API 650 Tank Anchorage Ratio

[D_YU]

Hi,

This is with regard to the anchorage ratio J (Table E6) in API 650 V13. My understanding is J = 0.785 (Pi/4)corresponds to eccentricity of D/4, while J = 1.54 (close to Pi/2 = 1.57) corresponds to eccentricity of D/2 but with a small (0.03/1.54 = 2%) difference. What is the significance of making such a small offset? This makes no sense to me or I missed something?

 

[HTURKAK]

I hope my respond does not disappoint you but you are missing something,

The summary for derivation of the expression for J ( Anchorage Ratio, or say overturning coeff) ;

- b = axial force developing at the tank shell per unit length of circumference b = WT + M/(Pi*R**2) API 650 uses the same expression using dia and Pi=3.14 than b= WT + 4M/Pi(D**2)= WT + 1.273M/(D**2)

- If you set the uplift force developing with seismic OT moment equal to the resisting wt ( wt of tank shell and roof portion + liquid wt resisting to the OT )

4M/(Pi*(D**2)) = Wt + Wl ⇒ M/(D**2)(Wt + Wl ) = Pi/4 =0.785

- When J greater than 0.785 , API 650 limits the eccentricity of the load to a point within the footprint of the shell.
Pi/2 or conservatively 1.54 .( the figure was 1.572 at old versions )

- Next time , prefer to post your storage tanks threads to the Storage tank forum.

...






He is like a man building a house, who dug deep and laid the foundation on the rock. And when the flood arose, the stream beat vehemently against that house, and could not shake it, for it was founded on the rock..

Luke 6:48

 

[D_YU]

Thanks for your answer HTURKAK (Structural). I will post my thread under the right topics in the future.
I actually understood where the J criteria coming from. However, the fact that API650 decided to use 1.54 instead of 1.57 confuses me. Why not using 1.50 if just for being conservative, or stay with 1.57 (Pi/2) to be less confusing, like 0.785 being exact Pi/4?

 

[JStephen]

It's kind of a moot point. As you approach 1.54 or 1.57 or whatever, the compressive force in the shell increases dramatically and that is expected to be the limiting factor rather than the exact J ratio.

 

[HTURKAK]

- J limit was 1.57 at API 650 old editions while J was 1.54 at AWWA . 1.54 or 1.57 only figures defined by API 650Committee.
- If you get J > 1.54, the tank is not stable but you can modify the bottom annular plate width and thickness in acceptable limits or provide mech. anchors .
..


He is like a man building a house, who dug deep and laid the foundation on the rock. And when the flood arose, the stream beat vehemently against that house, and could not shake it, for it was founded on the rock..

Luke 6:48

 

[D_YU]

So why API changed J from 1.57 to 1.54? If it was to align with AWWA, then why AWWA used 1.54 not 1.57? I know the difference is minor and has no effect on design.

 

[JStephen]

In "Basis of Seismic Design Provisions for Welded Steel Storage Tanks" by Wozniak and Mitchell, they derive an equation similar to (but not identical to) E.6.2.2.1-2a in API-650.
In introducing that equation, which is an approximation, they state, "The relationship may be approximated with good accuracy up to a value of the moment parameter of 1.54 with the following formula..."
Which implies that perhaps they limited the parameter to 1.54 so that their equation stayed within the "well-behaved" region of the parameters. (IE, compressive stress goes to infinity at pi/2, so they were cutting it off at some arbitrary point prior.)