probably doesn't do
that.

If you have a four foot long by eight foot tall wall in line with a 20 foot
long x 8 ft tall wall, all four terms come into play in determining the
relative stiffnesses. As you stated, the flexural deflection (function of
h^3/b) and hold down deflections (function of h/b) may not be insignificant
in the short shear wall and there might not be any uplift at all in the
longer one (the last term going to zero except for the plate crushing
component). If that's the case, then using the capacities would still
overestimate the stiffness of the short shear wall and not transfer enough
load to the long shear wall. Using a 4 ft. wall coupled with a 20 ft. wall,
using 10d @ 4", the difference in stiffness (on a per foot basis) could be
as much as 30%. This analogy could also be used for shear walls on different
grid lines when using the RDA.

I know how difficult it can be to come to terms with the four term equation
(no pun intended). The nail slip formula is non-linear, but can easily be
programmed. Even if you consider it linear to capacity, that is probably
just slightly conservative. The chord member term is linear. The hold down
term is zero until there's uplift, and then I would say it would be safe to
consider its stiffness linear to its capacity. Plate crushing is linear. As
far as proprietary systems, I would say use a linear stiffness to capacity
unless you have any better data (holddown contribution?). The proprietary
systems (Hardy, Strong Wall, etc.) are short elements so there will be
uplift and flexure. Of course, if all the shear walls in your structure are
nice and long, you're right, there's not much difference.

I am by no means a programmer, but here's how I would do it. I would write a
spreadsheet with all of the shear walls on one grid line on one work sheet
(much like I do for masonry shear piers). I would set up each shear wall
section in a column and collect all the data from my other calculations. I
would tie the shear wall data to my shear wall schedule. I would set the
sheet up so that I could calculate the stiffness of each shear wall segment
and then the total stiffness of the grid line. I would feed in the results
from my FDA and have the load redistributed to the element based on relative
stiffness.

I would then compare the shear stress (PLF) based on the redistributed loads
and compare it to the capacity in my shear wall schedule. If the load in
_any_ shear wall element exceeds the capacity, I would bump up the shear
wall specification for all the elements on that grid line. Once I had all
the shear walls "compliant", I would then do the RDA using the stiffnesses,
return the values to this sheet and compare the results to the capacities.
If any are overstressed, I would again adjust the shear wall specification.
I would be very surprised if this took very many iterations at all. I'm sure
I haven't done this as often as you and I'm sure there are pitfalls, but I
really can't see how this is any more complicated than making an assumption
in the beginning which not only *may* be flawed but also *may* not achieve
the intended goal of enveloping the loads.

FWIW, the reason I first started looking at shear wall stiffnesses is that,
to my surprise, many combinations of shear walls and hold downs
(particularly non-Struct I panels and HD hold downs) won't meet 0.025H even
if they are 2:1.

Just my \$0.25.

I can't believe I'm taking this side of the FDA/RDA argument. Sheesh!

Regards,

T. William (Bill) Allen, S.E. (CA #2607)
ALLEN DESIGNS (http://www.AllenDesigns.com)
San Juan Capistrano, CA

:-----Original Message-----
:From: G M [mailto:newabhaju(--nospam--at)hotmail.com]
:Sent: Wednesday, May 05, 2004 9:10 PM
:To: seaint(--nospam--at)seaint.org
:Subject: RE: Rigid vs. Flexible Diaphragm
:
:Bill:
:
:Let me first agree with you that whether you use FDA or RDA, good detailing
:is king.
:
:A major contribution of plywood wall deflection is from nail slip followed
:by the  contribution of the holddown deflection; the contribution of shear
:deflection and flexural deflection is generally small and is dependent on
:the aspect ratio.  It is the nail slip that causes a whole lot of problem
:in
:calculating the wall rigidity.
:
:Let us say a shear demand is 400 plf.   1/2" ply w/ 10d nails at 4" o.c.
:with a capacity of 460 plf will probably be specified.  The actual rigidity
:calc should be based on the nail slip w/ 400 plf; the rigidity based on
:capacity will be lower as the nail slip will now be based on a load of 460
:plf.  When I first developed my program, I used the actual stiffness ( -
:this is also not 100% correct because the holddown contribution is based on
:the Simpson's catalog which is based on capacity ).  This procedure
:required
:several iteration because the change of rigidity of one wall caused the
:redistribution of forces which then further changed rigidity (due to nail
:slip).  I must say that I did have doubts about the wisdom of using RDA
:because of the number of iterations required.
:
:The use of capacity based rigidity made iteration manageable - generally
:only one iteration is required.  But then I am not using the actual
:rigidity
:- and that is why I said the validity may be questioned.
:
:The more I tinkered with my program (more automation), the more I realised
:that capacity based rigidity is a better way to go inspite of the flaw I
:described above.  Some of the reasons I feel capacity based rigidity is the
:way to go are:
:
:1. The holddown deflection contribution is based on capacity.  When I
:talked
:to Simpson, they did not have deflection values for load other than the
:capacity.
:
:2. Proprietary wall deflection values are based on capacity.
:
:3. Moment frame/cantiliver columns can now easily be incorported - once you
:know the section, just plug in the rigidity into the program.
:
:4. If the building consists of plywood shear walls only, most of the walls
:will have a reduced rigidity and the error will tend to balance out.
:
:5. If the building consists of a mix of plywood walls and proprietary
:walls,
:it doe not make sense to use the demand rigidity of the plywood walls and
:capacity rigidty of proprietary walls.
:
:
:Gautam Manandhar, SE
:
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