
 DOESTD102395
(3)
Numerical modeling
The median response spectrum shape is calculated from numerical models such as
bandwidthlimitedwhitenoise/random vibration theory models benchmarked
against response spectra from actual ground motion records associated with
magnitudes, distances, and soil profiles as similar to those of the site under study.
For this method, the input parameters, the numerical model used, and the validation
of the appropriateness of the model shall be documented.
A3.1.3.2a. As an example, the procedure for constructing a standardized DBE response spectrum based
on Newmark and Hall (1978), using the authors' original units, is summarized below:
(1) Determine the horizontal ground motion parameters: PGA, PGV, and PGD.
a. Obtain the design basis mean peak ground acceleration (PGA) in units of "g"
based on a site specific probabilistic seismic hazard assessment.
b. For a competent alluvium site with Vs (shear wave velocity) < 3500 ft/sec,
determine the peak ground velocity (PGV) in "in/sec" and peak ground
displacement (PGD) in "in" by the following formulas:
PGV = 48 PGA
PGD = 36 PGA
c. For a rock site with Vs > 3500 ft/sec, determine PGV and PGD by the following
formulas:
PGV = 36 PGA
PGD = 20 PGA
(2) Determine the maximum amplified response acceleration (amax), velocity (vmax), and
displacement (dmax) for median spectra (50th percentile):
amax = PGA (3.21  0.68 ln )
vmax = PGV (2.31  0.41 ln )
dmax = PGD (1.82  0.27 ln )
where "" is the critical damping ratio in "percent" and "ln" is the natural logarithm.
A7

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