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Re: 10/lw term in calculation of rho

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Re: 1997 UBC 1630.1.1:


Rho is independent of the base shear for all structural systems.
Rho is a property of and is dependent ONLY upon the geometry 
(location) and stiffness of the vertical elements (frames or 
walls).  For shear walls, stiffness is dependent upon length 
as well as other factors.  Obviously this only applies if the 
elements are assumed to be in a force range where deformations 
are linear-elastic.

If one has a shear wall building with a calculated rho of 1.1 
(for example), rho will remain the same even if the force level
increases.  This is because the denominator will increase by 
the same percentage as the numerator for all r(i) calculations.

I fail to see how rho will increase if the loads are increased 
due to discovering a rho greater than 1.

The point of the provision is to nudge the designer to ADD 
walls upon calculating a rho greater than 1.  In this case, 
if the configuration is changed through the addition of walls, 
rho will decrease, as you pointed out, assuming walls are added 
or lengthened in the vicinity of the most-highly-stressed wall.

Mark Swingle, SE
Oakland, CA

P.S.  Please do not assume from the above response that I am 
in favor of this provision in its current form.  There are 
several ways in which this provision is rife with potential 
pitfalls and in which it is weak technically.


Chuck Utzman wrote on 28 Oct 1999:

The two guys that ran the S.F seminar didn't know wood very well at all.
As Bill Allen correctly pointed out in previous comments on this subject,
doesn't "penalize" short walls at all.  What this provision really does is
a limit on the the maximum shear in any wall at each level.  Set rho = 1
find that Vmax = 2 x story load/square root of the base area.
It actually works very well for design purposes. Once you know the story
and base area, find Vmax, add up the total length of shearwalls for each
and find Vave. at each level, if it exceeds Vmax. you're going to add some
wall length on that floor to keep rho under 1. As long as you don't mix long
and short walls (under 6') and keep the eccentricity down, you'll find this
works very accurately.  If you let rho exceed 1, then the wall loads go up
rho goes up again--it usually takes several iterations to converge (or hit
1.5).  You almost have to set up spreadsheets to do lateral analysis now.
Chuck Utzman, P.E.