Seismic Design of Storage Tanks: EQ E.4.5.1-1b 3

[HTCivil]

I'm looking at the 11th ed. of API Std.650. I'm confused by the equation for Impuslive Natural Period (E.4.5.1-1b) given as:

Ti = 1/27.8 * CiH/sqrt(tu/D) * sqrt(E)

Units (by definition in Sec E.2.2): My values:
Ti: sec 1.23x10^6 s
Ci: unitless 7.20
H: ft 46.72 ft
tu: in 0.419 in
D: ft 150 ft
E: Definition gives kPa for U.S. Custom, I'm assuming psi
is what they meant, it's irrelevant to my question.
29x10^6 psi

First: How can period increase with an increase in elastic modulus? It seems to me that E should be somewhere in the denominator, not the numerator. Remarks?

Second: Does the coefficient out front account for the fact that the units, accourding to definitions, don't cancel out? For example tu/D is in units of in/ft. I would naturally want to convert one into the other by multiplying or dividing by 12 so that the units cancel out. But I don't know if the conversions are covered by that coeficient out front. It would make things easy to be able to just plug in a value based on the by definition units. For example if your thickness, tu, is 5/8" and your diameter, is 100 ft, then you plug into tu/D, (5/8)/100, and you're good. Would be nice, yes, but is it reality? School taught me to always cancel units, but by that logic, how does one arrive at units of seconds when none of the parameters have seconds in their units?

Third: What does "Rho = 9.35" mean?

Any remarks and/or insight would be much appreciated. Hopefully I'm just overanalyzing this thing and there's a simple solution to my problem.

HT

 

[JoeTank]

There are numerous editorial errors in Appendix E of the 11th Edition of API-650. The errors will be corrected by an addendum, soon to issued by API. i suggest you wait, or contact API for an advance copy. Don't fret about the inconsistent units in API. Many of the eqautions are not dimensionally consistent due to the long-standing use of always using D an H in feet (not inches).

Joe Tank

 

[JStephen]

The E term should be in the denominator. See the equivalent equation in this document:

http://www.dec.fct.unl.pt/seccoes/S_Estruturas/Dinamica/Util/SeismicAnalysisTanks.pdf

API does have a "draft" version of Addendum 1 somewhere on their website if you can find it. I think you have to look under "committees" and go from there.

 

[Shahin71]

Great Article

 

[chicopee]

E-modulus of elasticity of steel=30 x 10^6 psi

 

[chicopee]

or 29 x 10^6 psi, either value.

 

[fatihbazman]

Draft addendum is located on

http://committees.api.org/standards/CRE/scast/refdocs/650e11wA1PgProof 2.pdf

this link in API committe web site. You should use this version at least.

http://fatih.bazman.net

 

[HTCivil]

JStephen, thanks for that article. Just for the record, the equation found there for impulsive period is the same as the one found in the tenth edition of the API 650, the same one that they "corrected" in the errata for that edition, dated 4/07. I guess I'll continue to use the tenth edition equation until the API can rectify this issue.
HT

 

[HTCivil]

The equation in the draft addendum given by fatihbazman appears to be correct. The period I calculated with the values I have in the first post comes out to be 0.34 sec. This seems to me to be good. I'm hesitant to use it until it's no further part of a "draft" addendum, but I get the same answer from the tenth edition equation if I make sure the units are consistent. So it would appear that the 1/27.8 coefficient accounts for the inconsistency of the units. Thanks to everyone.
-HT

 

[IFRs]

I'm curious - API does not use the impulsive period for any of the calculations but includes it for some reason - why are you so interested in it?

Addendum 1 has been published and is available. In this version, equation E.4.5.1-1b appears to have the sqrt(E) in the denominator.

I use MathCAD and so usually use the SI version of the equations and always "prove" the equations using at least one USC example without units. Very occasionally I have to "fudge" an equation and artificially add a unit. Since the impulsive period is not used for tank design, I passed it by.

Where is th "rho" you are curious about?

 

[JStephen]

The impulsive period is used for site-specific response- see E.4.6.2 in the 11th Edition. The impulsive period doesn't enter directly into the calculation, but is used to find Sa.

The "rho" is in the 11th Edition, right out beside the impulsive period equation, it says "Rho = 9.35" for no apparent reason.