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Fw: R-values in Seismic Provisions

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Just to throw a little gasoline on the fire...

Take a look at UBC97 Table 16-N for the R factor associated with
Cantinlevered column elements.  The table lists the factor as 2.2.  

If I were to design a single cantilevered column, supporting a mass, fixed
at the base, EXACTLY for the Vb associated with an R factor of 2.2, using
USD, then THEORETICALLY it would have yielded at a base shear value of the
elastic base shear/2.2, right?  This of course is according to UBC97 (not
necessarily in reality).

Ron Hamburger has a good point in that there are factors which make the
yield strength of a seismic resistant system higher than we assume for
design: phi factors reduce capacity forcing us to increase the strength,
the fact that I will likely put more reinforcement in the column than
required (eg 16#9 bars as opposed to 15.2#9 bars), overstrength of the
reinforcement (actual yield of say 66ksi as opposed to 60ksi).

These would be the only factors which would increase the ACTUAL yield base
shear (resulting in a decrease of R), since there is only one column so no
redistribution of forces can occur, and since I am assuming there are no
non-structural elements.  One could expect to get period elongation, due to
the decrease in Keff, over the course of the earthquake. There would also
be some damping I imagine (which, interestingly, would lead to a higher
maximum displacement).

It would seem reasonable, in my mind, that the above factors (overstrength,
period elongation, damping) would drop the R factor down from 2.2 to 2.

So, at least according to UBC97, it would seem that an R factor of about 2
is appropriate for an "elastic" response, at least the way I see it. 
Anyone agree/disagree?

T. Eric Gillham PE

> From: Bill Sherman <SHERMANWC(--nospam--at)>
> To: seaint(--nospam--at)
> Subject: Re: R-values in Seismic Provisions
> Date: Wednesday, September 16, 1998 4:36 AM
> Ronald O. Hamburger, thank you for your thoughts on this - but I am still

> somewhat unconvinced.  Your first comment relates to the "approximate
> formulae".  But the noted R-value was not specified to necessarily be
> for designs using the approximate period formulae.  Some designs could
> more accurate period calculations or could be relatively rigid
> which are not impacted by the approximate formulae.  (And as pointed out
> another responder, other features may actually reduce the actual period.)

> I do agree with your second comment that "Most structures incorporate 
> substantial overstrength."  However, I am not sure this overstrength can
> generalized and I am not sure whether it is typically by as much as a
> of 2.  Thus I would concur that reality is that full elasticity generally

> would occur at an R-value greater than 1.0 (but may not be as high as
> This can be a significant issue if one is attempting to keep a structure 
> "nearly fully elastic" in a design.  Since yielding is permitted in
> strength design, an R-value of 1.0 is certainly implied as the
> value for full elasticity.   
> (The speaker said that an Rw = 3.0 used to be the estimated limit of
> behavior using allowable stress design, now reduced to R = 2.0 for load
> factor 
> design.)