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# RE: Fundamental period of tanks

• To: <seaint(--nospam--at)seaint.org>
• Subject: RE: Fundamental period of tanks
• From: Tom.Hunt(--nospam--at)fluor.com
• Date: Fri, 28 Dec 2007 11:20:09 -0800

Dave,

No, the two are different.  The following is the formula for Ti (I will send you the Ci chart on a direct e-mail):

Ti = [Ci x H x (square root p / square root E) ] / square root (2tu / D)

Thomas Hunt, S.E.
Fluor

12/28/2007 09:12 AM
 To cc Subject RE: Fundamental period of tanks

Are you then saying that "T-sub-c" (natural period of first sloshing mode) is equal to "T-sub-i" (fundamental period of the tank & impulsive component of contents) in ASCE 7-05, Section 15.7.6.1?  My original question was related to "T-sub-i", which appears to require some form of displacement determination, and I am not sure it can be accurately obtained without some complicated form of analysis.  If we are to say that "T-sub-c" = "T-sub-i", determining the seismic base shear appears to be a lot simpler.  I'm sure there must be something I'm missing ...

-----Original Message-----
From:
Harold Sprague [mailto:spraguehope(--nospam--at)hotmail.com]
Sent:
Thursday, December 27, 2007 1:36 PM
To:
seaint(--nospam--at)seaint.org
Subject:
RE: Fundamental period of tanks

Dave,
Tom is on target as usual.

It was never the intent to discourage the use of the formulas in API or AWWA.  The intent of the NERHP and the ASCE 7 was to foster updating to the more current ground motions and to present equations on how to employ the new ground motions.  As the API and AWWA have developed, the NEHRP and ASCE have referenced those documents.

In the future, the NEHRP will represent more of the cutting edge of code development using the ASCE 7 as the base.  You will also find the NFPA 59A currently provides some information regarding vertical seismic ground motions not present in the current codes, but can drive the design of liquid containing structures especially in areas of close proximity to thrust or subduction faults.

Regards,
Harold Sprague

To: seaint(--nospam--at)seaint.org
Subject: Re: Fundamental period of tanks
From: Tom.Hunt(--nospam--at)fluor.com
Date: Thu, 27 Dec 2007 12:43:59 -0800

Dave,

>From API 650, the first mode sloshing wave period (Tc), in seconds, is taken from the below formula:

Tc = Ks x square root of D

Ks = 0.578 / square root of tanh(3.68H/D)

Thomas Hunt, S.E.

Fluor

12/27/2007 12:04 PM

 To cc Subject Fundamental period of tanks

Hello everyone,

Those of you who deal with non-building structures:  How are you spending your time determining the fundamental period of flat-bottom tanks (T-sub-i in ASCE 7-05, Section 15.7)?  Are you actually modeling and calculating the value or using simplified equations from material standards (i.e. AWWA or API)?  ASCE 7 appears to really discourage the use of simplified equations.

Thanks,

LANE ENGINEERS, INC.

Tulare, CA  93274

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