Ametank Model Example 2 API 650 Calculation Report

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SUMMARY OF DESIGN DATA AND REMARKS

ROOF DESIGN

ROOF SUMMARY OF RESULTS

SHELL COURSE DESIGN

SHELL SUMMARY OF RESULTS

BOTTOM DESIGN

BOTTOM SUMMARY OF RESULTS

WIND MOMENT

SEISMIC SITE GROUND MOTION

SEISMIC CALCULATIONS

ANCHOR BOLT DESIGN

ANCHOR BOLT SUMMARY OF RESULTS

CAPACITIES AND WEIGHTS

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Warnings!!

Initial Data

1.- Design internal pressure is greater than maximum allowable working pressure (MAWP). 2.- Design external pressure is greater than maximum allowable working vacuum (MAWV). Shell Course Data

1.- Please revise the shell thk, 3 courses have problems.

2.- The required minimum thickness based on external pressure is greater than the available thickness and the shell must be stiffened.

Top Member Data

1.- Design pressure is greater that maximum allowable pressure 2.- Reinforcement needed due to insufficient cross sectional area.

3.- Reinforcement needed due to insufficient combined stiffener shell moment of inertia. Intermediate Stiffener Data

1.- Number of intermediate stiffeners is less than required. Revise shell thicknesses or add stiffeners. Structure Data

1.- Please revise the Structure, there is a problem in the sizes. Shell Clean Outs

Clean-Out-0001

1.- Please revise the bottom plate thickness, has problem. Shell Pipe Overflows

Pipe-Overflow-0001

1.- Re Pad thickness is less than min req'd.

SUMMARY OF DESIGN DATA AND REMARKS

Back

Job : 2014-6-20-9-46

Date of Calcs. : 8/11/11

Mfg. or Insp. Date : Designer : TCB

Project : Tag Number :

Plant : PURCHASER DESCRIPTION CITY AND STATE Plant Location :

Site :

Design Basis : API-650 12th Edition, March 2013

TANK NAMEPLATE INFORMATION

Pressure Combination Factor 0.4

Design Standard API-650 12th Edition, March 2013 Appendices Used

Roof A36 : 0.1875 in

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Shell (2) A36 : 0.5625 in

Shell (3) A36 : 0.3125 in

Shell (4) A36 : 0.3125 in

Shell (5) A36 : 0.3125 in

Bottom A36 : 0.25 in

Design Internal Pressure = 0.1 psi or 2.7682 inh2o

Design External Pressure = -0.06 psi or -1.6609 inh2o

MAWP = 0.0764 psi or 2.1165 inh2o

MAWV = -0.0575 psi or -1.5915 inh2o

D of Tank = 150 ft

OD of Tank = 150.125 ft

ID of Tank = 150 ft

CL of Tank = 150.0625 ft

Shell Height = 40 ft

S.G of Contents = 1

Max Liq. Level = 40 ft

Min Liq. Level = 2 ft

Design Temperature = 120 ºF

Tank Joint Efficiency = 1

Ground Snow Load = 0 psf

Roof Live Load = 20 psf

Additional Roof Dead Load = 0 psf

Basic Wind Velocity = 125 mph

Wind Importance Factor = 1

Using Seismic Method: API-650 - ASCE7 Mapped(Ss & S1)

DESIGNER REMARKS

Remarks or Comments

SUMMARY OF SHELL RESULTS

She ll # Widt h (in) Materi al C A (in ) J E Min Yield Strengt h (psi) Tensile Strengt h (psi) Sd (psi) St (psi) Weigh t (Lbf) Weigh t CA (Lbf) t-min Erectio n (in) t-Des (in) t-Test (in) t-min Seismi c (in) t-min Ext-Pe (in) t-min (in) t-Actu al (in) Statu s 1 96 A36 0 1 36,000 58,000 23,20 0 24,90 0 115,29 7 115,29 7 0.3125 0.655 6 0.610 8 0.5087 0.435 9 0.655 6 0.75 OK 2 96 A36 0 1 36,000 58,000 23,20 0 24,90 0 86,482 86,482 0.3125 0.521 1 0.485 5 0.4062 0.435 9 0.521 1 0.562 5 OK 3 96 A36 0 1 36,000 58,000 23,20 0 24,90 0 48,052 48,052 0.3125 0.386 6 0.360 2 0.3029 0.435 9 0.435 9 0.312 5 FAIL 4 96 A36 0 1 36,000 58,000 23,20 0 24,90 0 48,052 48,052 0.3125 0.252 2 0.234 9 0.199 0.435 9 0.435 9 0.312 5 FAIL 5 93 A36 0 1 36,000 58,000 23,20 0 24,90 0 46,550 46,550 0.3125 0.117 7 0.109 6 0.0948 0.435 9 0.435 9 0.312 5 FAIL

Total Weight of Shell = 344,435.3686 lbf

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Plates Material = A36

Structural Material = A36

t.required = 0.1875 in

t.actual = 0.1875 in

Roof corrosion allowance = 0 in

Roof Joint Efficiency = 1

Plates Overlap Weight = 2,136.0223 lbf

Plates Weight = 135,679.1475 lbf

RAFTERS:

Qty At Radius (ft) Size Length (ft) W (lbf/ft) Ind. Weight (lbf) Total Weight (lbf)

40 37.5 W10X12 35.2765 12 423.3185 16,932.7414

80 74.9052 W10X22 40.926 22 900.374 72,029.9234

Rafters Total Weight = 88,962.6649 lbf

GIRDERS:

8 37.5 W12X50 28.7012 50 1,435.0628 11,480.5029

Girders Total Weight = 11,480.5029 lbf

COLUMNS:

1 0 10" SCH STD 43.6853 40.5207 1,770.1605 1,770.1605

8 37.5 10" SCH STD 40.4587 40.5207 1,640.1602 13,121.2819

Columns Total Weight = 14,891.4425 lbf

Bottom Type : Flat Bottom Annular

Bottom Material = A36

t.required = 0.236 in

t.actual = 0.25 in

Bottom corrosion allowance = 0 in

Bottom Joint Efficiency = 1

Total Weight of Bottom = 175,797.7572 lbf

TOP END STIFFENER : Detail D

Size = l3x3x3/8 Material = A36

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STRUCTURALLY SUPPORTED CONICAL ROOF

Back

A = Actual Part. Area of Roof-to-shell Juncture per API-650 (in^2)

A-min = Minimum participating area (in^2) per API-650 5.10.5.2

a-min-A = Minimum participating area due to full design pressure per API-650 F.5.1 (in^2)

a-min-Roof = Minimum participating area per API-650 App. F.5.2 (in^2)

Add-DL = Added Dead load (psf)

Alpha = 1/2 the included apex angle of cone (degrees)

Aroof = Contributing Area due to roof plates (in^2)

Ashell = Contributing Area due to shell plates (in^2)

CA = Roof corrosion allowance (in)

D = Tank Nominal Diameter per API-650 5.6.1.1 Note 1 (ft)

density = Density of roof (lbf/in3)

DL = Dead load (psf)

e.1b = Gravity Roof Load (1) - Balanced (psf)

e.1u = Gravity Roof Load (1) - Unbalanced (psf)

e.2b = Gravity Roof Load (2) - Balanced (psf)

e.2u = Gravity Roof Load (2) - Unbalanced (psf)

Fp = Pressure Combination Factor

Fy = smallest of the yield strength (psi)

Fy-roof = Minimum yield strength for shell material (Table 5-2b) (psi)

Fy-shell = Minimum yield strength for shell material (Table 5-2b) (psi)

Fy-stiff = Minimum yield strength for stiffener material (Table 5-2b) (psi)

hr = Roof height (ft)

ID = Tank Inner Diameter (ft)

Insulation = Roof Insulation (ft)

JEr = Roof joint efficiency

Lr = Entered Roof Live Load (psf)

Lr-1 = Computed Roof Live Load, including External Pressure

Max-p = Max Roof Load due to participating Area (psf)

Net-Uplift = Uplift due to internal pressure minus nominal weight of shell, roof and attached framing (lbf), per API-650 F.1.2

P = Minimum participating area (psf)

P-ext-2 = Max external pressure due to roof shell joint area (psi)

P-F41 = Max design pressure limited by the roof-to-shell joint (inH2O)

P-F42 = Max design pressure due to Uplift per API-650 F.4.2 (inH2O)

P-F51 = Max design pressure reversing a-min-A calculation (psf)

P-max-ext-T = Total max external pressure due to roof actual thickness and roof participating area (psi)

P-max-internal = Maximum design pressure and test procedure per API-650 F.4, F.5. (psf)

P-Std = Max pressure pressure allowed per API-650 App. F.1 & F.7 (psi)

P-Uplift = Uplift case per API-650 1.1.1 (lbf) P-weight = Dead load of roof plate (Psf)

Pe = External Pressure (psf)

pt = Roof cone pitch (in) rise per 12 (in)

Pv = Internal Pressure (psf)

R = Roof horizontal radius (ft)

Ra = Roof surface area (in^2)

Roof-wc = Weight corroded of roof plates (lbf)

S = Ground Snow Load per ASCE 7-05 Fig 7-1 (psf)

Sb = Balanced Design Snow Load per API-650 Section 5.2.1.h.1 (psf)

Shell-wc = Weight corroded of shell (lbf)

Su = Unbalanced Design Snow Load per API-650 Section 5.2.1.h.2 (psf)

T = Balanced Roof Design Load per API-650 Appendix R (psf)

t-calc = Minimum nominal roof plates thickness per API-650 Section 5.10.5.1 (in)

t-Ins = thickness of Roof Insulation (ft)

Theta = Angle of cone to the horizontal (degrees)

U = Unbalanced Roof Design Load per API-650 Appendix R (psf)

Wc = Maximum width of participating shell per API-650 Fig. F-2 (in)

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Roof Design Per API-650

Note: Tank Pressure Combination Factor Fp = 0.4

D = 150 ft

ID = 150 ft

CA = 0 in

R = 75.0677 ft

Fp = 0.4

JEr = 1

JEs = 1

JEst = 1

Insulation = 0 ft

Add-DL = 0 psf

Lr = 20 psf

S = 0 psf

Sb = 0 psf

Su = 0 psf

density = 0.2833 lbf/in3

P-weight = 7.6779 Psf

Pe = 8.64 psf

pt = 0.75 in rise per 12 in

t-actual = 0.1875 in Fy-roof = 36,000 psi

Fy-shell = 36,000 psi

Fy-stiff = 36,000 psi

Shell-wc = 344,435.3686 lbf

Roof-wc = 135,679.1475 lbf

P-Std = 2.5 psi, Per API-650 F.1.3

t-1 = 0.3125 in CA-1 = 0 in Sd = 23200 psi

Theta = TAN^-1 (pt/12)

Theta = TAN^-1 (0.75/12)

Theta = 3.5763 degrees

Alpha = 90 - Theta

Alpha = 90 - 3.5763

Alpha = 86.4237 degrees

Ap-Vert = D^2 * TAN(Theta)/4

Ap-Vert = 150^2 * TAN(3.5763)/4

Ap-Vert = 351.5625 ft^2

Horizontal Projected Area of Roof per API-650 5.2.1.f

Xw = D * 0.5

Xw = 150 * 0.5

Xw = 75 ft

Ap = PI * (D/2)^2

Ap = PI * (150/2)^2

Ap = 17,671.4586 ft^2

DL = Insulation + P-weight + Add-DL

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DL = 7.6779 psf

Roof Loads per API-650 5.2.2

e.1b = DL + MAX(Sb , Lr) + (0.4 * Pe)

e.1b = 7.6779 + MAX(0 , 20) + (0.4 * 8.64)

e.1b = 31.1339 psf

e.2b = DL + Pe + (0.4 * MAX(Sb , Lr))

e.2b = 7.6779 + 8.64 + (0.4 * MAX(0 , 20))

e.2b = 24.3179 psf

T = MAX(e.1b , e.2b)

T = MAX(31.1339 , 24.3179)

T = 31.1339 psf

e.1u = DL + MAX(Su , Lr) + (0.4 * Pe)

e.1u = 7.6779 + MAX(0 , 20) + (0.4 * 8.64)

e.1u = 31.1339 psf

e.2u = DL + Pe + (0.4 * MAX(Su , Lr))

e.2u = 7.6779 + 8.64 + (0.4 * MAX(0 , 20))

e.2u = 24.3179 psf

U = MAX(e.1u , e.2u)

U = MAX(31.1339 , 24.3179)

U = 31.1339 psf

Lr-1 = MAX(T , U)

Lr-1 = MAX(31.1339 , 31.1339)

Lr-1 = 31.1339 psf

Ra = PI * R * SQRT(R^2 + hr^2) Ra = PI * 75.0677 * SQRT(75.0677^2 + 4.6917^2) Ra = 2,554,260.9252 in^2 or 17738 ft^2

Roof Plates Weight = density * Ra * t-actual

Roof Plates Weight = 0.2833 * 2,554,260.9252 * 0.1875

Roof plates Weight = 135,679.1475 lbf

BAY 2 DETAILS

MINIMUM # OF RAFTERS

l = Maximum rafter spacing per API-650 5.10.4.4 (in)

l-actual-2 = Actual rafter spacing (in)

Max-T1-2 = Due to roof thickness (psf) N-actual-2 = Actual number of rafter

N-min-2 = Minimum number of rafter

P = Uniform pressure as determined from load combinations described in Appendix R (psi)

P-ext-1-2 = Due to roof thickness vacuum limited by actual rafter spacing (psf)

R-2 = Outer radius (in)

RLoad-Max-2 = Maximun roof load based on actual rafter spacing (psf)

t-calc-2 = Minimum roof thickness based on actual rafter spacing (in)

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P = Lr-1

P = 0.2162 psi

R-2 = 898.8625 in

l = MIN(((t-Roof - CA-Roof) * SQRT((1.5 * Fy-Roof)/P)) , 84)

l = MIN(((0.1875 - 0) * SQRT((1.5 * 36,000) / 0.2162)) , 84)

l = MIN(93.705 , 84)

l = 84 in

N-min-2 = (2 * PI * R-2)/l

N-min-2 = (2 * PI * 898.8625)/84

N-min-2 = 68

N-min-2 must be a multiple of 8, therefore N-min-2 = 72.

N-actual-2 = 80

l-actual-2 = (2 * PI * R-2)/N-actual-2

l-actual-2 = (2 * PI * 898.8625)/80

l-actual-2 = 70.5965 in

Minimum roof thickness based on actual rafter spacing

t-calc-2 = l-actual-2/SQRT((1.5 * Fy-Roof)/P) + CA-Roof

t-calc-2 = 70.5965/SQRT((1.5 * 36,000)/0.2162) + 0

t-calc-2 = 0.1413 in

NOTE: Governs for roof plate thickness.

RLoad-Max-2 = (1.5 * Fy-Roof)/(l-actual-2/(t-Roof - CA-Roof))^2

RLoad-Max-2 = (1.5 * 36,000)/(70.5965/(0.1875 - 0))^2

RLoad-Max-2 = 54.852 psf

Max-T1-2 = RLoad-Max-2

Max-T1-2 = 54.852 psf

P-ext-1-2 = Max-T1-2 - DL - (0.4 * MAX(Sb , Lr))

P-ext-1-2 = 54.852 - 7.6779 - (0.4 * MAX(0 , 20))

P-ext-1-2 = -39.1741 psf

Pa-rafter-3-2 = P-ext-1-2

Pa-rafter-3-2 = -39.1741 psf

t-required-2 = MAX(0.1413 , (0.1875 + 0))

t-required-2 = 0.1875 in

RAFTER DESIGN

Average-p-width-2 = Average plate width (ft)

Average-r-s-inner-2 = Average rafter spacing on inner girder (ft)

Average-r-s-shell-2 = Average rafter spacing on shell (ft)

Max-P-2 = Load allowed for each rafter in ring (psi)

Max-r-span-2 = Maximum rafter span (ft)

Max-T1-rafter-2 = Due to roof thickness (psf) Mmax-rafter-2 = Maximum moment bending (in-lbf)

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P-ext-2-2 = Vacuum limited by rafter type (psf)

R-Inner-2 = Inner radius (ft)

Rafter-Weight-2 = (lb/ft)

Sx-rafter-actual-2 = Actual elastic section modulus about the x axis (in^3)

Sx-rafter-Req'd-2 = Required elastic section modulus about the x axis (in^3)

W-Max-rafter-2 = Maximum stress allowed for each rafter in ring (lbf/in)

W-rafter-2 = (lbf/in)

SPAN TO SHELL

P = 0.2162 psi

Rafter-Weight-2 = 22 lbf/ft

R-2 = 903 in

R-Inner2 = 447 in

Max-r-span-2 = (R-2 - R-Inner-2)/COS(Theta)

Max-r-span-2 = (903 - 447)/COS(3.5763)

Max-r-span-2 = 40.9261 ft

Average-r-s-inner-2 = (2 * PI * R-Inner-2)/N-actual-2

Average-r-s-inner-2 = (2 * PI * 447)/80

Average-r-s-inner-2 = 2.9256 ft

Average-r-s-shell-2 = (2 * PI * R-2)/N-actual-2

Average-r-s-shell-2 = (2 * PI * 903)/80

Average-r-s-shell-2 = 5.9101 ft

Average-p-width-2 = (Average-r-s-inner-2 + Average-r-s-shell-2)/2

Average-p-width-2 = (2.9256 + 5.9101)/2

Average-p-width-2 = 4.4179 ft

W-rafter-2 = (P * Average-p-width-2) + Rafter-Weight-2

W-rafter-2 = (0.2162 * 53.0148) + 1.8333

W-rafter-2 = 13.2954 lbf/in

Mmax-rafter-2 = (W-rafter-2 * Max-r-span-2^2)/8

Mmax-rafter-2 = (13.2954 * 491.1132^2)/8

Mmax-rafter-2 = 400,844 in-lbf

Sx-rafter-Req'd-2 = Mmax-rafter-2/Sd

Sx-rafter-Req'd-2 = 400,844/23,200

Sx-rafter-Req'd-2 = 17.2778 in^3

Sx-actual-2 = 23.2 in^3

W-Max-rafter-2 = (Sx-rafter-actual-2 * Sd * 8)/Max-r-span-2^2)

W-Max-rafter-2 = (23.2 * 23,200 * 8)/491.1132^2)

W-Max-rafter-2 = 17.8526 lbf/in

Max-P-2 = (W-Max-rafter-2 - Rafter-Weight-2)/Average-p-width-2

Max-P-2 = 0.3022 psi

Max-T1-rafter-2 = Max-P-2

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P-ext-2-2 = Max-T1-rafter-2 - DL - (Fp * MAX(S , Lr))

P-ext-2-2 = 43.5168 - 7.6779 - (0.4 * MAX(0 , 20))

P-ext-2-2 = -27.8345 psf

P2-rafter-3-2 = P-ext-2-2

P2-rafter-3-2 = -27.8345 psf

Limited by rafter type

GIRDER DESIGN

Average-p-width-previous-2 = Average plate width (ft)

C1-2 = (in)

C2-2 = (in)

F-Max-girder-2 = Maximum load allowed for each girder in ring (lbf)

Girder-Length-2 = Girder length (ft)

Girder-W-2 = Girder weight (lb)

Girder-W-previous-2 = Girder weight (lb)

Max-P-girder-2 = Load allowed for each rafter in ring (psi)

Max-r-span/2-actual-2 = Average maximum rafter span (ft)

Max-r-span/2-previous-2 = Average maximum rafter span previous (ft)

Max-T1-girder-2 = Due to roof thickness (psf) Mmax-girder-2 = Maximum moment bending (in-lbf)

N-columns-actual-2 = Actual number of columns

N-columns-previous-2 = Previous number of columns

N-previous-2 = Previous number of rafter

Num-Gird-actual-2 = Actual Number of girders

Num-Gird-Req-actual-2 = Required Number of girders

Num-Gird-Req-previous-2 = Required Number of girders previous

P-ext-4-2 = Vacuum limited by girder type (psi)

Pa-girder-2-2 = Vacuum limited by girder type (psi)

R-Inner-previous-2 = Inner radius (ft)

R-previous-2 = Outer radius (ft)

Sx-girder-actual-2 = Actual elastic section modulus about the x axis (in^3)

Sx-girder-Req'd-2 = Required elastic section modulus about the x axis (in^3)

W-girder-2 = Total load including weight of girder (lbf/in)

W-Max-girder-2 = Maximum stress allowed for each girder in ring (lbf/in)

W-rafter-actual-2 = (lbf/in)

W-rafter-previous-2 = (lbf/in)

W1-2 = Total rafter and roof load per girder length (lbf/in)

Wi-2 = Load due to inner rafters and roof (lbf)

Wo-2 = Load due to outer rafters and roof (lbf)

Num-Gird-actual-2 = 8

N-columns-actual-2 = 8

Girder-Length-2 = 344.4151 ft

Girder-W-2 = 50 lbf/ft

Wi-2 = W-rafter-previous-2 * Max-r-span/2-previous-2 * (Num-of-Rafters-Previous-2 / Number-of-columns)

Wi-2 = 9.2357 * 226.5 * (40 / 8)

Wi-2 = 10,390.1988 lbf

C2-2 = [(Radial-distance-next - Radial-distance-actual) / 2] * Num-Gird-Req-actual-2

C2-2 = [(900.0 - 450.0) / 2] * 10

C2-2 = 2250 in

Wo-2 = W-rafter-actual-2 * C2-2

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Wo-2 = 29,914.7288 lbf

W1-2 = (Wi-2 + Wo-2)/Girder-Length-2

W1-2 = (10,390.1988 + 29,914.7288)/344.4151

W1-2 = 117.0242 lbf/in

W-girder-2 = W1-2 + Girder-W-2

W-girder-2 = 117.0242 + 4.1666

W-girder-2 = 121.1909 lbf/in

Mmax-girder-2 = (W-girder-2 * Girder-Length-2^2)/8

Mmax-girder-2 = (121.1909 * 344.4151^2)/8

Mmax-girder-2 = 1,796,985 in-lbf

Sx-girder-Req'd-2 = Mmax-girder-2/Sd

Sx-girder-Req'd-2 = 1,796,985/23,200

Sx-girder-Req'd-2 = 77.4563 in^3

Sx-girder-actual-2 = 64.2 in^3

W-Max-girder-2 = (Sx-girder-actual-2 * Sd * 8)/Girder-Length-2^2

W-Max-girder-2 = (64.2 * 23,200 * 8)/344.4151^2

W-Max-girder-2 = 100.4497 lbf/in

Let C1-2 = Max-r-span/2-previous-2 * Num-Gird-Req-previous-2

C1-2 = 226.5 * 5

C1-2 = 1125 in

Let C2-2 = [(Radial-distance-next - Radial-distance-actual) / 2] * Num-Gird-Req-actual-2

C2-2 = [(900.0 - 450.0) / 2] * 10

C2-2 = 2250 in

F-Max-girder-2 = (W-Max-girder-2 - Girder-W-2) * Girder-Length-2

F-Max-girder-2 = (100.4497 - 4.1666) * 344.4151

F-Max-girder-2 = 33,161.3307 lbf

Solve for Max-P:

Max-P-girder-2 = (F-Max-girder-2 - (Girder-W-2 * Girder-W-previous-2) - (C1-2 * Girder-W-2))/((C2-2 * Average-p-width-previous-2) + (C1-2 * Average-p-width-2))

Max-P-girder-2 = (33,161.3307 - (50 * 0) - (1125 * 50))/((2250 * 38.0918) + (1125 * 4.4179))

Max-P-girder-2 = 0.1664 psi

COLUMN DESIGN

A-actual-2 = Actual area of column (in^2)

A-req-2 = Required area of column (in^2)

C-length-2 = Column length (in)

E-c = Modulus of elasticity of the column material (psi)

Fa-2 = Allowable compressive stress per API-650 5.10.3.4 (psi)

Fy-c = Allowable design stress (psi)

Max-P-column-2 = Maximum Load allowed for each column in ring (psi)

Max-T1-column-2 = Due to roof thickness (psf)

P-c-2 = Total roof load supported by each column (lbf)

P-ext-3-2 = Vacuum limited by column type (psf)

Pa-column-3-2 = Vacuum limited by column type (psi)

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Radius-Gyr-2 = Radius of gyration

Radius-Gyr-req-2 = Radius of gyration required

W-column-2 = Total weight of column (lbf)

W-Max-column-2 = Maximum weight allowed for each column in ring (lbf)

Wi-2 = Load due to inner rafters and roof (lbf)

Wo-2 = Load due to outer rafters and roof (lbf)

W1-2 = Total rafter and roof load per girder length (lbf/in)

W-girder-2 = Total load including weight of girder (lbf/in)

AT GIRDER RING OUTER Radius = 75.25 ft

W-column-2 = 1,640.1602 lbf

Fy-c = 35,000 psi

E-c = 28,600,000.38 psi

A-actual-2 = 11.9083 in^2

C-length-2 = 40.4587 ft

Radius-Gyr-2 = 3.6717 in

If C-length-2/Radius-Gyr-2 must be less than 180, then

Radius-Gyr-req-2 = C-length-2/180

Radius-Gyr-req-2 = 40.4587/180

Radius-Gyr-req-2 = 2.6972 in

Per API-650 5.10.3.3

R-c-2 = C-length-2/Radius-Gyr-2

R-c-2 = 40.4587/3.6717

R-c-2 = 132.2306

Rafter-L-2 = (- R-2 - R-Inner2)/COS(Theta)

Rafter-L-2 = (- 898.8625 - 408.7058)/COS(3.5763)

Rafter-L-2 = 491.1131 in

Wi-2 = W-rafter-previous-2 * Max-r-span/2-previous-2 * (Num-of-Rafters-Previous-2 / Number-of-columns)

Wi-2 = 9.2357 * 226.5 * (40 / 8)

Wi-2 = 10,390.1988 lbf

C2-2 = [(Radial-distance-next - Radial-distance-actual) / 2] * Num-Gird-Req-actual-2

C2-2 = [(900.0 - 450.0) / 2] * 10

C2-2 = 2250 in

Wo-2 = W-rafter-actual-2 * C2-2

Wo-2 = 13.2954 * 2250 Wo-2 = 29,914.7288 lbf

W1-2 = (Wi-2 + Wo-2)/Girder-Length-2

W1-2 = (10,390.1988 + 29,914.7288)/344.4151

W1-2 = 117.0242 lbf/in

W-girder-2 = W1-2 + Girder-W-2

W-girder-2 = 117.0242 + 4.1666

W-girder-2 = 121.1909 lbf/in

P-c-2 = W-column-2 + (W-girder-2 * Girder-Length-2)

P-c-2 = 1,640.1602 + (121.1909 * 344.4151)

(14)

Since R-c-2 > 120, using API-650 Formulas in 5.10.3.4

Fa-2 = (/ (* 12 (EXPT PI 2) E-c) (* 23 (EXPT R-c-2 2)))

Fa-2 = (/ (* 12 (EXPT PI 2) 28,600,000.38) (* 23 (EXPT 132.2306 2)))

Per API-650 M.3.5

Fa is not modified Since Design Temp. <= 200 ºF.

(API-650 M.3.5 N.A.)

Fa-2 = 8,971.4086 psi

A-req-2 = P-c-2/Fa-2

A-req-2 = 43,380.1508/8,971.4086

A-req-2 = 4.8354 in^2

W-Max-column-2 = (Fa-2 * A-actual-2) - W-column-2

W-Max-column-2 = (8,971.4086 * 11.9083) - 1,640.1602

W-Max-column-2 = 105,193.9348 lbf

Max-P-column-2 = ((W-Max-column-2/((Rafter-L-2 * N-actual-2)/2)) - Rafter-Weight-2)/(AVERAGE Average-r-s-inner-2 , Average-r-s-shell-2)

Max-P-column-2 = ((105,193.9348/((491.1131 * 80)/2)) - 22)/(AVERAGE 2.675 , 5.883)

Max-P-column-2 = 0.5005 psi

Max-T1-column-2 = Max-P-column-2

Max-T1-column-2 = 72.072 psf

P-ext-3-2 = Max-T1-column-2 - DL - (Fp * MAX(S , Lr))

P-ext-3-2 = 72.072 - 7.6779 - (0.4 * MAX(0 , 20))

P-ext-3-2 = -56.3917 psf

Pa-column-3-2 = P-ext-3-2

Pa-column-3-2 = -56.3917 psf

Limited by column type

BAY 1 DETAILS

MINIMUM # OF RAFTERS

l = Maximum rafter spacing per API-650 5.10.4.4 (in)

l-actual-1 = Actual rafter spacing (in)

Max-T1-1 = Due to roof thickness (psf) N-actual-1 = Actual number of rafter

N-min-1 = Minimum number of rafter

P = Uniform pressure as determined from load combinations described in Appendix R (psi)

P-ext-1-1 = Due to roof thickness vacuum limited by actual rafter spacing (psf)

RLoad-Max-1 = Maximun roof load based on actual rafter spacing (psf)

t-calc-1 = Minimum roof thickness based on actual rafter spacing (in)

FOR GIRDER RING OUTER Radius = 37.5 ft

(15)

P = Lr-1

P = 0.2162 psi

R-1 = 450 in

l = MIN(((t-Roof - CA-Roof) * SQRT((1.5 * Fy-Roof)/P)) , 84)

l = MIN(((0.1875 - 0) * SQRT((1.5 * 36,000) / 0.2162)) , 84)

l = MIN(93.705 , 84)

l = 84 in

N-min-1 = (2 * PI * R-1)/l

N-min-1 = (2 * PI * 450)/84

N-min-1 = 34

N-min-1 must be a multiple of 8, therefore N-min-1 = 40.

N-actual-1 = 40

l-actual-1 = (2 * PI * R-1)/N-actual-1

l-actual-1 = (2 * PI * 450)/40

l-actual-1 = 70.6858 in

Minimum roof thickness based on actual rafter spacing

t-calc-1 = l-actual-1/SQRT((1.5 * Fy-Roof)/P) + CA-Roof

t-calc-1 = 70.6858/SQRT((1.5 * 36,000)/0.2162) + 0

t-calc-1 = 0.1414 in

NOTE: Governs for roof plate thickness.

RLoad-Max-1 = (1.5 * Fy-Roof)/(l-actual-1/(t-Roof - CA-Roof))^2

RLoad-Max-1 = (1.5 * 36,000)/(70.6858/(0.1875 - 0))^2

RLoad-Max-1 = 54.7134 psf

Max-T1-1 = RLoad-Max-1

Max-T1-1 = 54.7134 psf

P-ext-1-1 = Max-T1-1 - DL - (0.4 * MAX(Sb , Lr))

P-ext-1-1 = 54.7134 - 7.6779 - (0.4 * MAX(0 , 20))

P-ext-1-1 = -39.0356 psf

Pa-rafter-3-1 = P-ext-1-1

Pa-rafter-3-1 = -39.0356 psf

t-required-1 = MAX(0.1414 , (0.1875 + 0))

t-required-1 = 0.1875 in

RAFTER DESIGN

Average-p-width-1 = Average plate width (ft)

Average-r-s-inner-1 = Average rafter spacing on inner girder (ft)

Average-r-s-shell-1 = Average rafter spacing on shell (ft)

Max-P-1 = Load allowed for each rafter in ring (psi)

Max-r-span-1 = Maximum rafter span (ft)

Max-T1-rafter-1 = Due to roof thickness (psf) Mmax-rafter-1 = Maximum moment bending (in-lbf)

(16)

P-ext-2-1 = Vacuum limited by rafter type (psf)

R-Inner-1 = Inner radius (ft)

Rafter-Weight-1 = (lb/ft)

Sx-rafter-actual-1 = Actual elastic section modulus about the x axis (in^3)

Sx-rafter-Req'd-1 = Required elastic section modulus about the x axis (in^3)

W-Max-rafter-1 = Maximum stress allowed for each rafter in ring (lbf/in)

W-rafter-1 = (lbf/in)

SPAN TO GIRDER RING OUTER Radius = 37.75 ft

P = 0.2162 psi

Rafter-Weight-1 = 12 lbf/ft

R-1 = 453 in

R-Inner1 = 32 in

Max-r-span-1 = (R-1 - R-Inner-1)/COS(Theta)

Max-r-span-1 = (453 - 32)/COS(3.5763)

Max-r-span-1 = 35.2765 ft

Average-r-s-inner-1 = (2 * PI * R-Inner-1)/N-actual-1

Average-r-s-inner-1 = (2 * PI * 32)/40

Average-r-s-inner-1 = 0.4189 ft

Average-r-s-shell-1 = (2 * PI * R-1)/N-actual-1

Average-r-s-shell-1 = (2 * PI * 453)/40

Average-r-s-shell-1 = 5.9298 ft

Average-p-width-1 = (Average-r-s-inner-1 + Average-r-s-shell-1)/2

Average-p-width-1 = (0.4189 + 5.9298)/2

Average-p-width-1 = 3.1743 ft

W-rafter-1 = (P * Average-p-width-1) + Rafter-Weight-1

W-rafter-1 = (0.2162 * 38.0916) + 1

W-rafter-1 = 9.2357 lbf/in

Mmax-rafter-1 = (W-rafter-1 * Max-r-span-1^2)/8

Mmax-rafter-1 = (9.2357 * 423.318^2)/8

Mmax-rafter-1 = 206,879 in-lbf

Sx-rafter-Req'd-1 = Mmax-rafter-1/Sd

Sx-rafter-Req'd-1 = 206,879/23,200

Sx-rafter-Req'd-1 = 8.9172 in^3

Sx-actual-1 = 10.9 in^3

W-Max-rafter-1 = (Sx-rafter-actual-1 * Sd * 8)/Max-r-span-1^2)

W-Max-rafter-1 = (10.9 * 23,200 * 8)/423.318^2)

W-Max-rafter-1 = 11.2893 lbf/in

Max-P-1 = (W-Max-rafter-1 - Rafter-Weight-1)/Average-p-width-1

Max-P-1 = 0.2701 psi

Max-T1-rafter-1 = Max-P-1

(17)

P-ext-2-1 = Max-T1-rafter-1 - DL - (Fp * MAX(S , Lr))

P-ext-2-1 = 38.8944 - 7.6779 - (0.4 * MAX(0 , 20))

P-ext-2-1 = -23.2195 psf

P2-rafter-3-1 = P-ext-2-1

P2-rafter-3-1 = -23.2195 psf

Limited by rafter type

GIRDER DESIGN

NOT REQUIRED FOR CENTER COLUMN

CENTER COLUMN

A-actual-1 = Actual area of column (in^2)

A-req-1 = Required area of column (in^2)

C-length-1 = Column length (in)

E-c = Modulus of elasticity of the column material (psi)

Fa-1 = Allowable compressive stress per API-650 5.10.3.4 (psi)

Fy-c = Allowable design stress (psi)

Max-P-column-1 = Maximum Load allowed for each column in ring (psi)

Max-T1-column-1 = Due to roof thickness (psf)

P-c-1 = Total roof load supported by each column (lbf)

P-ext-3-1 = Vacuum limited by column type (psf)

Pa-column-3-1 = Vacuum limited by column type (psi)

R-c-1 = Per API-650 5.10.3.3

Radius-Gyr-1 = Radius of gyration

Radius-Gyr-req-1 = Radius of gyration required

W-column-1 = Total weight of column (lbf)

W-Max-column-1 = Maximum weight allowed for each column in ring (lbf)

W-column-1 = 1,770.1605 lbf

Fy-c = 35,000 psi

E-c = 28,600,000.38 psi

A-actual-1 = 11.9083 in^2

C-length-1 = 43.6853 ft

Radius-Gyr-1 = 3.6717 in

If C-length-1/Radius-Gyr-1 must be less than 180, then

Radius-Gyr-req-1 = C-length-1/180

Radius-Gyr-req-1 = 43.6853/180

Radius-Gyr-req-1 = 2.9124 in

Per API-650 5.10.3.3

R-c-1 = C-length-1/Radius-Gyr-1

R-c-1 = 43.6853/3.6717

R-c-1 = 142.776

Rafter-L-1 = (- R-1 - R-Inner1)/COS(Theta)

Rafter-L-1 = (- 450 - 0)/COS(3.5763)

(18)

Rafter-L-1 = 423.3185 in

P-c-1 = W-column-1 + (Rafter-L-1 * W-rafter-1 * N-actual-1)/2

P-c-1 = 1,770.1605 + (423.3185 * 9.2357 * 40)/2

P-c-1 = 79,963.2946 lbf

Since R-c-1 > 120, using API-650 Formulas in 5.10.3.4

Fa-1 = (/ (* 12 (EXPT PI 2) E-c) (* 23 (EXPT R-c-1 2)))

Fa-1 = (/ (* 12 (EXPT PI 2) 28,600,000.38) (* 23 (EXPT 142.776 2)))

Per API-650 M.3.5

Fa is not modified Since Design Temp. <= 200 ºF.

(API-650 M.3.5 N.A.)

Fa-1 = 8,152.9746 psi

A-req-1 = P-c-1/Fa-1

A-req-1 = 79,963.2946/8,152.9746

A-req-1 = 9.8079 in^2

W-Max-column-1 = (Fa-1 * A-actual-1) - W-column-1

W-Max-column-1 = (8,152.9746 * 11.9083) - 1,770.1605

W-Max-column-1 = 95,317.7892 lbf

Max-P-column-1 = ((W-Max-column-1/((Rafter-L-1 * N-actual-1)/2)) - Rafter-Weight-1)/(AVERAGE Average-r-s-inner-1 , Average-r-s-shell-1)

Max-P-column-1 = ((95,317.7892/((423.3185 * 40)/2)) - 12)/(AVERAGE 0 , 5.8905)

Max-P-column-1 = 0.2693 psi

Max-T1-column-1 = Max-P-column-1

Max-T1-column-1 = 38.7792 psf

P-ext-3-1 = Max-T1-column-1 - DL - (Fp * MAX(S , Lr))

P-ext-3-1 = 38.7792 - 7.6779 - (0.4 * MAX(0 , 20))

P-ext-3-1 = -23.1024 psf

Pa-column-3-1 = P-ext-3-1

Pa-column-3-1 = -23.1024 psf

Limited by column type

P-max-ext-T = MAX(P-ext-1-1 , P-ext-2-1 , P-ext-3-1 , P-ext-1-2 , P-ext-2-2 , P-ext-3-2)

P-max-ext-T = MAX(-39.0356 , -23.2195 , -23.1024 , -39.1741 , -27.8345 , -56.3917)

P-max-ext-T = -0.1604 psi or -23.1024 psf

Warning!!

1.- Please revise the Structure, there is a problem in the sizes.

TOP MEMBER DESIGN

CA_roof (Thickness of roof plate) = 0 in CA_shell (Thickness of shell plate) = 0 in D (Shell nominal diameter) = 150.0625 ft

(19)

ID (Shell inside diameter) = 150.0 ft

Theta angle (Angle between the roof and a horizontal plane at the roof-to-shell junction) = 3.5763 deg tc (Thickness of shell plate) = 0.3125 in

th (Thickness of roof plate) = 0.1875 in

Shell inside radius

Rc = ID / 2 = 1800.0 / 2 = 900.0 in Shell nominal diameter (D) = 150.0625 ft

Length of normal to roof

R2 = Rc / SIN(Theta angle) = 900.0 / SIN(3.5763) = 14428.0976 in

Thickness of corroded roof plate

th_corroded = th - CA_roof = 0.1875 - 0 = 0.1875 in

Thickness of corroded shell plate

tc_corroded = tc - CA_shell = 0.3125 - 0 = 0.3125 in

Maximum width of participating roof API-650 Figure F-2

Wh = MIN((0.3 * SQRT((R2 * th_corroded))) , 12) = MIN((0.3 * SQRT((14428.0976 * 0.1875))) , 12) = 12 in

Maximum width of participating shell API-650 Figure F-2

Wc = 0.6 * SQRT((Rc * tc_corroded)) = 0.6 * SQRT((900.0 * 0.3125)) = 10.0623 in

Nominal weight of shell plates and framing

DLS = Ws + W_framing = 344435.3687 + 59409.7227 = 403845.0914 lbf

Nominal weight of roof plates and attached structural

DLR = Wr + W_structural = 135679.1475 + 677.7268 = 136356.8743 lbf

Compression Ring Detail d Properties

ID (Shell inside diameter) = 150.0 ft Size (Compression ring size) = l3x3x3/8 Wc (Length of contributing shell) = 10.0623 in Wh (Length of contributing roof) = 12 in tc (Thickness of shell plate) = 0.3125 in th (Thickness of roof plate) = 0.1875 in Angle vertical leg size (l_vert) = 3.0 in Angle horizontal leg size (l_horz) = 3.0 in Angle thickness (t_angle) = 0.375 in Angle area (A_angle) = 2.11 in^2 Angle centroid (c_angle) = 0.884 in

Angle moment of inertia (I_angle) = 1.75 in^4

Length of contributing shell reduced

wc_reduced = Wc - l_vert = 10.0623 - 3.0 = 7.0623 in

Contributing shell moment of inertia

I_shell = (wc_reduced * (tc_corroded^3)) / 12 = (7.0623 * (0.3125^3)) / 12

= 0.018 in^4

Contributing shell area

(20)

Contributing roof area

A_roof = Wh * th_corroded = 12 * 0.1875 = 2.25 in^2

Detail total area

A_detail = A_shell + A_roof + A_angle = 2.207 + 2.25 + 2.11 = 6.567 in^2

Find combined moment of inertia about shell inside axis with negative value toward center

Description Variable

Equation

Value Unit

Shell centroid

d_shell

tc_corroded / 2

0.1563 in

Stiffener centroid

d_stiff

(the-reference (current-object) '(superior

angle-centroid) t t t nil 'default-the-error

nil)

0.8840 in

moment of inertia of

first body

I_1

I_angle + (A_angle * (d_stiff^2))

3.3989 in^4

moment of inertia of

second body

I_2

I_shell + (A_shell * (d_shell^2))

0.0718 in^4

Total area

A_sum

A_angle + A_shell

4.3170 in^2

Sum of moments of

inertia's

I_sum

I_1 + I_2

3.4707 in^4

Combined centroid

c_combined

((d_stiff * A_angle) + (d_shell * A_shell))

/ (A_angle + A_shell)

0.5120 in

Combined moment of

inertia

I_combined I_sum - (A_sum * (c_combined^2))

2.3393 in^4

Distance from neutral

axis to edge 1 (inside)

e1 l_horz

-

c_combined

2.4880 in

Distance from neutral

axis to edge 2 (outside)

e2 l_horz

-

e1

0.5120 in

Combined stiffener

shell section modulus

S

I_combined / MAX(e1 , e2)

0.9402 in^3

Roof Design Requirements

Appendix F Requirements

A_actual (Area resisting compressive force) = 6.567 in^2 D (Tank nominal diameter) = 150.0625 ft

DLR (Nominal weight of roof plates and attached structural) = 136356.8743 lbf DLS (Nominal weight of shell plates and framing) = 403845.0914 lbf

Fy (Minimum specified yield-strength of the materials in the roof-to-shell junction) = 36000 psi ID (Tank inside diameter) = 150.0 ft

Mw (Wind moment) = 6.6057000203E6 ft.lbf P (Design pressure) = 0.1 psi

Theta angle (Angle between the roof and a horizontal plane at the roof-to-shell junction) = 3.5763 deg W_framing (Weight of framing supported by the shell and roof) = 59409.7227 lbf

W_structural (Weight of roof attached structural) = 677.7268 lbf Wr (Roof plates weight) = 135679.1475 lbf

(21)

Uplift due to internal pressure API-650 F.1.2

P_uplift = P * pi * ((ID^2) / 4) = 0.1 * pi * ((1800.0^2) / 4) = 254469.0049 lbf

Weight of roof shell and attached-framing

W_total = Wr + Ws + W_framing

= 135679.1475 + 344435.3687 + 59409.7227 = 539524.2389 lbf

Net uplift due to internal pressure

Net_uplift = MAX((P_uplift - W_total) , 0)

= MAX((254469.0049 - 539524.2389) , 0) = 0 lbf

Wr < P_uplift <= W_total , Tank design should meet F.2 to F.6 requirements.

Maximum design pressure API 650 F.4.1

P_F41 = ((0.962 * A_actual * Fy * TAN(Theta angle)) / (D^2)) + ((0.245 * DLR) / (D^2)) = ((0.962 * 6.567 * 36000 * TAN(3.5763)) / (150.0625^2)) + ((0.245 * 136356.8743) / (150.0625^2))

= 2.1148 inH2O

Maximum design pressure for unanchored tank API 650 F.4.2

P_F42 = (((0.1632 * DLS) / (D^2)) + ((0.245 * DLR) / (D^2))) - ((0.2938 * Mw) / (D^3))

= (((0.1632 * 403845.0914) / (150.0625^2)) + ((0.245 * 136356.8743) / (150.0625^2))) - ((0.2938 * 6.6057000203E6) / (150.0625^3))

= 3.836 inH2O

Maximum design pressure

P_max = MIN(P_F41 , P_F42) = MIN(2.1148 , 3.836) = 2.1148 inH2O P > P_max ==> Design pressure is greater that maximum allowable pressure

*** WARNING *** : Design pressure is greater that maximum allowable pressure

Required area API 650 F.5.1

A_F51 = ((D^2) * (P - ((0.245 * DLR) / (D^2)))) / (0.962 * Fy * TAN(Theta angle))

= ((150.0625^2) * (2.7682 - ((0.245 * 136356.8743) / (150.0625^2)))) / (0.962 * 36000 * TAN(3.5763))

= 13.3657 in^2

A_actual < A_F51 ==> Compression region actual cross sectional area is not sufficient.

*** WARNING *** : Reinforcement needed due to insufficient cross sectional area. As per API-650 5.2.1 c), Maximum design internal pressure (P_std) = 2.5 psi

Maximum allowable internal pressure for the actual resisting area API 650 F.5.1

P_F51 = ((0.962 * Fy * TAN(Theta angle) * A_actual) / (D^2)) + ((0.245 * DLR) / (D^2)) = ((0.962 * 36000 * TAN(3.5763) * 6.567) / (150.0625^2)) + ((0.245 * 136356.8743) / (150.0625^2))

= 2.1148 inH2O

Maximum allowable internal pressure

P_max_internal = MIN(P_std , P_F51 , P_max) = MIN(2.5 , 0.0764 , 0.0764)

= 0.0764 psi

(22)

A_resisting (Detail resisting area) = 6.567 in^2 D (Nominal Tank Diameter) = 150.0625 ft

E (Modulus of Elasticity of Roof Plate Material) = 2.879999924E7 lb/in^2 H (Shell Height) = 40 ft

I_combined (Combined stiffener shell moment of inertia) = 2.3393 in^4 N (Waves Quantity) = 10.0

P (Total design external pressure for design of shell) = 37.0932 psf Pr (Total design external pressure for design of roof) = 31.1339 lb/ft^2 f (Smallest Allowable Tensile Stress) = 23200 psi

Radial Load Imposed on End Stiffener by Shell API 650 Section V.8.2.3.1

V1 = (Ps * H) / 48 = (37.0932 * 40) / 48 = 30.911 lb/in

End Stiffener Region Required Moment of Inertia API 650 Section V.8.2.3.2

Ireqd = (684 * V1 * (D^3)) / (E * ((N^2) - 1))

= (684 * 30.911 * (150.0625^3)) / (2.879999924E7 * ((10.0^2) - 1)) = 25.0586 in^4

I_combined < Ireqd ==> Combined stiffener shell moment of inertia is not sufficient.

*** WARNING *** : Reinforcement needed due to insufficient combined stiffener shell moment of inertia.

End Stiffener Region Required Cross Sectional Area API 650 Section V.8.2.3.3.1

Areqd = (6 * V1 * D) / f = (6 * 30.911 * 150.0625) / 23200.0 = 1.1996 in^2

Top stiffener required cross sectional area

A_stiff = (Areqd) = (1.1996) = 1.1996 in^2

A_resisting >= A_stiff ==> Compression region actual cross sectional area is sufficient.

Warning!!

1.- Design pressure is greater that maximum allowable pressure 2.- Reinforcement needed due to insufficient cross sectional area.

3.- Reinforcement needed due to insufficient combined stiffener shell moment of inertia.

SUMMARY OF ROOF RESULTS

Back

Material = A36

Structural Material = A36

t-actual = 0.1875 in

t-required = 0.1875 in

t-calc = 0.1875 in

P-Max-Internal = 0.0764 psi

P-Max-External = -0.1604 psi

Roof Plates Weight = 135,679.1475 lbf

Weight of Rafters = 88,962.6649 lbf

Weight of Girders = 11,480.5029 lbf

(23)

SHELL COURSE DESIGN (Bottom course is #1)

Back

API-650 ONE FOOT METHOD

D = Tank Nominal diameter (ft) per API-650 5.6.1.1 Note 1

H = Max liquid level (ft)

I-p = Design internal pressure (psi)

L = Factor

I-p = 0.1 psi

D = 150 ft

H = 40 ft

L = (6 * D (t-1 - Ca-1))^0.5

L = (6 * 150 (0.75 - 0))^0.5 = 25.9808

Course # 1

Ca-1 = Corrosion allowance per API-650 5.3.2 (in)

G = Design specific gravity of the liquid to be stored

H' = Effective liquid head at design pressure (ft)

hmax-1 = Max liquid level based on shell thickness (ft)

JE = Joint efficiency

pmax-1 = Max pressure at design (psi)

pmax-int-shell-1 = Max internal pressure at design (psi)

Sd = Allowable design stress for the design condition per API-650 Table 5-2a (psi)

St = Allowable stress for the hydrostatic test condition per API-650 5.6.2.2 (psi)

t-1 = Shell actual thickness (in)

t-calc-1 = Shell thickness design condition td (in)

t-seismic-1 = See E.6.2.4 table in SEISMIC calculations.

t-test-1 = Shell thickness hydrostatic test condition (in)

Material = A36

Width = 8 ft

Ca-1 = 0 in

JE = 1 t-1 = 0.75 in

Sd = 23,200 psi

St = 24,900 psi

Design Condition G = 1 (per API-650)

H' = H

H' = 40

H' = 40 ft

t-calc-1 = (2.6 * D * (H' - 1) * G)/Sd + Ca-1 (per API-650 5.6.3.2)

t-calc-1 = (2.6 * 150 * (40 - 1) * 1)/23,200 + 0

t-calc-1 = 0.6556 in

hmax-1 = Sd * (t-1 - CA-1)/(2.6 * D * G) + 1

hmax-1 = 23,200 * (0.75 - 0)/(2.6 * 150 * 1) + 1

hmax-1 = 45.6154 ft

pmax-1 = (hmax-1 - H) * 0.433 * G

pmax-1 = (45.6154 - 40) * 0.433 * 1

pmax-1 = 2.4315 psi

pmax-int-shell-1 = pmax-1

(24)

pmax-int-shell-1 = 2.4315 psi

Hydrostatic Test Condition G = 1

H' = H

H' = 40

H' = 40 ft

t-test-1 = (2.6 * D * (H' - 1))/St

t-test-1 = (2.6 * 150 * (40 - 1))/24,900

t-test-1 = 0.6108 in

Course # 2

Material = A36

Width = 8 ft

Ca-2 = 0 in

JE = 1 t-2 = 0.5625 in

Sd = 23,200 psi

St = 24,900 psi

H' = H

H' = 32

H' = 32 ft

t-calc-2 = (2.6 * 150 * (32 - 1) * 1)/23,200 + 0

t-calc-2 = 0.5211 in

hmax-2 = Sd * (t-2 - CA-2)/(2.6 * D * G) + 1

hmax-2 = 23,200 * (0.5625 - 0)/(2.6 * 150 * 1) + 1

hmax-2 = 34.4615 ft

pmax-2 = (hmax-2 - H) * 0.433 * G

pmax-2 = (34.4615 - 32) * 0.433 * 1

pmax-2 = 1.0658 psi

pmax-int-shell-2 = MIN(pmax-int-shell-1 pmax-2)

pmax-int-shell-2 = MIN(2.4315 1.0658)

(25)

H' = H

H' = 32

H' = 32 ft

t-test-2 = (2.6 * D * (H' - 1))/St

t-test-2 = (2.6 * 150 * (32 - 1))/24,900

t-test-2 = 0.4855 in

Course # 3

Material = A36

Width = 8 ft

Ca-3 = 0 in

JE = 1 t-3 = 0.3125 in

Sd = 23,200 psi

St = 24,900 psi

H' = H

H' = 24

H' = 24 ft

t-calc-3 = (2.6 * 150 * (24 - 1) * 1)/23,200 + 0

t-calc-3 = 0.3866 in

hmax-3 = Sd * (t-3 - CA-3)/(2.6 * D * G) + 1

hmax-3 = 23,200 * (0.3125 - 0)/(2.6 * 150 * 1) + 1

hmax-3 = 19.5897 ft

pmax-3 = (hmax-3 - H) * 0.433 * G

pmax-3 = (19.5897 - 24) * 0.433 * 1

pmax-3 = -1.9096 psi

pmax-int-shell-3 = MIN(1.0658 -1.9096)

pmax-int-shell-3 = 0 psi (Since pmax-int-shell-3 < 0, pmax-int-shell-3 = 0 psi)

(26)

H' = H

H' = 24

H' = 24 ft

t-test-3 = (2.6 * D * (H' - 1))/St

t-test-3 = (2.6 * 150 * (24 - 1))/24,900

t-test-3 = 0.3602 in

Course # 4

Material = A36

Width = 8 ft

Ca-4 = 0 in

JE = 1 t-4 = 0.3125 in

Sd = 23,200 psi

St = 24,900 psi

H' = H

H' = 16

H' = 16 ft

t-calc-4 = (2.6 * 150 * (16 - 1) * 1)/23,200 + 0

t-calc-4 = 0.2522 in

hmax-4 = Sd * (t-4 - CA-4)/(2.6 * D * G) + 1

hmax-4 = 23,200 * (0.3125 - 0)/(2.6 * 150 * 1) + 1

hmax-4 = 19.5897 ft

pmax-4 = (hmax-4 - H) * 0.433 * G

pmax-4 = (19.5897 - 16) * 0.433 * 1

pmax-4 = 1.5544 psi

pmax-int-shell-4 = MIN(0 1.5544)

pmax-int-shell-4 = 0 psi

H' = H

(27)

H' = 16 ft

t-test-4 = (2.6 * D * (H' - 1))/St

t-test-4 = (2.6 * 150 * (16 - 1))/24,900

t-test-4 = 0.2349 in

Course # 5

Material = A36

Width = 7.75 ft

Ca-5 = 0 in

JE = 1 t-5 = 0.3125 in

Sd = 23,200 psi

St = 24,900 psi

H' = H

H' = 8

H' = 8 ft

t-calc-5 = (2.6 * 150 * (8 - 1) * 1)/23,200 + 0

t-calc-5 = 0.1177 in

hmax-5 = Sd * (t-5 - CA-5)/(2.6 * D * G) + 1

hmax-5 = 23,200 * (0.3125 - 0)/(2.6 * 150 * 1) + 1

hmax-5 = 19.5897 ft

pmax-5 = (hmax-5 - H) * 0.433 * G

pmax-5 = (19.5897 - 8) * 0.433 * 1

pmax-5 = 5.0184 psi

pmax-int-shell-5 = MIN(0 5.0184)

pmax-int-shell-5 = 0 psi

H' = H

H' = 8

(28)

t-test-5 = (2.6 * D * (H' - 1))/St

t-test-5 = (2.6 * 150 * (8 - 1))/24,900

t-test-5 = 0.1096 in

SUMMARY OF SHELL RESULTS

Back

t-min-Seismic = See API-650 E.6.1.4, table in SEISMIC calculations.

Shell API-650 Summary (Bottom is 1)

She ll # Widt h (in) Materi al C A (in ) J E Min Yield Strengt h (psi) Tensile Strengt h (psi) Sd (psi) St (psi) Weigh t (Lbf) Weigh t CA (Lbf) t-min Erectio n (in) t-Des (in) t-Test (in) t-min Seismi c (in) t-min Ext-Pe (in) t-min (in) t-Actu al (in) Statu s 1 96 A36 0 1 36,000 58,000 23,20 0 24,90 0 115,29 7 115,29 7 0.3125 0.655 6 0.610 8 0.5087 0.435 9 0.655 6 0.75 OK 2 96 A36 0 1 36,000 58,000 23,20 0 24,90 0 86,482 86,482 0.3125 0.521 1 0.485 5 0.4062 0.435 9 0.521 1 0.562 5 OK 3 96 A36 0 1 36,000 58,000 23,20 0 24,90 0 48,052 48,052 0.3125 0.386 6 0.360 2 0.3029 0.435 9 0.435 9 0.312 5 FAIL 4 96 A36 0 1 36,000 58,000 23,20 0 24,90 0 48,052 48,052 0.3125 0.252 2 0.234 9 0.199 0.435 9 0.435 9 0.312 5 FAIL 5 93 A36 0 1 36,000 58,000 23,20 0 24,90 0 46,550 46,550 0.3125 0.117 7 0.109 6 0.0948 0.435 9 0.435 9 0.312 5 FAIL Total Weight = 344,435.3686 Lbf

Warning!!

1.- Please revise the shell thk, 3 courses have problems.

2.- The required minimum thickness based on external pressure is greater than the available thickness and the shell must be stiffened.

API-650 APPENDIX V FOR EXTERNAL PRESSURE

V = Wind load velocity (mph)

W = Wind pressure (psf)

Pe = External Pressure (psi)

Ps = Shell design pressure (psf)

t-width = Shell ring actual width (ft)

t-course = Shell ring actual thickness (in)

t-uniform = as-built thickness, unless otherwise specified, of the thinnest shell course, (in)

Wtr = Transposed width of each shell course (ft)

Hts = Height of the transformed shell (ft)

V = 125 mph

Pe = 8.64 psf

W = 31 * (V/120)^2

W = 31 * (125/120)^2

W = 33.6372 psf

Ps = MAX(Pe , (W + (Fp * Pe)))

Ps = MAX(8.64 , (33.6372 + (0.4 * 8.64)))

Ps = 37.0932 psf

(29)

Hts = SUM(Wtr)

Transforming courses (1) to (5)

Wtr-1 = 8 * (0.3125 / 0.75)^2.5 = 0.8965 ft

Wtr-2 = 8 * (0.3125 / 0.5625)^2.5 = 1.8404 ft

Wtr-3 = 8 * (0.3125 / 0.3125)^2.5 = 8 ft

Wtr-4 = 8 * (0.3125 / 0.3125)^2.5 = 8 ft

Wtr-5 = 8 * (0.3125 / 0.3125)^2.5 = 8 ft

Hts = 26.7369 ft

INTERMEDIATE STIFFENER CALCULATIONS PER API-650 APP. V.8

A-reqd-(n) = Required area (in^2)

A-stiff-(n) = Area required by Stiffener (in^2)

A-stiff-actual-(n) = Actual area (in^2)

Bottom-OD = Bottom floor OD diameter per API-650 5.6.1.1 Note 1 (ft)

D = Nominal diameter per API-650 5.6.1.1 Note 1 (ft)

E = Modulus of elasticity of the roof plate material (psi)

EFC = Elastic failure

F-btm = Allowable stress for bottom floor (psi)

F-roof = Allowable stress for thinnest shell (psi)

F-stiff = Allowable stress for stiffener (psi)

Fc = Smallest allowable compressive stress (psi)

Fp = Pressure Combination Ratio

Fy-shell = Minimum yield strength for shell material (Table 5-2b) (psi)

Fy-stiff = Minimum yield strength for stiffener material (Table 5-2b) (psi)

Hs = Maximum unstiffened shell height (ft)

Hts = Height of the transformed shell (ft)

I-actual-(n) = Actual moment of inertia (in^4)

I-reqd-(n) = Required moment of inertia (in^4)

JEb = Bottom joint efficiency

JEn = Bottom shell course joint efficiency

JEr = Roof joint efficiency

JEs = Top shell course joint efficiency

Ls = Actual spacing (ft)

Lx = Maximum stiffener spacing on transposed shell (ft)

L_act = Actual Transform Height Spacing between Stiffeners (ft)

N = Number of waves

NS = Number of stiffeners required

NS-actual = Actual Number of stiffeners

Pe = External Pressure (psf)

Ps = Shell design pressure (psf)

Ps-Max = Maximum allowable external pressure for unstiffened shell (psf)

PSI-C = Stability factor

PSI1 = Stability factor under condition 1 (V.8.1)

PSI2 = Stability factor under condition 2 (V.8.1)

Pv-Max-1 = Maximum allowable external pressure for unstiffened shell under condition 1 (psf)

Pv-Max-2 = Maximum allowable external pressure for unstiffened shell under condition 2 (psf)

Pv-Max-C = Final maximum allowable external pressure for unstiffened shell (psi)

Q-(n) = Radial load imposed on intermediate stiffeners by the shell (lbf/ft)

t-min-ext = Minimum thickness due to design pressure (in) t-min-ext-stiff = Minimum thickness due to stiffener (in) ts-(n) = Actual shell course thickness (in)

ts1 = Top shell course thickness (in)

tsmin = Smallest actual shell course thickness (in) tsn = Bottom shell course thickness (in)

(30)

W-shell-(n) = Contributing shell at stiffener n (in)

W = 33.6372 psf

Hts = 26.7369 ft

Wtr-1 = t-width-(n) * (t-top/ts-(n))^2.5

Wtr = Hts = 26.7369 ft

Fp = 0.4

D = 150 ft

ts1 = 0.3125 in tsn = 0.75 in CA = 0 in tsmin = 0.3125 in JEr = 1

JEs = 1

F-roof = 23,200 psi

Fy-shell = 36,000 psi

E = 28,799,999 psi

F-stiff = 0 psi

Fy-stiff = 0 psi

F-btm = 23,200 psi

JEn = 1

JEb = 1

Bottom-OD = 145.7083 ft

V.8.1 UNSTIFFENED SHELLS

Pe = 8.64 psf

Ps = 37.0932 psf

V.8.1.1 Criteria (Elastic failure when EFC >= 0.19,

otherwise must use ASME section VIII Div 1.)

EFC = (D / tsmin)^0.75 * [(HtS / D) * (Fy-shell / E)^0.5]

EFC = (150 / 0.3125)^0.75 * [(26.7369 / 150) * (36,000 / 28,799,999)^0.5]

EFC = 0.6463

Since EFC >= 0.19 using App. V method.

Condition 1: Wind plus specified external (Vacuum) pressure

Since Pe > 5.2 & Pe <= 15, (Pe + 15)/20

PSI1 = (Pe + 15)/20

PSI1 = (8.64 + 15)/20

PSI1 = 1.182

V.8.1.2 Maximum external pressure

Ps-Max = (0.6 * E)/[PSI1 * (HtS/D) * (D/tsmin)^2.5]

Ps-Max = (0.6 * 28,799,999)/[1.182 * (26.7369/150) * (150/0.3125)^2.5]

Ps-Max = 16.2481 psf

Pv-Max-1 = MIN(Ps-Max , (Ps-Max - W)/Fp)

Pv-Max-1 = MIN(16.2481 , (16.2481 - 33.6372)/0.4)

Pv-Max-1 = -43.4726 psf or -0.3019 psi

Pv-Max-2 = (0.6 * E)/[PSI2 * (HTS/D) * (D/tsmin)^2.5]

Pv-Max-2 = (0.6 * 28,799,999)/[3 * (26.7369/150) * (150/0.3125)^2.5]

(31)

Pv-Max-C = MIN(Pv-Max-1 , Pv-Max-2)

Pv-Max-C = MIN(-43.4726 , 6.4018)

Pv-Max-C = -43.4726 psf or -0.3019 psi

Condition 2: Specified external (Vacuum) pressure only

PSI2 = 3

V.8.1.3 Minimum thickness due to design pressure

Since Pe < Ps

t-min-1-ext = (1.23 * (PSI1 * HTS * Ps)^0.4 * D^0.6) / E^0.4

t-min-1-ext = (1.23 * (1.182 * 26.7369 * 37.0932)^0.4 * 150^0.6) / 28,799,999^0.4 t-min-1-ext = 0.4359 in

t-min-2-ext = (1.23 * (PSI2 * HTS * Pe)^0.4 * D^0.6) / E^0.4

t-min-2-ext = (1.23 * (3 * 26.7369 * 8.64)^0.4 * 150^0.6) / 28,799,999^0.4 t-min-2-ext = 0.3533 in

t-min-ext = MAX(t-min-1-ext , t-min-2-ext)

t-min-ext = MAX(0.4359 , 0.3533)

t-min-ext = 0.4359

CIRCUMFERENTIALLY STIFFENED SHELLS

Since no Int. stiffener are specified,

L_act = Wrt

L_act = 26.7369 ft

Number of Intermediate Stiffeners NOT Sufficient Since Hsafe < L_act

Warning: Stiffener spacing is greater than permitted height of unstiffened shell

V.8.2.2.3 Radial load

Q = N.A., Since no Int. stiffeners are specified.

V.8.2.2.4 Contributing shell at stiffener

W-shell = N.A., Since no Int. stiffeners are specified.

SUMMARY OF SHELL STIFFENING RESULTS

Number of Intermediate stiffeners req'd (NS) = 2

Warning!!

(32)

FLAT BOTTOM: ANNULAR PLATE DESIGN

Back

Ann-a = Area of annular ring (in^2) Ann-d = Density of annular ring (lbf/in3)

Ann-t-actual = Actual annular ring thickness (in)

Ann-t-min = Minimum annular ring plates thickness per API-650 5.5.3 TABLE 5-1b (in)

Ann-w-actual = Actual annular ring width (in)

Ann-w-min = Minimum annular ring width per API-650 5.5.2 (in) Ba = Area of bottom (in^2)

Bottom-OD = Bottom diameter (ft)

ca-1 = Bottom (1st) shell course corrosion allowance ca-Ann = Annular ring corrosion allowance (in)

Ca-bottom = Bottom corrosion allowance (in)

D = Nominal diameter per API-650 5.6.1.1 Note 1 (ft)

D-bottom = Density of bottom (lbf/in3)

H = Max liquid level (ft)

R = Nominal radius (ft)

S = Maximum Stress in first shell course per API 650 Table 5.1.b S1 = Product stress in the first shell course per API 650 Table 5.1.b

S2 = Hydrostatic test stress in the first shell course per API 650 Table 5.1.b

Sd = Allowable design stress for the design condition in bottom (1st) shell course (psi) per API 650 5.6.3.2

St = Allowable stress for the hydrostatic test condition in bottom (1st) shell course (psi) per API 650 5.6.3.2

t-1 = Bottom (1st) shell course thickness (in) t-actual = Actual bottom thickness (in)

t-calc = Minimum nominal bottom plates thickness per API-650 5.4.1 (in)

t-min = Minimum nominal bottom plates thickness per API-650 5.4.1 (in)

t-test-1 = Bottom (1st) shell course test thickness (in) td-1 = Bottom (1st) shell course design thickness (in) Material = A36

t-actual = 0.25 in

Annular Ring Material = A36

Ann-t-actual = 0.375 in

Ann-w-actual = 30 in

Calculation of Hydrostatic Test Stress & Product Stress (per API-650 Section 5.5.1)

Bottom-OD = 145.7083 ft

JE = 1

D-bottom = 0.283 lbf/in3

t-1 = 0.75 in

ca-1 = 0 in

G = 1

H = 40 ft

H' = 40 ft

St = 24,900 psi

Sd = 23,200 psi

Ca-bottom = 0 in

ca-Ann = 0 in

Ann-d = 0.2 lbf/in3

Product stress in first shell course

(33)

S1 = ((0.6556 - 0) / (0.75 - 0)) * 23,200

S1 = 20,280 psi

Hydrostatic test stress in first shell course

S2 = (t-test-1 / t-1) * St

S2 = (0.6108 / 0.75) * 24,900

S2 = 20,280 psi

S = Max (S1, S2)

S = Max (20,280 , 20,280)

S = 20,280 psi

API-650 Table 5.1b required thickness of annular ring excluding corrosion allowance is 0.236 in

Annular ring required thickness = 0.236 + ca-Ann = 0.236 + 0

Annular ring required thickness = 0.236 in

Weight of Bottom plate

BA = PI * ((Bottom-OD / 2) - Ann-w-actual)^2

BA = PI * ((1748.5 / 2) - 30)^2

BA = 2,239,195.4929 in^2

Ann-a = PI/4 * Bottom-OD^2 - BA

Ann-a = PI/4 * 1748.5^2 - 2,239,195.4929

Ann-a = 161,964.8092 in^2

weight = (D-bottom * t-actual * BA) + (Ann-d * Ann-t-actual * Ann-A)

weight = (0.283 * 0.25 * 2,239,195.4929) + (0.2 * 0.375 * 161,964.8092)

weight = 175,797.7572 lbf

API-650

t-min = 0.236 + Ca-bottom

t-min = 0.236 + 0

t-min = 0.236 in

t-calc = t-min

t-calc = 0.236 in

Per API 650 appendix V.9.1

P-btm = D-bottom * t-actual + P_liq_min

P-btm = 0.283 * 0.25 + 0.8669

P-btm = 0.9378 psi

ABS(E-p) < P-btm Then there is no uplift

API-650 5.5

Ann-t-min = 0.236 in

Ann-w-min = (390 * Ann-t-actual)/(H * G)^0.5

(34)

Ann-w-min = 24 in Note: API-650 until the inner radius of the shell.

Ann-w-min = 28.25 in Note: including chime distance, overlap and shell thickness.

SUMMARY OF BOTTOM RESULTS

Back

Material = A36

t-actual = 0.25 in

t-req = 0.236 in

Annular Ring Material = A36

Ann-t-actual = 0.375 in

Ann-w-actual = 30 in

Ann-t-min = 0.236 in

Ann-w-min = 28.25 in

NET UPLIFT DUE TO INTERNAL PRESSURE

Net-Uplift = 0 lbf, (See roof report for calculations)

WIND MOMENT (Per API-650 SECTION 5.11)

Back

A = Area resisting the compressive force, as illustrated in Figure F.1

P-F41 = Design pressure determined in F.4.1

P-v = Internal pressure

Wind Velocity per API-650 ASCE 7-05

V_entered = 125 mph I = 1

Vs (Wind Velocity) = SQRT(I) * V_entered = 125 mph

Vf = (Vs / 120)^2

Vf = (125 / 120)^2

Vf (Velocity Factor) = 1.0851

PWS = 18 * Vf

PWS = 19.5312 psf

PWR = 30 * Vf

PWR = 32.552 psf

API-650 5.2.1.k Uplift Check

P-F41 = (0.962 * A * Fy * TAN(Theta))/D^2 + (0.245 * DLR)/D^2

P-F41 = ((0.962 * 6.567 * 36,000 * TAN(3.5763))/150^2) + ((0.245 * 136357) / 150^2)

P-F41 = 0.0765 psi = 11.0098 psf

Wind-Uplift = MIN(PWR , (1.6 * P-F41 - Pv))

Wind-Uplift = MIN(32.552 , 3.2157)

Wind-Uplift = 3.2157 psf

Ap-Vert (Vertical Projected Area of Roof) = 351.5625 ft^2

Horizontal Projected Area of Roof (Per API-650 5.2.1.f)

Xw (Moment Arm of UPLIFT wind force on roof) = 75 ft

Ametank Model Example 2 API 650 Calculation Report

TABLE OF CONTENTS

SUMMARY OF DESIGN DATA AND REMARKS

ROOF DESIGN

ROOF SUMMARY OF RESULTS

SHELL COURSE DESIGN

SHELL SUMMARY OF RESULTS

BOTTOM DESIGN

BOTTOM SUMMARY OF RESULTS

WIND MOMENT

SEISMIC SITE GROUND MOTION

SEISMIC CALCULATIONS

ANCHOR BOLT DESIGN

ANCHOR BOLT SUMMARY OF RESULTS

CAPACITIES AND WEIGHTS

Warnings!!

SUMMARY OF DESIGN DATA AND REMARKS

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STRUCTURALLY SUPPORTED CONICAL ROOF

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