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# Re: Seismic Response Spectrum

• To: seaint(--nospam--at)seaint.org
• Subject: Re: Seismic Response Spectrum
• From: bcainse(--nospam--at)aol.com
• Date: Tue, 23 May 2006 13:25:23 -0400

Rich-
Assuming a Poisson Distribution of earthquakes, one possible method to convert between various periods is:

-RT
(1-p) =e

Where p = probabability of occurence in period T years, expressed as a fraction
R = Annual probability of occurence, events/tear = 1/ Mean Recurrence Interval
e = 2.71828...   I.e., the base of natural logs

For your two earthquakes, the value of R is
R1= 0.0105 events/yr  This would correspond to an earthquake of 0.17g PGA with a probability of 41% in 50 years
R2= 0.00105 event/yr  This would correspond to an earthquake of 0.28g PGA with a probability of 5.1% in 50 years

Given that earthquake data is not all that precise, you could probably plot the peak ground acceleration vs probability for a given period (e.g., the 50 years shown above) on Arithmetic (one scale) vs probability (other scale) paper and obtain an estimate of the 2%/50 year or any other event with reasonable accuracy by assuming a straight line variation.  Doing this results in a PGA of about 0.315g for 2% in 50 years (mean recurrence interval = 2,475 years, or approximately the 1 in 2,500 year event) or 0.255g for 10% in 50 years (mean recurrence = 475 years, or approximately the 1 in 500 year event).

IIRC, not having the IBC in currently in front of me, I think the IBC design EQ spectrum is taken as 2/3 of the 2/50 event or about 0.19g.  From the probability plot assuming the straight line variation, this would correspond to an event with a probability of about 32% in 50 years (mean recurrence = 130 years).

A note of caution in seismically active areas such as the near fault regions of California, the probabilistic methods don't work well as the design EQ may be much closer to the 2/50 event (i.e., it is not a straight line variation).

Regards,
Bill Cain, S.E.
Berkeley CA

-----Original Message-----
From: Rich Lewis <seaint03(--nospam--at)lewisengineering.com>
To: seaint(--nospam--at)seaint.org
Sent: Tue, 23 May 2006 09:50:52 -0500
Subject: Seismic Response Spectrum

I was given seismic design criteria for an overseas project that is not typical of what is used in the IBC code.  The design criteria given to me is:

Peak Horizontal Ground Acceleration:

0.17(g) - 10% over 10 years.
0.28(g) - 10% over 100 years.

I was wondering how this information can be utilized in an equivalent static force analysis.  IBC uses an acceleration response spectrum having a 2 percent probability of exceedance within a 50 year period.  Seems to me I’m mixing apples and oranges with this criterion.  My seismic texts don’t show a method for taking raw data like this and translating it into an equivalent static force system.  Is it possible?

Thanks.

Rich