ANALYSIS OF ROUND ATTACHMENT ON CYLINDRICAL SHELL INTERACTION PER WRC BULLETIN 297
ATTACHMENT DESCRIPTION 8" STEAM OUTLET
NOZZLE MATERIAL: SA106-B ALLOWABLE STRESS: Sv = 118.00 Mpa (PG-23)
SHELL & PAD MATERIAL: SA516-70 ALLOWABLE STRESS: Sv = 138.00 Mpa (PG-23)
SHELL OUTSIDE DIAMETERDa = 1200.00 mm COR. ALLOWANCE: ca = 0.00 mm
SHELL NOMINAL THICKNESt'= 10.00 mm MILL UNDERTOL.: mu = 0.00 mm
NOZZLE OUTSIDE DIAMETEd = 170.00 mm COR. ALLOWANCE: ca,n = 0.00 mm
WALL THICKNESS: tn = 10.00 mm MILL UNDERTOL.: mu,n = 0.00 mm
OPTION: SET NOZZLE PRESSURE INDICE TO (1) P d / 2 t ; P d / 4 t or (2) P D / 2 T ; P D / 4T 1
Option 2 is a more conservative approach, used on software such as Autopipe Nozzle
Option 1 is a less conservative approach, used on software such as PV Elite
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IS THERE A REINFORCING PAD ? REINFORING PAD OUTSIDE DIAMETER: Dp = 530.00 mm
YES REINFORCING PAD THICKNESS: tp' = 10.00 mm
GEOMETRY CHECK OF PAD: 1.65 √ 0,5 Di (ta + tp) = 179.24 mm OK
APPLICABLE FORCES & LOADS TABLE
DESIGN PRESSURE: p 1.00 Mpa
RADIAL LOAD (+ / - ): Fr 9000.00 N
LONGITUDINAL SHEAR LOAD: Fl 9000.00 N
CIRCUMFERENTIAL SHEAR LOAD: Fc 9000.00 N
LONGITUDINAL MOMENT: Ml 750000.00 Nmm
CIRCUMFERENTIAL MOMENT: Mc 750000.00 Nmm
TORTIONAL MOMENT: Mt 750000.00 Nmm
GEOMETRY DATA Positive radial force = Towards outside of vessel!
CYLINDRICAL SHELL ANALYSIS THICKNESS: ta = t' - ca - mu = 10.00 mm
CALCULATION THICKNESS FOR ATTACHMENT TO SHELL INTERACTION: T = ta + tp = 20.00 mm
CALCULATION THICKNESS FOR PAD TO SHELL INTERACTION: T = ta = 10.00 mm
CALCULATION THICKNESS NOZZLE: t= 10.00 mm
CALCULATION THICKNESS WHEN PAD APPLIES: t = 0,5 (Dp - d) + t = 190.00 mm
SHELL CORRODED INSIDE DIAMETER: Di = Da - 2 ta = 1180.00 mm
MEAN CORRODED RADIUS FOR ATTACHMENT TO SHELL INTERACTION: D = (Di + ta + tp)= 1200.00 mm
MEAN CORRODED RADIUS FOR PAD TO SHELL INTERACTION: D = (Di + ta) = 1190.00 mm
EQUIVALENT NOZZLE DIAMETER WHEN PAD APPLIES: d = Dp = 530.00 mm
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NOZZLE ON PAD OR SHELL
GEOMETRY FACTORS / ATTACHMENT TO SHELL INTERACTION: STRESS CONCENTRACTION FACTORS:
d/t = 17.00 T/t = 2.000 λ = (d/D)√D/T 1.097 Vessel Ke: 1.00 Nozzle Ke: 1.00
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SHEAR STRESSES:
SHELL τ =2 Fl / π d T = 1.69 τ =2 Fc / π d T = 1.69 τ = 2 Mt / π d² T = 0.83
NOZZLE: τ =2 Fl / π d t = 3.37 τ =2 Fc / π d t = 3.37 τ = 2 Mt / π d² t = 1.65
RADIAL STRESSES FROM AXIAL LOAD Fr { SHELL (1) / NOZZLE (5) }
(1) nr = (NrT/P) 0.085 MEMBRANE: 1.91 Mpa σr = P / T² nr (+ / -) P / T² mr (equation 1, membrane +/-
(1) mr = (Mr/P) 0.089 BENDING: 12.02 Mpa bending components)
(5) nr = (NrT/P) 0.085 MEMBRANE: 1.69 Mpa σr = σα = P / t² ( t / πd ) (+/-) P / t ² ( 6mr - 3nr ) (equation
(5) mr = (Mr/P) 0.089 BENDING: 25.11 Mpa 5, membrane +/- bending components)
RADIAL STRESSES FROM BENDING MOMENT Mc { SHELL (3) / NOZZLE (6) }
(3) nr = (NrTd/Mc) 0.119 MEMBRANE: 1.31 Mpa σr = Μi / T² d nr (+/-) Mi / T² d 6 mr (equation 3,
(3) mr = (Mrd/Mc) 0.196 BENDING: 12.97 Mpa membrane +/- bending components)
(6) nr = (NrTd/Mc) 0.119 MEMBRANE: 3.30 Mpa σr = σα = Mi / t² d ( 4 t / πd ) (+/-) Mi / t² d ( 6mr - 3nr )
(6) mr = (Mrd/Mc) 0.196 BENDING: 36.13 Mpa (equation 6, membrane +/- bending components)
RADIAL STRESSES FROM LONGITUDINAL MOMENT Ml { SHELL (3) / NOZZLE (6) }
(3) nr = (NrTd/ML 0.078 MEMBRANE: 0.86 Mpa σr = Μi / T² d nr (+/-) Mi / T² d 6 mr (equation 3,
(3) mr = (Mrd/ML) 0.127 BENDING: 8.40 Mpa membrane +/- bending components)
(6) nr = (NrTd/ML 0.078 MEMBRANE: 3.30 Mpa σr = σα = Mi / t² d ( 4 t / πd ) (+/-) Mi / t² d ( 6mr - 3nr )
(6) mr = (Mrd/ML) 0.127 BENDING: 23.29 Mpa (equation 6, membrane +/- bending components)
CIRCUMFERENTIAL STRESSES FROM AXIAL LOAD Fr { SHELL (2) / NOZZLE (7) }
(2) nθ = (ΝθT/P) 0.155 MEMBRANE: 3.49 Mpa σθ = P / T² nθ (+/-) P / T² 6 mθ (equation 2, membrane
(2) mθ = (Mθ/P) 0.053 BENDING: 7.16 Mpa +/- bending components)
(7) nθ = (ΝθT/P) 0.155 MEMBRANE: 3.49 Mpa σθ = σc = P / T² nθ (equation 7, membrane component
(7) mθ = (Mθ/P) 0.000 BENDING: 0.00 Mpa only)
CIRCUMFERENTIAL STRESSES FROM BENDING MOMENT Mc { SHELL (4) / NOZZLE (8) }
(4) nθ = (ΝθTd/Mc 0.167 MEMBRANE: 1.84 Mpa σθ = Μi / T² d nθ (+/-) Mi / T² d 6 mθ (equation 4,
(4) mθ = (Mθd/Mc 0.132 BENDING: 8.74 Mpa membrane +/- bending components)
(8) nθ = (ΝθTd/Mc 0.167 MEMBRANE: 1.84 Mpa σθ = σc = Mi / T² d nθ (equation 8, membrane component
(8) mθ = (Mθd/Mc 0.000 BENDING: 0.00 Mpa only)
CIRCUMFERENTIAL STRESSES FROM BENDING MOMENT ML { SHELL (4) / NOZZLE (8) }
(4) nθ = (ΝθTd/ML 0.276 MEMBRANE: 3.04 Mpa σθ = Μi / T² d nθ (+/-) Mi / T² d 6 mθ (equation 4,
(4) mθ = (Mθd/ML 0.080 BENDING: 5.29 Mpa membrane +/- bending components)
(8) nθ = (ΝθTd/ML 0.276 MEMBRANE: 3.04 Mpa σθ = σc = Mi / T² d nθ (equation 8, membrane component
(8) mθ = (Mθd/ML 0.000 BENDING: 0.00 Mpa only)
STRESSES RESULTING FOR THE INNER SURFACE:
σr (Mpa) σθ (Mpa)
Load Part Equation Equation
Membrane Bending Total Membrane Bending Total
Vessel (1) 1.91 12.02 -10.10 (2) 3.49 7.16 -3.67
Fr
Nozzle (5) 1.69 25.11 -23.42 (7) 3.49 0.00 3.49
Vessel (3) 1.31 12.97 -11.66 (4) 1.84 8.74 -6.89
Mc
Nozzle (6) 3.30 36.13 -32.83 (8) 1.84 0.00 1.84
Vessel (3) 0.86 8.40 -7.54 (4) 3.04 5.29 -2.25
ML
Nozzle (6) 3.30 23.29 -19.99 (8) 3.04 0.00 3.04
STRESSES RESULTING FOR THE OUTER SURFACE:
σr (Mpa) σθ (Mpa)
Load Part Equation Equation
Membrane Bending Total Membrane Bending Total
Vessel (1) 1.91 12.02 13.93 (2) 3.49 7.16 10.64
Fr
Nozzle (5) 1.69 25.11 26.80 (7) 3.49 0.00 3.49
Vessel (3) 1.31 12.97 14.28 (4) 1.84 8.74 10.58
Mc
Nozzle (6) 3.30 36.13 39.44 (8) 1.84 0.00 1.84
Vessel (3) 0.86 8.40 9.26 (4) 3.04 5.29 8.34
ML
Nozzle (6) 3.30 23.29 26.60 (8) 3.04 0.00 3.04
CHECK OF SHELL AT JUNCTION WITH NOZZLE OR CHECK OF SHELL WITH PAD AT JUNCTION WITH NOZZLE:
CIRCUMFERENTIAL STRESSES:
0 90 180 270
Stress due to:
Inside Outside Inside Outside Inside Outside Inside Outside
Fr 3.49 3.49 3.49 3.49 3.49 3.49 3.49 3.49
Membrane
Mc 1.84 1.84 -1.84 -1.84
σθ
Ml -3.04 -3.04 3.04 3.04
Primary membrane σθ = 0.44 0.44 5.33 5.33 6.53 6.53 1.65 1.65
From pressure: σθ,p = 30.00 30.00 30.00 30.00 30.00 30.00 30.00 30.00
σpθ,m = σθ + σθ,p = 30.44 30.44 35.33 35.33 36.53 36.53 31.65 31.65
Fr -7.16 7.16 -7.16 7.16 -7.16 7.16 -7.16 7.16
Bending σθ Mc -8.74 8.74 8.74 -8.74
Ml 5.29 -5.29 -5.29 5.29
Local bending σθ,b = -1.86 1.86 -15.89 15.89 -12.45 12.45 1.58 -1.58
Total σθ,m = σpθ,m + σθ,b 28.58 32.30 19.44 51.22 24.08 48.98 33.23 30.07
LONGITUDINAL STRESSES:
0 90 180 270
Stress due to:
Inside Outside Inside Outside Inside Outside Inside Outside
Fr 1.91 1.91 1.91 1.91 1.91 1.91 1.91 1.91
Membrane σr Mc 1.31 1.31 -1.31 -1.31
Ml -0.86 -0.86 0.86 0.86
Primary membrane σr = 1.05 1.05 3.23 3.23 2.77 2.77 0.60 0.60
From pressure: σr,p = 15.00 15.00 15.00 15.00 15.00 15.00 15.00 15.00
σpr,m = σr + σr,p = 16.05 16.05 18.23 18.23 17.77 17.77 15.60 15.60
Fr -12.02 12.02 -12.02 12.02 -12.02 12.02 -12.02 12.02
Bending σr Mc -12.97 12.97 12.97 -12.97
Ml 8.40 -8.40 -8.40 8.40
Local bending σr,b = -3.61 3.61 -24.99 24.99 -20.42 20.42 0.96 -0.96
Total σr,m = σpr,m + σr,b 12.44 19.66 -6.76 43.21 -2.65 38.19 16.56 14.64
SHEAR STRESSES:
0 90 180 270
Stress due to:
Inside Outside Inside Outside Inside Outside Inside Outside
Mt 0.83 0.83 0.83 0.83 0.83 0.83 0.83 0.83
Shear τ Fc 1.69 1.69 -1.69 -1.69
Fl -1.69 -1.69 1.69 1.69
Total shear τ = 2.51 2.51 -0.86 -0.86 -0.86 -0.86 2.51 2.51
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CLASSIC WRC & AS PER BS5500
MAXIMUM STRESS INTENSITY
Max Stress intensity formula 28.96 32.78 19.47 51.31 24.11 49.05 33.60 30.46
Max Stress intensity formula 12.06 19.18 6.79 43.12 2.67 38.12 16.19 14.25
Max Stress intensity formula 16.90 13.60 26.26 8.19 26.78 10.92 17.41 16.22
Maximum stress intensity: 28.96 32.78 26.26 51.31 26.78 49.05 33.60 30.46
Max stress intensity: 51.31 Check < 3f or 2.25 f for PD5500
BUCKLING STRESS (PD5500 ONLY)
Buckling stress σbkθ = σθ + 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
Buckling stress σbkr = σr + σ 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
Max buckling: 0.00 Check < - 0.9 yield (only PD5500)
BUCKLING STRESS INTENSITY (WRC297 ONLY)
Max Stress intensity formula 1.86 3.61 15.89 24.99 12.45 20.42 1.58 0.96
Max Stress intensity formula 3.61 1.86 24.99 15.89 20.42 12.45 0.96 1.58
Max Stress intensity formula 1.75 1.75 9.10 9.10 7.97 7.97 0.62 0.62
Maximum stress intensity: 3.61 3.61 24.99 24.99 20.42 20.42 1.58 1.58
Max buckling: 24.99 Check < 3f
MEMBRANE STRESS INTENSITY
Membrane stress intensity 1 30.87 30.87 35.37 35.37 36.57 36.57 32.03 32.03
Membrane stress intensity 2 15.63 15.63 18.18 18.18 17.73 17.73 15.22 15.22
Membrane stress intensity 3 15.24 15.24 17.19 17.19 18.84 18.84 16.81 16.81
Maximum stress intensity: 30.87 30.87 35.37 35.37 36.57 36.57 32.03 32.03
Max stress intensity: 36.57 Check < 1.5f (NO CHECK IN PD5500)
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FOR ASME VIII DIV.1 & DIV.2:
Circumferential Pm = σθ,p 30.00 30.00 30.00 30.00 30.00 30.00 30.00 30.00
Circumferential Pl = σθ 0.44 0.44 5.33 5.33 6.53 6.53 1.65 1.65
Circumferential Q = σθ,b -1.86 1.86 -15.89 15.89 -12.45 12.45 1.58 -1.58
Longitudinal Pm = σr,p 15.00 15.00 15.00 15.00 15.00 15.00 15.00 15.00
Longitudinal Pl = σr 1.05 1.05 3.23 3.23 2.77 2.77 0.60 0.60
Longitudinal Q = σr,b -3.61 3.61 -24.99 24.99 -20.42 20.42 0.96 -0.96
Shear Pl = τ(Fc) + τ(Fl) 1.69 1.69 -1.69 -1.69 -1.69 -1.69 1.69 1.69
Shear Q = τ(Mt) 0.83 0.83 0.83 0.83 0.83 0.83 0.83 0.83
PRIMARY GENERAL MEMBRANE STRESS INTENSITY (Pm)
Membrane stress intensity 1 30.00 30.00 30.00 30.00 30.00 30.00 30.00 30.00
Membrane stress intensity 2 15.00 15.00 15.00 15.00 15.00 15.00 15.00 15.00
Membrane stress intensity 3 15.00 15.00 15.00 15.00 15.00 15.00 15.00 15.00
Max Pm = 30.00 30.00 30.00 30.00 30.00 30.00 30.00 30.00
PRIMARY GENERAL MEMBRANE + PRIMARY LOCAL STRESS INTENSITY (Pm + Pl)
Membrane stress intensity 1 30.64 30.64 35.49 35.49 36.68 36.68 31.82 31.82
Membrane stress intensity 2 15.86 15.86 18.06 18.06 17.62 17.62 15.42 15.42
Membrane stress intensity 3 14.78 14.78 17.43 17.43 19.06 19.06 16.40 16.40
Max Pm + Pl 30.64 30.64 35.49 35.49 36.68 36.68 31.82 31.82
PRIMARY GENERAL MEMBRANE + PRIMARY LOCAL STRESS INTENSITY (Pm + Pl) + SECONDARY MEMBRANE AND BENDING (Q)
Membrane stress intensity 1 28.96 32.78 19.47 51.31 24.11 49.05 33.60 30.46
Membrane stress intensity 2 12.06 19.18 6.79 43.12 2.67 38.12 16.19 14.25
Membrane stress intensity 3 16.90 13.60 26.26 8.19 26.78 10.92 17.41 16.22
Max Pm + Pl + Q 28.96 32.78 26.26 51.31 26.78 49.05 33.60 30.46
Max Pm 30.00 < S,all Max Pm + Pl 36.68 < 1.5 S,all Max Pm + Pl + Q 51.31 < 3 S,all
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CHECK OF NOZZLE AT JUNCTION:
CIRCUMFERENTIAL STRESSES:
0 90 180 270
Stress due to:
Inside Outside Inside Outside Inside Outside Inside Outside
Fr 3.49 3.49 3.49 3.49 3.49 3.49 3.49 3.49
Membrane
Mc 1.84 1.84 -1.84 -1.84
σθ
Ml -3.04 -3.04 3.04 3.04
Primary membrane σθ = 0.44 0.44 5.33 5.33 6.53 6.53 1.65 1.65
From pressure: σθ,p = 8.50 8.50 8.50 8.50 8.50 8.50 8.50 8.50
σpθ,m = σθ + σθ,p = 8.94 8.94 13.83 13.83 15.03 15.03 10.15 10.15
Fr 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
Bending σθ Mc 0.00 0.00 0.00 0.00
Ml 0.00 0.00 0.00 0.00
Local bending σθ,b = 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
Total σθ,m = σpθ,m + σθ,b 8.94 8.94 13.83 13.83 15.03 15.03 10.15 10.15
LONGITUDINAL STRESSES:
0 90 180 270
Stress due to:
Inside Outside Inside Outside Inside Outside Inside Outside
Fr 1.69 1.69 1.69 1.69 1.69 1.69 1.69 1.69
Membrane σr Mc 3.30 3.30 -3.30 -3.30
Ml -3.30 -3.30 3.30 3.30
Primary membrane σr = -1.62 -1.62 4.99 4.99 4.99 4.99 -1.62 -1.62
From pressure: σr,p = 4.25 4.25 4.25 4.25 4.25 4.25 4.25 4.25
σpr,m = σr + σr,p = 2.63 2.63 9.24 9.24 9.24 9.24 2.63 2.63
Fr -25.11 25.11 -25.11 25.11 -25.11 25.11 -25.11 25.11
Bending σr Mc -36.13 36.13 36.13 -36.13
Ml 23.29 -23.29 -23.29 23.29
Local bending σr,b = -1.82 1.82 -61.24 61.24 -48.40 48.40 11.02 -11.02
Total σr,m = σpr,m + σr,b 0.82 4.45 -52.00 70.48 -39.16 57.64 13.65 -8.39
SHEAR STRESSES:
0 90 180 270
Stress due to:
Inside Outside Inside Outside Inside Outside Inside Outside
Mt 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65
Shear τ Fc 3.37 3.37 -3.37 -3.37
Fl -3.37 -3.37 3.37 3.37
Total shear τ = 5.02 5.02 -1.72 -1.72 -1.72 -1.72 5.02 5.02
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CLASSIC WRC & AS PER BS5500
MAXIMUM STRESS INTENSITY
Max Stress intensity formula 11.34 12.20 13.87 70.53 15.09 57.71 17.22 11.42
Max Stress intensity formula 1.58 1.19 52.05 13.78 39.22 14.96 6.58 9.66
Max Stress intensity formula 12.92 11.01 65.92 56.76 54.31 42.75 10.64 21.08
Maximum stress intensity: 12.92 12.20 65.92 70.53 54.31 57.71 17.22 21.08
Max stress intensity: 70.53 Check < 3f or 2.25 f , where f = nozzle allowable stress !!!
BUCKLING STRESS (PD5500 ONLY)
Buckling stress σbkθ = σθ + 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
Buckling stress σbkr = σr + σ -3.43 0.20 0.00 0.00 0.00 0.00 9.40 -12.64
Max buckling: -12.64 Check < - 0.9 yield (only PD5500) , check with nozzle yield
BUCKLING STRESS INTENSITY (WRC297 ONLY)
Max Stress intensity formula 0.00 1.82 0.00 61.24 0.00 48.40 11.02 0.00
Max Stress intensity formula 1.82 0.00 61.24 0.00 48.40 0.00 0.00 11.02
Max Stress intensity formula 1.82 1.82 61.24 61.24 48.40 48.40 11.02 11.02
Maximum stress intensity: 1.82 1.82 61.24 61.24 48.40 48.40 11.02 11.02
Max buckling: 61.24 Check < 3f , check with nozzle allowable stress
MEMBRANE STRESS INTENSITY
Membrane stress intensity 1 11.72 11.72 14.40 14.40 15.50 15.50 12.66 12.66
Membrane stress intensity 2 0.14 0.14 8.67 8.67 8.77 8.77 0.12 0.12
Membrane stress intensity 3 11.86 11.86 5.73 5.73 6.73 6.73 12.54 12.54
Maximum stress intensity: 11.86 11.86 14.40 14.40 15.50 15.50 12.66 12.66
Max stress intensity: 15.50 Check < 1.5f (NO CHECK IN PD5500)
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FOR ASME VIII DIV.1 & DIV.2:
Circumferential Pm = σθ,p 8.50 8.50 8.50 8.50 8.50 8.50 8.50 8.50
Circumferential Pl = σθ 0.44 0.44 5.33 5.33 6.53 6.53 1.65 1.65
Circumferential Q = σθ,b 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
Longitudinal Pm = σr,p 4.25 4.25 4.25 4.25 4.25 4.25 4.25 4.25
Longitudinal Pl = σr -1.62 -1.62 4.99 4.99 4.99 4.99 -1.62 -1.62
Longitudinal Q = σr,b -1.82 1.82 -61.24 61.24 -48.40 48.40 11.02 -11.02
Shear Pl = τ(Fc) + τ(Fl) 3.37 3.37 -3.37 -3.37 -3.37 -3.37 3.37 3.37
Shear Q = τ(Mt) 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65
PRIMARY GENERAL MEMBRANE STRESS INTENSITY (Pm)
Membrane stress intensity 1 8.50 8.50 8.50 8.50 8.50 8.50 8.50 8.50
Membrane stress intensity 2 4.25 4.25 4.25 4.25 4.25 4.25 4.25 4.25
Membrane stress intensity 3 4.25 4.25 4.25 4.25 4.25 4.25 4.25 4.25
Max Pm = 8.50 8.50 8.50 8.50 8.50 8.50 8.50 8.50
PRIMARY GENERAL MEMBRANE + PRIMARY LOCAL STRESS INTENSITY (Pm + Pl)
Membrane stress intensity 1 10.40 10.40 15.61 15.61 16.58 16.58 11.44 11.44
Membrane stress intensity 2 1.17 1.17 7.46 7.46 7.69 7.69 1.34 1.34
Membrane stress intensity 3 9.23 9.23 8.16 8.16 8.89 8.89 10.09 10.09
Max Pm + Pl 10.40 10.40 15.61 15.61 16.58 16.58 11.44 11.44
PRIMARY GENERAL MEMBRANE + PRIMARY LOCAL STRESS INTENSITY (Pm + Pl) + SECONDARY MEMBRANE AND BENDING (Q)
Membrane stress intensity 1 11.34 12.20 13.87 70.53 15.09 57.71 17.22 11.42
Membrane stress intensity 2 1.58 1.19 52.05 13.78 39.22 14.96 6.58 9.66
Membrane stress intensity 3 12.92 11.01 65.92 56.76 54.31 42.75 10.64 21.08
Max Pm + Pl + Q 12.92 12.20 65.92 70.53 54.31 57.71 17.22 21.08
Max Pm 8.50 < S,all Max Pm + Pl 16.58 < 1.5 S,all Max Pm + Pl + Q 70.53 < 3 S,all
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