192 TANK 2014 SP1, API-650/653 Analysis Licensee: SPLM Licensee ID: 101 Job: 44-01-T-2491 Date: Jun 19,2015 Time: 10:22a

NOZZLE FLEXIBILITIES & LOADS - Appendix P API-650 12th Edition, Errata, July 2013

DESIGN TEST USER

DATA FOR NOZZLE: A1 Radial Stiffness (N./cm. ) 0.20669E+06 0.20669E+06 0.20669E+06 Long. Bending Stiff(N.m./deg ) 52401. 52401. 52401. Circ. Bending Stiff(N.m./deg ) 18587. 18587. 18587. Radial Deflection (mm. ) 0.58878 0.58878 0.58878 Long. Rotation (deg. ) 0.65277E-02 0.65277E-02 0.65277E-02

Radial Force Multp (1/N. ) 0.53658E-04 0.53658E-04 0.53658E-04 Long. Moment Multp (1/N.m. ) 0.21078E-03 0.21078E-03 0.21078E-03 Circ. Moment Multp (1/N.m. ) 0.18040E-03 0.18040E-03 0.18040E-03

Radial Force Limit (N. ) 1863.7 1863.7 1863.7 +Long. Moment Limit(N.m. ) 474.42 474.42 474.42 -Long. Moment Limit(N.m. ) -474.42 -474.42 -474.42 Circ. Moment Limit (N.m. ) 554.32 554.32 554.32

DATA FOR NOZZLE: S1 Radial Stiffness (N./cm. ) 0.27506E+06 0.27506E+06 0.27506E+06 Long. Bending Stiff(N.m./deg ) 24146. 24146. 24146. Circ. Bending Stiff(N.m./deg ) 16477. 16477. 16477. Radial Deflection (mm. ) 0.28573 0.28573 0.28573 Long. Rotation (deg. ) 0.65277E-02 0.65277E-02 0.65277E-02

Radial Force Multp (1/N. ) 0.13143E-03 0.13143E-03 0.13143E-03 Long. Moment Multp (1/N.m. ) 0.75540E-03 0.75540E-03 0.75540E-03 Circ. Moment Multp (1/N.m. ) 0.33952E-03 0.33952E-03 0.33952E-03

Radial Force Limit (N. ) 760.89 760.89 760.89 +Long. Moment Limit(N.m. ) 132.38 132.38 132.38 -Long. Moment Limit(N.m. ) -132.38 -132.38 -132.38 Circ. Moment Limit (N.m. ) 294.54 294.54 294.54

DATA FOR NOZZLE: S2 Radial Stiffness (N./cm. ) 0.23098E+06 0.23098E+06 0.23098E+06 Long. Bending Stiff(N.m./deg ) 66933. 66933. 66933. Circ. Bending Stiff(N.m./deg ) 23372. 23372. 23372. Radial Deflection (mm. ) 1.0911 1.0911 1.0911 Long. Rotation (deg. ) 0.42243E-02 0.42243E-02 0.42243E-02

Radial Force Multp (1/N. ) 0.26541E-04 0.26541E-04 0.26541E-04 Long. Moment Multp (1/N.m. ) 0.96455E-04 0.96455E-04 0.96455E-04 Circ. Moment Multp (1/N.m. ) 0.90126E-04 0.90126E-04 0.90126E-04

Radial Force Limit (N. ) 3767.8 3767.8 3767.8 +Long. Moment Limit(N.m. ) 1036.8 1036.8 1036.8 -Long. Moment Limit(N.m. ) -1036.8 -1036.8 -1036.8 Circ. Moment Limit (N.m. ) 1109.6 1109.6 1109.6

DATA FOR NOZZLE: S3 Radial Stiffness (N./cm. ) 0.27506E+06 0.27506E+06 0.27506E+06 Long. Bending Stiff(N.m./deg ) 24146. 24146. 24146. Circ. Bending Stiff(N.m./deg ) 16477. 16477. 16477. Radial Deflection (mm. ) 0.57739 0.57739 0.57739 Long. Rotation (deg. ) 0.65277E-02 0.65277E-02 0.65277E-02

Radial Force Multp (1/N. ) 0.65037E-04 0.65037E-04 0.65037E-04 Long. Moment Multp (1/N.m. ) 0.37382E-03 0.37382E-03 0.37382E-03 Circ. Moment Multp (1/N.m. ) 0.16801E-03 0.16801E-03 0.16801E-03

Radial Force Limit (N. ) 1537.6 1537.6 1537.6 +Long. Moment Limit(N.m. ) 267.51 267.51 267.51 -Long. Moment Limit(N.m. ) -267.51 -267.51 -267.51 Circ. Moment Limit (N.m. ) 595.19 595.19 595.19

DATA FOR NOZZLE: D1 Radial Stiffness (N./cm. ) 0.46875E+06 0.46875E+06 0.46875E+06 Long. Bending Stiff(N.m./deg ) 14880. 14880. 14880. Circ. Bending Stiff(N.m./deg ) 26037. 26037. 26037. Radial Deflection (mm. ) 0.58607 0.58607 0.58607 Long. Rotation (deg. ) -0.17331 -0.17331 -0.17331

Radial Force Multp (1/N. ) 0.33617E-04 0.33617E-04 0.33617E-04 Long. Moment Multp (1/N.m. ) 0.33999E-03 0.33999E-03 0.33999E-03 Circ. Moment Multp (1/N.m. ) 0.75120E-04 0.75120E-04 0.75120E-04

Radial Force Limit (N. ) 16148. 16148. 16148. +Long. Moment Limit(N.m. ) 2181.3 2181.3 2181.3 -Long. Moment Limit(N.m. ) -1596.6 -1596.6 -1596.6 Circ. Moment Limit (N.m. ) 8549.4 8549.4 8549.4

DATA FOR NOZZLE: D2 Radial Stiffness (N./cm. ) 0.48061E+06 0.48061E+06 0.48061E+06 Long. Bending Stiff(N.m./deg ) 19223. 19223. 19223. Circ. Bending Stiff(N.m./deg ) 27089. 27089. 27089. Radial Deflection (mm. ) 0.58607 0.58607 0.58607 Long. Rotation (deg. ) -0.17331 -0.17331 -0.17331

Radial Force Multp (1/N. ) 0.31466E-04 0.31466E-04 0.31466E-04 Long. Moment Multp (1/N.m. ) 0.25006E-03 0.25006E-03 0.25006E-03 Circ. Moment Multp (1/N.m. ) 0.76319E-04 0.76319E-04 0.76319E-04

Radial Force Limit (N. ) 16349. 16349. 16349. +Long. Moment Limit(N.m. ) 3079.3 3079.3 3079.3 -Long. Moment Limit(N.m. ) -2057.2 -2057.2 -2057.2 Circ. Moment Limit (N.m. ) 8415.1 8415.1 8415.1

DATA FOR NOZZLE: N1A Radial Stiffness (N./cm. ) 0.40363E+06 0.40363E+06 0.40363E+06 Long. Bending Stiff(N.m./deg ) 13006. 13006. 13006. Circ. Bending Stiff(N.m./deg ) 21892. 21892. 21892. Radial Deflection (mm. ) 0.23560 0.23560 0.23560 Long. Rotation (deg. ) 0.65277E-02 0.65277E-02 0.65277E-02

Radial Force Multp (1/N. ) 0.16926E-03 0.16926E-03 0.16926E-03 Long. Moment Multp (1/N.m. ) 0.17139E-02 0.17139E-02 0.17139E-02 Circ. Moment Multp (1/N.m. ) 0.39284E-03 0.39284E-03 0.39284E-03

Radial Force Limit (N. ) 590.80 590.80 590.80 +Long. Moment Limit(N.m. ) 58.347 58.347 58.347 -Long. Moment Limit(N.m. ) -58.347 -58.347 -58.347 Circ. Moment Limit (N.m. ) 254.55 254.55 254.55

DATA FOR NOZZLE: N1B Radial Stiffness (N./cm. ) 0.40363E+06 0.40363E+06 0.40363E+06 Long. Bending Stiff(N.m./deg ) 13006. 13006. 13006. Circ. Bending Stiff(N.m./deg ) 21892. 21892. 21892. Radial Deflection (mm. ) 0.25838 0.25838 0.25838 Long. Rotation (deg. ) 0.65277E-02 0.65277E-02 0.65277E-02

Radial Force Multp (1/N. ) 0.15434E-03 0.15434E-03 0.15434E-03 Long. Moment Multp (1/N.m. ) 0.15627E-02 0.15627E-02 0.15627E-02 Circ. Moment Multp (1/N.m. ) 0.35820E-03 0.35820E-03 0.35820E-03

Radial Force Limit (N. ) 647.94 647.94 647.94 +Long. Moment Limit(N.m. ) 63.990 63.990 63.990 -Long. Moment Limit(N.m. ) -63.990 -63.990 -63.990 Circ. Moment Limit (N.m. ) 279.17 279.17 279.17

DATA FOR NOZZLE: N1C Radial Stiffness (N./cm. ) 0.40363E+06 0.40363E+06 0.40363E+06 Long. Bending Stiff(N.m./deg ) 13006. 13006. 13006. Circ. Bending Stiff(N.m./deg ) 21892. 21892. 21892. Radial Deflection (mm. ) 0.28117 0.28117 0.28117 Long. Rotation (deg. ) 0.65277E-02 0.65277E-02 0.65277E-02

Radial Force Multp (1/N. ) 0.14183E-03 0.14183E-03 0.14183E-03 Long. Moment Multp (1/N.m. ) 0.14361E-02 0.14361E-02 0.14361E-02 Circ. Moment Multp (1/N.m. ) 0.32917E-03 0.32917E-03 0.32917E-03

Radial Force Limit (N. ) 705.07 705.07 705.07 +Long. Moment Limit(N.m. ) 69.633 69.633 69.633 -Long. Moment Limit(N.m. ) -69.633 -69.633 -69.633 Circ. Moment Limit (N.m. ) 303.79 303.79 303.79

DATA FOR NOZZLE: N2A Radial Stiffness (N./cm. ) 0.11086E+06 0.11086E+06 0.11086E+06 Long. Bending Stiff(N.m./deg ) 1777.3 1777.3 1777.3 Circ. Bending Stiff(N.m./deg ) 3571.0 3571.0 3571.0 Radial Deflection (mm. ) 2.2141 2.2141 2.2141 Long. Rotation (deg. ) 0.19127E-01 0.19127E-01 0.19127E-01

Radial Force Multp (1/N. ) 0.70015E-04 0.70015E-04 0.70015E-04 Long. Moment Multp (1/N.m. ) 0.10418E-02 0.10418E-02 0.10418E-02 Circ. Moment Multp (1/N.m. ) 0.21831E-03 0.21831E-03 0.21831E-03

Radial Force Limit (N. ) 1428.3 1428.3 1428.3 +Long. Moment Limit(N.m. ) 95.988 95.988 95.988 -Long. Moment Limit(N.m. ) -95.988 -95.988 -95.988 Circ. Moment Limit (N.m. ) 458.07 458.07 458.07

DATA FOR NOZZLE: N2B Radial Stiffness (N./cm. ) 0.11086E+06 0.11086E+06 0.11086E+06 Long. Bending Stiff(N.m./deg ) 1777.3 1777.3 1777.3 Circ. Bending Stiff(N.m./deg ) 3571.0 3571.0 3571.0 Radial Deflection (mm. ) 2.1253 2.1253 2.1253 Long. Rotation (deg. ) -0.11263 -0.11263 -0.11263

Radial Force Multp (1/N. ) 0.68940E-04 0.68940E-04 0.68940E-04 Long. Moment Multp (1/N.m. ) 0.10258E-02 0.10258E-02 0.10258E-02 Circ. Moment Multp (1/N.m. ) 0.21496E-03 0.21496E-03 0.21496E-03

Radial Force Limit (N. ) 1450.5 1450.5 1450.5 +Long. Moment Limit(N.m. ) 143.01 143.01 143.01 -Long. Moment Limit(N.m. ) -97.485 -97.485 -97.485 Circ. Moment Limit (N.m. ) 465.21 465.21 465.21

DATA FOR NOZZLE: I1 Radial Stiffness (N./cm. ) 0.40363E+06 0.40363E+06 0.40363E+06 Long. Bending Stiff(N.m./deg ) 13006. 13006. 13006. Circ. Bending Stiff(N.m./deg ) 21892. 21892. 21892. Radial Deflection (mm. ) 0.63435 0.63435 0.63435 Long. Rotation (deg. ) 0.65277E-02 0.65277E-02 0.65277E-02

Radial Force Multp (1/N. ) 0.62864E-04 0.62864E-04 0.62864E-04 Long. Moment Multp (1/N.m. ) 0.63653E-03 0.63653E-03 0.63653E-03 Circ. Moment Multp (1/N.m. ) 0.14590E-03 0.14590E-03 0.14590E-03

Radial Force Limit (N. ) 1590.7 1590.7 1590.7 +Long. Moment Limit(N.m. ) 157.10 157.10 157.10 -Long. Moment Limit(N.m. ) -157.10 -157.10 -157.10 Circ. Moment Limit (N.m. ) 685.39 685.39 685.39

TANK(c) Intergraph CADWorx & Analysis Solutions, Inc. 2014

5 TANK 2014 SP1, API-650/653 Analysis Licensee: SPLM Licensee ID: 201 Job: 44-01-T-2491 Date: Jun 19,2015 Time: 10:22a

Nozzle Stiffness Calculations:

Design Case [Nozzle 1 ] per Appendix P:

Nozzle stiffness coefficients per P.2.4:

Outside radius of nozzle [a]: = D / 2 = 12.8/2 = 6.4 in. [323.9 mm.]

Nominal tank radius [R]: = Nominal tank diameter / 2 = 492.1/2 = 246.1 in. [12500.0 mm.]

L / 2a coefficient: = L / 2 * a = 192.913/2 * 6.375 = 15.1

As L/2a >= 1.5, use second set of curves.

a / R coefficient: = a / R = 6.4/246.063 = 0.026

R / t coefficient: = R / t = 246.063/0.669 = 367.6

From figure P-2D [KR/E(2a)]: = 0.322E-03

From figure P-2E [KL/E(2a)^3]: = 0.446E-03

From figure P-2F [KC/E(2a)^3]: = 0.158E-03

Stiffness coefficient for the radial thrust load per P.2.9.2.1 [KR]: = Coeff. from graph * E * 2 * a = 0.322E-03 * 28756854 * 2 * 6.375 = 0.11803E+06 lbf./in. [0.20669E+06 N./cm.]

Stiffness coefficient for the longitudinal moment per P.2.9.2.1 [KL]: = Coeff. from graph * E * ( 2.0 * a )^3 = 0.446E-03 * 28756854 * ( 2.0 * 6.375 )^3 = 0.46381E+06 in.lbf./deg [0.52401E+05 N.m./deg]

Stiffness coefficient for the circumferential moment per P.2.9.2.1 [KC]: = Coeff. from graph * E * ( 2 * a )^3 = 0.158E-03 * 28756854 * ( 2 * 6.375 )^3 = 0.16451E+06 in.lbf./deg [0.18587E+05 N.m./deg]

Characteristic parameter per P.2.3 [beta]: = 1.285 / (Rt)^0.5 = 1.285/(246.063 * 0.669 )^0.5 = 0.10013E+00 1/in. [0.39422E-02 1/mm.]

Unrestrained radial growth of the shell per P.2.5.1 [W]: = (0.036*G*H*R^2)/Et * [1-(e^-(beta*L)) * cos(beta*L) - (L/H)] + alpha * R * delta[T] = (0.036*1.006 *396.375 *246.063^2)/28756854 *0.669 * [1-(e^-(0.100 *192.913 )) * cos(0.100 *192.913 ) - (192.913/396.37 )] + 0.663E-05 * 246.063 * 0.000 = 0.02318 in. [0.58878 mm.]

Unrestrained shell rotation of the shell per P.2.5.2 [theta]: = (0.036*G*H*R^2)/E*t * [(1/H)-(beta*e^-(beta*L)) * [cos(beta*L)+sin(beta*L)]] = (0.036*1.006 *396.375 *246.063^2)/28756854 *0.669 * [(1/396.375 )-(0.100 *e^-(0.100 *192.913 )) * [cos(0.100 *192.913 )+sin(0.100 *192.913 )]] = 0.65277E-02 deg

Value of lamda per P.2.3 [lamda]: = a/(Rt)^0.5 = 6.375/(246.063 * 0.669 )^0.5 = 0.497

Coefficient XA per P.2.3: = L + a = 192.913 + 6.375 = 199.288 in. [5061.925 mm.]

Coefficient XB per P.2.3: = L - a = 192.913 - 6.375 = 186.538 in. [4738.075 mm.]

Coefficient XC per P.2.3: = L = 192.913 in. [4900.000 mm.]

Coefficients YF and YL from figure P-4A based on lamda: YF = 1.103 YL = 3.467

Coefficient YC from figure P-4B based on lamda: YC = 4.051

Pressure end load on the opening per P.2.3: = pi * a^2 * P = 3.1415 * 6.375^2 * 7.391 = 943.694 lbf. [4197.551 N.]

Radial force nomogram limit values per figure P-3A: = max[(1 - 0.75)(XA / (Rt)^0.5), 0.1] = max[(1 - 0.75)(199.288/(246.063 *0.669 )^0.5), 0.1] = 0.100

Longitudinal nomogram limit values per figure P-3A: = max[(1 - 0.75)(XB / (Rt)^0.5), 0.1] = max[(1 - 0.75)(186.538/(246.063 *0.669 )^0.5), 0.1] = 0.100

Circumferential moment nomogram limit value per figure P-3B: = max[(1 - 0.75)(XC / (Rt)^0.5), 0.1] = max[(1 - 0.75)(192.913/(246.063 *0.669 )^0.5), 0.1] = 0.100

Radial force multiplier per figure P-3A: = lamda / (2 * YF * FP) = 0.497/(2 * 1.103 * 943.694 ) = 0.23867E-03 1/lbf. [0.53658E-04 1/N.]

Longitudinal moment multiplier per figure P-3A: = lamda / (a * 12.0 * YL * FP) = 0.497/(6.375 * 12.0 * 3.467 * 943.694 ) = 0.28577E-03 1/ft.lb. [0.21078E-03 1/N.m.]

Circumferential moment multiplier per figure P-3B: = lamda / (a * 12.0 * YC * FP) = 0.497/(6.375 * 12.0 * 4.051 * 943.694 ) = 0.24458E-03 1/ft.lb. [0.18040E-03 1/N.m.]

Radial force limit [ML = 0 and MC = 0] per figure P-3A [FRmax]: = Radial force nomogram limit value / Radial force multp. = 0.100/0.239E-03 = 0.41899E+03 lbf. [0.18637E+04 N.]

Positive Long. moment limit [MC = 0 and FR = 0] per figure P-3A [MLmax]: = Long. moment nomogram limit value / Long. moment multiplier = 0.100/0.286E-03 = 0.34993E+03 ft.lb. [0.47442E+03 N.m.]

Negative Long. moment limit [ML = 0 and MC = 0] per figure P-3A [MLmin]: = - Radial Force nomogram limit value / Long. moment multiplier = -0.100/0.286E-03 = -.34993E+03 ft.lb. [-0.47442E+03 N.m.]

Circ. moment limit [ML = 0 and FR = 0] per figure P-3B [MCmax]: = Circ. moment nomogram limit value / Circ. moment multiplier = 0.100/0.245E-03 = 0.40887E+03 ft.lb. [0.55432E+03 N.m.]

Test Case [Nozzle 1 ] per Appendix P:

Nozzle stiffness coefficients per P.2.4:

Outside radius of nozzle [a]: = D / 2 = 12.8/2 = 6.4 in. [323.9 mm.]

Nominal tank radius [R]: = Nominal tank diameter / 2 = 492.1/2 = 246.1 in. [12500.0 mm.]

L / 2a coefficient: = L / 2 * a = 192.913/2 * 6.375 = 15.1

As L/2a >= 1.5, use second set of curves.

a / R coefficient: = a / R = 6.4/246.063 = 0.026

R / t coefficient: = R / t = 246.063/0.669 = 367.6

From figure P-2D [KR/E(2a)]: = 0.322E-03

From figure P-2E [KL/E(2a)^3]: = 0.446E-03

From figure P-2F [KC/E(2a)^3]: = 0.158E-03

Stiffness coefficient for the radial thrust load per P.2.9.2.1 [KR]: = Coeff. from graph * E * 2 * a = 0.322E-03 * 28756854 * 2 * 6.375 = 0.11803E+06 lbf./in. [0.20669E+06 N./cm.]

Stiffness coefficient for the longitudinal moment per P.2.9.2.1 [KL]: = Coeff. from graph * E * ( 2.0 * a )^3 = 0.446E-03 * 28756854 * ( 2.0 * 6.375 )^3 = 0.46381E+06 in.lbf./deg [0.52401E+05 N.m./deg]

Stiffness coefficient for the circumferential moment per P.2.9.2.1 [KC]: = Coeff. from graph * E * ( 2 * a )^3 = 0.158E-03 * 28756854 * ( 2 * 6.375 )^3 = 0.16451E+06 in.lbf./deg [0.18587E+05 N.m./deg]

Characteristic parameter per P.2.3 [beta]: = 1.285 / (Rt)^0.5 = 1.285/(246.063 * 0.669 )^0.5 = 0.10013E+00 1/in. [0.39422E-02 1/mm.]

Unrestrained radial growth of the shell per P.2.5.1 [W]: = (0.036*G*H*R^2)/Et * [1-(e^-(beta*L)) * cos(beta*L) - (L/H)] + alpha * R * delta[T] = (0.036*1.006 *396.375 *246.063^2)/28756854 *0.669 * [1-(e^-(0.100 *192.913 )) * cos(0.100 *192.913 ) - (192.913/396.37 )] + 0.663E-05 * 246.063 * 0.000 = 0.02318 in. [0.58878 mm.]

Unrestrained shell rotation of the shell per P.2.5.2 [theta]: = (0.036*G*H*R^2)/E*t * [(1/H)-(beta*e^-(beta*L)) * [cos(beta*L)+sin(beta*L)]] = (0.036*1.006 *396.375 *246.063^2)/28756854 *0.669 * [(1/396.375 )-(0.100 *e^-(0.100 *192.913 )) * [cos(0.100 *192.913 )+sin(0.100 *192.913 )]] = 0.65277E-02 deg

Value of lamda per P.2.3 [lamda]: = a/(Rt)^0.5 = 6.375/(246.063 * 0.669 )^0.5 = 0.497

Coefficient XA per P.2.3: = L + a = 192.913 + 6.375 = 199.288 in. [5061.925 mm.]

Coefficient XB per P.2.3: = L - a = 192.913 - 6.375 = 186.538 in. [4738.075 mm.]

Coefficient XC per P.2.3: = L = 192.913 in. [4900.000 mm.]

Coefficients YF and YL from figure P-4A based on lamda: YF = 1.103 YL = 3.467

Coefficient YC from figure P-4B based on lamda: YC = 4.051

Pressure end load on the opening per P.2.3: = pi * a^2 * P = 3.1415 * 6.375^2 * 7.391 = 943.694 lbf. [4197.551 N.]

Radial force nomogram limit values per figure P-3A: = max[(1 - 0.75)(XA / (Rt)^0.5), 0.1] = max[(1 - 0.75)(199.288/(246.063 *0.669 )^0.5), 0.1] = 0.100

Longitudinal nomogram limit values per figure P-3A: = max[(1 - 0.75)(XB / (Rt)^0.5), 0.1] = max[(1 - 0.75)(186.538/(246.063 *0.669 )^0.5), 0.1] = 0.100

Circumferential moment nomogram limit value per figure P-3B: = max[(1 - 0.75)(XC / (Rt)^0.5), 0.1] = max[(1 - 0.75)(192.913/(246.063 *0.669 )^0.5), 0.1] = 0.100

Radial force multiplier per figure P-3A: = lamda / (2 * YF * FP) = 0.497/(2 * 1.103 * 943.694 ) = 0.23867E-03 1/lbf. [0.53658E-04 1/N.]

Longitudinal moment multiplier per figure P-3A: = lamda / (a * 12.0 * YL * FP) = 0.497/(6.375 * 12.0 * 3.467 * 943.694 ) = 0.28577E-03 1/ft.lb. [0.21078E-03 1/N.m.]

Circumferential moment multiplier per figure P-3B: = lamda / (a * 12.0 * YC * FP) = 0.497/(6.375 * 12.0 * 4.051 * 943.694 ) = 0.24458E-03 1/ft.lb. [0.18040E-03 1/N.m.]

Radial force limit [ML = 0 and MC = 0] per figure P-3A [FRmax]: = Radial force nomogram limit value / Radial force multp. = 0.100/0.239E-03 = 0.41899E+03 lbf. [0.18637E+04 N.]

Positive Long. moment limit [MC = 0 and FR = 0] per figure P-3A [MLmax]: = Long. moment nomogram limit value / Long. moment multiplier = 0.100/0.286E-03 = 0.34993E+03 ft.lb. [0.47442E+03 N.m.]

Negative Long. moment limit [ML = 0 and MC = 0] per figure P-3A [MLmin]: = - Radial Force nomogram limit value / Long. moment multiplier = -0.100/0.286E-03 = -.34993E+03 ft.lb. [-0.47442E+03 N.m.]

Circ. moment limit [ML = 0 and FR = 0] per figure P-3B [MCmax]: = Circ. moment nomogram limit value / Circ. moment multiplier = 0.100/0.245E-03 = 0.40887E+03 ft.lb. [0.55432E+03 N.m.]

User Case [Nozzle 1 ] per Appendix P:

Nozzle stiffness coefficients per P.2.4:

Outside radius of nozzle [a]: = D / 2 = 12.8/2 = 6.4 in. [323.9 mm.]

Nominal tank radius [R]: = Nominal tank diameter / 2 = 492.1/2 = 246.1 in. [12500.0 mm.]

L / 2a coefficient: = L / 2 * a = 192.913/2 * 6.375 = 15.1

As L/2a >= 1.5, use second set of curves.

a / R coefficient: = a / R = 6.4/246.063 = 0.026

R / t coefficient: = R / t = 246.063/0.669 = 367.6

From figure P-2D [KR/E(2a)]: = 0.322E-03

From figure P-2E [KL/E(2a)^3]: = 0.446E-03

From figure P-2F [KC/E(2a)^3]: = 0.158E-03

Stiffness coefficient for the radial thrust load per P.2.9.2.1 [KR]: = Coeff. from graph * E * 2 * a = 0.322E-03 * 28756854 * 2 * 6.375 = 0.11803E+06 lbf./in. [0.20669E+06 N./cm.]

Stiffness coefficient for the longitudinal moment per P.2.9.2.1 [KL]: = Coeff. from graph * E * ( 2.0 * a )^3 = 0.446E-03 * 28756854 * ( 2.0 * 6.375 )^3 = 0.46381E+06 in.lbf./deg [0.52401E+05 N.m./deg]

Stiffness coefficient for the circumferential moment per P.2.9.2.1 [KC]: = Coeff. from graph * E * ( 2 * a )^3 = 0.158E-03 * 28756854 * ( 2 * 6.375 )^3 = 0.16451E+06 in.lbf./deg [0.18587E+05 N.m./deg]

Characteristic parameter per P.2.3 [beta]: = 1.285 / (Rt)^0.5 = 1.285/(246.063 * 0.669 )^0.5 = 0.10013E+00 1/in. [0.39422E-02 1/mm.]

Unrestrained radial growth of the shell per P.2.5.1 [W]: = (0.036*G*H*R^2)/Et * [1-(e^-(beta*L)) * cos(beta*L) - (L/H)] + alpha * R * delta[T] = (0.036*1.006 *396.375 *246.063^2)/28756854 *0.669 * [1-(e^-(0.100 *192.913 )) * cos(0.100 *192.913 ) - (192.913/396.37 )] + 0.663E-05 * 246.063 * 0.000 = 0.02318 in. [0.58878 mm.]

Unrestrained shell rotation of the shell per P.2.5.2 [theta]: = (0.036*G*H*R^2)/E*t * [(1/H)-(beta*e^-(beta*L)) * [cos(beta*L)+sin(beta*L)]] = (0.036*1.006 *396.375 *246.063^2)/28756854 *0.669 * [(1/396.375 )-(0.100 *e^-(0.100 *192.913 )) * [cos(0.100 *192.913 )+sin(0.100 *192.913 )]] = 0.65277E-02 deg

Value of lamda per P.2.3 [lamda]: = a/(Rt)^0.5 = 6.375/(246.063 * 0.669 )^0.5 = 0.497

Coefficient XA per P.2.3: = L + a = 192.913 + 6.375 = 199.288 in. [5061.925 mm.]

Coefficient XB per P.2.3: = L - a = 192.913 - 6.375 = 186.538 in. [4738.075 mm.]

Coefficient XC per P.2.3: = L = 192.913 in. [4900.000 mm.]

Coefficients YF and YL from figure P-4A based on lamda: YF = 1.103 YL = 3.467

Coefficient YC from figure P-4B based on lamda: YC = 4.051

Pressure end load on the opening per P.2.3: = pi * a^2 * P = 3.1415 * 6.375^2 * 7.391 = 943.694 lbf. [4197.551 N.]

Radial force nomogram limit values per figure P-3A: = max[(1 - 0.75)(XA / (Rt)^0.5), 0.1] = max[(1 - 0.75)(199.288/(246.063 *0.669 )^0.5), 0.1] = 0.100

Longitudinal nomogram limit values per figure P-3A: = max[(1 - 0.75)(XB / (Rt)^0.5), 0.1] = max[(1 - 0.75)(186.538/(246.063 *0.669 )^0.5), 0.1] = 0.100

Circumferential moment nomogram limit value per figure P-3B: = max[(1 - 0.75)(XC / (Rt)^0.5), 0.1] = max[(1 - 0.75)(192.913/(246.063 *0.669 )^0.5), 0.1] = 0.100

Radial force multiplier per figure P-3A: = lamda / (2 * YF * FP) = 0.497/(2 * 1.103 * 943.694 ) = 0.23867E-03 1/lbf. [0.53658E-04 1/N.]

Longitudinal moment multiplier per figure P-3A: = lamda / (a * 12.0 * YL * FP) = 0.497/(6.375 * 12.0 * 3.467 * 943.694 ) = 0.28577E-03 1/ft.lb. [0.21078E-03 1/N.m.]

Circumferential moment multiplier per figure P-3B: = lamda / (a * 12.0 * YC * FP) = 0.497/(6.375 * 12.0 * 4.051 * 943.694 ) = 0.24458E-03 1/ft.lb. [0.18040E-03 1/N.m.]

Radial force limit [ML = 0 and MC = 0] per figure P-3A [FRmax]: = Radial force nomogram limit value / Radial force multp. = 0.100/0.239E-03 = 0.41899E+03 lbf. [0.18637E+04 N.]

Positive Long. moment limit [MC = 0 and FR = 0] per figure P-3A [MLmax]: = Long. moment nomogram limit value / Long. moment multiplier = 0.100/0.286E-03 = 0.34993E+03 ft.lb. [0.47442E+03 N.m.]

Negative Long. moment limit [ML = 0 and MC = 0] per figure P-3A [MLmin]: = - Radial Force nomogram limit value / Long. moment multiplier = -0.100/0.286E-03 = -.34993E+03 ft.lb. [-0.47442E+03 N.m.]

Circ. moment limit [ML = 0 and FR = 0] per figure P-3B [MCmax]: = Circ. moment nomogram limit value / Circ. moment multiplier = 0.100/0.245E-03 = 0.40887E+03 ft.lb. [0.55432E+03 N.m.]

Design Case [Nozzle 2 ] per Appendix P:

Nozzle stiffness coefficients per P.2.4:

Outside radius of nozzle [a]: = D / 2 = 6.6/2 = 3.3 in. [168.3 mm.]

Nominal tank radius [R]: = Nominal tank diameter / 2 = 492.1/2 = 246.1 in. [12500.0 mm.]

L / 2a coefficient: = L / 2 * a = 297.638/2 * 3.313 = 44.9

As L/2a >= 1.5, use second set of curves.

a / R coefficient: = a / R = 3.3/246.063 = 0.013

R / t coefficient: = R / t = 246.063/0.669 = 367.6

From figure P-2D [KR/E(2a)]: = 0.824E-03

From figure P-2E [KL/E(2a)^3]: = 0.146E-02

From figure P-2F [KC/E(2a)^3]: = 0.999E-03

Stiffness coefficient for the radial thrust load per P.2.9.2.1 [KR]: = Coeff. from graph * E * 2 * a = 0.824E-03 * 28756854 * 2 * 3.313 = 0.15707E+06 lbf./in. [0.27506E+06 N./cm.]

Stiffness coefficient for the longitudinal moment per P.2.9.2.1 [KL]: = Coeff. from graph * E * ( 2.0 * a )^3 = 0.146E-02 * 28756854 * ( 2.0 * 3.313 )^3 = 0.21371E+06 in.lbf./deg [0.24146E+05 N.m./deg]

Stiffness coefficient for the circumferential moment per P.2.9.2.1 [KC]: = Coeff. from graph * E * ( 2 * a )^3 = 0.999E-03 * 28756854 * ( 2 * 3.313 )^3 = 0.14584E+06 in.lbf./deg [0.16477E+05 N.m./deg]

Characteristic parameter per P.2.3 [beta]: = 1.285 / (Rt)^0.5 = 1.285/(246.063 * 0.669 )^0.5 = 0.10013E+00 1/in. [0.39422E-02 1/mm.]

Unrestrained radial growth of the shell per P.2.5.1 [W]: = (0.036*G*H*R^2)/Et * [1-(e^-(beta*L)) * cos(beta*L) - (L/H)] + alpha * R * delta[T] = (0.036*1.006 *396.375 *246.063^2)/28756854 *0.669 * [1-(e^-(0.100 *297.638 )) * cos(0.100 *297.638 ) - (297.638/396.37 )] + 0.663E-05 * 246.063 * 0.000 = 0.01125 in. [0.28573 mm.]

Unrestrained shell rotation of the shell per P.2.5.2 [theta]: = (0.036*G*H*R^2)/E*t * [(1/H)-(beta*e^-(beta*L)) * [cos(beta*L)+sin(beta*L)]] = (0.036*1.006 *396.375 *246.063^2)/28756854 *0.669 * [(1/396.375 )-(0.100 *e^-(0.100 *297.638 )) * [cos(0.100 *297.638 )+sin(0.100 *297.638 )]] = 0.65277E-02 deg

Value of lamda per P.2.3 [lamda]: = a/(Rt)^0.5 = 3.313/(246.063 * 0.669 )^0.5 = 0.258

Coefficient XA per P.2.3: = L + a = 297.638 + 3.313 = 300.951 in. [7644.149 mm.]

Coefficient XB per P.2.3: = L - a = 297.638 - 3.313 = 294.325 in. [7475.850 mm.]

Coefficient XC per P.2.3: = L = 297.638 in. [7560.000 mm.]

Coefficients YF and YL from figure P-4A based on lamda: YF = 1.785 YL = 7.382

Coefficient YC from figure P-4B based on lamda: YC = 16.425

Pressure end load on the opening per P.2.3: = pi * a^2 * P = 3.1415 * 3.313^2 * 3.587 = 123.683 lbf. [550.142 N.]

Radial force nomogram limit values per figure P-3A: = max[(1 - 0.75)(XA / (Rt)^0.5), 0.1] = max[(1 - 0.75)(300.951/(246.063 *0.669 )^0.5), 0.1] = 0.100

Longitudinal nomogram limit values per figure P-3A: = max[(1 - 0.75)(XB / (Rt)^0.5), 0.1] = max[(1 - 0.75)(294.325/(246.063 *0.669 )^0.5), 0.1] = 0.100

Circumferential moment nomogram limit value per figure P-3B: = max[(1 - 0.75)(XC / (Rt)^0.5), 0.1] = max[(1 - 0.75)(297.638/(246.063 *0.669 )^0.5), 0.1] = 0.100

Radial force multiplier per figure P-3A: = lamda / (2 * YF * FP) = 0.258/(2 * 1.785 * 123.683 ) = 0.58458E-03 1/lbf. [0.13143E-03 1/N.]

Longitudinal moment multiplier per figure P-3A: = lamda / (a * 12.0 * YL * FP) = 0.258/(3.313 * 12.0 * 7.382 * 123.683 ) = 0.10241E-02 1/ft.lb. [0.75540E-03 1/N.m.]

Circumferential moment multiplier per figure P-3B: = lamda / (a * 12.0 * YC * FP) = 0.258/(3.313 * 12.0 * 16.425 * 123.683 ) = 0.46030E-03 1/ft.lb. [0.33952E-03 1/N.m.]

Radial force limit [ML = 0 and MC = 0] per figure P-3A [FRmax]: = Radial force nomogram limit value / Radial force multp. = 0.100/0.585E-03 = 0.17106E+03 lbf. [0.76089E+03 N.]

Positive Long. moment limit [MC = 0 and FR = 0] per figure P-3A [MLmax]: = Long. moment nomogram limit value / Long. moment multiplier = 0.100/0.102E-02 = 0.97643E+02 ft.lb. [0.13238E+03 N.m.]

Negative Long. moment limit [ML = 0 and MC = 0] per figure P-3A [MLmin]: = - Radial Force nomogram limit value / Long. moment multiplier = -0.100/0.102E-02 = -.97643E+02 ft.lb. [-0.13238E+03 N.m.]

Circ. moment limit [ML = 0 and FR = 0] per figure P-3B [MCmax]: = Circ. moment nomogram limit value / Circ. moment multiplier = 0.100/0.460E-03 = 0.21725E+03 ft.lb. [0.29454E+03 N.m.]

Test Case [Nozzle 2 ] per Appendix P:

Nozzle stiffness coefficients per P.2.4:

Outside radius of nozzle [a]: = D / 2 = 6.6/2 = 3.3 in. [168.3 mm.]

Nominal tank radius [R]: = Nominal tank diameter / 2 = 492.1/2 = 246.1 in. [12500.0 mm.]

L / 2a coefficient: = L / 2 * a = 297.638/2 * 3.313 = 44.9

As L/2a >= 1.5, use second set of curves.

a / R coefficient: = a / R = 3.3/246.063 = 0.013

R / t coefficient: = R / t = 246.063/0.669 = 367.6

From figure P-2D [KR/E(2a)]: = 0.824E-03

From figure P-2E [KL/E(2a)^3]: = 0.146E-02

From figure P-2F [KC/E(2a)^3]: = 0.999E-03

Stiffness coefficient for the radial thrust load per P.2.9.2.1 [KR]: = Coeff. from graph * E * 2 * a = 0.824E-03 * 28756854 * 2 * 3.313 = 0.15707E+06 lbf./in. [0.27506E+06 N./cm.]

Stiffness coefficient for the longitudinal moment per P.2.9.2.1 [KL]: = Coeff. from graph * E * ( 2.0 * a )^3 = 0.146E-02 * 28756854 * ( 2.0 * 3.313 )^3 = 0.21371E+06 in.lbf./deg [0.24146E+05 N.m./deg]

Stiffness coefficient for the circumferential moment per P.2.9.2.1 [KC]: = Coeff. from graph * E * ( 2 * a )^3 = 0.999E-03 * 28756854 * ( 2 * 3.313 )^3 = 0.14584E+06 in.lbf./deg [0.16477E+05 N.m./deg]

Characteristic parameter per P.2.3 [beta]: = 1.285 / (Rt)^0.5 = 1.285/(246.063 * 0.669 )^0.5 = 0.10013E+00 1/in. [0.39422E-02 1/mm.]

Unrestrained radial growth of the shell per P.2.5.1 [W]: = (0.036*G*H*R^2)/Et * [1-(e^-(beta*L)) * cos(beta*L) - (L/H)] + alpha * R * delta[T] = (0.036*1.006 *396.375 *246.063^2)/28756854 *0.669 * [1-(e^-(0.100 *297.638 )) * cos(0.100 *297.638 ) - (297.638/396.37 )] + 0.663E-05 * 246.063 * 0.000 = 0.01125 in. [0.28573 mm.]

Unrestrained shell rotation of the shell per P.2.5.2 [theta]: = (0.036*G*H*R^2)/E*t * [(1/H)-(beta*e^-(beta*L)) * [cos(beta*L)+sin(beta*L)]] = (0.036*1.006 *396.375 *246.063^2)/28756854 *0.669 * [(1/396.375 )-(0.100 *e^-(0.100 *297.638 )) * [cos(0.100 *297.638 )+sin(0.100 *297.638 )]] = 0.65277E-02 deg

Value of lamda per P.2.3 [lamda]: = a/(Rt)^0.5 = 3.313/(246.063 * 0.669 )^0.5 = 0.258

Coefficient XA per P.2.3: = L + a = 297.638 + 3.313 = 300.951 in. [7644.149 mm.]

Coefficient XB per P.2.3: = L - a = 297.638 - 3.313 = 294.325 in. [7475.850 mm.]

Coefficient XC per P.2.3: = L = 297.638 in. [7560.000 mm.]

Coefficients YF and YL from figure P-4A based on lamda: YF = 1.785 YL = 7.382

Coefficient YC from figure P-4B based on lamda: YC = 16.425

Pressure end load on the opening per P.2.3: = pi * a^2 * P = 3.1415 * 3.313^2 * 3.587 = 123.683 lbf. [550.142 N.]

Radial force nomogram limit values per figure P-3A: = max[(1 - 0.75)(XA / (Rt)^0.5), 0.1] = max[(1 - 0.75)(300.951/(246.063 *0.669 )^0.5), 0.1] = 0.100

Longitudinal nomogram limit values per figure P-3A: = max[(1 - 0.75)(XB / (Rt)^0.5), 0.1] = max[(1 - 0.75)(294.325/(246.063 *0.669 )^0.5), 0.1] = 0.100

Circumferential moment nomogram limit value per figure P-3B: = max[(1 - 0.75)(XC / (Rt)^0.5), 0.1] = max[(1 - 0.75)(297.638/(246.063 *0.669 )^0.5), 0.1] = 0.100

Radial force multiplier per figure P-3A: = lamda / (2 * YF * FP) = 0.258/(2 * 1.785 * 123.683 ) = 0.58458E-03 1/lbf. [0.13143E-03 1/N.]

Longitudinal moment multiplier per figure P-3A: = lamda / (a * 12.0 * YL * FP) = 0.258/(3.313 * 12.0 * 7.382 * 123.683 ) = 0.10241E-02 1/ft.lb. [0.75540E-03 1/N.m.]

Circumferential moment multiplier per figure P-3B: = lamda / (a * 12.0 * YC * FP) = 0.258/(3.313 * 12.0 * 16.425 * 123.683 ) = 0.46030E-03 1/ft.lb. [0.33952E-03 1/N.m.]

Radial force limit [ML = 0 and MC = 0] per figure P-3A [FRmax]: = Radial force nomogram limit value / Radial force multp. = 0.100/0.585E-03 = 0.17106E+03 lbf. [0.76089E+03 N.]

Positive Long. moment limit [MC = 0 and FR = 0] per figure P-3A [MLmax]: = Long. moment nomogram limit value / Long. moment multiplier = 0.100/0.102E-02 = 0.97643E+02 ft.lb. [0.13238E+03 N.m.]

Negative Long. moment limit [ML = 0 and MC = 0] per figure P-3A [MLmin]: = - Radial Force nomogram limit value / Long. moment multiplier = -0.100/0.102E-02 = -.97643E+02 ft.lb. [-0.13238E+03 N.m.]

Circ. moment limit [ML = 0 and FR = 0] per figure P-3B [MCmax]: = Circ. moment nomogram limit value / Circ. moment multiplier = 0.100/0.460E-03 = 0.21725E+03 ft.lb. [0.29454E+03 N.m.]

User Case [Nozzle 2 ] per Appendix P:

Nozzle stiffness coefficients per P.2.4:

Outside radius of nozzle [a]: = D / 2 = 6.6/2 = 3.3 in. [168.3 mm.]

Nominal tank radius [R]: = Nominal tank diameter / 2 = 492.1/2 = 246.1 in. [12500.0 mm.]

L / 2a coefficient: = L / 2 * a = 297.638/2 * 3.313 = 44.9

As L/2a >= 1.5, use second set of curves.

a / R coefficient: = a / R = 3.3/246.063 = 0.013

R / t coefficient: = R / t = 246.063/0.669 = 367.6

From figure P-2D [KR/E(2a)]: = 0.824E-03

From figure P-2E [KL/E(2a)^3]: = 0.146E-02

From figure P-2F [KC/E(2a)^3]: = 0.999E-03

Stiffness coefficient for the radial thrust load per P.2.9.2.1 [KR]: = Coeff. from graph * E * 2 * a = 0.824E-03 * 28756854 * 2 * 3.313 = 0.15707E+06 lbf./in. [0.27506E+06 N./cm.]

Stiffness coefficient for the longitudinal moment per P.2.9.2.1 [KL]: = Coeff. from graph * E * ( 2.0 * a )^3 = 0.146E-02 * 28756854 * ( 2.0 * 3.313 )^3 = 0.21371E+06 in.lbf./deg [0.24146E+05 N.m./deg]

Stiffness coefficient for the circumferential moment per P.2.9.2.1 [KC]: = Coeff. from graph * E * ( 2 * a )^3 = 0.999E-03 * 28756854 * ( 2 * 3.313 )^3 = 0.14584E+06 in.lbf./deg [0.16477E+05 N.m./deg]

Characteristic parameter per P.2.3 [beta]: = 1.285 / (Rt)^0.5 = 1.285/(246.063 * 0.669 )^0.5 = 0.10013E+00 1/in. [0.39422E-02 1/mm.]

Unrestrained radial growth of the shell per P.2.5.1 [W]: = (0.036*G*H*R^2)/Et * [1-(e^-(beta*L)) * cos(beta*L) - (L/H)] + alpha * R * delta[T] = (0.036*1.006 *396.375 *246.063^2)/28756854 *0.669 * [1-(e^-(0.100 *297.638 )) * cos(0.100 *297.638 ) - (297.638/396.37 )] + 0.663E-05 * 246.063 * 0.000 = 0.01125 in. [0.28573 mm.]

Unrestrained shell rotation of the shell per P.2.5.2 [theta]: = (0.036*G*H*R^2)/E*t * [(1/H)-(beta*e^-(beta*L)) * [cos(beta*L)+sin(beta*L)]] = (0.036*1.006 *396.375 *246.063^2)/28756854 *0.669 * [(1/396.375 )-(0.100 *e^-(0.100 *297.638 )) * [cos(0.100 *297.638 )+sin(0.100 *297.638 )]] = 0.65277E-02 deg

Value of lamda per P.2.3 [lamda]: = a/(Rt)^0.5 = 3.313/(246.063 * 0.669 )^0.5 = 0.258

Coefficient XA per P.2.3: = L + a = 297.638 + 3.313 = 300.951 in. [7644.149 mm.]

Coefficient XB per P.2.3: = L - a = 297.638 - 3.313 = 294.325 in. [7475.850 mm.]

Coefficient XC per P.2.3: = L = 297.638 in. [7560.000 mm.]

Coefficients YF and YL from figure P-4A based on lamda: YF = 1.785 YL = 7.382

Coefficient YC from figure P-4B based on lamda: YC = 16.425

Pressure end load on the opening per P.2.3: = pi * a^2 * P = 3.1415 * 3.313^2 * 3.587 = 123.683 lbf. [550.142 N.]

Radial force nomogram limit values per figure P-3A: = max[(1 - 0.75)(XA / (Rt)^0.5), 0.1] = max[(1 - 0.75)(300.951/(246.063 *0.669 )^0.5), 0.1] = 0.100

Longitudinal nomogram limit values per figure P-3A: = max[(1 - 0.75)(XB / (Rt)^0.5), 0.1] = max[(1 - 0.75)(294.325/(246.063 *0.669 )^0.5), 0.1] = 0.100

Circumferential moment nomogram limit value per figure P-3B: = max[(1 - 0.75)(XC / (Rt)^0.5), 0.1] = max[(1 - 0.75)(297.638/(246.063 *0.669 )^0.5), 0.1] = 0.100

Radial force multiplier per figure P-3A: = lamda / (2 * YF * FP) = 0.258/(2 * 1.785 * 123.683 ) = 0.58458E-03 1/lbf. [0.13143E-03 1/N.]

Longitudinal moment multiplier per figure P-3A: = lamda / (a * 12.0 * YL * FP) = 0.258/(3.313 * 12.0 * 7.382 * 123.683 ) = 0.10241E-02 1/ft.lb. [0.75540E-03 1/N.m.]

Circumferential moment multiplier per figure P-3B: = lamda / (a * 12.0 * YC * FP) = 0.258/(3.313 * 12.0 * 16.425 * 123.683 ) = 0.46030E-03 1/ft.lb. [0.33952E-03 1/N.m.]

Radial force limit [ML = 0 and MC = 0] per figure P-3A [FRmax]: = Radial force nomogram limit value / Radial force multp. = 0.100/0.585E-03 = 0.17106E+03 lbf. [0.76089E+03 N.]

Positive Long. moment limit [MC = 0 and FR = 0] per figure P-3A [MLmax]: = Long. moment nomogram limit value / Long. moment multiplier = 0.100/0.102E-02 = 0.97643E+02 ft.lb. [0.13238E+03 N.m.]

Negative Long. moment limit [ML = 0 and MC = 0] per figure P-3A [MLmin]: = - Radial Force nomogram limit value / Long. moment multiplier = -0.100/0.102E-02 = -.97643E+02 ft.lb. [-0.13238E+03 N.m.]

Circ. moment limit [ML = 0 and FR = 0] per figure P-3B [MCmax]: = Circ. moment nomogram limit value / Circ. moment multiplier = 0.100/0.460E-03 = 0.21725E+03 ft.lb. [0.29454E+03 N.m.]

Design Case [Nozzle 3 ] per Appendix P:

Nozzle stiffness coefficients per P.2.4:

Outside radius of nozzle [a]: = D / 2 = 14.0/2 = 7.0 in. [355.6 mm.]

Nominal tank radius [R]: = Nominal tank diameter / 2 = 492.1/2 = 246.1 in. [12500.0 mm.]

L / 2a coefficient: = L / 2 * a = 23.622/2 * 7.000 = 1.7

As L/2a >= 1.5, use second set of curves.

a / R coefficient: = a / R = 7.0/246.063 = 0.028

R / t coefficient: = R / t = 246.063/0.709 = 347.2

From figure P-2D [KR/E(2a)]: = 0.328E-03

From figure P-2E [KL/E(2a)^3]: = 0.430E-03

From figure P-2F [KC/E(2a)^3]: = 0.150E-03

Stiffness coefficient for the radial thrust load per P.2.9.2.1 [KR]: = Coeff. from graph * E * 2 * a = 0.328E-03 * 28756854 * 2 * 7.000 = 0.13190E+06 lbf./in. [0.23098E+06 N./cm.]

Stiffness coefficient for the longitudinal moment per P.2.9.2.1 [KL]: = Coeff. from graph * E * ( 2.0 * a )^3 = 0.430E-03 * 28756854 * ( 2.0 * 7.000 )^3 = 0.59243E+06 in.lbf./deg [0.66933E+05 N.m./deg]

Stiffness coefficient for the circumferential moment per P.2.9.2.1 [KC]: = Coeff. from graph * E * ( 2 * a )^3 = 0.150E-03 * 28756854 * ( 2 * 7.000 )^3 = 0.20687E+06 in.lbf./deg [0.23372E+05 N.m./deg]

Characteristic parameter per P.2.3 [beta]: = 1.285 / (Rt)^0.5 = 1.285/(246.063 * 0.709 )^0.5 = 0.97311E-01 1/in. [0.38311E-02 1/mm.]

Unrestrained radial growth of the shell per P.2.5.1 [W]: = (0.036*G*H*R^2)/Et * [1-(e^-(beta*L)) * cos(beta*L) - (L/H)] + alpha * R * delta[T] = (0.036*1.006 *396.375 *246.063^2)/28756854 *0.709 * [1-(e^-(0.097 *23.622 )) * cos(0.097 *23.622 ) - (23.622/396.37 )] + 0.663E-05 * 246.063 * 0.000 = 0.04296 in. [1.09110 mm.]

Unrestrained shell rotation of the shell per P.2.5.2 [theta]: = (0.036*G*H*R^2)/E*t * [(1/H)-(beta*e^-(beta*L)) * [cos(beta*L)+sin(beta*L)]] = (0.036*1.006 *396.375 *246.063^2)/28756854 *0.709 * [(1/396.375 )-(0.097 *e^-(0.097 *23.622 )) * [cos(0.097 *23.622 )+sin(0.097 *23.622 )]] = 0.42243E-02 deg

Value of lamda per P.2.3 [lamda]: = a/(Rt)^0.5 = 7.000/(246.063 * 0.709 )^0.5 = 0.530

Coefficient XA per P.2.3: = L + a = 23.622 + 7.000 = 30.622 in. [777.800 mm.]

Coefficient XB per P.2.3: = L - a = 23.622 - 7.000 = 16.622 in. [422.200 mm.]

Coefficient XC per P.2.3: = L = 23.622 in. [600.000 mm.]

Coefficients YF and YL from figure P-4A based on lamda: YF = 1.077 YL = 3.334

Coefficient YC from figure P-4B based on lamda: YC = 3.568

Pressure end load on the opening per P.2.3: = pi * a^2 * P = 3.1415 * 7.000^2 * 13.541 = 2084.518 lbf. [9271.938 N.]

Radial force nomogram limit values per figure P-3A: = max[(1 - 0.75)(XA / (Rt)^0.5), 0.1] = max[(1 - 0.75)(30.622/(246.063 *0.709 )^0.5), 0.1] = 0.100

Longitudinal nomogram limit values per figure P-3A: = max[(1 - 0.75)(XB / (Rt)^0.5), 0.1] = max[(1 - 0.75)(16.622/(246.063 *0.709 )^0.5), 0.1] = 0.100

Circumferential moment nomogram limit value per figure P-3B: = max[(1 - 0.75)(XC / (Rt)^0.5), 0.1] = max[(1 - 0.75)(23.622/(246.063 *0.709 )^0.5), 0.1] = 0.100

Radial force multiplier per figure P-3A: = lamda / (2 * YF * FP) = 0.530/(2 * 1.077 * 2084.518 ) = 0.11805E-03 1/lbf. [0.26541E-04 1/N.]

Longitudinal moment multiplier per figure P-3A: = lamda / (a * 12.0 * YL * FP) = 0.530/(7.000 * 12.0 * 3.334 * 2084.518 ) = 0.13077E-03 1/ft.lb. [0.96455E-04 1/N.m.]

Circumferential moment multiplier per figure P-3B: = lamda / (a * 12.0 * YC * FP) = 0.530/(7.000 * 12.0 * 3.568 * 2084.518 ) = 0.12219E-03 1/ft.lb. [0.90126E-04 1/N.m.]

Radial force limit [ML = 0 and MC = 0] per figure P-3A [FRmax]: = Radial force nomogram limit value / Radial force multp. = 0.100/0.118E-03 = 0.84707E+03 lbf. [0.37678E+04 N.]

Positive Long. moment limit [MC = 0 and FR = 0] per figure P-3A [MLmax]: = Long. moment nomogram limit value / Long. moment multiplier = 0.100/0.131E-03 = 0.76470E+03 ft.lb. [0.10368E+04 N.m.]

Negative Long. moment limit [ML = 0 and MC = 0] per figure P-3A [MLmin]: = - Radial Force nomogram limit value / Long. moment multiplier = -0.100/0.131E-03 = -.76470E+03 ft.lb. [-0.10368E+04 N.m.]

Circ. moment limit [ML = 0 and FR = 0] per figure P-3B [MCmax]: = Circ. moment nomogram limit value / Circ. moment multiplier = 0.100/0.122E-03 = 0.81840E+03 ft.lb. [0.11096E+04 N.m.]

Test Case [Nozzle 3 ] per Appendix P:

Nozzle stiffness coefficients per P.2.4:

Outside radius of nozzle [a]: = D / 2 = 14.0/2 = 7.0 in. [355.6 mm.]

Nominal tank radius [R]: = Nominal tank diameter / 2 = 492.1/2 = 246.1 in. [12500.0 mm.]

L / 2a coefficient: = L / 2 * a = 23.622/2 * 7.000 = 1.7

As L/2a >= 1.5, use second set of curves.

a / R coefficient: = a / R = 7.0/246.063 = 0.028

R / t coefficient: = R / t = 246.063/0.709 = 347.2

From figure P-2D [KR/E(2a)]: = 0.328E-03

From figure P-2E [KL/E(2a)^3]: = 0.430E-03

From figure P-2F [KC/E(2a)^3]: = 0.150E-03

Stiffness coefficient for the radial thrust load per P.2.9.2.1 [KR]: = Coeff. from graph * E * 2 * a = 0.328E-03 * 28756854 * 2 * 7.000 = 0.13190E+06 lbf./in. [0.23098E+06 N./cm.]

Stiffness coefficient for the longitudinal moment per P.2.9.2.1 [KL]: = Coeff. from graph * E * ( 2.0 * a )^3 = 0.430E-03 * 28756854 * ( 2.0 * 7.000 )^3 = 0.59243E+06 in.lbf./deg [0.66933E+05 N.m./deg]

Stiffness coefficient for the circumferential moment per P.2.9.2.1 [KC]: = Coeff. from graph * E * ( 2 * a )^3 = 0.150E-03 * 28756854 * ( 2 * 7.000 )^3 = 0.20687E+06 in.lbf./deg [0.23372E+05 N.m./deg]

Characteristic parameter per P.2.3 [beta]: = 1.285 / (Rt)^0.5 = 1.285/(246.063 * 0.709 )^0.5 = 0.97311E-01 1/in. [0.38311E-02 1/mm.]

Unrestrained radial growth of the shell per P.2.5.1 [W]: = (0.036*G*H*R^2)/Et * [1-(e^-(beta*L)) * cos(beta*L) - (L/H)] + alpha * R * delta[T] = (0.036*1.006 *396.375 *246.063^2)/28756854 *0.709 * [1-(e^-(0.097 *23.622 )) * cos(0.097 *23.622 ) - (23.622/396.37 )] + 0.663E-05 * 246.063 * 0.000 = 0.04296 in. [1.09110 mm.]

Unrestrained shell rotation of the shell per P.2.5.2 [theta]: = (0.036*G*H*R^2)/E*t * [(1/H)-(beta*e^-(beta*L)) * [cos(beta*L)+sin(beta*L)]] = (0.036*1.006 *396.375 *246.063^2)/28756854 *0.709 * [(1/396.375 )-(0.097 *e^-(0.097 *23.622 )) * [cos(0.097 *23.622 )+sin(0.097 *23.622 )]] = 0.42243E-02 deg

Value of lamda per P.2.3 [lamda]: = a/(Rt)^0.5 = 7.000/(246.063 * 0.709 )^0.5 = 0.530

Coefficient XA per P.2.3: = L + a = 23.622 + 7.000 = 30.622 in. [777.800 mm.]

Coefficient XB per P.2.3: = L - a = 23.622 - 7.000 = 16.622 in. [422.200 mm.]

Coefficient XC per P.2.3: = L = 23.622 in. [600.000 mm.]

Coefficients YF and YL from figure P-4A based on lamda: YF = 1.077 YL = 3.334

Coefficient YC from figure P-4B based on lamda: YC = 3.568

Pressure end load on the opening per P.2.3: = pi * a^2 * P = 3.1415 * 7.000^2 * 13.541 = 2084.518 lbf. [9271.938 N.]

Radial force nomogram limit values per figure P-3A: = max[(1 - 0.75)(XA / (Rt)^0.5), 0.1] = max[(1 - 0.75)(30.622/(246.063 *0.709 )^0.5), 0.1] = 0.100

Longitudinal nomogram limit values per figure P-3A: = max[(1 - 0.75)(XB / (Rt)^0.5), 0.1] = max[(1 - 0.75)(16.622/(246.063 *0.709 )^0.5), 0.1] = 0.100

Circumferential moment nomogram limit value per figure P-3B: = max[(1 - 0.75)(XC / (Rt)^0.5), 0.1] = max[(1 - 0.75)(23.622/(246.063 *0.709 )^0.5), 0.1] = 0.100

Radial force multiplier per figure P-3A: = lamda / (2 * YF * FP) = 0.530/(2 * 1.077 * 2084.518 ) = 0.11805E-03 1/lbf. [0.26541E-04 1/N.]

Longitudinal moment multiplier per figure P-3A: = lamda / (a * 12.0 * YL * FP) = 0.530/(7.000 * 12.0 * 3.334 * 2084.518 ) = 0.13077E-03 1/ft.lb. [0.96455E-04 1/N.m.]

Circumferential moment multiplier per figure P-3B: = lamda / (a * 12.0 * YC * FP) = 0.530/(7.000 * 12.0 * 3.568 * 2084.518 ) = 0.12219E-03 1/ft.lb. [0.90126E-04 1/N.m.]

Radial force limit [ML = 0 and MC = 0] per figure P-3A [FRmax]: = Radial force nomogram limit value / Radial force multp. = 0.100/0.118E-03 = 0.84707E+03 lbf. [0.37678E+04 N.]

Positive Long. moment limit [MC = 0 and FR = 0] per figure P-3A [MLmax]: = Long. moment nomogram limit value / Long. moment multiplier = 0.100/0.131E-03 = 0.76470E+03 ft.lb. [0.10368E+04 N.m.]

Negative Long. moment limit [ML = 0 and MC = 0] per figure P-3A [MLmin]: = - Radial Force nomogram limit value / Long. moment multiplier = -0.100/0.131E-03 = -.76470E+03 ft.lb. [-0.10368E+04 N.m.]

Circ. moment limit [ML = 0 and FR = 0] per figure P-3B [MCmax]: = Circ. moment nomogram limit value / Circ. moment multiplier = 0.100/0.122E-03 = 0.81840E+03 ft.lb. [0.11096E+04 N.m.]

User Case [Nozzle 3 ] per Appendix P:

Nozzle stiffness coefficients per P.2.4:

Outside radius of nozzle [a]: = D / 2 = 14.0/2 = 7.0 in. [355.6 mm.]

Nominal tank radius [R]: = Nominal tank diameter / 2 = 492.1/2 = 246.1 in. [12500.0 mm.]

L / 2a coefficient: = L / 2 * a = 23.622/2 * 7.000 = 1.7

As L/2a >= 1.5, use second set of curves.

a / R coefficient: = a / R = 7.0/246.063 = 0.028

R / t coefficient: = R / t = 246.063/0.709 = 347.2

From figure P-2D [KR/E(2a)]: = 0.328E-03

From figure P-2E [KL/E(2a)^3]: = 0.430E-03

From figure P-2F [KC/E(2a)^3]: = 0.150E-03

Stiffness coefficient for the radial thrust load per P.2.9.2.1 [KR]: = Coeff. from graph * E * 2 * a = 0.328E-03 * 28756854 * 2 * 7.000 = 0.13190E+06 lbf./in. [0.23098E+06 N./cm.]

Stiffness coefficient for the longitudinal moment per P.2.9.2.1 [KL]: = Coeff. from graph * E * ( 2.0 * a )^3 = 0.430E-03 * 28756854 * ( 2.0 * 7.000 )^3 = 0.59243E+06 in.lbf./deg [0.66933E+05 N.m./deg]

Stiffness coefficient for the circumferential moment per P.2.9.2.1 [KC]: = Coeff. from graph * E * ( 2 * a )^3 = 0.150E-03 * 28756854 * ( 2 * 7.000 )^3 = 0.20687E+06 in.lbf./deg [0.23372E+05 N.m./deg]

Characteristic parameter per P.2.3 [beta]: = 1.285 / (Rt)^0.5 = 1.285/(246.063 * 0.709 )^0.5 = 0.97311E-01 1/in. [0.38311E-02 1/mm.]

Unrestrained radial growth of the shell per P.2.5.1 [W]: = (0.036*G*H*R^2)/Et * [1-(e^-(beta*L)) * cos(beta*L) - (L/H)] + alpha * R * delta[T] = (0.036*1.006 *396.375 *246.063^2)/28756854 *0.709 * [1-(e^-(0.097 *23.622 )) * cos(0.097 *23.622 ) - (23.622/396.37 )] + 0.663E-05 * 246.063 * 0.000 = 0.04296 in. [1.09110 mm.]

Unrestrained shell rotation of the shell per P.2.5.2 [theta]: = (0.036*G*H*R^2)/E*t * [(1/H)-(beta*e^-(beta*L)) * [cos(beta*L)+sin(beta*L)]] = (0.036*1.006 *396.375 *246.063^2)/28756854 *0.709 * [(1/396.375 )-(0.097 *e^-(0.097 *23.622 )) * [cos(0.097 *23.622 )+sin(0.097 *23.622 )]] = 0.42243E-02 deg

Value of lamda per P.2.3 [lamda]: = a/(Rt)^0.5 = 7.000/(246.063 * 0.709 )^0.5 = 0.530

Coefficient XA per P.2.3: = L + a = 23.622 + 7.000 = 30.622 in. [777.800 mm.]

Coefficient XB per P.2.3: = L - a = 23.622 - 7.000 = 16.622 in. [422.200 mm.]

Coefficient XC per P.2.3: = L = 23.622 in. [600.000 mm.]

Coefficients YF and YL from figure P-4A based on lamda: YF = 1.077 YL = 3.334

Coefficient YC from figure P-4B based on lamda: YC = 3.568

Pressure end load on the opening per P.2.3: = pi * a^2 * P = 3.1415 * 7.000^2 * 13.541 = 2084.518 lbf. [9271.938 N.]

Radial force nomogram limit values per figure P-3A: = max[(1 - 0.75)(XA / (Rt)^0.5), 0.1] = max[(1 - 0.75)(30.622/(246.063 *0.709 )^0.5), 0.1] = 0.100

Longitudinal nomogram limit values per figure P-3A: = max[(1 - 0.75)(XB / (Rt)^0.5), 0.1] = max[(1 - 0.75)(16.622/(246.063 *0.709 )^0.5), 0.1] = 0.100

Circumferential moment nomogram limit value per figure P-3B: = max[(1 - 0.75)(XC / (Rt)^0.5), 0.1] = max[(1 - 0.75)(23.622/(246.063 *0.709 )^0.5), 0.1] = 0.100

Radial force multiplier per figure P-3A: = lamda / (2 * YF * FP) = 0.530/(2 * 1.077 * 2084.518 ) = 0.11805E-03 1/lbf. [0.26541E-04 1/N.]

Longitudinal moment multiplier per figure P-3A: = lamda / (a * 12.0 * YL * FP) = 0.530/(7.000 * 12.0 * 3.334 * 2084.518 ) = 0.13077E-03 1/ft.lb. [0.96455E-04 1/N.m.]

Circumferential moment multiplier per figure P-3B: = lamda / (a * 12.0 * YC * FP) = 0.530/(7.000 * 12.0 * 3.568 * 2084.518 ) = 0.12219E-03 1/ft.lb. [0.90126E-04 1/N.m.]

Radial force limit [ML = 0 and MC = 0] per figure P-3A [FRmax]: = Radial force nomogram limit value / Radial force multp. = 0.100/0.118E-03 = 0.84707E+03 lbf. [0.37678E+04 N.]

Positive Long. moment limit [MC = 0 and FR = 0] per figure P-3A [MLmax]: = Long. moment nomogram limit value / Long. moment multiplier = 0.100/0.131E-03 = 0.76470E+03 ft.lb. [0.10368E+04 N.m.]

Negative Long. moment limit [ML = 0 and MC = 0] per figure P-3A [MLmin]: = - Radial Force nomogram limit value / Long. moment multiplier = -0.100/0.131E-03 = -.76470E+03 ft.lb. [-0.10368E+04 N.m.]

Circ. moment limit [ML = 0 and FR = 0] per figure P-3B [MCmax]: = Circ. moment nomogram limit value / Circ. moment multiplier = 0.100/0.122E-03 = 0.81840E+03 ft.lb. [0.11096E+04 N.m.]

Design Case [Nozzle 4 ] per Appendix P:

Nozzle stiffness coefficients per P.2.4:

Outside radius of nozzle [a]: = D / 2 = 6.6/2 = 3.3 in. [168.3 mm.]

Nominal tank radius [R]: = Nominal tank diameter / 2 = 492.1/2 = 246.1 in. [12500.0 mm.]

L / 2a coefficient: = L / 2 * a = 196.850/2 * 3.313 = 29.7

As L/2a >= 1.5, use second set of curves.

a / R coefficient: = a / R = 3.3/246.063 = 0.013

R / t coefficient: = R / t = 246.063/0.669 = 367.6

From figure P-2D [KR/E(2a)]: = 0.824E-03

From figure P-2E [KL/E(2a)^3]: = 0.146E-02

From figure P-2F [KC/E(2a)^3]: = 0.999E-03

Stiffness coefficient for the radial thrust load per P.2.9.2.1 [KR]: = Coeff. from graph * E * 2 * a = 0.824E-03 * 28756854 * 2 * 3.313 = 0.15707E+06 lbf./in. [0.27506E+06 N./cm.]

Stiffness coefficient for the longitudinal moment per P.2.9.2.1 [KL]: = Coeff. from graph * E * ( 2.0 * a )^3 = 0.146E-02 * 28756854 * ( 2.0 * 3.313 )^3 = 0.21371E+06 in.lbf./deg [0.24146E+05 N.m./deg]

Stiffness coefficient for the circumferential moment per P.2.9.2.1 [KC]: = Coeff. from graph * E * ( 2 * a )^3 = 0.999E-03 * 28756854 * ( 2 * 3.313 )^3 = 0.14584E+06 in.lbf./deg [0.16477E+05 N.m./deg]

Characteristic parameter per P.2.3 [beta]: = 1.285 / (Rt)^0.5 = 1.285/(246.063 * 0.669 )^0.5 = 0.10013E+00 1/in. [0.39422E-02 1/mm.]

Unrestrained radial growth of the shell per P.2.5.1 [W]: = (0.036*G*H*R^2)/Et * [1-(e^-(beta*L)) * cos(beta*L) - (L/H)] + alpha * R * delta[T] = (0.036*1.006 *396.375 *246.063^2)/28756854 *0.669 * [1-(e^-(0.100 *196.850 )) * cos(0.100 *196.850 ) - (196.850/396.37 )] + 0.663E-05 * 246.063 * 0.000 = 0.02273 in. [0.57739 mm.]

Unrestrained shell rotation of the shell per P.2.5.2 [theta]: = (0.036*G*H*R^2)/E*t * [(1/H)-(beta*e^-(beta*L)) * [cos(beta*L)+sin(beta*L)]] = (0.036*1.006 *396.375 *246.063^2)/28756854 *0.669 * [(1/396.375 )-(0.100 *e^-(0.100 *196.850 )) * [cos(0.100 *196.850 )+sin(0.100 *196.850 )]] = 0.65277E-02 deg

Value of lamda per P.2.3 [lamda]: = a/(Rt)^0.5 = 3.313/(246.063 * 0.669 )^0.5 = 0.258

Coefficient XA per P.2.3: = L + a = 196.850 + 3.313 = 200.163 in. [5084.150 mm.]

Coefficient XB per P.2.3: = L - a = 196.850 - 3.313 = 193.537 in. [4915.850 mm.]

Coefficient XC per P.2.3: = L = 196.850 in. [5000.000 mm.]

Coefficients YF and YL from figure P-4A based on lamda: YF = 1.785 YL = 7.382

Coefficient YC from figure P-4B based on lamda: YC = 16.425

Pressure end load on the opening per P.2.3: = pi * a^2 * P = 3.1415 * 3.313^2 * 7.248 = 249.934 lbf. [1111.707 N.]

Radial force nomogram limit values per figure P-3A: = max[(1 - 0.75)(XA / (Rt)^0.5), 0.1] = max[(1 - 0.75)(200.163/(246.063 *0.669 )^0.5), 0.1] = 0.100

Longitudinal nomogram limit values per figure P-3A: = max[(1 - 0.75)(XB / (Rt)^0.5), 0.1] = max[(1 - 0.75)(193.537/(246.063 *0.669 )^0.5), 0.1] = 0.100

Circumferential moment nomogram limit value per figure P-3B: = max[(1 - 0.75)(XC / (Rt)^0.5), 0.1] = max[(1 - 0.75)(196.850/(246.063 *0.669 )^0.5), 0.1] = 0.100

Radial force multiplier per figure P-3A: = lamda / (2 * YF * FP) = 0.258/(2 * 1.785 * 249.934 ) = 0.28929E-03 1/lbf. [0.65037E-04 1/N.]

Longitudinal moment multiplier per figure P-3A: = lamda / (a * 12.0 * YL * FP) = 0.258/(3.313 * 12.0 * 7.382 * 249.934 ) = 0.50681E-03 1/ft.lb. [0.37382E-03 1/N.m.]

Circumferential moment multiplier per figure P-3B: = lamda / (a * 12.0 * YC * FP) = 0.258/(3.313 * 12.0 * 16.425 * 249.934 ) = 0.22779E-03 1/ft.lb. [0.16801E-03 1/N.m.]

Radial force limit [ML = 0 and MC = 0] per figure P-3A [FRmax]: = Radial force nomogram limit value / Radial force multp. = 0.100/0.289E-03 = 0.34568E+03 lbf. [0.15376E+04 N.]

Positive Long. moment limit [MC = 0 and FR = 0] per figure P-3A [MLmax]: = Long. moment nomogram limit value / Long. moment multiplier = 0.100/0.507E-03 = 0.19731E+03 ft.lb. [0.26751E+03 N.m.]

Negative Long. moment limit [ML = 0 and MC = 0] per figure P-3A [MLmin]: = - Radial Force nomogram limit value / Long. moment multiplier = -0.100/0.507E-03 = -.19731E+03 ft.lb. [-0.26751E+03 N.m.]

Circ. moment limit [ML = 0 and FR = 0] per figure P-3B [MCmax]: = Circ. moment nomogram limit value / Circ. moment multiplier = 0.100/0.228E-03 = 0.43901E+03 ft.lb. [0.59519E+03 N.m.]

Test Case [Nozzle 4 ] per Appendix P:

Nozzle stiffness coefficients per P.2.4:

Outside radius of nozzle [a]: = D / 2 = 6.6/2 = 3.3 in. [168.3 mm.]

Nominal tank radius [R]: = Nominal tank diameter / 2 = 492.1/2 = 246.1 in. [12500.0 mm.]

L / 2a coefficient: = L / 2 * a = 196.850/2 * 3.313 = 29.7

As L/2a >= 1.5, use second set of curves.

a / R coefficient: = a / R = 3.3/246.063 = 0.013

R / t coefficient: = R / t = 246.063/0.669 = 367.6

From figure P-2D [KR/E(2a)]: = 0.824E-03

From figure P-2E [KL/E(2a)^3]: = 0.146E-02

From figure P-2F [KC/E(2a)^3]: = 0.999E-03

Stiffness coefficient for the radial thrust load per P.2.9.2.1 [KR]: = Coeff. from graph * E * 2 * a = 0.824E-03 * 28756854 * 2 * 3.313 = 0.15707E+06 lbf./in. [0.27506E+06 N./cm.]

Stiffness coefficient for the longitudinal moment per P.2.9.2.1 [KL]: = Coeff. from graph * E * ( 2.0 * a )^3 = 0.146E-02 * 28756854 * ( 2.0 * 3.313 )^3 = 0.21371E+06 in.lbf./deg [0.24146E+05 N.m./deg]

Stiffness coefficient for the circumferential moment per P.2.9.2.1 [KC]: = Coeff. from graph * E * ( 2 * a )^3 = 0.999E-03 * 28756854 * ( 2 * 3.313 )^3 = 0.14584E+06 in.lbf./deg [0.16477E+05 N.m./deg]

Characteristic parameter per P.2.3 [beta]: = 1.285 / (Rt)^0.5 = 1.285/(246.063 * 0.669 )^0.5 = 0.10013E+00 1/in. [0.39422E-02 1/mm.]

Unrestrained radial growth of the shell per P.2.5.1 [W]: = (0.036*G*H*R^2)/Et * [1-(e^-(beta*L)) * cos(beta*L) - (L/H)] + alpha * R * delta[T] = (0.036*1.006 *396.375 *246.063^2)/28756854 *0.669 * [1-(e^-(0.100 *196.850 )) * cos(0.100 *196.850 ) - (196.850/396.37 )] + 0.663E-05 * 246.063 * 0.000 = 0.02273 in. [0.57739 mm.]

Unrestrained shell rotation of the shell per P.2.5.2 [theta]: = (0.036*G*H*R^2)/E*t * [(1/H)-(beta*e^-(beta*L)) * [cos(beta*L)+sin(beta*L)]] = (0.036*1.006 *396.375 *246.063^2)/28756854 *0.669 * [(1/396.375 )-(0.100 *e^-(0.100 *196.850 )) * [cos(0.100 *196.850 )+sin(0.100 *196.850 )]] = 0.65277E-02 deg

Value of lamda per P.2.3 [lamda]: = a/(Rt)^0.5 = 3.313/(246.063 * 0.669 )^0.5 = 0.258

Coefficient XA per P.2.3: = L + a = 196.850 + 3.313 = 200.163 in. [5084.150 mm.]

Coefficient XB per P.2.3: = L - a = 196.850 - 3.313 = 193.537 in. [4915.850 mm.]

Coefficient XC per P.2.3: = L = 196.850 in. [5000.000 mm.]

Coefficients YF and YL from figure P-4A based on lamda: YF = 1.785 YL = 7.382

Coefficient YC from figure P-4B based on lamda: YC = 16.425

Pressure end load on the opening per P.2.3: = pi * a^2 * P = 3.1415 * 3.313^2 * 7.248 = 249.934 lbf. [1111.707 N.]

Radial force nomogram limit values per figure P-3A: = max[(1 - 0.75)(XA / (Rt)^0.5), 0.1] = max[(1 - 0.75)(200.163/(246.063 *0.669 )^0.5), 0.1] = 0.100

Longitudinal nomogram limit values per figure P-3A: = max[(1 - 0.75)(XB / (Rt)^0.5), 0.1] = max[(1 - 0.75)(193.537/(246.063 *0.669 )^0.5), 0.1] = 0.100

Circumferential moment nomogram limit value per figure P-3B: = max[(1 - 0.75)(XC / (Rt)^0.5), 0.1] = max[(1 - 0.75)(196.850/(246.063 *0.669 )^0.5), 0.1] = 0.100

Radial force multiplier per figure P-3A: = lamda / (2 * YF * FP) = 0.258/(2 * 1.785 * 249.934 ) = 0.28929E-03 1/lbf. [0.65037E-04 1/N.]

Longitudinal moment multiplier per figure P-3A: = lamda / (a * 12.0 * YL * FP) = 0.258/(3.313 * 12.0 * 7.382 * 249.934 ) = 0.50681E-03 1/ft.lb. [0.37382E-03 1/N.m.]

Circumferential moment multiplier per figure P-3B: = lamda / (a * 12.0 * YC * FP) = 0.258/(3.313 * 12.0 * 16.425 * 249.934 ) = 0.22779E-03 1/ft.lb. [0.16801E-03 1/N.m.]

Radial force limit [ML = 0 and MC = 0] per figure P-3A [FRmax]: = Radial force nomogram limit value / Radial force multp. = 0.100/0.289E-03 = 0.34568E+03 lbf. [0.15376E+04 N.]

Positive Long. moment limit [MC = 0 and FR = 0] per figure P-3A [MLmax]: = Long. moment nomogram limit value / Long. moment multiplier = 0.100/0.507E-03 = 0.19731E+03 ft.lb. [0.26751E+03 N.m.]

Negative Long. moment limit [ML = 0 and MC = 0] per figure P-3A [MLmin]: = - Radial Force nomogram limit value / Long. moment multiplier = -0.100/0.507E-03 = -.19731E+03 ft.lb. [-0.26751E+03 N.m.]

Circ. moment limit [ML = 0 and FR = 0] per figure P-3B [MCmax]: = Circ. moment nomogram limit value / Circ. moment multiplier = 0.100/0.228E-03 = 0.43901E+03 ft.lb. [0.59519E+03 N.m.]

User Case [Nozzle 4 ] per Appendix P:

Nozzle stiffness coefficients per P.2.4:

Outside radius of nozzle [a]: = D / 2 = 6.6/2 = 3.3 in. [168.3 mm.]

Nominal tank radius [R]: = Nominal tank diameter / 2 = 492.1/2 = 246.1 in. [12500.0 mm.]

L / 2a coefficient: = L / 2 * a = 196.850/2 * 3.313 = 29.7

As L/2a >= 1.5, use second set of curves.

a / R coefficient: = a / R = 3.3/246.063 = 0.013

R / t coefficient: = R / t = 246.063/0.669 = 367.6

From figure P-2D [KR/E(2a)]: = 0.824E-03

From figure P-2E [KL/E(2a)^3]: = 0.146E-02

From figure P-2F [KC/E(2a)^3]: = 0.999E-03

Stiffness coefficient for the radial thrust load per P.2.9.2.1 [KR]: = Coeff. from graph * E * 2 * a = 0.824E-03 * 28756854 * 2 * 3.313 = 0.15707E+06 lbf./in. [0.27506E+06 N./cm.]

Stiffness coefficient for the longitudinal moment per P.2.9.2.1 [KL]: = Coeff. from graph * E * ( 2.0 * a )^3 = 0.146E-02 * 28756854 * ( 2.0 * 3.313 )^3 = 0.21371E+06 in.lbf./deg [0.24146E+05 N.m./deg]

Stiffness coefficient for the circumferential moment per P.2.9.2.1 [KC]: = Coeff. from graph * E * ( 2 * a )^3 = 0.999E-03 * 28756854 * ( 2 * 3.313 )^3 = 0.14584E+06 in.lbf./deg [0.16477E+05 N.m./deg]

Characteristic parameter per P.2.3 [beta]: = 1.285 / (Rt)^0.5 = 1.285/(246.063 * 0.669 )^0.5 = 0.10013E+00 1/in. [0.39422E-02 1/mm.]

Unrestrained radial growth of the shell per P.2.5.1 [W]: = (0.036*G*H*R^2)/Et * [1-(e^-(beta*L)) * cos(beta*L) - (L/H)] + alpha * R * delta[T] = (0.036*1.006 *396.375 *246.063^2)/28756854 *0.669 * [1-(e^-(0.100 *196.850 )) * cos(0.100 *196.850 ) - (196.850/396.37 )] + 0.663E-05 * 246.063 * 0.000 = 0.02273 in. [0.57739 mm.]

Unrestrained shell rotation of the shell per P.2.5.2 [theta]: = (0.036*G*H*R^2)/E*t * [(1/H)-(beta*e^-(beta*L)) * [cos(beta*L)+sin(beta*L)]] = (0.036*1.006 *396.375 *246.063^2)/28756854 *0.669 * [(1/396.375 )-(0.100 *e^-(0.100 *196.850 )) * [cos(0.100 *196.850 )+sin(0.100 *196.850 )]] = 0.65277E-02 deg

Value of lamda per P.2.3 [lamda]: = a/(Rt)^0.5 = 3.313/(246.063 * 0.669 )^0.5 = 0.258

Coefficient XA per P.2.3: = L + a = 196.850 + 3.313 = 200.163 in. [5084.150 mm.]

Coefficient XB per P.2.3: = L - a = 196.850 - 3.313 = 193.537 in. [4915.850 mm.]

Coefficient XC per P.2.3: = L = 196.850 in. [5000.000 mm.]

Coefficients YF and YL from figure P-4A based on lamda: YF = 1.785 YL = 7.382

Coefficient YC from figure P-4B based on lamda: YC = 16.425

Pressure end load on the opening per P.2.3: = pi * a^2 * P = 3.1415 * 3.313^2 * 7.248 = 249.934 lbf. [1111.707 N.]

Radial force nomogram limit values per figure P-3A: = max[(1 - 0.75)(XA / (Rt)^0.5), 0.1] = max[(1 - 0.75)(200.163/(246.063 *0.669 )^0.5), 0.1] = 0.100

Longitudinal nomogram limit values per figure P-3A: = max[(1 - 0.75)(XB / (Rt)^0.5), 0.1] = max[(1 - 0.75)(193.537/(246.063 *0.669 )^0.5), 0.1] = 0.100

Circumferential moment nomogram limit value per figure P-3B: = max[(1 - 0.75)(XC / (Rt)^0.5), 0.1] = max[(1 - 0.75)(196.850/(246.063 *0.669 )^0.5), 0.1] = 0.100

Radial force multiplier per figure P-3A: = lamda / (2 * YF * FP) = 0.258/(2 * 1.785 * 249.934 ) = 0.28929E-03 1/lbf. [0.65037E-04 1/N.]

Longitudinal moment multiplier per figure P-3A: = lamda / (a * 12.0 * YL * FP) = 0.258/(3.313 * 12.0 * 7.382 * 249.934 ) = 0.50681E-03 1/ft.lb. [0.37382E-03 1/N.m.]

Circumferential moment multiplier per figure P-3B: = lamda / (a * 12.0 * YC * FP) = 0.258/(3.313 * 12.0 * 16.425 * 249.934 ) = 0.22779E-03 1/ft.lb. [0.16801E-03 1/N.m.]

Radial force limit [ML = 0 and MC = 0] per figure P-3A [FRmax]: = Radial force nomogram limit value / Radial force multp. = 0.100/0.289E-03 = 0.34568E+03 lbf. [0.15376E+04 N.]

Positive Long. moment limit [MC = 0 and FR = 0] per figure P-3A [MLmax]: = Long. moment nomogram limit value / Long. moment multiplier = 0.100/0.507E-03 = 0.19731E+03 ft.lb. [0.26751E+03 N.m.]

Negative Long. moment limit [ML = 0 and MC = 0] per figure P-3A [MLmin]: = - Radial Force nomogram limit value / Long. moment multiplier = -0.100/0.507E-03 = -.19731E+03 ft.lb. [-0.26751E+03 N.m.]

Circ. moment limit [ML = 0 and FR = 0] per figure P-3B [MCmax]: = Circ. moment nomogram limit value / Circ. moment multiplier = 0.100/0.228E-03 = 0.43901E+03 ft.lb. [0.59519E+03 N.m.]

Design Case [Nozzle 5 ] per Appendix P:

Nozzle stiffness coefficients per P.2.4:

Outside radius of nozzle [a]: = D / 2 = 3.5/2 = 1.8 in. [88.9 mm.]

Nominal tank radius [R]: = Nominal tank diameter / 2 = 492.1/2 = 246.1 in. [12500.0 mm.]

L / 2a coefficient: = L / 2 * a = 6.299/2 * 1.750 = 1.8

As L/2a >= 1.5, use second set of curves.

a / R coefficient: = a / R = 1.8/246.063 = 0.007

R / t coefficient: = R / t = 246.063/0.709 = 347.2

From figure P-2D [KR/E(2a)]: = 0.266E-02

From figure P-2E [KL/E(2a)^3]: = 0.612E-02

From figure P-2F [KC/E(2a)^3]: = 0.107E-01

Stiffness coefficient for the radial thrust load per P.2.9.2.1 [KR]: = Coeff. from graph * E * 2 * a = 0.266E-02 * 28756854 * 2 * 1.750 = 0.26768E+06 lbf./in. [0.46875E+06 N./cm.]

Stiffness coefficient for the longitudinal moment per P.2.9.2.1 [KL]: = Coeff. from graph * E * ( 2.0 * a )^3 = 0.612E-02 * 28756854 * ( 2.0 * 1.750 )^3 = 0.13170E+06 in.lbf./deg [0.14880E+05 N.m./deg]

Stiffness coefficient for the circumferential moment per P.2.9.2.1 [KC]: = Coeff. from graph * E * ( 2 * a )^3 = 0.107E-01 * 28756854 * ( 2 * 1.750 )^3 = 0.23046E+06 in.lbf./deg [0.26037E+05 N.m./deg]

Characteristic parameter per P.2.3 [beta]: = 1.285 / (Rt)^0.5 = 1.285/(246.063 * 0.709 )^0.5 = 0.97311E-01 1/in. [0.38311E-02 1/mm.]

Unrestrained radial growth of the shell per P.2.5.1 [W]: = (0.036*G*H*R^2)/Et * [1-(e^-(beta*L)) * cos(beta*L) - (L/H)] + alpha * R * delta[T] = (0.036*1.006 *396.375 *246.063^2)/28756854 *0.709 * [1-(e^-(0.097 *6.299 )) * cos(0.097 *6.299 ) - (6.299/396.37 )] + 0.663E-05 * 246.063 * 0.000 = 0.02307 in. [0.58607 mm.]

Unrestrained shell rotation of the shell per P.2.5.2 [theta]: = (0.036*G*H*R^2)/E*t * [(1/H)-(beta*e^-(beta*L)) * [cos(beta*L)+sin(beta*L)]] = (0.036*1.006 *396.375 *246.063^2)/28756854 *0.709 * [(1/396.375 )-(0.097 *e^-(0.097 *6.299 )) * [cos(0.097 *6.299 )+sin(0.097 *6.299 )]] = -0.17331E+00 deg

Value of lamda per P.2.3 [lamda]: = a/(Rt)^0.5 = 1.750/(246.063 * 0.709 )^0.5 = 0.133

Coefficient XA per P.2.3: = L + a = 6.299 + 1.750 = 8.049 in. [204.450 mm.]

Coefficient XB per P.2.3: = L - a = 6.299 - 1.750 = 4.549 in. [115.550 mm.]

Coefficient XC per P.2.3: = L = 6.299 in. [160.000 mm.]

Coefficients YF and YL from figure P-4A based on lamda: YF = 3.250 YL = 14.460

Coefficient YC from figure P-4B based on lamda: YC = 65.447

Pressure end load on the opening per P.2.3: = pi * a^2 * P = 3.1415 * 1.750^2 * 14.171 = 136.337 lbf. [606.427 N.]

Radial force nomogram limit values per figure P-3A: = max[(1 - 0.75)(XA / (Rt)^0.5), 0.1] = max[(1 - 0.75)(8.049/(246.063 *0.709 )^0.5), 0.1] = 0.543

Longitudinal nomogram limit values per figure P-3A: = max[(1 - 0.75)(XB / (Rt)^0.5), 0.1] = max[(1 - 0.75)(4.549/(246.063 *0.709 )^0.5), 0.1] = 0.742

Circumferential moment nomogram limit value per figure P-3B: = max[(1 - 0.75)(XC / (Rt)^0.5), 0.1] = max[(1 - 0.75)(6.299/(246.063 *0.709 )^0.5), 0.1] = 0.642

Radial force multiplier per figure P-3A: = lamda / (2 * YF * FP) = 0.133/(2 * 3.250 * 136.337 ) = 0.14953E-03 1/lbf. [0.33617E-04 1/N.]

Longitudinal moment multiplier per figure P-3A: = lamda / (a * 12.0 * YL * FP) = 0.133/(1.750 * 12.0 * 14.460 * 136.337 ) = 0.46095E-03 1/ft.lb. [0.33999E-03 1/N.m.]

Circumferential moment multiplier per figure P-3B: = lamda / (a * 12.0 * YC * FP) = 0.133/(1.750 * 12.0 * 65.447 * 136.337 ) = 0.10184E-03 1/ft.lb. [0.75120E-04 1/N.m.]

Radial force limit [ML = 0 and MC = 0] per figure P-3A [FRmax]: = Radial force nomogram limit value / Radial force multp. = 0.543/0.150E-03 = 0.36304E+04 lbf. [0.16148E+05 N.]

Positive Long. moment limit [MC = 0 and FR = 0] per figure P-3A [MLmax]: = Long. moment nomogram limit value / Long. moment multiplier = 0.742/0.461E-03 = 0.16089E+04 ft.lb. [0.21813E+04 N.m.]

Negative Long. moment limit [ML = 0 and MC = 0] per figure P-3A [MLmin]: = - Radial Force nomogram limit value / Long. moment multiplier = -0.543/0.461E-03 = -.11777E+04 ft.lb. [-0.15966E+04 N.m.]

Circ. moment limit [ML = 0 and FR = 0] per figure P-3B [MCmax]: = Circ. moment nomogram limit value / Circ. moment multiplier = 0.642/0.102E-03 = 0.63060E+04 ft.lb. [0.85494E+04 N.m.]

Test Case [Nozzle 5 ] per Appendix P:

Nozzle stiffness coefficients per P.2.4:

Outside radius of nozzle [a]: = D / 2 = 3.5/2 = 1.8 in. [88.9 mm.]

Nominal tank radius [R]: = Nominal tank diameter / 2 = 492.1/2 = 246.1 in. [12500.0 mm.]

L / 2a coefficient: = L / 2 * a = 6.299/2 * 1.750 = 1.8

As L/2a >= 1.5, use second set of curves.

a / R coefficient: = a / R = 1.8/246.063 = 0.007

R / t coefficient: = R / t = 246.063/0.709 = 347.2

From figure P-2D [KR/E(2a)]: = 0.266E-02

From figure P-2E [KL/E(2a)^3]: = 0.612E-02

From figure P-2F [KC/E(2a)^3]: = 0.107E-01

Stiffness coefficient for the radial thrust load per P.2.9.2.1 [KR]: = Coeff. from graph * E * 2 * a = 0.266E-02 * 28756854 * 2 * 1.750 = 0.26768E+06 lbf./in. [0.46875E+06 N./cm.]

Stiffness coefficient for the longitudinal moment per P.2.9.2.1 [KL]: = Coeff. from graph * E * ( 2.0 * a )^3 = 0.612E-02 * 28756854 * ( 2.0 * 1.750 )^3 = 0.13170E+06 in.lbf./deg [0.14880E+05 N.m./deg]

Stiffness coefficient for the circumferential moment per P.2.9.2.1 [KC]: = Coeff. from graph * E * ( 2 * a )^3 = 0.107E-01 * 28756854 * ( 2 * 1.750 )^3 = 0.23046E+06 in.lbf./deg [0.26037E+05 N.m./deg]

Characteristic parameter per P.2.3 [beta]: = 1.285 / (Rt)^0.5 = 1.285/(246.063 * 0.709 )^0.5 = 0.97311E-01 1/in. [0.38311E-02 1/mm.]

Unrestrained radial growth of the shell per P.2.5.1 [W]: = (0.036*G*H*R^2)/Et * [1-(e^-(beta*L)) * cos(beta*L) - (L/H)] + alpha * R * delta[T] = (0.036*1.006 *396.375 *246.063^2)/28756854 *0.709 * [1-(e^-(0.097 *6.299 )) * cos(0.097 *6.299 ) - (6.299/396.37 )] + 0.663E-05 * 246.063 * 0.000 = 0.02307 in. [0.58607 mm.]

Unrestrained shell rotation of the shell per P.2.5.2 [theta]: = (0.036*G*H*R^2)/E*t * [(1/H)-(beta*e^-(beta*L)) * [cos(beta*L)+sin(beta*L)]] = (0.036*1.006 *396.375 *246.063^2)/28756854 *0.709 * [(1/396.375 )-(0.097 *e^-(0.097 *6.299 )) * [cos(0.097 *6.299 )+sin(0.097 *6.299 )]] = -0.17331E+00 deg

Value of lamda per P.2.3 [lamda]: = a/(Rt)^0.5 = 1.750/(246.063 * 0.709 )^0.5 = 0.133

Coefficient XA per P.2.3: = L + a = 6.299 + 1.750 = 8.049 in. [204.450 mm.]

Coefficient XB per P.2.3: = L - a = 6.299 - 1.750 = 4.549 in. [115.550 mm.]

Coefficient XC per P.2.3: = L = 6.299 in. [160.000 mm.]

Coefficients YF and YL from figure P-4A based on lamda: YF = 3.250 YL = 14.460

Coefficient YC from figure P-4B based on lamda: YC = 65.447

Pressure end load on the opening per P.2.3: = pi * a^2 * P = 3.1415 * 1.750^2 * 14.171 = 136.337 lbf. [606.427 N.]

Radial force nomogram limit values per figure P-3A: = max[(1 - 0.75)(XA / (Rt)^0.5), 0.1] = max[(1 - 0.75)(8.049/(246.063 *0.709 )^0.5), 0.1] = 0.543

Longitudinal nomogram limit values per figure P-3A: = max[(1 - 0.75)(XB / (Rt)^0.5), 0.1] = max[(1 - 0.75)(4.549/(246.063 *0.709 )^0.5), 0.1] = 0.742

Circumferential moment nomogram limit value per figure P-3B: = max[(1 - 0.75)(XC / (Rt)^0.5), 0.1] = max[(1 - 0.75)(6.299/(246.063 *0.709 )^0.5), 0.1] = 0.642

Radial force multiplier per figure P-3A: = lamda / (2 * YF * FP) = 0.133/(2 * 3.250 * 136.337 ) = 0.14953E-03 1/lbf. [0.33617E-04 1/N.]

Longitudinal moment multiplier per figure P-3A: = lamda / (a * 12.0 * YL * FP) = 0.133/(1.750 * 12.0 * 14.460 * 136.337 ) = 0.46095E-03 1/ft.lb. [0.33999E-03 1/N.m.]

Circumferential moment multiplier per figure P-3B: = lamda / (a * 12.0 * YC * FP) = 0.133/(1.750 * 12.0 * 65.447 * 136.337 ) = 0.10184E-03 1/ft.lb. [0.75120E-04 1/N.m.]

Radial force limit [ML = 0 and MC = 0] per figure P-3A [FRmax]: = Radial force nomogram limit value / Radial force multp. = 0.543/0.150E-03 = 0.36304E+04 lbf. [0.16148E+05 N.]

Positive Long. moment limit [MC = 0 and FR = 0] per figure P-3A [MLmax]: = Long. moment nomogram limit value / Long. moment multiplier = 0.742/0.461E-03 = 0.16089E+04 ft.lb. [0.21813E+04 N.m.]

Negative Long. moment limit [ML = 0 and MC = 0] per figure P-3A [MLmin]: = - Radial Force nomogram limit value / Long. moment multiplier = -0.543/0.461E-03 = -.11777E+04 ft.lb. [-0.15966E+04 N.m.]

Circ. moment limit [ML = 0 and FR = 0] per figure P-3B [MCmax]: = Circ. moment nomogram limit value / Circ. moment multiplier = 0.642/0.102E-03 = 0.63060E+04 ft.lb. [0.85494E+04 N.m.]

User Case [Nozzle 5 ] per Appendix P:

Nozzle stiffness coefficients per P.2.4:

Outside radius of nozzle [a]: = D / 2 = 3.5/2 = 1.8 in. [88.9 mm.]

Nominal tank radius [R]: = Nominal tank diameter / 2 = 492.1/2 = 246.1 in. [12500.0 mm.]

L / 2a coefficient: = L / 2 * a = 6.299/2 * 1.750 = 1.8

As L/2a >= 1.5, use second set of curves.

a / R coefficient: = a / R = 1.8/246.063 = 0.007

R / t coefficient: = R / t = 246.063/0.709 = 347.2

From figure P-2D [KR/E(2a)]: = 0.266E-02

From figure P-2E [KL/E(2a)^3]: = 0.612E-02

From figure P-2F [KC/E(2a)^3]: = 0.107E-01

Stiffness coefficient for the radial thrust load per P.2.9.2.1 [KR]: = Coeff. from graph * E * 2 * a = 0.266E-02 * 28756854 * 2 * 1.750 = 0.26768E+06 lbf./in. [0.46875E+06 N./cm.]

Stiffness coefficient for the longitudinal moment per P.2.9.2.1 [KL]: = Coeff. from graph * E * ( 2.0 * a )^3 = 0.612E-02 * 28756854 * ( 2.0 * 1.750 )^3 = 0.13170E+06 in.lbf./deg [0.14880E+05 N.m./deg]

Stiffness coefficient for the circumferential moment per P.2.9.2.1 [KC]: = Coeff. from graph * E * ( 2 * a )^3 = 0.107E-01 * 28756854 * ( 2 * 1.750 )^3 = 0.23046E+06 in.lbf./deg [0.26037E+05 N.m./deg]

Characteristic parameter per P.2.3 [beta]: = 1.285 / (Rt)^0.5 = 1.285/(246.063 * 0.709 )^0.5 = 0.97311E-01 1/in. [0.38311E-02 1/mm.]

Unrestrained radial growth of the shell per P.2.5.1 [W]: = (0.036*G*H*R^2)/Et * [1-(e^-(beta*L)) * cos(beta*L) - (L/H)] + alpha * R * delta[T] = (0.036*1.006 *396.375 *246.063^2)/28756854 *0.709 * [1-(e^-(0.097 *6.299 )) * cos(0.097 *6.299 ) - (6.299/396.37 )] + 0.663E-05 * 246.063 * 0.000 = 0.02307 in. [0.58607 mm.]

Unrestrained shell rotation of the shell per P.2.5.2 [theta]: = (0.036*G*H*R^2)/E*t * [(1/H)-(beta*e^-(beta*L)) * [cos(beta*L)+sin(beta*L)]] = (0.036*1.006 *396.375 *246.063^2)/28756854 *0.709 * [(1/396.375 )-(0.097 *e^-(0.097 *6.299 )) * [cos(0.097 *6.299 )+sin(0.097 *6.299 )]] = -0.17331E+00 deg

Value of lamda per P.2.3 [lamda]: = a/(Rt)^0.5 = 1.750/(246.063 * 0.709 )^0.5 = 0.133

Coefficient XA per P.2.3: = L + a = 6.299 + 1.750 = 8.049 in. [204.450 mm.]

Coefficient XB per P.2.3: = L - a = 6.299 - 1.750 = 4.549 in. [115.550 mm.]

Coefficient XC per P.2.3: = L = 6.299 in. [160.000 mm.]

Coefficients YF and YL from figure P-4A based on lamda: YF = 3.250 YL = 14.460

Coefficient YC from figure P-4B based on lamda: YC = 65.447

Pressure end load on the opening per P.2.3: = pi * a^2 * P = 3.1415 * 1.750^2 * 14.171 = 136.337 lbf. [606.427 N.]

Radial force nomogram limit values per figure P-3A: = max[(1 - 0.75)(XA / (Rt)^0.5), 0.1] = max[(1 - 0.75)(8.049/(246.063 *0.709 )^0.5), 0.1] = 0.543

Longitudinal nomogram limit values per figure P-3A: = max[(1 - 0.75)(XB / (Rt)^0.5), 0.1] = max[(1 - 0.75)(4.549/(246.063 *0.709 )^0.5), 0.1] = 0.742

Circumferential moment nomogram limit value per figure P-3B: = max[(1 - 0.75)(XC / (Rt)^0.5), 0.1] = max[(1 - 0.75)(6.299/(246.063 *0.709 )^0.5), 0.1] = 0.642

Radial force multiplier per figure P-3A: = lamda / (2 * YF * FP) = 0.133/(2 * 3.250 * 136.337 ) = 0.14953E-03 1/lbf. [0.33617E-04 1/N.]

Longitudinal moment multiplier per figure P-3A: = lamda / (a * 12.0 * YL * FP) = 0.133/(1.750 * 12.0 * 14.460 * 136.337 ) = 0.46095E-03 1/ft.lb. [0.33999E-03 1/N.m.]

Circumferential moment multiplier per figure P-3B: = lamda / (a * 12.0 * YC * FP) = 0.133/(1.750 * 12.0 * 65.447 * 136.337 ) = 0.10184E-03 1/ft.lb. [0.75120E-04 1/N.m.]

Radial force limit [ML = 0 and MC = 0] per figure P-3A [FRmax]: = Radial force nomogram limit value / Radial force multp. = 0.543/0.150E-03 = 0.36304E+04 lbf. [0.16148E+05 N.]

Positive Long. moment limit [MC = 0 and FR = 0] per figure P-3A [MLmax]: = Long. moment nomogram limit value / Long. moment multiplier = 0.742/0.461E-03 = 0.16089E+04 ft.lb. [0.21813E+04 N.m.]

Negative Long. moment limit [ML = 0 and MC = 0] per figure P-3A [MLmin]: = - Radial Force nomogram limit value / Long. moment multiplier = -0.543/0.461E-03 = -.11777E+04 ft.lb. [-0.15966E+04 N.m.]

Circ. moment limit [ML = 0 and FR = 0] per figure P-3B [MCmax]: = Circ. moment nomogram limit value / Circ. moment multiplier = 0.642/0.102E-03 = 0.63060E+04 ft.lb. [0.85494E+04 N.m.]

Design Case [Nozzle 6 ] per Appendix P:

Nozzle stiffness coefficients per P.2.4:

Outside radius of nozzle [a]: = D / 2 = 4.5/2 = 2.2 in. [114.3 mm.]

Nominal tank radius [R]: = Nominal tank diameter / 2 = 492.1/2 = 246.1 in. [12500.0 mm.]

L / 2a coefficient: = L / 2 * a = 6.299/2 * 2.250 = 1.4

As 1.0 < L/2a < 1.5, interpolate between both sets of curves.

a / R coefficient: = a / R = 2.2/246.063 = 0.009

R / t coefficient: = R / t = 246.063/0.709 = 347.2

Interpolated values from the figure per P-2A and P-2D [KR/E(2a)]: = 0.212E-02

Interpolated values from the figure per P-2B and P-2E [KL/E(2a)^3]: = 0.372E-02

Interpolated values from the figure P-2C and P-2F [KC/E(2a)^3]: = 0.524E-02

Stiffness coefficient for the radial thrust load per P.2.9.2.1 [KR]: = Coeff. from graph * E * 2 * a = 0.212E-02 * 28756854 * 2 * 2.250 = 0.27445E+06 lbf./in. [0.48061E+06 N./cm.]

Stiffness coefficient for the longitudinal moment per P.2.9.2.1 [KL]: = Coeff. from graph * E * ( 2.0 * a )^3 = 0.372E-02 * 28756854 * ( 2.0 * 2.250 )^3 = 0.17014E+06 in.lbf./deg [0.19223E+05 N.m./deg]

Stiffness coefficient for the circumferential moment per P.2.9.2.1 [KC]: = Coeff. from graph * E * ( 2 * a )^3 = 0.524E-02 * 28756854 * ( 2 * 2.250 )^3 = 0.23977E+06 in.lbf./deg [0.27089E+05 N.m./deg]

Characteristic parameter per P.2.3 [beta]: = 1.285 / (Rt)^0.5 = 1.285/(246.063 * 0.709 )^0.5 = 0.97311E-01 1/in. [0.38311E-02 1/mm.]

Unrestrained radial growth of the shell per P.2.5.1 [W]: = (0.036*G*H*R^2)/Et * [1-(e^-(beta*L)) * cos(beta*L) - (L/H)] + alpha * R * delta[T] = (0.036*1.006 *396.375 *246.063^2)/28756854 *0.709 * [1-(e^-(0.097 *6.299 )) * cos(0.097 *6.299 ) - (6.299/396.37 )] + 0.663E-05 * 246.063 * 0.000 = 0.02307 in. [0.58607 mm.]

Unrestrained shell rotation of the shell per P.2.5.2 [theta]: = (0.036*G*H*R^2)/E*t * [(1/H)-(beta*e^-(beta*L)) * [cos(beta*L)+sin(beta*L)]] = (0.036*1.006 *396.375 *246.063^2)/28756854 *0.709 * [(1/396.375 )-(0.097 *e^-(0.097 *6.299 )) * [cos(0.097 *6.299 )+sin(0.097 *6.299 )]] = -0.17331E+00 deg

Value of lamda per P.2.3 [lamda]: = a/(Rt)^0.5 = 2.250/(246.063 * 0.709 )^0.5 = 0.170

Coefficient XA per P.2.3: = L + a = 6.299 + 2.250 = 8.549 in. [217.150 mm.]

Coefficient XB per P.2.3: = L - a = 6.299 - 2.250 = 4.049 in. [102.850 mm.]

Coefficient XC per P.2.3: = L = 6.299 in. [160.000 mm.]

Coefficients YF and YL from figure P-4A based on lamda: YF = 2.701 YL = 11.893

Coefficient YC from figure P-4B based on lamda: YC = 38.969

Pressure end load on the opening per P.2.3: = pi * a^2 * P = 3.1415 * 2.250^2 * 14.171 = 225.373 lbf. [1002.461 N.]

Radial force nomogram limit values per figure P-3A: = max[(1 - 0.75)(XA / (Rt)^0.5), 0.1] = max[(1 - 0.75)(8.549/(246.063 *0.709 )^0.5), 0.1] = 0.514

Longitudinal nomogram limit values per figure P-3A: = max[(1 - 0.75)(XB / (Rt)^0.5), 0.1] = max[(1 - 0.75)(4.049/(246.063 *0.709 )^0.5), 0.1] = 0.770

Circumferential moment nomogram limit value per figure P-3B: = max[(1 - 0.75)(XC / (Rt)^0.5), 0.1] = max[(1 - 0.75)(6.299/(246.063 *0.709 )^0.5), 0.1] = 0.642

Radial force multiplier per figure P-3A: = lamda / (2 * YF * FP) = 0.170/(2 * 2.701 * 225.373 ) = 0.13996E-03 1/lbf. [0.31466E-04 1/N.]

Longitudinal moment multiplier per figure P-3A: = lamda / (a * 12.0 * YL * FP) = 0.170/(2.250 * 12.0 * 11.893 * 225.373 ) = 0.33903E-03 1/ft.lb. [0.25006E-03 1/N.m.]

Circumferential moment multiplier per figure P-3B: = lamda / (a * 12.0 * YC * FP) = 0.170/(2.250 * 12.0 * 38.969 * 225.373 ) = 0.10347E-03 1/ft.lb. [0.76319E-04 1/N.m.]

Radial force limit [ML = 0 and MC = 0] per figure P-3A [FRmax]: = Radial force nomogram limit value / Radial force multp. = 0.514/0.140E-03 = 0.36755E+04 lbf. [0.16349E+05 N.]

Positive Long. moment limit [MC = 0 and FR = 0] per figure P-3A [MLmax]: = Long. moment nomogram limit value / Long. moment multiplier = 0.770/0.339E-03 = 0.22713E+04 ft.lb. [0.30793E+04 N.m.]

Negative Long. moment limit [ML = 0 and MC = 0] per figure P-3A [MLmin]: = - Radial Force nomogram limit value / Long. moment multiplier = -0.514/0.339E-03 = -.15174E+04 ft.lb. [-0.20572E+04 N.m.]

Circ. moment limit [ML = 0 and FR = 0] per figure P-3B [MCmax]: = Circ. moment nomogram limit value / Circ. moment multiplier = 0.642/0.103E-03 = 0.62069E+04 ft.lb. [0.84151E+04 N.m.]

Test Case [Nozzle 6 ] per Appendix P:

Nozzle stiffness coefficients per P.2.4:

Outside radius of nozzle [a]: = D / 2 = 4.5/2 = 2.2 in. [114.3 mm.]

Nominal tank radius [R]: = Nominal tank diameter / 2 = 492.1/2 = 246.1 in. [12500.0 mm.]

L / 2a coefficient: = L / 2 * a = 6.299/2 * 2.250 = 1.4

As 1.0 < L/2a < 1.5, interpolate between both sets of curves.

a / R coefficient: = a / R = 2.2/246.063 = 0.009

R / t coefficient: = R / t = 246.063/0.709 = 347.2

Interpolated values from the figure per P-2A and P-2D [KR/E(2a)]: = 0.212E-02

Interpolated values from the figure per P-2B and P-2E [KL/E(2a)^3]: = 0.372E-02

Interpolated values from the figure P-2C and P-2F [KC/E(2a)^3]: = 0.524E-02

Stiffness coefficient for the radial thrust load per P.2.9.2.1 [KR]: = Coeff. from graph * E * 2 * a = 0.212E-02 * 28756854 * 2 * 2.250 = 0.27445E+06 lbf./in. [0.48061E+06 N./cm.]

Stiffness coefficient for the longitudinal moment per P.2.9.2.1 [KL]: = Coeff. from graph * E * ( 2.0 * a )^3 = 0.372E-02 * 28756854 * ( 2.0 * 2.250 )^3 = 0.17014E+06 in.lbf./deg [0.19223E+05 N.m./deg]

Stiffness coefficient for the circumferential moment per P.2.9.2.1 [KC]: = Coeff. from graph * E * ( 2 * a )^3 = 0.524E-02 * 28756854 * ( 2 * 2.250 )^3 = 0.23977E+06 in.lbf./deg [0.27089E+05 N.m./deg]

Characteristic parameter per P.2.3 [beta]: = 1.285 / (Rt)^0.5 = 1.285/(246.063 * 0.709 )^0.5 = 0.97311E-01 1/in. [0.38311E-02 1/mm.]

Unrestrained radial growth of the shell per P.2.5.1 [W]: = (0.036*G*H*R^2)/Et * [1-(e^-(beta*L)) * cos(beta*L) - (L/H)] + alpha * R * delta[T] = (0.036*1.006 *396.375 *246.063^2)/28756854 *0.709 * [1-(e^-(0.097 *6.299 )) * cos(0.097 *6.299 ) - (6.299/396.37 )] + 0.663E-05 * 246.063 * 0.000 = 0.02307 in. [0.58607 mm.]

Unrestrained shell rotation of the shell per P.2.5.2 [theta]: = (0.036*G*H*R^2)/E*t * [(1/H)-(beta*e^-(beta*L)) * [cos(beta*L)+sin(beta*L)]] = (0.036*1.006 *396.375 *246.063^2)/28756854 *0.709 * [(1/396.375 )-(0.097 *e^-(0.097