# Re: Definition of A sub B in Rho evaluation

• To: <seaint(--nospam--at)seaint.org>
• Subject: Re: Definition of A sub B in Rho evaluation
• From: "Paul Feather" <pfeather(--nospam--at)san.rr.com>
• Date: Fri, 21 Jul 2000 11:30:46 -0700
```Paul Reilly wrote:
>
> Larger Ab reduces the ratio of total shear (story level 1) to the unit
> shear of the wall being considered.   For a single shearwall, increasing
Ab
> reduces the value of rho.  Rho is intentionally (and unjustly) punitive to
> light-frame construction and as the demand forces are artificially
> increased by a big rho, you may have the opportunity to increase Ab (by
> interpretation), which may counter a reduction in the value of rho, which
> will reduce demand forces, that may require less hardware to facilitate
> capacities, that may be interpreted as less conservative, because you have
> realized a minor reduction of  the monstrous fairy tale of rho...  eg.  A
> fair price may be seventy-five cents.   They charged you a dollar.  For
> twenty-cents more, you may realize a five-cent return.  It (rho) is a
> bureaucratic masterpiece.
>

I am not sure I follow all this, but my interpretation would be different.

r is simply a ratio, (vi / V)  For a given number of resisting elements the
size of Ab should not effect r.  If the building is larger (increased Ab),
the base shear V is larger (more building), and the element shear is
proportionally larger (higher base shear with same number of resisting
elements = higher element shear).  r is essentially constant. I am assuming
no increase in wall length or number of elements for purposes of discussion.

Since rho is calculated as 2 - 20/r*sqrt(Ab),  as Ab increases rho will
increase getting closer to 2.  This in turn will increase the base shear V
and the element shear vi.

I do not see how a larger Ab is unconservative.

For example I like to look at a box with walls on four sides.  If the box is
10 x 10, Ab is small and the box is fairly redundant.  If the box is 100 x
100, Ab is larger and the box is considered less redundant.  This makes
sense to me if you think in terms of demand on single elements (diaphragm,
chords, drags, etc.)

Anyway, my two cents worth,

Paul Feather

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