Semi-Elliptical Head
Results from Nozzle FleX for mesh size 3 (medium) are compared to results manually extracted from SAP 2000 Version 25 in the left hand column. The model was also imported to the general purpose FEA package Mecway Version 21. In the right hand column, results from Mecway are compared to Nozzle FleX. Finally there is a comparison of results for longitudinal bending with a mesh size 1 (fine) model.
Results show agreement to within 3% and in most cases less than 1%. See the Nozzle FleX listing at the end for full details of the model.
| SAP 2000 | MECWAY |
| Radial stiffness (force applied 10000N): | Radial stiffness (force applied 10000N): |
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| Take average of radial displacement at 4 points: At X=304.6,Z=0: Dx = -0.01841, Dy = -0.12195 (res 0.1233) radial = -0.12195sin83.46 -0.01841cos83.46 = 0.1233mm At X=200,Z=104.6: Dx=-0.01395, Dy = -0.12769 (res=0.1284), radial = -0.1284mm At X =95.5, Z=0: Dx=-0.009, dy = -0.13331 (res 0.1336) At X=200, Z -104.6, Dx=-0.01395, Dy = -0.12769 (res=0.1284), radial = -0.1284mm Avg = 0.128425 mm -> stiffness = 77866 (0.2% less than Nozzle Flex 78026 ) | Normal to shell at 83.46deg Centre of intersection at x=200, y=436.18 Apply load at 305mm above centre (y=741.18) Radial load 10000N = -1139N X, -9935N Y Thus an offsetting moment must be applied of -1139*0.305=-347.4Nm about Z-axis. Average radial displacement at same 4 points: Node 1: Dx=-0.0182, Dy=-0.1212, res =0.1226 Node 593: Dx=-0.0138, Dy=-0.1267, res=0.1274 Node 1281:Dx=-0.0090, Dy=-0.1321, res=0.1324 Node 1975:Dx=-0.0138, Dy=-0.1267, res=0.1274 Average = 0.12745mm ->stiffness = 78462N/mm (0.6% greater than Nozzle Flex 78026) |
| Longitudinal stiffness (moment applied 10000Nm): | Longitudinal stiffness (moment applied 10000Nm): |
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| SAP2000 Displacements at intersection nodes on X-axis DX = 0.2068, DY = 0.9794, RZ = 0.00502RADS DX = -0.02605, DY = -1.10135, RZ = 0.00527RADS INTERSECTION ‘DIAMETER’ LINE DELTA X=210.1, Y=-24.153 ANGLE TO X-AXIS AS PER ADJACENT MECWAY CALC = -6.558° RELATIVE DISPLACEMENT DX = 0.233, DY = 2.081 ENDING INTERSECTION DIAMETER LINE DELTA X= 210.1+0.233 = 210.333, DELTA Y = -24.153+2.081 = -22.072 ANGLE TO X-AXIS ENDING: ATAN -22.072/210.333 = -5.991° ROTATION ABOUT Z-AXIS = 0.5673° -> STIFFNESS = 17627NM/DEG. (~AS PER NOZZLE FLEX) | Displacements at intersection nodes on X-axis DX = 0.2045, DY = 0.9708, DZ=0, CO-ORDS X=304.550, Y=420.795 DX= -0.0258, DY= -1.0895, DZ=0, CO-ORDS X=95.450, Y=444.948 INTERSECTION ‘DIAMETER’ LINE DELTA X=210.1, Y=-24.153 (RES=211.484) ANGLE TO X-AXIS STARTING: ATAN -24.153/210.1 = -6.558° RELATIVE DISPLACEMENT DX = 0.2303, DY = 2.0603 (RES=2.0731) ENDING INTERSECTION DIAMETER LINE DELTA X= 210.1+0.2303 = 210.330, DELTA Y = -24.153+2.0603 = -22.093 ANGLE TO X-AXIS ENDING: ATAN -22.093/210.33 = -5.996° ROTATION ABOUT Z-AXIS = 0.562° (= ATAN 2.0731/211.484) -> STIFFNESS = 17804NM/DEG. (1% HIGHER THAN SAP2000) |
| Longitudinal SCF: | Longitudinal SCF: |
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| Max principal stress outside weld zone = 480.4MPa SCF check, Branch section modulus =pi.(219.1^4-199.1^4)/(219.1.32) = 328475 mm3. Sb = M/Z=10e6/328475=30.44 -> SCF=480.4/30.44 = 15.78 = NOZZLEFLEX VALUE | Max principal stress outside weld zone = 467.2MPa SCF check, Branch section modulus =328475 mm3 Sb = M/Z=10e6/328475=30.44 -> SCF=467.2/30.44 = 15.35 = (2.7% lower than NozzleFlex 15.78) |
| Circumferential stiffness (load applied 10000Nm): | Circumferential stiffness (load applied 10000Nm): |
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| Mc=10000Nm. Radial angle 83.46deg to X -> Circ angle 173.54deg Mx = 10000cos173.54 = -9935Nm, My = 10000sin173.54=1139Nm Pt 116100 Dx=0.11728,Dy=1.02166, Dz=0.091 Pt 148100 Dx=-0.11728,Dy=-1.02166,Dz=0.091 Rel displacement Dx=0.23456,Dy=2.04332 (RES 2.0567) Rotation = asin 2.0567/209.1=0.5636deg ->k=10000/0.5636 = 17744Nm/deg (0.6% lower than Nozzleflex 17845) Minor difference because Nozzleflex considers effect of all nodes around circumference | Mc=10000Nm. Radial angle 83.46deg to X -> Circ angle 173.54deg Mx = 10000cos173.54 = -9935Nm, My = 10000sin173.54=1139Nm Node 593,X=200,Y=433.04,Z=104.55 Dx=0.11591, Dy=1.01196, Dz=0.08964 Node 1975,X=200,Y=433.04,Z=-104.55 Dx=-0.11591, Dy=-1.01196, Dz=0.08964 Diameter = 2*104.55=209.10mm Relative displacement Dx=0.23182, Dy=2.02392 (RES 2.03715). In radial direction this is 2.02392sin83.46 + 0.23182cos83.46 = 2.03715mm Rotation = asin 2.03715/209.1=0.5582deg -> k=10000/0.5582=17915 Nm/deg (0.4% higher than NozzleFlex 17845) |
| Circumf SCF | Circumf SCF |
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| Max principal stress outside weld zone = 467.3MPa SCF check, Branch section modulus =pi.(219.1^4-199.1^4)/(219.1.32) = 328475 mm3. Sb = M/Z=10e6/328475=30.44 -> SCF=467.3/30.44 = 15.35 = NOZZLEFLEX VALUE | Max principal stress outside weld zone = 454.1MPa SCF check, Branch section modulus =328475 mm3 Sb = M/Z=10e6/328475=30.44 -> SCF=454.1/30.44 = 14.92 = (2.8% lower than NozzleFlex 15.35) |
| Torsional stiffness (torsion 10000Nm applied): | Torsional stiffness (torsion 10000Nm applied): |
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| Mt=10000Nm, angle to horizontal = 83.46deg My = 10000sin83.54 = 9935Nm, Mx = 10000cos83.54=1139Nm Take average of 4 points On X-axis Pt100100, X=304.55,Y=420.795,Z=0. Dx=Dy=0. Dz = -0.00836 Pt132100, X=95.45,Y=444.948,Z=0. Dx=Dy=0. Dz = 0.01038 Length of ‘diameter’ = 210.49mm. Relative Dz= 0.01038+0.00836=0.01874 Rotation = asin 0.01874/210.49=0.00510 Parallel to Z-axis Pt116100, X=200, Y=433.04, Z=104.55. Dx=0.00962, Dy=-0.00137, Dz =0.00074. Pt148100, X=200, Y-433.04, Z=-104.55, Dx=-0.00962,Dy=0.00137,Dz=0.00074. Relative Dx =0.01924 & Dy = -0.00274, RES=0.01943, Diameter = 209.1mm. Rotation = asin 0.01943/209.1=0.00532 Average = 0.00521DEG ->k=1918642Nm/deg; (1.5% greater than Nozzleflex 1889935) As torsional stiffness of the vessel intersection is high compared to the nozzle neck, results are sensitive to small differences between shell and beam element stiffnesses in shear /torsion. | Take average of 4 points On X-axis Pt100100, Dz=-0.00836 (Dx=Dy=0) Pt132100, Dz= 0.01040 (Dx=Dy=0) Relative Dz= 0.01040+0.00836=0.01876 Rotation = asin 0.01876/210.49=0.00511 Parallel to Z-axis Pt116100,Dx=0.00963, Dy=-0.00133, Dz=0.00076 Pt148100, Dx=-0.00963, Dy=0.00133, Dz=0.00076 Relative Dx =0.01926 & Dy = -0.00266, RES=0.01944, Rotation = asin 0.01944/209.1=0.00533 Average = 0.00522 -> k=1916300Nm/deg. (1.4% greater than Nozzleflex 1889935) |
| Repeat longitudinal check for mesh size 1: | Repeat longitudinal check for mesh size 1: |
| Nozzle Flex K=17662 (0.1% greater than mesh size 3). Displacements Pt100100, DX=0.20677,DY=0.97938 Pt 164100, DX=-0.02598, DY=-1.09905 RELATIVE DISPLACEMENT DELTA X = 0.2327, DELTA Y =2.0784 STARTING ANGLE TO X-AXIS AS PER PREV. CALC = -6.558° ENDING INTERSECTION DIAMETER LINE DELTA X= 210.1+0.233 = 210.333, DELTA Y = -24.153+2.078 = -22.075 ANGLE TO X-AXIS ENDING: ATAN -22.075/210.333 = -5.991° ROTATION ABOUT Z-AXIS = 0.5665° LOAD = 10KNM -> STIFFNESS = 17652NM/DEG. (~AS PER NOZZLE FLEX) | Node 1, DX=0.2060, DY=0.9789 Node 4725, DX=-0.0265, DY=-1.1011 REL DISPL DELTA X=, DELTA Y = 0.2325, DELTA Y = 2.0800 STARTING ANGLE TO X-AXIS AS PER PREV. CALC = -6.558° ENDING INTERSECTION DIAMETER LINE DELTA X= 210.1+0.2325 = 210.3325, DELTA Y = -24.153+2.080 = -22.073 ANGLE TO X-AXIS ENDING: ATAN -22.073/210.3325 = -5.9909° ROTATION ABOUT Z-AXIS = 0.5671° LOAD = 10KNM -> STIFFNESS = 17633NM/DEG. (0.2% LOWER THAN NOZZLEFLEX) |
| Longitudinal SCF (mesh size 1): | Longitudinal SCF (mesh size 1): |
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| SCF_ib = 16.07 (1.8% greater than value 15.78 at mesh size 3) Max principal stress outside weld zone = 489.3MPa SCF check, Branch section modulus =pi.(219.1^4-199.1^4)/(219.1.32) = 328475 mm3. Sb = M/Z=10e6/328475=30.44 -> SCF=489.3/30.44 = 16.07 = NOZZLEFLEX VALUE | Max principal stress outside weld zone = 493.6MPa SCF check, Branch section modulus =328475 mm3 Sb = M/Z=10e6/328475=30.44 -> SCF=493.6/30.44 = 16.22 = (0.9% greater than NozzleFlex) |
Nozzle Flex listing and results for mesh size 3:
Nozzle FleX Plugin for SAP2000
Version 2.0, by Xtrados Pty Ltd.
INPUTS
Geometry type: SEhead
Nozzle angle: Vertical
Mesh size (1-5) : 3
Poisson's ratio : 0.3
Young's modulus (MPa): 206850
Branch standout (mm): 300
Ellipsoidal ratio : 2
Fillet weld leg (mm): 0
Hillside offset (mm): 200
Re-pad thickness (mm): 0
Re-pad width (mm): 0
Branch thk. (mm): 10
Branch OD (mm): 219.1
Shell thk. (mm): 10
Shell OD (mm): 1800
OUTPUTS
Radial stiffness: 78026 (N/mm)
Longit. stiffness: 17641 (Nm/deg.)
Circum. stiffness: 17845 (Nm/deg.)
Torsional stiffness: 1889935 (Nm/deg.)
SCF_ab: 22.06
SCF_ib: 15.78
SCF_ob: 15.35
SCF_tb: 1.05
In-plane flexibility factor: 35.22
Out-plane flexibility factor: 34.82
Torsional flexibility factor: 1
Other model details
Branch standout (mm): as above
Radial angle from horizontal (deg): 83.46
Nozzle Flex listing and results for mesh size 1:
Nozzle FleX Plugin for SAP2000
Version 2.0, by Xtrados Pty Ltd.
INPUTS
Geometry type: SEhead
Nozzle angle: Vertical
Mesh size (1-5) : 1
Poisson's ratio : 0.3
Young's modulus (MPa): 206850
Branch standout (mm): 300
Ellipsoidal ratio : 2
Fillet weld leg (mm): 0
Hillside offset (mm): 200
Re-pad thickness (mm): 0
Re-pad width (mm): 0
Branch thk. (mm): 10
Branch OD (mm): 219.1
Shell thk. (mm): 10
Shell OD (mm): 1800
OUTPUTS
Radial stiffness: 77895 (N/mm)
Longit. stiffness: 17662 (Nm/deg.)
Circum. stiffness: 17862 (Nm/deg.)
Torsional stiffness: 1912483 (Nm/deg.)
SCF_ab: 22.43
SCF_ib: 16.07
SCF_ob: 15.63
SCF_tb: 1.04
In-plane flexibility factor: 35.18
Out-plane flexibility factor: 34.78
Torsional flexibility factor: 1
Other model details
Branch standout (mm): as above
Radial angle from horizontal (deg): 83.46
Cylindrical Intersection
The nozzle stiffness outputs from Nozzle FleX are compared to values manually calculated from the SAP2000 model. See the Nozzle FleX listing at the end for full details of the model.
Manually calculated stiffnesses are less than Nozzle FleX outputs by the following amounts
- Radial: 0.25%
- Circumferential: 0.0%
- Longitudinal: 2.8%
- Torsional: 4.9%
The manual calculations consider only deflections at two or four points on the circumference, whereas Nozzle FleX considers the entire circumference. There can also be small differences in results between beam and shell models, which tends to exaggerate differences for stiff rotational axes (ie torsional).
| SAP2000 Results and hand calculations |
Radial stiffness (force applied 10000N): |
| Average points at 0 and 90 deg Pt 100100, Dy=-0.38547mm Pt 116100, Dy=-0.38916mm Average = 0.38732mm Note that Nozzle FleX intersection stiffness results Do Not include header / vessel deflections, and therefore we must subtract deflection of the header (6m long DN400 x 10mm thick cylinder with central load). The classical beam deflection (ignoring shear effects) is not accurate enough here, instead we run a beam model in SAP2000 and get deflection 0.2525mm (vs 0.2222mm using classical beam equations).  Subtract theoretical header defln 0.2525mm, giving nett radial 0.1348mm ->k=10000/0.1348 = 74173N/mm (0.25% less than NozzleFlex 74360) |
Circumferential stiffness (load applied 10000Nm): |
| Intersection points at Z=0 Pt 100100, X=45, Y=193.02 Displ Dx=0.8031, Dy=1.3824 Pt 132100, X=-45, Y=193.02 Dx=0.8031, Dy=-1.3824 Dia = 90mm; radius 45mm Rotation = atan(1.3824/45) = 1.7596deg. -> k=10000/1.76 = 5682Nm/deg Subtract theoretical header rotation ML/(4JG) = 0.02207deg; nett rotation = 1.7375deg -> k=10000/1.7375 = 5755Nm/deg (~NozzleFlex 5752) |
Longitudinal stiffness (moment applied 10000Nm): |
| Intersection points at X=0 Pt 116100, Y=198.2, Z=45.0 Dy=0.51881, Dz=-0.05477 Pt 148100, Y=198.2, Z=-45 Dy=-0.51881, Dz=-0.05477 Radius 45mm Rotation = atan(0.51881/45) = 0.66054 Subtract theoretical header rotation ML/(16EI) = 0.00424deg; nett rotation = 0.65630deg ->k=10000/0.6563 = 15237Nm/deg (2.8% less than NozzleFlex 15680) |
Torsional stiffness (torsion 10000Nm applied): |
| Average points at 0 and 90 deg Pt 100100, Dz=-0.0230mm Rotation = atan (0.023/45)=0.02928deg Pt 116100, Dx=0.05357mm Rotation = atan (0.05357/45)=0.06837deg Average = 0.04883deg Subtract theoretical header rot’n 0.00424deg Nett rotation = 0.04459deg ->k=10000/0.04459 = 224266 (4.9% less than Nozzle Flex 235808) As torsional stiffness of the intersection is high compared to the nozzle neck, results are sensitive to small differences between shell and beam element stiffnesses in shear /torsion. |
Nozzle FleX Plugin for SAP2000
Version 2.0, by Xtrados Pty Ltd.
INPUTS
Geometry type: Cylinder
Nozzle angle: Normal
Mesh size (1-5) : 3
Poisson's ratio : 0.3
Young's modulus (MPa): 206850
Branch standout (mm): 200
Distance to rigid end 2 (mm): 3000
Distance to rigid end 1 (mm): 3000
Fillet weld leg (mm): 0
Hillside offset (mm): 0
Re-pad thickness (mm): 0
Re-pad width (mm): 0
Cut through shell? : Y
Branch thk. (mm): 10
Branch OD (mm): 100
Shell thk. (mm): 10
Shell OD (mm): 406.4
OUTPUTS
Radial stiffness: 74360 (N/mm)
Longit. stiffness: 15680 (Nm/deg.)
Circum. stiffness: 5752 (Nm/deg.)
Torsional stiffness: 235808 (Nm/deg.)
SCF_ab: 17.99
SCF_ib: 4.55
SCF_ob: 8.1
SCF_tb: 1.22
In-plane flexibility factor: 7.41
Out-plane flexibility factor: 20.21
Torsional flexibility factor: 1
Other model details
Branch standout (mm): as above
Distance to rigid end 1 (mm): as above
Distance to rigid end 2 (mm): as above