This document provides the calculation of ringwall soil bearing pressure for the attached SFA model named "Ringwall Foundation_verification".

Equation from AP 650

Equation from SFA calculation sheet

__Procedure for the calculation based on the equation shown in the SFA calc sheet for the attached SFA file__

Basic data:

Internal diameter of the tank = 20.422 m

Hence, Internal Radius = 20.422/2 = 10.211 m

Wall thickness of the tank = 12.7 mm

Hence, External Radius = 10.211 + (12.7/1000) = 10.2237 m

Internal area of the tank = Pi() * 10.211*10.211 = 327.5567 sq.m

Circumference of the tank wall at the centerline of the tank wall =

2 * pi() * 0.5 * (10.211 + 10.2237) = 64.1975 m

Width of ring wall = (Available from the calc sheet’s Ringwall soil bearing check output and from the drawing) = 0.991 m or 39 inches (0.9906 m to be exact)

**Term 1 – see highlighted item below**

This is the force per unit circumferential length due to weight of the empty tank. The weight is reported as 1437.658 kN in the calc sheet for the attached model. Hence,

w_{t} = (Weight / circumference of the centerline of the tank wall) * Load factor for dead load for load comb 104

w_{t} = (1437.658 / 64.1975) * 1.0 = 22.3943 kN/m

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**Term 2 – see highlighted item below**

This is the force caused by the weight of a 1 m circumferential length of the ringwall divided by its width. In other words, it is simply the depth of the ring wall * 1.0 m circumferential length * density of concrete * Load factor for dead load for load comb 104

Ringwall depth = 1.829 m

Density of concrete = 23.563 kN/m3

W_{fdni} = 1.829 * 23.563 * 1.0 = 43.09673 kN/m

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**Term 3**

As shown in the figure below, this is the force caused by the weight of the fluid contained inside the tank at operating condition acting over the portion of the ring wall projecting into the inside of the tank (defined using the alphabet L in the picture below)

Wp is just the pressure at the level of the bottom of tank shell (or top of ringwall)

Weight of liquid (product) at operating condition = 33961.73 kN

Area inside the tank = 327.5567 sq.m

L = Half the width of the ringwall minus eccentricity = (0.5 * 39 inches) – (0.25ft*12) = 16.5 inches = 0.4191 m

Thus, Wp * L * Load factor for dead load for case 104 = (33961.73/327.5567) * 0.4191 * 1.0 =

43.45313 kN/m

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**Term 4**

In the above,

SNLC stands for load factor for snow load

w_{s} stands for force per unit circumferential length due to weight of snow

Total weight of snow on the tank roof = 334.069 kN

Thus, w_{s} = 334.069 / 64.1975 m = 5.20377 kN/m

SNLC = 0.1 for the snow load component of load comb 104 (from the load combination table)

Thus, SNLC * w_{s} = 0.520377 kN/m

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** Term 5**

Av is reported in the calculation sheet as 0.372

EQLC = load factor for the seismic load component for load comb 104 (from the load comb table)

Thus, term 5 = 1 + (0.4*0.372*1.0) = 1.1488

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** Term 6**

Wp = internal pressure in the tank = 0.0

Hence, Term 6 = 0.0

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** Term 7**

Mrw = Moment at top of ring wall due to the various loads. For load comb 104, this value comes solely from the seismic load term. From the calc sheet, the value reported for the moment acting on top of the ringwall (see table titled “Applied Loads at Top of Ringwall – Service Stress Level”) is 3807.813 kN-m

(D – L + Fw/2) = 20.422 – 0.4191 + (0.5*39*25.4/1000) = 20.4982 m

Where D = Internal diameter of tank wall, L is the offset shown in figure for

Thus, Term 7 = 1.273 * 3807.813 / (20.4982*20.4982) = 11.53646 kN/m

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**Term 8**

Fw is the width of the footing = 39 inches = 0.9906 m

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Final result:

Sum of terms 1 to 4 = (22.39429766 + 43.096727 + 43.4531327 + 0.520376934) = 109.4645 kN/m

Numerator = (109.4645*1.1488) + 0.00 + 11.53646 = 137.2893 kN/m

Denominator = 0.9906

Final result = 109.4645/0.9906 = 138.5921 kN/m2

Value reported by SFA = 133.597 kN/m2 (See figure below)