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RE: "Sloshing Effects"
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- Subject: RE: "Sloshing Effects"
- From: "Lutz, James" <JLUTZ(--nospam--at)earthtech.com>
- Date: Wed, 31 Jan 2001 08:58:25 -0800
There isn't anything terribly new on this subject. The methodology in AWWA and API tank design standards is basically that developed by George Housner back in the 1950's and published in papers by him and subsequently as part of "TID-7024 Nuclear Reactors and Earthquakes," which I think you can get from NTIS. I have an old copy of this that was donated to me by another engineer, and there were some corrections to some of Housner's formulas which may not be in the published version. A couple of Housner's original papers on this subject are included in a collection of his works published by ASCE. Housner's methodology assumes the tank is rigid, and subsequent papers have suggested that it may be unconservative for taller steel reservoirs where there is some interaction and amplification of force due to the flexibility of the structure. There are also some papers out there that have a little bit to say about soil-structure interaction. If you can get to a decent engineering library, there are a number of good papers in the literature, generally ASCE journals, on the subject of seismic effects in tanks. Names I have stumbled across include Haroun, Veletsos, Young, Clough, and Wozniak. Haroun was a student of Housner's and still does a little research in this area. You should also look at the AWWA standards for prestressed concrete tanks, D-110 and D-115, which address a few issues not mentioned in D-100, like adjustments for base isolation. The fundamental physics for tank seismic effects is expressed in the Navier-Stokes equations of fluid dynamics, higher order partial differential equations which are essentially impossible to solve. There are only a couple of published solutions for very simple vessel shapes and harmonic motion. Housner made some simplifying assumptions about the physics and used some alternate energy methods to come up with solutions for ground level circular and rectangular tanks under simple harmonic motion with certain damping assumptions. The resulting "simple" equations are still full of hyperbolic functions. Resulting pressures and forces are supposed to be accurate in a range of about 5 percent or so, and model tests have supported this. Considering the vagaries of real earthquakes, however, I even wonder about that. AWWA standards have used Housner's approach to develop simpler formulas for base shear and overturning moment, but don't include formulas for wall pressures, so you still have to resort to TID-7024 to figure out the variation of wall pressure with water elevation. Sloshing wave formulas are all based on first mode effects, and it is important that you provide adequate freeboard to keep the wave from contacting the roof (something I have a hard time convincing my clients of--all they see is wasted storage volume). I have recently been involved in a project where we used computational fluid dynamics modeling, sort of a liquid version of finite elements, to see how the liquid behaved when subjected to forcing functions of various frequencies. Typically, the freeboard concern has usually been directed toward preventing uplift and failure of the roof to wall connection. The thing we discovered from the CFD analysis was that a water pressure spike is also transmitted to the walls and bottom of the tank if the wave can contact the roof. Also, in certain cases, you can get higher mode waves. The other thing CFD impressed on me is that a long period earthquake is not your friend when it comes to large tanks. Unlike the natural period of the tank structure, which is very low, the natural period of the fluid can be fairly high. As you approach the natural frequency of the fluid, the sloshing wave and seismic loads can get out of hand in a hurry. -----Original Message----- From: Frank Griffin [mailto:fsg(--nospam--at)freese.com] Sent: Tuesday, January 30, 2001 5:59 PM To: 'seaint(--nospam--at)seaint.org' Subject: "Sloshing Effects" Can someone guide me to any reference materials pertaining to seismic effects of liquids in storage tanks? UBC '97 makes mention of, "inertial effects of the contained fluid." IBC 2000 (which is the code in effect for my project) makes mention of, "sloshing period of the stored liquid," and states that, "The tank shall be designed to resist the effects of sloshing." Furthermore, AWWA D100-96 states, "The design of ground-supported flat-bottom tanks recognizes the reduction in seismic load due to the sloshing of the contained liquid. This design procedure is referred to as the effective mass method." There are some references in the Appendix, but nothing more recent than 1984. Thanks in advance for any help you can provide. Frank Griffin Ft. Worth, Texas
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