API 650 5.12.2 uplift per anchor

[eberger]

As per API 650 clause 5.12 tank anchorage, table 5-21a shows uplift load calculation formula including seismic case as U=(4xMrw/D)-W2(1-0.4Av).

The load per anchor equation (tb=U/N) appears to assume that all anchors will share the uplift load equally. However, if I have a cylindrical tank with equally spaced anchors, and a moment in one direction, won't only half( (or less) of the anchors be acting in tension, while the other half of the tank will be in compression? How does tb or N (# of anchors) account for this?

 

[JStephen]

The definition of U is misleading. It shown as "net uplift". It should be "maximum uplift per bolt times the number of bolts", so that when divided by the number of bolts, it results in net uplift per bolt.

If you treat the anchor bolts as a uniform thin ring of metal, radius R, thickness t, the total area is 2*pi*R*t.
The moment of inertia is pi*R^3*t. Section modulus is then pi*R^2*t.
So maximum stress in that thin ring is M/(pi*R^2*t) - P/(2*pi()*R*t)
Multiplying the maximum stress times the total area gives you the fictitious force U which is (M/(pi*R^2*t) - P/(2*pi()*R*t)) * (2*pi*R*t) = 2M/R - P or 4M/D - P.
This is adjusted for pressure and vertical acceleration.
If calculating net uplift on the bolt pattern for concrete design, you'll need to account for distance from the centerline, etc. If pressure is low and moment is high, only some of the bolts will actually be in tension.

 

[eberger]

"If pressure is low and moment is high", which pressure are you referring to?

Couldn't I just treat the tank as a cantilevered beam/pipe with a moment, and use the moment calculated from ANNEX E to calculate the max tension at the fixed side?

 

[JStephen]

The pressure I'm referring to is interior roof pressure, the P and Pt terms in those anchor equations.

"Couldn't I just treat the tank as a cantilevered beam/pipe with a moment, and use the moment calculated from ANNEX E to calculate the max tension at the fixed side?"- that is basically what the equation above is doing.

 

[eberger]

using API 650 ch5,
net uplift=128kips
uplift per bolt=16k

I have 8 equally spaced anchors. If I assume 2 of the anchors are located perpendicular to the load relative to the tank, then there will be no force acting on them. of the remaining (6) anchors, three of them will be in compression (load carried through the base of the tank) and three will be in tension.

How do I distribute the uplift forces to these (3) anchors to determine the maximum uplift that will occur?

I have (1) anchor at 6' from center of tank and (2) anchors at 4.27'.

M/D= 440ft-k/12ft=36.7K tension

T=C

4.24/6=0.706

A+2B=36.7k
A=0.706B

A=15.1k
B=10.8K