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

 

[HTURKAK]

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

API 650 assumes the uplift force is ( the max . nominal line stress stress * perimeter area - vertical seismic effect )

- If you neglect the vertical seismic effect, and assume the perimeter as thin shell the section modulus S= pi* (D**2)*t/4

- The max. stress = M / S = 4 Mrw/(pi* (D**2)*t)

- Max. uplift assuming max. stress can occur any point on the perimeter U = ( 4 Mrw/(pi* (D**2)*t)) ( thin wall area = pi*D*t) = 4 Mrw/D

If net uplift=128kips and there are 8 equally spaced anchors , the load per anchor shall be calculated Tb = U/N = 128/8=16 kips.

In your case ( diameter 12 ft, ) should not be API 650 tank and if this approach does not convince you , you may look PV code.

 

[Geoff13]

I don't like API's method of expressing anchor bolt loads. Using tb = U/N leads to a misunderstanding of what's going on. Please think of tb as the formulas in Table 5.21 with "divided by N" added throughout each one.

Thus for the seismic moment the first term becomes 4M/(ND). If you take a circle of equally spaced anchor bolts and calculate the minimum section modulus (I forget if the axes are between bolts or thru bolts for the minimum, but you can easily check) it happens to be a very simple RN/2. Thus tb = M/S = 4M/(ND) and tb is the maximum bolt load properly accounting for the perpendicular bolts resisting no load.

 

[tmgczb]

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?

I want to inquire, when using LRFD method to calculate reinforcement for tank foundation, load factor for dead load is not 1, 0.9D+1.0E for instance. Is the requirement to multiply 1+0.4Av to dead load still applicable or not? Should it be (0.9+0.4Av)D OR 0.9*(1+0.4Av)D?

 

[HTURKAK]

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..

API 650 assumes any of the anchors can experience max. uplift load . ( In this case , seismic load can be at any direction ) With this assumption , total uplift load U is calculated based on max. uplift and the load per anchor is be calculated Tb = U/N

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?

In reality , say a crescent area resist to compression . In order to the anchors can take compression, tank perimeter shall be supported on compression nuts ( double nut one for tension at the above of anchor bracket the other under the bracket ).

API 650 uses working stress design. I will suggest you to look PIP STE03020 for design procedure and worked examples .