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RE: Site soil report response spectra and API 650 Appendix E
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 Subject: RE: Site soil report response spectra and API 650 Appendix E
 From: "Lutz, James" <James.Lutz(nospamat)earthtech.com>
 Date: Wed, 12 Feb 2003 17:43:00 0800
If you
have access to TID 7024, the Nuclear Reactors and Earthquakes document
referenced in API 650, there are formulas for calculating base shear and wall
pressures given the ground motion parameters. The mass is broken up into
two forces, an impulsive force proportional to the peak ground acceleration
times the impulsive mass, and a convective force proportional to
the impulsive mass times the maximum spectral displacement of the water
surface. The impulsive and convective masses are as defined in API 650, which
uses graphs based on TID 7024 formulas.
The
impulsive mass is assumed to move as a rigid body with a period of 0 seconds.
The convective mass has a natural period which can be calculated from formulas
in the manual, and the maximum displacement can be estimated from the peak
pseudovelocity divided by the circular frequency of the convective mass. The
method is only applied to the first mode of vibration. You can pick the peak
acceleration and velocity values off the site specific response spectrum if it's
plotted in tripartite form. I think a fairly low damping percentage is usually
used, say 2%. I would interpret forces computed on this basis to be ultimate
loads.
This
is simplified, 50 year old methodology that ignores amplification effects due to
the flexibility of the tank shell, which can be a factor in steel tanks,
especially taller ones. It also ignores other effects such as longer periods
caused by rocking of the tank, ovaling effects and higher modes. Near as I can
tell, almost nobody investigates these effects for practical design problems. I
have run some CFD models for tanks and even for some reservoirs of modest
proportions have been surprised to see higher mode behavior in the fluid surface
when the motion gets rockin' and rollin'. When you run a time history on one of
these things, you can get multiple waves, waves adding to one another as they
are reflected, extreme pressure on walls and roof in cases of inadequate
freeboard, etc. It ca be far more complicated behavior that the simplified code
formulas would suggest.
If you
wanted to do a finite element tank model that included computational fluid
dynamics modeling, you are talking about very high end and expensive
software.
You
might also want to take a look at the more recent seismic design
provisions in ACI 350.301. This is for concrete tanks, but has some good
information. It uses the same formulas from TID 7024, which originated with
George Housner at Cal Tech, but has corrected a couple of the
coefficients per some changes Housner made after TID 7024 was
published.

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