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RE: Site soil report response spectra and API 650 Appendix E

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 pseudo-velocity 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 350.3-01. 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. 
-----Original Message-----
From: Robert M. Hanson [mailto:Bob(--nospam--at)KappaEngineers.com]
Sent: Wednesday, February 12, 2003 11:35 AM
To: seaint list
Subject: Site soil report response spectra and API 650 Appendix E


Inspecting a tank that is a flat bottom, grade supported, at 117 ft dia and 42 ft tall, floating roof, contents SG at .9.

I would like to find out if there is some information on how to simply apply a soil reports response spectra for a site to Appendix E of API 650 (10 th edition) without having to do full dynamic model for the tank and its contents. If any one does the full model what software is currently used for the hydrodynamic forces and such.




Robert M. Hanson, SE

Kappa Engineers

(310) 233-3800 x109