ETANK FULL REPORT - 3300
ETank2000 MU 1.9.14 (26 Oct 2010)
TABLE OF CONTENTS
TABLE OF CONTENTS
ETANK SETTINGS SUMMARY
SUMMARY OF DESIGN DATA and REMARKS
SUMMARY OF RESULTS
ROOF DESIGN PER API 650
ROOF DESIGN SUMMARY
SHELL COURSE DESIGN
SHELL COURSE SUMMARY
FLAT BOTTOM: NON-ANNULAR PLATE DESIGN
FLAT BOTTOM: NON-ANNULAR SUMMARY
SEISMIC CALCULATIONS PER API-650 11TH ED., ADDENDUM 2
ANCHOR BOLT DESIGN
CAPACITIES and WEIGHTS
MAWP & MAWV SUMMARY FOR 3300
ETANK SETTINGS SUMMARY
To Change These ETank Settings, Go To Tools->Options, Behavior Tab.
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No 650 Appendix F Calcs when Tank P = 0 -> Default : False
-> This Tank : False
* * NOTE: Ignored (Since App. F calcs apply per 650 1.1.1.)
Repad 650 Design Basis
-> Default for Tank Roof Nozzles : Use API Default 1/4 in.
-> This Tank : Use API Default 1/4 in.
Show MAWP / MAWV Calcs : True
Enforce API Minimum thicknesses : True
Enforce API Maximum Roof thickness : True
Enforce Minimum Self Supp. Cone Pitch (2 in 12) : True
Force Non-Annular Btm. to Meet API-650 5.5.1 : False
Set t.actual to t.required Values : False
Maximum 650 App. S or App. M Multiplier is 1 : True
Enforce API Maximum Nozzle Sizes : True
Max. Self Supported Roof thickness : 5 in.
Max. Tank Corr. Allowance : 5 in.
External pressure calcs subtract C.A. per V.5 : False
Use Gauge Material for min thicknesses : False
Enforce API Minimum Live Load : True
Enforce API Minimum Anchor Chair Design Load
= Bolt Yield Load : True
SUMMARY OF DESIGN DATA and REMARKS
Job : 3300
Date of Calcs. : 26/07/2011 , 11:41
Mfg. or Insp. Date : 24/11/1993
Designer : JEFFCOAT SMITT
Project : 48' OD BY 32' TALL
Plant Location : COLUMBIA, SC
Site : COLUMBIA, SC
Design Basis : API-650 11th Edition, Addendum 2, Nov 2009
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- TANK NAMEPLATE INFORMATION
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- Operating Ratio: 0,4
- Design Standard:
- API-650 11th Edition, Addendum 2, Nov 2009 -
- API-650 Appendices Used: F.1.2, E, M, V -
- Roof : A-240 Type 304: 0,375in. -
- Shell (4): A-240 Type 304: 0,25in. -
- Shell (3): A-240 Type 304: 0,25in. -
- Shell (2): A-240 Type 304: 0,3125in. -
- Shell (1): A-240 Type 304: 0,336in. -
- Bottom : A-240 Type 304: 0,25in. -
------
Design Internal Pressure = 0,25 PSI or 6,93 IN. H2O
Design External Pressure = -0,1 PSI or -2,77 IN. H2O
MAWP = 0,8368 PSI or 23,19 IN. H2O
MAWV = -0,2879 PSI or -7,98 IN. H2O
OD of Tank = 48 ft
Shell Height = 32 ft
S.G. of Contents = 1,15
Max. Liq. Level = 32 ft
Design Temperature = 300 °F
Tank Joint Efficiency = 0,85
* * Warning * *
SHELL HOOP STRESSES EXCEED ALLOWABLE DUE TO SEISMIC MOMENT.
CHECK HOOP STRESS SECTION OF SEISMIC REPORT.
Ground Snow Load = 10 lbf/ft^2
Roof Live Load = 25 lbf/ft^2
Design Roof Dead Load = 0 lbf/ft^2
Basic Wind Velocity = 110 mph
Wind Importance Factor = 1
Using Seismic Method: API-650 11th Ed. - ASCE7 Mapped (Ss & S1)
Seismic Use Group:
Site Class: D
T_L = 12 sec
Ss = 124 %g
S1 = 50 %g
S0 = 49,6 %g
Av = 0,23 %g
Q = 0,6666
Importance Factor = 1
DESIGN NOTES
NOTE 1 : There are tank calculation warnings.
Search for * * Warning * * notes.
NOTE 2 : Tank is not subject to API-650 Appendix F.7
** NOTE **
A Minimum Liquid Level of 1 ft. has been used for this model
as entered on the Shell Design Screen.
DESIGNER REMARKS
SUMMARY OF RESULTS
Shell Material Summary (Bottom is 1)
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Shell Width Material Sd St Weight CA
# (ft) (psi) (psi) (lbf) (in)
------
4 8 A-240 Type 304 20.300 27.000 12.915 0,0625
3 8 A-240 Type 304 20.300 27.000 12.915 0,0625
2 8 A-240 Type 304 20.300 27.000 16.142 0,0625
1 8 A-240 Type 304 20.300 27.000 17.355 0,0625
------
Total Weight 59.327
Shell API 650 Summary (Bottom is 1)
------
Shell t.design t.test t.external t.seismic t.required t.actual
# (in.) (in.) (in.) (in.) (in.) (in.)
------
4 0,1249 0,0412 0,1291 0,1591 0,1875 0,25
3 0,1914 0,0847 0,1291 0,2495 0,2495 0,25
2 0,258 0,1282 0,1291 0,336 0,336 0,3125
1 0,3245 0,1717 0,1291 0,4177 0,4177 0,336
------
Self Supported Domed Roof; Material = A-240 Type 304
t.required = 0,3238 in.
t.actual = 0,375 in.
Roof Joint Efficiency = 0,85
Weight = 31.009 lbf
Bottom Type: Flat Bottom: Non-Annular
Bottom Floor Material = A-240 Type 304
t.required = 0,1875 in.
t.actual = 0,25 in.
Bottom Joint Efficiency = 0,85
Total Weight of Bottom = 19.583 lbf
ANCHOR BOLTS: (24) 1,5in. UNC Bolts, A-36
TOP END STIFFENER: L3x2x3/8, A-240 Type 304, 936, lbf
QTY (3) INTERMEDIATE STIFFENERS: A-240 Type 304
Stiffener #1: BAR 4x3/8, 813, lbf, Elev. = 11,98 ft.
Stiffener #2: BAR 4x3/8, 813, lbf, Elev. = 19,8 ft.
Stiffener #3: BAR 4x3/8, 813, lbf, Elev. = 25,9 ft.
ROOF DESIGN PER API 650
DOMED ROOF: A-240 Type 304
JEr = Roof Joint Efficiency = 0,85
Lr = Entered Roof Live Load = 25 lbf/ft^2
Lr_1 = Computed Roof Live Load, including External Pressure
S = Ground Snow Load (per ASCE 7-05 Fig. 7-1)
= 10 lbf/ft^2
Sb = Balanced Design Snow Load (per API-650 Sec. 5.2.1.h.1)
= 0.84 * S = 8,4 lbf/ft^2
Su = Unbalanced Design Snow Load (per API-650 Sec. 5.2.1.h.2)
= 1,5*Sb = 12,6 lbf/ft^2
Dead_Load = Insulation + Plate_Weight + Added_Dead_Load
= (8)(2/12) + 16,065 + 0
= 17,4033 lbf/ft^2
Roof Loads (per API-650 Appendix R)
Pe = PV*144 = 0,1*144 = 14,4 lbf/ft^2
e.1b = DL + MAX(Sb,Lr) + 0,4*Pe
= 17,4033 + 25 + 0,4*14,4000
= 48,163 lbf/ft^2
e.2b = DL + Pe + 0,4*MAX(Sb,Lr)
= 17,4033 + 14,4000 + 0,4*25
= 41,803 lbf/ft^2
T = Balanced Roof Design Load (per API-650 Appendix R)
= MAX(e.1b,e.2b)
= 48,163 lbf/ft^2
e.1u = DL + MAX(Su,Lr) + 0,4*Pe
= 17,4033 + 25 + 0,4*14,4000
= 48,163 lbf/ft^2
e.2u = DL + Pe + 0,4*MAX(Su,Lr)
= 17,4033 + 14,4000 + 0,4*25
= 41,803 lbf/ft^2
U = Unbalanced Roof Design Load (per API-650 Appendix R)
= MAX(e.1u,e.2u)
= 48,163 lbf/ft^2
Lr_1 = MAX(T,U) = 48,163 lbf/ft^2
Dish Radius (Rs) = 48 ft
Alpha = 60,0000 degrees (angle between the Normal to the roof and
a horizontal line at the
roof-to-shell juncture)
Theta = 30,0000 degrees (angle between the Normal to the roof and
a vertical line at the
roof-to-shell juncture)
Rs = R1 = R2 = 576 in.
Rc = ID/2 = 287,75 in.
<Weight, Surface Area, and Projected Areas of Roof>
hR = Height of Roof
= R - SQRT[R^2 - (OD/2)^2]
= 48 - SQRT[48^2 - (48/2)^2]
= 6,419 ft
t_ins = Thickness of Roof Insulation
= 0,1667 ft
Ap_Vert = Vertical Projected Area of Roof
= PI*([R + t_ins]^2)(Alpha/360) - OD*([R + t_ins] - hR)/2
= PI*(48,1667^2)(59,9859/360) - 48*(48,1667 - 6,419)/2
= 212,5351 ft^2
Horizontal Projected Area of Roof (Per API-650 5.2.1.f)
Xw = Moment Arm of UPLIFT wind force on roof
= 0.5*OD
= 0.5*48
= 24 ft
Ap = Projected Area of roof for wind moment
= PI*R^2
= PI*24^2
= 1.810 ft^2
Roof_Area = 288*PI*R*hR
= 288*PI*48*6,413
= 277.948 in^2
Weight = (Density)(t)(Roof_Area)
= (0,2975)(0,375)(277.948)
= 31.009 lbf (New)
= 25.840 lbf (Corroded)
< Uplift on Tank > (per API-650 F.1.2)
NOTE: This flat bottom tank is assumed supported by the bottom plate.
If tank not supported by a flat bottom, then uplift calculations
will be N.A., and for reference only.
For flat bottom tank with self supported roof,
Net_Uplift = Uplift due to design pressure less
Corroded weight of shell and roof plates.
= P * PI / 4 * D ^ 2 * 144 «
- Corr. shell - Corr. roof weight
= 0,25 * 3,1416 / 4 * 2.304 * 144 «
- 46.417 - 25.840
= -7.113 lbf
< Uplift Case per API-650 1.1.1 >
P_Uplift = 65.144 lbf
W_Roof_Plates (corroded) = 25.840 lbf
W_Shell (corroded) = 46.417 lbf
Since W_Roof < P_Uplift <= W_Roof + W_Shell,
Tank Roof should meet App. F.1.2 and F.2-F.6 requirements.
<Minimum Thickness of Roof Plate>
ME = 28.000.000/26.600.000 = 1,0526 (per API-650 App. S.3.6.6)
<Section 5.10.6.1>
t-Calc1 = ME * SQRT[T/45]*R/200 + CA
= 1,0526 * SQRT[48,163/45]*48/200 + 0,0625
= 0,3238 in.
t-Calc2 = ME * SQRT[U/45]*R/230 + CA
= 1,0526 * SQRT[48,163/45]*48/230 + 0,0625
= 0,2898 in.
t-CalcExt = MAX(t-Calc1,t-Calc2)
= 0,3238 in.
t-Calc = 0,3238 in.
Max_f (due to roof thickness)
= 200(t-CA)/ME/R
= 200(0,3125)/1,0526/48
= 1,237
Max_T1 (due to roof thickness)
= Max_f^2 * 45
= 1,237^2 * 45
= 68,8576 lbf/ft^2
P_ext_1 (Vacuum limited by roof thickness)
= -[Max_T1 - DL - 0,4 * Max(Snow_Load,Lr)]/144
= -[68,8576 - 17,4033 - 0,4 * Max(8,4,25)]/144
= -0,2879 PSI or -7,98 IN. H2O
P_max_ext = -0,2879 PSI or -7,98 IN. H2O
<Actual Participating Area of Roof-to-Shell Juncture>
(From API-650 Figure F-2)
Wc = 0,6 * SQRT[Rc * (t-CA)] (Top Shell Course)
= 0,6 * SQRT[287,75 * (0,25 - 0,0625)]
= 4,4072 in.
(From API-650 Figure F-2)
Wh = 0,3 * SQRT[R2 * (t-CA)] (or 12", whichever is less)
= 0,3 * SQRT[576 * (0,375 - 0,0625)]
= MIN(4,0249, 12)
= 4,0249 in.
Top End Stiffener: L3x2x3/8
Aa = (Cross-sectional Area of Top End Stiffener)
= 1,73 in^2
Using API-650 Fig. F-2, Detail d End Stiffener Detail
Ashell = Contributing Area due to shell plates
= Wc*(t_shell - CA)
= 4,4072 * (0,25 - 0,0625)
= 0,826 in^2
Aroof = Contributing Area due to roof plates
= Wh*(t_roof - CA)
= 4,0249 * (0,375 - 0,0625)
= 1,258 in^2
A = Actual Part. Area of Roof-to-Shell Juncture (per API-650)
= Aa + Aroof + Ashell
= 1,73 + 1,258 + 0,826
= 3,814 in^2
MINIMUM PARTICIPATING AREA Dome Roof ( Per API-650 Section 5.10.6.2 )
p = MAX(U,T)
Fa = Min(Fy_roof,Fy_shell,Fy_stiff)
= Min(22.500,22.500,22.500)
= 22.500 psi
A_min = Minimum Participating Area
= p*D^2/(8*Fa*TAN(Theta))
= 48,163*48^2/(8*22.500*TAN(30,0000))
= 1,068 in^2
MaxT_A = Max Roof Load due to Participating Area
( reversing API-650 Section 5.10.6.2 )
= 1500*45*A/(D*R)
= 1500*45*3,814/(48*48)
= 111,738 lbf/ft^2
P_ext_2 (Due to MaxT_A)
= -[Max_T1 - DL - 0,4 * Max(Snow_Load,Lr)]/144
= -[111,738 - 17,4033 - 0,4 * Max(8,4,25)]/144
= -0,5857 PSI (Due to Participating Area)
NOTE: Per API-650 1.1.1, Tank must comply with F.4 through F.5.2
< API-650 App. F >
Fy = Min(Fy_roof,Fy_shell,Fy_stiff)
= Min(22.500,22.500,22.500)
= 22.500 psi
A_min_a = Min. Participating Area due to full Design Pressure.
(per API-650 F.5.1, and Fig. F-2)
= [OD^2(P - 8*t)]/[0,962*22.500*TAN(Theta)]
= [48^2(6,93 - 8*0,375)]/[0,962*22.500*0,5774]
= 0,725 in^2
A_min = MAX(1,068,0,725,0)
= 1,068 in^2 (per API-650 App F.5.2)
P_F51 = Max. Design Pressure, reversing A_min_a calculation.
= A * [0,962*22.500*TAN(Theta)]/OD^2 + 8*t_h
= 3,814 * [0,962*22.500*0,5774]/48^2 + 8*0,3125
= 0,8368 PSI or 23,19 IN. H2O
< Maximum Design Pressure > (per F.4.1)
P_F41 = 0,962*22.500*A*TAN(Theta)/D^2 + 8*t_h
= 0,962*22.500*(3,814)*(0,5774)/(48^2) + 8*(0,3125)
= 0,8368 PSI or 23,19 IN. H2O
P_F42 = N.A. (Tank is Anchored)
P_Std = Max. Pressure allowed (Per API-650 App. F.1.3 & F.7)
= 2,5 PSI or 69,28 IN. H2O
P_max_internal = MIN(P_F51, P_F41, P_Std)
= MIN(23,19, 23,19, 69,28)
= 0,8368 PSI or 23,19 IN. H2O
P_max_ext = MAX(-0,2879,-0,5857)
= -0,2879 PSI or -7,98 IN. H2O
* * * API 650 APPENDIX V * * *
<Section V.7.3.1>
Pr = Max Roof Load = Lr_1
t_Dome1 = 4,47*R*SQRT[(Pr/E)]
= 4,47*48*SQRT[(48,163/26.600.000)]
= 0,2887 in.
t_Dome = MAX(t-Calc, t_Dome1)
= MAX(0,3238, 0,2887)
= 0,3238 in.
<Participating Area Required per App. V>
f (Allowable Design Stress) = 20.300 psi
ts1 (Top Shell Course thickness) = 0,25 in.
tr (Roof Actual Thickness) = 0,375 in.
JEr (Roof Joint Efficiency) = 0,85
JEs (Top Shell Course Joint Efficiency) = 0,85
JEst (Roof Comp. Ring Joint Efficiency) = 0,85
(Section V.7.3.2)
A_Reqd = Pr*R*D/(3,375*f)
= 48,163*48*48/(3,375*20.300)
= 1,6197 in^2
(Section V.7.3.3)
X_Dome = 2,1*(R*tr)^0,5
= 2,1*(48*0,375)^0,5
= 8,9095 in
(Section V.7.3.4)
X_Shell = 1,47*SQRT[OD*ts1]
= 1,47*SQRT[48*0,25]
= 5,0922 in
(Section V.7.3.5)
A_stiff_reqd = (A_Reqd - JEs*ts1*X_Shell - JEr*tr*X_Dome)/JEst
= (1,6197 - 0,85*0,25*5,0922 - 0,85*0,375*8,9095)/0,85
= -2,7086 in^2
Since A_stiff_reqd <=0, No Roof Stiffener Required
A_stiff_actual = 1,73 in^2
using L3x2x3/8 angle
A_actual = JEs*ts1*X_Shell + JEr*tr*X_Dome + A_stiff_actual*JEst
= 0,85*0,25*5,0922 + 0,85*0,375*8,9095 + 1,73*0,85
= 5,3925 in^2
<TOP END STIFFENER CALCULATIONS>
<V.8.2.2.1 Number of Waves>
N^2 = SQRT[5,33*D^3/(tsmin*Hts^2)]
= SQRT[5,33*48^3/(0,25*24,3998^2)]
= 62,93
N = 7,93
<V.8.2.3 Contributing Shell at Stiffener>
w_shell = 1,47*(D*ts1)^0,5
= 1,47*(48*0,25)^0,5
= 5,0922 in.
<V.8.2.3.1 Radial Load, VI>
VI = Ps * H/48
= 31,81 * 32/48
= 21,2067 lbf/ft
<V.8.2.3.2 Required Moment of Inertia>
I_reqd = 648*VI*D^3/[E*(N^2-1)]
= 648*21,2067*48^3/[26.600.000*(7,93^2-1)]
= 0,923 in^4
I_actual = 1,981 in^4
using L3x2x3/8, ts1 = 0,25 in., & W = 5,0922 in.
<V.8.2.3.3.1 Area Required>
define f = Min(f_roof, f_shell, f_stiff)
= Min(20.300, 20.300, 20.300)
= 20.300 psi
A_reqd = 6*VI*D/f
= 6*21,2067*48/20.300
= 0,3009 in^4
<V.8.2.3.3.2 Area required by stiffener>
A_stiff_reqd = A_reqd - JEs*ts1*X_Shell - JEr*t_roof*X_Dome
= 0,3009 - 0,85*0,25*5,0922 - 0,85*0,375*8,9095
= -3,62 in^2
Since A_stiff_reqd <=0, No Roof Stiffener Required
A_stiff = 1,73 in^2
using L3x2x3/8
A_actual = JEs*ts1*X_Shell + JEr*tr*X_Dome + A_stiff_actual
= 0,85*0,25*5,0922 + 0,85*0,375*8,9095 + 1,73
= 5,652 in^2
t.required = 0,3238 in.
ROOF DESIGN SUMMARY
t.required = 0,3238 in.
t.actual = 0,375 in.
P_max_internal = 0,8368 PSI or 23,19 IN. H2O
P_max_external = -0,2879 PSI or -7,98 IN. H2O
SHELL COURSE DESIGN
VDP Criteria (per API-650 5.6.4.1)
L = (6*D*(t-ca))^0,5
= (6*48*(0,336-0,0625))^0,5
= 8,8751
H = Max Liquid Level =32 ft
L / H <= 2
Course # 1
Material: A-240 Type 304; Width = 8 ft.
Corrosion Allow. = 0,0625 in.
Joint Efficiency = 0,85
API-650 ONE FOOT METHOD
Sd = 20.300 PSI (allowable design stress per API-650 App. S Table S-2a)
St = 27.000 PSI (allowable test stress)
DESIGN CONDITION
G = 1,15 (per API-650)
< Design Condition G = 1,15 >
H' = Effective liquid head at design pressure
= H + 2,31*P(psi)/G
= 32 + 2.31*0,25/1,15 = 32,5ft
t-Calc = 2,6*OD*(H' - 1)*G/(Sd*E) + CA (per API-650 S.3.2)
= 2,6*48*(32,5 - 1)*1,15/(20.300*0,85) + 0,0625
= 0,3245 in.
hMax_1 = E*Sd*(t_1 - CA_1)/(2,6*OD*G) + 1
= 0,85*20.300*(0,336 - 0,0625) / (2,6 * 48 * 1,15) + 1
= 33,8821 ft.
Pmax_1 = (hMax_1 - H) * 0,433 * G
= (33,8821 - 32) * 0,433 * 1,15
= 0,9372 PSI
Pmax_int_shell = Pmax_1
Pmax_int_shell = 0,9372 PSI
HYDROSTATIC TEST CONDITION
< Design Condition G = 1 >
H' = Effective liquid head at design pressure
= H + 2,31*P(psi)/G
= 32 + 2.31*0,25/1 = 32,58ft
t.test = 2,6*48*(32,58 - 1)/(27.000*0,85) = 0,1717 in.
Course # 2
Material: A-240 Type 304; Width = 8 ft.
Corrosion Allow. = 0,0625 in.
Joint Efficiency = 0,85
API-650 ONE FOOT METHOD
Sd = 20.300 PSI (allowable design stress per API-650 App. S Table S-2a)
St = 27.000 PSI (allowable test stress)
DESIGN CONDITION
G = 1,15 (per API-650)
< Design Condition G = 1,15 >
H' = Effective liquid head at design pressure
= H + 2,31*P(psi)/G
= 24 + 2.31*0,25/1,15 = 24,5ft
t-Calc = 2,6*OD*(H' - 1)*G/(Sd*E) + CA (per API-650 S.3.2)
= 2,6*48*(24,5 - 1)*1,15/(20.300*0,85) + 0,0625
= 0,258 in.
hMax_2 = E*Sd*(t_2 - CA_2)/(2,6*OD*G) + 1
= 0,85*20.300*(0,3125 - 0,0625) / (2,6 * 48 * 1,15) + 1
= 31,0568 ft.
Pmax_2 = (hMax_2 - H) * 0,433 * G
= (31,0568 - 24) * 0,433 * 1,15
= 3,5139 PSI
Pmax_int_shell = Min(Pmax_int_shell, Pmax_2)
= Min(0,9372, 3,5139)
Pmax_int_shell = 0,9372 PSI
HYDROSTATIC TEST CONDITION
< Design Condition G = 1 >
H' = Effective liquid head at design pressure
= H + 2,31*P(psi)/G
= 24 + 2.31*0,25/1 = 24,58ft
t.test = 2,6*48*(24,58 - 1)/(27.000*0,85) = 0,1282 in.
Course # 3
Material: A-240 Type 304; Width = 8 ft.
Corrosion Allow. = 0,0625 in.
Joint Efficiency = 0,85
API-650 ONE FOOT METHOD
Sd = 20.300 PSI (allowable design stress per API-650 App. S Table S-2a)
St = 27.000 PSI (allowable test stress)
DESIGN CONDITION
G = 1,15 (per API-650)
< Design Condition G = 1,15 >
H' = Effective liquid head at design pressure
= H + 2,31*P(psi)/G
= 16 + 2.31*0,25/1,15 = 16,5ft
t-Calc = 2,6*OD*(H' - 1)*G/(Sd*E) + CA (per API-650 S.3.2)
= 2,6*48*(16,5 - 1)*1,15/(20.300*0,85) + 0,0625
= 0,1914 in.
hMax_3 = E*Sd*(t_3 - CA_3)/(2,6*OD*G) + 1
= 0,85*20.300*(0,25 - 0,0625) / (2,6 * 48 * 1,15) + 1
= 23,5426 ft.
Pmax_3 = (hMax_3 - H) * 0,433 * G
= (23,5426 - 16) * 0,433 * 1,15
= 3,7558 PSI
Pmax_int_shell = Min(Pmax_int_shell, Pmax_3)
= Min(0,9372, 3,7558)
Pmax_int_shell = 0,9372 PSI
HYDROSTATIC TEST CONDITION
< Design Condition G = 1 >
H' = Effective liquid head at design pressure
= H + 2,31*P(psi)/G
= 16 + 2.31*0,25/1 = 16,58ft
t.test = 2,6*48*(16,58 - 1)/(27.000*0,85) = 0,0847 in.
Course # 4
Material: A-240 Type 304; Width = 8 ft.
Corrosion Allow. = 0,0625 in.
Joint Efficiency = 0,85
API-650 ONE FOOT METHOD
Sd = 20.300 PSI (allowable design stress per API-650 App. S Table S-2a)
St = 27.000 PSI (allowable test stress)
DESIGN CONDITION
G = 1,15 (per API-650)
< Design Condition G = 1,15 >
H' = Effective liquid head at design pressure
= H + 2,31*P(psi)/G
= 8 + 2.31*0,25/1,15 = 8,5ft
t-Calc = 2,6*OD*(H' - 1)*G/(Sd*E) + CA (per API-650 S.3.2)
= 2,6*48*(8,5 - 1)*1,15/(20.300*0,85) + 0,0625
= 0,1249 in.
hMax_4 = E*Sd*(t_4 - CA_4)/(2,6*OD*G) + 1
= 0,85*20.300*(0,25 - 0,0625) / (2,6 * 48 * 1,15) + 1
= 23,5426 ft.
Pmax_4 = (hMax_4 - H) * 0,433 * G
= (23,5426 - 8) * 0,433 * 1,15
= 7,7394 PSI
Pmax_int_shell = Min(Pmax_int_shell, Pmax_4)
= Min(0,9372, 7,7394)
Pmax_int_shell = 0,9372 PSI
HYDROSTATIC TEST CONDITION
< Design Condition G = 1 >
H' = Effective liquid head at design pressure
= H + 2,31*P(psi)/G
= 8 + 2.31*0,25/1 = 8,58ft
t.test = 2,6*48*(8,58 - 1)/(27.000*0,85) = 0,0412 in.
<API-650 APPENDIX V FOR EXTERNAL PRESSURE>
W (Wind Pressure) = 31*(V/120)^2
= 31*(110/120)^2
= 26,05 lbf/ft^2
Pe (External Pressure) = 0,1 PSI, OR 2,77 In. H2O
= 14,4 lbf/ft^2
Ps (Shell Design Pressure) = MAX(Pe, W + 0,4*Pe)
= MAX(14,4, 26,05 + 0,4*14,4)
= MAX(14,4, 31,81)
= 31,81 lbf/ft^2
Wtr = Transposed Width of each Shell Course
= Width*[ t_top / t_course ]^2,5
Transforming Courses (1) to (4)
Wtr(1) = 8*[ 0,25/0,336 ]^2.5 = 3,8203 ft
Wtr(2) = 8*[ 0,25/0,3125 ]^2.5 = 4,5795 ft
Wtr(3) = 8*[ 0,25/0,25 ]^2.5 = 8 ft
Wtr(4) = 8*[ 0,25/0,25 ]^2.5 = 8 ft
Hts (Height of the Transformed Shell)
= SUM{Wtr} = 24,3998 ft
* * * SHELL STIFFENING PER API-650 APP. V.8 * * *
D (Tank OD) = 48 ft
SHELL MATERIAL (thinnest course) : A-240 Type 304
ts1 (Top Shell Thickness) = 0,25 in.
tsn (Bottom Shell Thickness) = 0,336 in.
tsmin (Smallest Actual Shell Thickness) = 0,25 in.
JEr (Roof Joint Efficiency) = 0,85
JEs (Top Shell Joint Efficiency) = 0,85
Hts (Transformed Shell Height) = 24,3998 ft
f_shell (Allowable Stress for thinnest Shell) = 20.300 psi
Fy_shell (Yield Stress for thinnest Shell) = 30.000 psi
E (Mod. of Elasticity for thinnest Shell) = 26.600.000 psi
TOP STIFFENER MATERIAL : A-240 Type 304
f_stiff (Allowable Stress for Stiffener) = 20.300 psi
Fy_stiff (Yield Stress for Stiffener) = 30.000 psi
SHELL STIFFENER MATERIAL : A-240 Type 304
f_stiff (Allowable Stress for Stiffener) = 20.300 psi
Fy_stiff (Yield Stress for Stiffener) = 30.000 psi
BOTTOM STIFFENER MATERIAL :
f_stiff (Allowable Stress for Stiffener) = 0 psi
Fy_stiff (Yield Stress for Stiffener) = 0 psi
BOTTOM PLATE MATERIAL : A-240 Type 304
f_btm (Allowable Stress for Bottom Floor) = 20.300 psi
Fy_shell (Yield Stress for Bottom Floor) = 30.000 psi
JEn (Bottom Shell Joint Efficiency) = 0,85
JEb (Bottom Joint Efficiency) = 0,85
Bottom Floor OD = 48,25 ft
<V.8.1 UNSTIFFENED SHELLS>
Pe (External Pressure) = 14,4 lbf/ft^2
Ps (Shell Design Pressure) = 31,81 lbf/ft^2
V.8.1.1 Criteria (Elastic Failure when EFC >= 0,19,
otherwise must use ASME Section VIII)
EFC = (D/tsmin)^0,75*[(Hts/D)*(Fy/E)^0,5]
= (48/0,25)^0,75*[(24,3998/48)*(30.000/26.600.000)^0,5]
= 0,8805
Since EFC >= 0,19, using App. V method.
Condition 1: Wind plus specified external (vacuum) pressure
Since Pe <= 15, PSI1 = (Pe + 15)/20 = 1,47
<V.8.1.2 Max External Pressure>
PS_Max = 0,6*E/[PSI1*(Hts/D)*(D/tsmin)^2,5]
= 0,6*26.600.000/[1,47*(24,3998/48)*(48/0,25)^2,5]
= 41,8136 lbf/ft^2
= 0,2904 psi
PV_max1 = Min(PS_Max, [PS_Max - W/144]/0,4)
= Min(0,2904, 0,2737)
= 0,2737 psi
Condition 2: Specified external (vacuum) pressure only
PSI2 = 3
<V.8.1.2 Max External Pressure>
PV_Max2 = 0,6*E/[PSI2*(Hts/D)*(D/tsmin)^2,5]
= 0,6*26.600.000/[3*(24,3998/48)*(48/0,25)^2,5]
= 20,4887 lbf/ft^2
= 0,1423 psi
PV_Max = Min(PV_Max1,PV_Max2)
= Min(0,2737,0,1423)
= 0,1423 psi
Since PSI1*Ps >= 3*Pe, PSI = PSI1 & Ps = Ps
<V.8.1.3 Min thickness due to Design Pressure>
t_min_ext = 1,23*[(PSI*Hts*Ps)^0,4]*(D^0,6)/(E^0,4)
= 1,23*[(1,47*24,3998*31,81)^0,4]*(48^0,6)/(26.600.000^0,4)
= 0,2247 in.
<V.8.2 CIRCUMFERENTIALLY STIFFENED SHELLS>
<V.8.2.1.2 Maximum Unstiffened Shell Height>
Hs = 0,6*(tsmin^2,5)*(E)/[(D^1,5)*Ps*PSI]
= 0,6*(0,25^2,5)*(26.600.000)/[(48^1,5)*31,81*1,47]
= 32,07 ft.
<V.8.2.1.3 Number of Stiffeners Required>
Ns = Hts/Hs - 1 (Rounded Up)
= 24,3998/32,07 - 1
= -0,2392, Rounded Up => 0
Actual Number of Stiffeners = 3
<V.8.2.1.4 Maximum Stiffener Spacing on transposed shell>
Lx = Hts/(Ns + 1)
= 24,3998/(0 + 1)
= 24,3998 ft
Evenly spaced uniform stiffeners,
Act. Spacing Ls = Hts/(N + 1)
= 24,3998/(3 + 1)
= 6,1 ft
t_min_ext_stiff = 1,23*[(PSI*Ls*Ps)^0,4]*(D^0,6)/(E^0,4)
= 1,23*[(1,47*6,1*31,81)^0,4]*(48^0,6)/(26.600.000^0,4)
= 0,1291 in.
PsMax = {[tsmin*(E^0,4)/[(D^0,6)*1,23]]^2,5}/(PSI*Ls)/144
= {[0,25*(26.600.000^0,4)/[(48^0,6)*1,23]]^2,5}/(1,47*6,1)/144
= 1,154 PSI
PV_max = Min(PsMax, [PsMax - W/144]/0.4)
= MIN(1,154, [1,154 - 26,05/144]/0,4)
= 1,154 PSI
<V.8.2.2 Intermediate Stiffener Ring Design>
<V.8.2.2.1 Number of Waves>
N^2 = SQRT[5,33*D^3/(tsmin*Hts^2)]
= SQRT[5,33*48^3/(0,25*24,3998^2)]
= 62,93
N = 7,93
<V.8.2.2.3 Radial Load>
For each stiffener, Q is calculated using Ls for each.
Q_1 = Ps * Ls_1/12
= 31,81 * 6,1/12
= 16,17 lbf/ft
Q_2 = Ps * Ls_2/12
= 31,81 * 6,1/12
= 16,17 lbf/ft
Q_3 = Ps * Ls_3/12
= 31,81 * 6,1/12
= 16,17 lbf/ft
<V.8.2.2.4 Contributing Shell at Stiffener>
w_shell_1 = 2*1,47*(D*ts_2)^0,5
= 2*1,47*(48*0,3125)^0,5
= 11,3866 in.
w_shell_2 = 2*1,47*(D*ts_3)^0,5
= 2*1,47*(48*0,25)^0,5
= 10,1845 in.
w_shell_3 = 2*1,47*(D*ts_4)^0,5
= 2*1,47*(48*0,25)^0,5
= 10,1845 in.
<V.8.2.2.5 Required Moment of Inertia>
I_reqd_1 = 648*Q*D^3/[E*(N^2-1)]
= 648*16,17*48^3/[26.600.000*(7,93^2-1)]
= 0,704 in^4
I_actual_1 = 6,935 in^4
using BAR 4x3/8, t = 0,3125 in., & W = 11,3866 in.
I_reqd_2 = 648*Q*D^3/[E*(N^2-1)]
= 648*16,17*48^3/[26.600.000*(7,93^2-1)]
= 0,704 in^4
I_actual_2 = 6,2756 in^4
using BAR 4x3/8, t = 0,25 in., & W = 10,1845 in.
I_reqd_3 = 648*Q*D^3/[E*(N^2-1)]
= 648*16,17*48^3/[26.600.000*(7,93^2-1)]
= 0,704 in^4
I_actual_3 = 6,2756 in^4
using BAR 4x3/8, t = 0,25 in., & W = 10,1845 in.
<V.8.2.2.6.1 Area Required>
For each stiffener, A_reqd is calculated using Q.
define fc = MAX(0,4Fy,15.000)
= MAX(0,4*30.000,15.000)
= 15.000 psi
A_reqd_1 = 6*Q_1*D/fc
= 6*16,17*48/15.000
= 0,31 in^2
define fc = MAX(0,4Fy,15.000)
= MAX(0,4*30.000,15.000)
= 15.000 psi
A_reqd_2 = 6*Q_2*D/fc
= 6*16,17*48/15.000
= 0,31 in^2
define fc = MAX(0,4Fy,15.000)
= MAX(0,4*30.000,15.000)
= 15.000 psi
A_reqd_3 = 6*Q_3*D/fc
= 6*16,17*48/15.000
= 0,31 in^2
<V.8.2.2.6.2 Area Required by Stiffener>
For each stiffener, A_stiff is calculated using shell t.
A_stiff_1 = A_reqd_1 - 26.84*ts_2*(D*ts_2)^0,5
= 0,31 - 26,84*0,3125*(48*0,3125)^0,5
= -32,175 in^2
Since A_stiff_1 <=0, No Stiffener Required
A_stiff_actual_1 = 1,5 in^2
using BAR 4x3/8.
A_stiff_2 = A_reqd_2 - 26.84*ts_3*(D*ts_3)^0,5
= 0,31 - 26,84*0,25*(48*0,25)^0,5
= -22,934 in^2
Since A_stiff_2 <=0, No Stiffener Required
A_stiff_actual_2 = 1,5 in^2
using BAR 4x3/8.
A_stiff_3 = A_reqd_3 - 26.84*ts_4*(D*ts_4)^0,5
= 0,31 - 26,84*0,25*(48*0,25)^0,5
= -22,934 in^2
Since A_stiff_3 <=0, No Stiffener Required
A_stiff_actual_3 = 1,5 in^2
using BAR 4x3/8.
SHELL COURSE SUMMARY
STIFFENER ELEVATIONS ON SHELL
------
Stiffener #1: BAR 4x3/8, Elev. = 11,98 ft.
Stiffener #2: BAR 4x3/8, Elev. = 19,8 ft.
Stiffener #3: BAR 4x3/8, Elev. = 25,9 ft.
SHELL COURSE #1 SUMMARY
------
t.seismic governs. See E.6.2.4 table in SEISMIC calculations.
t-Calc = MAX(t-Calc_650, t_min_ext, t.seismic)
= MAX(0,3245, 0,1291, 0,4177)
= 0,4177 in.
t-650min = 0,1875 in. (per API-650 Section 5.6.1.1, NOTE 4)
t.required = MAX(t.design, t.test, t.min650) = 0,4177 in.
t.actual = 0,336 in.
Weight = Density*PI*[(12*OD) - t]*12*Width*t
= 0,2975*PI*[(12*48)-0,336]*12*8*0,336
= 17.355 lbf (New)
= 14.128 lbf (Corroded)
SHELL COURSE #2 SUMMARY
------
t.seismic governs. See E.6.2.4 table in SEISMIC calculations.
t-Calc = MAX(t-Calc_650, t_min_ext, t.seismic)
= MAX(0,258, 0,1291, 0,336)
= 0,336 in.
t-650min = 0,1875 in. (per API-650 Section 5.6.1.1, NOTE 4)
t.required = MAX(t.design, t.test, t.min650) = 0,336 in.
t.actual = 0,3125 in.
Weight = Density*PI*[(12*OD) - t]*12*Width*t
= 0,2975*PI*[(12*48)-0,3125]*12*8*0,3125
= 16.142 lbf (New)
= 12.915 lbf (Corroded)
SHELL COURSE #3 SUMMARY
------
t.seismic governs. See E.6.2.4 table in SEISMIC calculations.
t-Calc = MAX(t-Calc_650, t_min_ext, t.seismic)
= MAX(0,1914, 0,1291, 0,2495)
= 0,2495 in.
t-650min = 0,1875 in. (per API-650 Section 5.6.1.1, NOTE 4)
t.required = MAX(t.design, t.test, t.min650) = 0,2495 in.
t.actual = 0,25 in.
Weight = Density*PI*[(12*OD) - t]*12*Width*t
= 0,2975*PI*[(12*48)-0,25]*12*8*0,25
= 12.915 lbf (New)
= 9.687 lbf (Corroded)
SHELL COURSE #4 SUMMARY
------
t.seismic governs. See E.6.2.4 table in SEISMIC calculations.
t-Calc = MAX(t-Calc_650, t_min_ext, t.seismic)
= MAX(0,1249, 0,1291, 0,1591)
= 0,1591 in.
t-650min = 0,1875 in. (per API-650 Section 5.6.1.1, NOTE 4)
t.required = MAX(t.design, t.test, t.min650) = 0,1875 in.
t.actual = 0,25 in.
Weight = Density*PI*[(12*OD) - t]*12*Width*t
= 0,2975*PI*[(12*48)-0,25]*12*8*0,25
= 12.915 lbf (New)
= 9.687 lbf (Corroded)
FLAT BOTTOM: NON-ANNULAR PLATE DESIGN
Bottom Plate Material : A-240 Type 304
Annular Bottom Plate Material : A-240 Type 304
<Weight of Bottom Plate>
Bottom_Area = PI/4*(Bottom_OD)^2
= PI/4*(579)^2
= 263.298 in^2
Weight = Density * t.actual * Bottom_Area
= 0,2975 * 0,25 * 263.298
= 19.583 lbf (New)
= 19.583 lbf (Corroded)
< API-650 >
Calculation of Hydrostatic Test Stress & Product Design Stress
(per API-650 Section 5.5.1)
t_1 : Bottom (1st) Shell Course thickness.
H'= Max. Liq. Level + P(psi)/(0,433)
= 32 + (0,25)/(0,433) = 32,5774 ft
St = Hydrostatic Test Stress in Bottom (1st) Shell Course
= (2,6)(OD)(H' - 1)/t_1
= (2,6)(48)(32,5774 - 1)/(0,336)
= 11.729 PSI. (Within 24900 PSI limit for Non-Annular Bottom)
Sd = Product Design Stress in Bottom (1st) Shell Course
= (2,6)(OD)(H' - 1)(G)/(t_1 - ca_1)
= (2,6)(48)(32,5774 - 1)(1,15)/(0,2735)
= 16.570 PSI. (Within 23200 PSI limit for Non-Annular Bottom)
------
<Non-Annular Bottom Plates>
t_min = 0,1875 + CA = 0,1875 + 0 = 0,1875 in. (per Section 5.4.1)
t-Calc = t_min = 0,1875 in.
t-Actual = 0,25 in.
< Vacuum Calculations > (per ASME Section VIII Div. 1)
Weight Resisting External Vacuum (Corr. Btm. Plate + Min. Liq. Level)
P_btm = 0,2975 * 0,25 + 0,4979
= 0,5723 PSI or 15,86 IN. H2O
P_ext = PV + P_btm = -0,1 + 0,5723 = 0,4723 PSI or 13,09 IN. H2O
Since P_ext > 0, P_ext = 0
td_ext = (t-Calc - CA) (1st course)
= (0,4177 - 0,0625)
= 0,3552 in.
ts = (t.actual - CA) (1st course)
= (0,336 - 0,0625)
= 0,2735 in.
C = 0,33 * td_ext / ts
= 0,33 * 0,3552 / 0,2735
= 0,4286
t-Vac = OD*SQRT(C*P_ext/SE) + CA
= (576)*SQRT[(0,4286)(0)/(20.300)(0,85)] + 0
= 0 in.
t-Calc = MAX(t-Calc, t-Vac)
= MAX(0,1875,0)
= 0,1875 in.
P_max_external (Vacuum limited by bottom plate thickness)
= -([(t - CA)/OD]^2*(S*E/C) + P_btm)
= -([(0,25 - 0)/576]^2*(20.300*0,85/0,4286) + 0,5723)
= -0,5799 PSI or -16,07 IN. H2O
------
Wtr = Transposed Width of each Shell Course
= Width*[ t_top / t_course ]^2,5
Transforming Courses (1) to (4)
Wtr(1) = 8*[ 0,25/0,336 ]^2.5 = 3,8203 ft
Wtr(2) = 8*[ 0,25/0,3125 ]^2.5 = 4,5795 ft
Wtr(3) = 8*[ 0,25/0,25 ]^2.5 = 8 ft
Wtr(4) = 8*[ 0,25/0,25 ]^2.5 = 8 ft
Hts (Height of the Transformed Shell)
= SUM{Wtr} = 24,3998 ft
<API-650 APPENDIX V FOR EXTERNAL PRESSURE>
W (Wind Pressure) = 31*(V/120)^2
= 31*(110/120)^2
= 26,05 lbf/ft^2
Pe (External Pressure) = 0,1 PSI, OR 2,77 In. H2O
= 14,4 lbf/ft^2
Ps (Shell Design Pressure) = MAX(Pe, W + 0,4*Pe)
= MAX(14,4, 26,05 + 0,4*14,4)
= MAX(14,4, 31,81)
= 31,81 lbf/ft^2
* * * BOTTOM END STIFFENING CALCULATIONS PER V.8 * * *
Using API-650 App. V for flat bottom tank stiffening.
<V.8.2.3 Contributing Shell at Stiffener>
w_shell = 1,47*(D*tsn)^0,5
= 1,47*(48*0,336)^0,5
= 5,9035 in.
<V.8.2.3.1 Radial Load, VI>
VI = Ps * H/48
= 31,81 * 32/48
= 21,2067 lbf/ft
<V.8.2.2.1 Number of Waves>
N^2 = SQRT[5,33*D^3/(tsmin*Hts^2)]
= SQRT[5,33*48^3/(0,25*24,3998^2)]
= 62,93
N = 7,93
<V.8.2.3.2 Required Moment of Inertia>
w_btm (Width of bottom available for I)
= 16*tb
= 4in.
I_reqd = 648*VI*D^3/[E*(N^2-1)]
= 648*21,2067*48^3/[26.600.000*(7,93^2-1)]
= 0,923 in^4
I_actual = 1,4253 in^4
using NONE, tsn = 0,336 in., & W_shell = 5,9035 in.
<V.8.2.3.3.1 Area Required>
define f = Min(Fy_bottom, Fy_shell, Fy_stiff)
= Min(20.300, 20.300, N.A.)
= 20.300 psi
A_reqd = 6*VI*D/f
= 6*21,2067*48/20.300
= 0,3009 in^4
<V.8.2.3.3.2 Area required by stiffener>
A_stiff_reqd = A_reqd - JEb*tb*w_btm - JEn*tsn*w_shell
= 0,3009 - 0,85*0,25*4 - 0,85*0,336*5,9035
= -2,24 in^2
Since A_stiff_reqd <=0, No Bottom Stiffener Required
A_stiff = 0 in^2
using NONE
A_actual = A_stiff + JEb*tb*w_btm + JEn*tsn*w_shell
= 0 + 0,85*0,25*4 + 0,85*0,336*5,9035
= 2,54 in^2
FLAT BOTTOM: NON-ANNULAR SUMMARY
Bottom Plate Material : A-240 Type 304
t.required = 0,1875 in.
t.actual = 0,25 in.
NET UPLIFT DUE TO INTERNAL PRESSURE
(See roof report for calculations)
Net_Uplift = -7.113 lbf
Anchorage NOT required for internal pressure.
WIND MOMENT (Per API-650 SECTION 5.11)
vs = Wind Velocity = 110 mph
vf = Velocity Factor = (vs/120)^2 = (110/120)^2 = 0,8403
Wind_Uplift = Iw * 30 * vf
= 1 * 30 * 0,8403
= 25,2083 lbf/ft^2
API-650 5.2.1.k Uplift Check
P_F41 = WCtoPSI(0,962*Fy*A*TAN(Theta)/D^2 + 8*t_h)
P_F41 = WCtoPSI(0,962*22.500*3,814*4/48^2 + 8*0,3125)
= 5,2617 PSI
Limit Wind_Uplift/144+P to 1.6*P_F41
Wind_Uplift/144 + P = 0,4251 PSI
1.6*P_F41 = 8,4187 PSI
Wind_Uplift/144 + P = MIN(Wind_Uplift/144 + P, 1.6*P_F41)
Wind_Uplift/144 = MIN(Wind_Uplift/144, 1.6*P_F41 - P)
Wind_Uplift = MIN(Wind_Uplift, (1.6*P_F41 - P) * 144)
= MIN(25,2083,1.176)
= 25,2083 lbf/ft^2
hR = Height of Roof
= R - SQRT[R^2 - (OD/2)^2]
= 48 - SQRT[48^2 - (48/2)^2]
= 6,419 ft
t_ins = Thickness of Roof Insulation
= 0,1667 ft
Ap_Vert = Vertical Projected Area of Roof
= PI*([R + t_ins]^2)(Alpha/360) - OD*([R + t_ins] - hR)/2
= PI*(48,1667^2)(59,9859/360) - 48*(48,1667 - 6,419)/2
= 212,5351 ft^2
Horizontal Projected Area of Roof (Per API-650 5.2.1.f)
Xw = Moment Arm of UPLIFT wind force on roof
= 0.5*OD
= 0.5*48
= 24 ft
Ap = Projected Area of roof for wind moment
= PI*R^2
= PI*24^2
= 1.810 ft^2
M_roof (Moment Due to Wind Force on Roof)
= (Wind_Uplift)(Ap)(Xw)
= (25,2083)(1.810)(24) = 1.094.782 ft-lbf
Xs (Moment Arm of Wind Force on Shell)
= H/2 = (32)/2 = 16 ft
As (Projected Area of Shell)
= H*(OD + t_ins / 6)
= (32)(48 + 2/6) = 1.547 ft^2
M_shell (Moment Due to Wind Force on Shell)
= (Iw)(vf)(18)(As)(Xs)
= (1)(0,8403)(18)(1.547)(16) = 374.293 ft-lbf
Mw (Wind moment)
= M_roof + M_shell = 1.094.782 + 374.293
= 1.469.075 ft-lbf
W = Net weight (PER API-650 5.11.3)
(Force due to corroded weight of shell and
shell-supported roof plates less
40% of F.1.2 Uplift force.)
= W_shell + W_roof - 0,4*P*(PI/4)(144)(OD^2)
= 46.417 + 25.840 - 0,25*(PI/4)(144)(48^2)
= 46.199 lbf
RESISTANCE TO OVERTURNING (per API-650 5.11.2)
An unanchored Tank must meet these two criteria:
1) 0,6*Mw + MPi < MDL/1,5
2) Mw + 0,4MPi < (MDL + MF)/2
Mw = Destabilizing Wind Moment = 1.469.075 ft-lbf
MPi = Destabilizing Moment about the Shell-to-Bottom Joint from Design «
Pressure.
= P*(PI*OD^2/4)*(144)*(OD/2)
= 0,25*(3,1416*48^2/4)*(144)*(24)
= 1.563.458 ft-lbf
MDL = Stabilizing Moment about the Shell-to-Bottom Joint from the Shell and «
Roof weight supported by the Shell.
= (W_shell + W_roof)*OD/2
= (46.417 + 25.840)*24
= 1.734.168 ft-lbf
tb = Bottom Plate thickness less C.A. = 0,25 in.
wl = Circumferential loading of contents along Shell-To-Bottom Joint.
= 4,67*tb*SQRT(Sy_btm*H_liq)
= 4,67*0,25*SQRT(22.500*32)
= 990,66 lbf/ft
MF = Stabilizing Moment due to Bottom Plate and Liquid Weight.
= (OD/2)*wl*PI*OD
= (24)(990,66)(3,1416)(48)
= 3.585.312 ft-lbf
Criteria 1
0,6*(1.469.075) + 1.563.458 < 1.734.168/1,5
Since 2.444.903 >= 1.156.112, Tank must be anchored.
Criteria 2
1.469.075 + 0,4 * 1.563.458 < (1.734.168 + 3.585.312)/2
Since 2.094.458 < 2.659.740, Tank is stable.
RESISTANCE TO SLIDING (per API-650 5.11.4)
F_wind = vF * 18 * As
= 0,8403 * 18 * 1.547
= 23.393 lbf
F_friction = Maximum of 40% of Weight of Tank
= 0,4 * (W_Roof_Corroded + W_Shell_Corroded +
W_Btm_Corroded + W_min_Liquid)
= 0,4 * (25.840 + 46.417 + 19.583 + 129.489)
= 88.532 lbf
No anchorage needed to resist sliding since
F_friction > F_wind
<Anchorage Requirement>
Anchorage required since Criteria 1, Criteria 2, or Sliding
are NOT acceptable.
Bolt Spacing = 10 ft, Min # Anchor Bolts = 15
SEISMIC CALCULATIONS PER API-650 11TH ED., ADDENDUM 2
< Mapped ASCE7 Method >
WEIGHTS
Ws = Weight of Shell (Incl. Shell Stiffeners & Insul.)
= 69.136 lbf
Wf = Weight of Floor (Incl. Annular Ring)
= 19.583 lbf
Wr = Weight Fixed Roof, framing and 10% of Design Live Load & Insul.
= 38.408 lbf
SEISMIC VARIABLES
SUG = Seismic Use Group (Importance factor depends on SUG)
=
Site Class = D
T_L = Regional Dependent Transition Period for Long Period Ground Motion
(per ASCE 7-05, Fig. 22-15)
= 12 sec.
Ss = Design Spectral Response Param. (5% damped) for Short Periods
(T=0.2 sec)(per ASCE7 Fig. 22-1)
= 1,24 Decimal %g
S1 = Design Spectral Response Param. (5% damped) for 1-Second Periods
(T=1.0 sec)(per ASCE7 Fig. 22-2)
= 0,5 Decimal %g
S0 = Design Spectral Response Param. (5% damped) for 0-Second Periods
(T=0.0 sec)
= 0,496 Decimal %g
Av = Vertical Earthquake Acceleration Coefficient
= 0,0023 Decimal %g
Q = Scaling factor from the MCE to design level spectral accelerations