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Re: R-values in Seismic Provisions

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On Sept. 14 Bill Sherman wrote:

> > An R of 1 would imply an elastic response. < 
> While I would agree with the above statement, I have heard some speakers on 
> seismic design state that an R-value of approximately 2.0 under the 1997 UBC 
> would relate to a "fully elastic response".  This does not make sense to me
>  can anyone explain the basis for this statement? 

There are several bases for such a statement-

1- The "actual" period of a structure is probably somewhat longer 
(maybe by as much as a factor of 2) than that calculated using the 
approximate period formulae.  Thus, the simple base shear formula 
(absent an R value) could somewhat overstate the response 

2- Most structures incorporate substantial overstrength.  Actual 
yield strengths of steel and concrete are somewhat higher than 
minimum specified strength.  Capacities of sections calclulated 
during design incorproate phi factors - that reduce strength below 
actual expected values.  Designs typically are not optimized as much 
as possible.  Engineers arbitrarily throw in more beef than the calcs 
may demand. 

 The overall effect of this is that most structures will 
not actually start to experience signficiant yielding until they see 
somewhat higher accelerations than the Z value in the code would 
indicate and will not experience full yield until substantially 
larger accelerations are experienced.  The factor of 2 probably 
overestimates the start of significant yielding but underestimates 
full yielding.  It is probably accurate to say that an R of 2 
represents "essentially elastic" behavior.
Ronald O. Hamburger, SE
Regional Manager
EQE International, Inc.
San Francisco, California