wrc 107 for vertical internal clip
DESCRIPTION
wrcTRANSCRIPT
Do not print this sheet, it contains only information as how to design elements of pressure vessel
INPUTS INPUT CELLS (UNLOCKED)
CALCULATIONS BY PROGRAM
FORMULAE, NOTATION
RESULTS
STEPS
1 Select "0 deg." sheet first. All other sheets will be changed by program
2 Input values in pink cells ----->
3 Results are shown at "Conclusion" Sheet
4 Reference of the calculations in this workbook is Pressure Vessel Manual by Moss
Select "0 deg." sheet first. All other sheets will be changed by program
Pressure Vessel Manual by Moss
3 of 25
Vessel Number: D412 At 0 degree
NotationRadial load lbinternal design pressure P psi
external longitudinal moment in-lbs
external circumferential moment in-lbsExternal torsional moment in-lbs
Internal Longitudinal moment in-lbs/in
Internal Circumferential Moment in-lbs/in
Longitudinal Shear force lbs
Cicumferential Shear Force lbsRadius of Fillet Weld r in
Mean Radius of Shell in
stress concentration factors
Co-efficients to determine β for rectangular attachments
Longitudinal Membrane Force in Shell lbs/in
Circumferential Membrace Force in Shell lbs/in
Torsional Shear Stress psi
Direct Shear Stress psi
Longitudinal normal stress psi
Circumferential Normal Stress psi
Multiplication Factors for Rectangular Attachments
One-Half Circumferential width of rectangular attachment in
One-Half Longitudinal width of rectangular attachment in
Thickness of Attachment h in
Equivalent Thickness of Shell & re-pad in
Thickness of re-pad in
Thickness of Shell t in
Leg of Fillet Weld w in
Ratios Based on Vessel & Attachment geometry
STRESSES IN CYLINDERICAL SHELL ON INTERNAL SUPPORTING CLIP (Vertical)
Pr
ML
Mc
MT
MX
Mø
VL
Vc
Rm
Kn, Kb
Kc, KL, K1, K2
Nx
Nø
τT
τS
σx
σø
CC , CL
C1
C2
te
tp
γ, β, β1, β2
Fig. Dimensions for clips
4 of 25
Inputinternal design pressure P 25 psiThickness of Shell t 0.55 inLeg of Fillet Weld w 0.315 in
Radius of Fillet Weld r 0.2 in
Load (on each plate) Pr 4400 lbs
Impact Factor I 1.2
Radial load (I x Pr) I x Pr 5280 lbinternal design pressure P 25 psiThickness of Attachment h 0.63 in
Mean Radius of Shell 84.2 in
One-Half Circumferential width of rectangular attachment h+2w+2t 2.36 in
One-Half Longitudinal width of rectangular attachment 2.76 inTwice the ratio Fillet Weld radius to Thickness of attachment 2r / h 2r / h 0.63
Membrane Stress concentration factor 1.65 From Fig. 5-20
Bending Stress concentration factor 1.40 From Fig. 5-20
Ratios Based on Vessel & Attachment geometry γ 153.09
Ratios Based on Vessel & Attachment geometry 0.03
Ratios Based on Vessel & Attachment geometry 0.03
Longitudinal Shear force, 5280.00 lbs
Circumferential Shear Force 264.00 lbs
c 0.86
External Longitudinal Moment 19430.40 in-lbs
External Circumferential Moment 16614.40 in-lbs
For Radial Load
β
0.91 1.48 1.003
1.68 1.20 1.001
1.76 0.88 0.999
1.2 1.25 1.001
β For Longitudinal Moment
β
β
β
0.89 0.031
0.92 0.031
0.98 0.030
1.05 0.033
β for Circumferential Momentβ
β
β
0.97 0.030
0.94 0.030
1.07 0.032
1.1 0.032
From graph 5-22 through 5-27 finding dimensionless membrane forces & bending moment
Radial Load (Input)from figure 5-22A 12
Pr
Rm
C1
C2
Kn
Kb
Rm / t
β1 C1/Rm
β2 C2/Rm
VL
VC
Ratio of β1 & β2 β1 / β2
ML 4C2Pr / 3
MC 4C1Pr / 3
From Table we compute values of β, selecting value of K1 & K2
If β1 / β2 < 1, then , [1-4/3 (1-c)(1-K2)]√(β1β2)
K1 K2 βNø
Nx
Mø
MX
From Table 5.9 Selecting value of CL & KL & compute value of β
For Nx and Nø3√(β1β2
2)
For Mø KL 3√(β1β2
2)
For Mx KL 3√(β1β2
2)
CL KL βNø
Nx
Mø
MX
For Nx and Nø3√(β1
2β2)
For Mø Kc 3√(β1
2β2)
For Mx Kc 3√(β1
2β2)
CC KC βNø
Nx
Mø
MX
NøRm/Pr
5 of 25
from figure 5-22B 15
from figure 5-23A 0.1
from figure 5-23B 0.061
Longitudinal Moment (Input)from figure 5-24A 5
from figure 5-24B 1.5
from figure 5-25A 0.06
from figure 5-25B 0.1
Circumferential Moment (Input)from figure 5-26A 1.5
from figure 5-26B 1.7
from figure 5-27A 0.11
from figure 5-27B 0.062.
Radial Load (Results)
membrane forces on the basis of figure 5-22A 752.49 lb/in
membrane forces on the basis of figure 5-22B 940.62 lb/in
membrane Stress on the basis of figure 5-22A 2257.48 psi
membrane forces on the basis of figure 5-22B 2821.85 psi
bending moment on the basis of figure 5-23A 528.00 in-lbs/in
bending moment on the basis of figure 5-23B 322.08 in-lbs/in
bending moment on the basis of figure 5-23A 14661.82 psi
bending moment on the basis of figure 5-23B 8943.71 psi
Longitudinal Moments (Results)
membrane forces on the basis of figure 5-24A 392.00 lb/in
membrane forces on the basis of figure 5-24B 121.56 lb/in
membrane Stress on the basis of figure 5-24A 15.00 psi
membrane forces on the basis of figure 5-24B 364.69 psi
bending moment on the basis of figure 5-25A 454.11 in-lbs/in
bending moment on the basis of figure 5-25B 706.40 in-lbs/in
bending moment on the basis of figure 5-25A 12610.07 psi
bending moment on the basis of figure 5-25B 19615.66 psi
Circumferential Moments (Results)
membrane forces on the basis of figure 5-26A 115.47 lb/in
membrane forces on the basis of figure 5-26B 126.82 lb/in
membrane Stress on the basis of figure 5-26A 346.40 psi
membrane forces on the basis of figure 5-26B 380.45 psi
bending moment on the basis of figure 5-27A 686.94 in-lbs/in
bending moment on the basis of figure 5-27B 376.62 in-lbs/in
bending moment on the basis of figure 5-27A 19075.23 psi
bending moment on the basis of figure 5-27B 10458.27 psi
Shear Stress Longitudinal
NxRm/Pr
Mø/Pr
Mx/Pr
NøRm2β / ML
NxRm2β / ML
MøRmβ / ML
MxRmβ / ML
NøRm2β / Mc
NxRm2β / Mc
MøRmβ / Mc
MxRmβ / Mc
Nø (NøRm/Pr) x Pr/Rm
Nx (NxRm/Pr) x Pr/Rm
σø KnNø / t
σx KnNx / t
Mø (Mø/Pr) x Pr
Mx (Mx/Pr) x Pr
σø 6KbMø / t2
σx 6KbMx / t2
Nø (NøRm2β / ML) x CLML / Rm
2β
Nx (NxRm2β / ML) x CLML / Rm
2β
σø KnNø / t
σx KnNx / t
Mø (MøRmβ / ML) x ML / Rmβ
Mx (MxRmβ / ML) x ML / Rmβ
σø 6KbMø / t2
σx 6KbMx / t2
Nø (NøRm2β / Mc) x CCMC / Rm
2β
Nx (NxRm2β / Mc) x CCMC / Rm
2β
σø KnNø / t
σx KnNx / t
Mø (MøRmβ / Mc) x Mc Rmβ
Mx (MxRmβ / Mc) x Mc Rmβ
σø 6KbMø / t2
σx 6KbMx / t2
6 of 25
Shear Stress, Longitudinal 1016.95 psi
Shear Stress Circumferential
Shear Stress, Circumferential 43.48 psi
τs τs= VL / 4C1t
τc τc= Vc / 4C2t
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8 of 25
From Fig. 5-20
From Fig. 5-20
9 of 25
At 90 degree
NotationRadial load lbinternal design pressure P psi
external longitudinal moment in-lbs
external circumferential moment in-lbsExternal torsional moment in-lbs
Internal Longitudinal moment in-lbs/in
Internal Circumferential Moment in-lbs/in
Longitudinal Shear force lbs
Cicumferential Shear Force lbsRadius of Fillet Weld r in
Mean Radius of Shell in
stress concentration factors
Co-efficients to determine β for rectangular attachments
Longitudinal Membrane Force in Shell lbs/in
Circumferential Membrace Force in Shell lbs/in
Torsional Shear Stress psi
Direct Shear Stress psi
Longitudinal normal stress psi
Circumferential Normal Stress psi
Multiplication Factors for Rectangular Attachments
One-Half Circumferential width of rectangular attachment in
One-Half Longitudinal width of rectangular attachment in
Thickness of Attachment h in
Equivalent Thickness of Shell & re-pad in
Thickness of re-pad in
Thickness of Shell t in
Leg of Fillet Weld w in
Ratios Based on Vessel & Attachment geometry
Inputinternal design pressure P 25 psi
Thickness of Shell t 0.55 in
Leg of Fillet Weld w 0.315 inRadius of Fillet Weld r 0.2 inLoad Pr 220 lbsImpact Factor I 1.2
Radial load (I x Pr) I x Pr 264 lbinternal design pressure P 25 psi
Thickness of Attachment h 0.63 in
Mean Radius of Shell 84.2 in
One-Half Circumferential width of rectangular attachment h+2w+2t 2.36 in
One-Half Longitudinal width of rectangular attachment 2.76 in
Twice the ratio Fillet Weld radius to Thickness of attachment 2r / h 2r / h 0.63
Membrane Stress concentration factor 1.65 From Fig. 5-20
Bending Stress concentration factor 1.40 From Fig. 5-20
Ratios Based on Vessel & Attachment geometry γ 153.09
Ratios Based on Vessel & Attachment geometry 0.03
Ratios Based on Vessel & Attachment geometry 0.03
Longitudinal Shear force, 264.00 lbs
Circumferential Shear Force 13.20 lbs
0.86
External Longitudinal Moment 971.52 in-lbs
External Circumferential Moment 830.72 in-lbs
For Radial Load
STRESSES IN CYLINDERICAL SHELLON INTERNAL SUPPORTING CLIPS
Pr
ML
Mc
MT
MX
Mø
VL
Vc
Rm
Kn, Kb
Kc, KL, K1, K2
Nx
Nø
τT
τS
σx
σø
CC , CL
C1
C2
te
tp
γ, β, β1, β2
Pr
Rm
C1
C2
Kn
Kb
Rm / t
β1 C1/Rm
β2 C2/Rm
VL
VC
Ratio of β1 & β2 β1 / β2 β1 / β2
ML 4C2Pr / 3
MC 4C1Pr / 4
10 of 25
0.91 1.48 1.0031.68 1.2 1.0011.76 0.88 0.9991.2 1.25 1.001
β For Longitudinal Moment
β
β
β
0.89 0.031
0.92 0.031
0.98 0.030
1.05 0.033
β for Circumferential Momentβ
β
β
0.97 0.030
0.94 0.030
1.07 0.032
1.1 0.032
From graph 5-22 through 5-27 finding dimensionless membrane forces & bending moment
Radial Load (Input)from figure 5-22A 12
from figure 5-22B 15
from figure 5-23A 0.1
from figure 5-23B 0.061
Longitudinal Moment (Input)from figure 5-24A 5
from figure 5-24B 1.5
from figure 5-25A 0.06
from figure 5-25B 0.1
Circumferential Moment (Input)from figure 5-26A 1.5
from figure 5-26B 1.7
from figure 5-27A 0.11
from figure 5-27B 0.062.
Radial Load (Results)
membrane forces on the basis of figure 5-22A 37.62 lb/in
membrane forces on the basis of figure 5-22B 47.03 lb/in
membrane Stress on the basis of figure 5-22A 112.87 psi
membrane forces on the basis of figure 5-22B 141.09 psi
bending moment on the basis of figure 5-23A 26.40 in-lbs/in
bending moment on the basis of figure 5-23B 16.10 in-lbs/in
From Table we compute values of β, selecting value of K1 & K2
If β1 / β2 < 1, then , β [1-4/3 (1-c)(1-K2)]√(β1β2)
K1 K2 βNø
Nx
Mø
MX
From Table 5.9 Selecting value of CL & KL & compute value of β
For Nx and Nø3√(β1β2
2)
For Mø KL 3√(β1β2
2)
For Mx KL 3√(β1β2
2)
CL KL βNø
Nx
Mø
MX
For Nx and Nø3√(β1
2β2)
For Mø Kc 3√(β1
2β2)
For Mx Kc 3√(β1
2β2)
CC KC βNø
Nx
Mø
MX
NøRm/Pr
NxRm/Pr
Mø/Pr
Mx/Pr
NøRm2β / ML
NxRm2β / ML
MøRmβ / ML
MxRmβ / ML
NøRm2β / Mc
NxRm2β / Mc
MøRmβ / Mc
MxRmβ / Mc
Nø (NøRm/Pr) x Pr/Rm
Nx (NxRm/Pr) x Pr/Rm
σø KnNø / t
σx KnNx / t
Mø (Mø/Pr) x Pr
Mx (Mx/Pr) x Pr
11 of 25
bending moment on the basis of figure 5-23A 733.09 psi
bending moment on the basis of figure 5-23B 447.19 psi
Longitudinal Moments (Results)
membrane forces on the basis of figure 5-24A 19.60 lb/in
membrane forces on the basis of figure 5-24B 6.08 lb/in
membrane Stress on the basis of figure 5-24A 15.00 psi
membrane forces on the basis of figure 5-24B 18.23 psi
bending moment on the basis of figure 5-25A 22.71 in-lbs/in
bending moment on the basis of figure 5-25B 35.32 in-lbs/in
bending moment on the basis of figure 5-25A 630.50 psi
bending moment on the basis of figure 5-25B 980.78 psi
Circumferential Moments (Results)
membrane forces on the basis of figure 5-26A 5.77 lb/in
membrane forces on the basis of figure 5-26B 6.34 lb/in
membrane Stress on the basis of figure 5-26A 17.32 psi
membrane forces on the basis of figure 5-26B 19.02 psi
bending moment on the basis of figure 5-27A 34.35 in-lbs/in
bending moment on the basis of figure 5-27B 18.83 in-lbs/in
bending moment on the basis of figure 5-27A 953.76 psi
bending moment on the basis of figure 5-27B 522.91 psi
Shear Stress Longitudinal
Shear Stress, Longitudinal 50.85 psi
Shear Stress Circumferential
Shear Stress, Circumferential 2.17 psi
σø 6KbMø / t2
σx 6KbMx / t2
Nø (NøRm2β / ML) x CLML / Rm
2β
Nx (NxRm2β / ML) x CLML / Rm
2β
σø KnNø / t
σx KnNx / t
Mø (MøRmβ / ML) x ML / Rmβ
Mx (MxRmβ / ML) x ML / Rmβ
σø 6KbMø / t2
σx 6KbMx / t2
Nø (NøRm2β / Mc) x CCMC / Rm
2β
Nx (NxRm2β / Mc) x CCMC / Rm
2β
σø KnNø / t
σx KnNx / t
Mø (MøRmβ / Mc) x Mc Rmβ
Mx (MxRmβ / Mc) x Mc Rmβ
σø 6KbMø / t2
σx 6KbMx / t2
τs τs= VL / 4C1t
τc τc= Vc / 4C2t
12 of 25
At 180 degree
NotationRadial load lbinternal design pressure P psi
external longitudinal moment in-lbs
external circumferential moment in-lbsExternal torsional moment in-lbs
Internal Longitudinal moment in-lbs/in
Internal Circumferential Moment in-lbs/in
Longitudinal Shear force lbs
Cicumferential Shear Force lbsRadius of Fillet Weld r in
Mean Radius of Shell in
stress concentration factors
Co-efficients to determine β for rectangular attachments
Longitudinal Membrane Force in Shell lbs/in
Circumferential Membrace Force in Shell lbs/in
Torsional Shear Stress psi
Direct Shear Stress psi
Longitudinal normal stress psi
Circumferential Normal Stress psi
Multiplication Factors for Rectangular Attachments
One-Half Circumferential width of rectangular attachment in
One-Half Longitudinal width of rectangular attachment in
Thickness of Attachment h in
Equivalent Thickness of Shell & re-pad in
Thickness of re-pad in
Thickness of Shell t in
Leg of Fillet Weld w in
Ratios Based on Vessel & Attachment geometry
Inputinternal design pressure P 25 psi
Thickness of Shell t 0.55 in
Leg of Fillet Weld w 0.315 in
Radius of Fillet Weld r 0.2 in
Load (on each plate) Pr 4400 lbs
Impact Factor I 1.2
Radial load (I x Pr) I x Pr 5280 lbinternal design pressure P 25 psi
Thickness of Attachment h 0.63 in
Mean Radius of Shell 84.2 in
One-Half Circumferential width of rectangular attachment h+2w+2t 2.36 in
One-Half Longitudinal width of rectangular attachment 2.76 in
Twice the ratio Fillet Weld radius to Thickness of attachment 2r / h 2r / h 0.634921
Membrane Stress concentration factor 1.65 From Fig. 5-20
Bending Stress concentration factor 1.4 From Fig. 5-20
Ratios Based on Vessel & Attachment geometry γ 153.0909
Ratios Based on Vessel & Attachment geometry 0.028029
Ratios Based on Vessel & Attachment geometry 0.032779
Longitudinal Shear force, 5280 lbs
Circumferential Shear Force 264 lbs
c 0.855072
External Longitudinal Moment 19430.4 in-lbs
External Circumferential Moment 16614.4 in-lbs
STRESSES IN CYLINDERICAL SHELL ON INTERNAL SUPPORTING CLIPS
Pr
ML
Mc
MT
MX
Mø
VL
Vc
Rm
Kn, Kb
Kc, KL, K1, K2
Nx
Nø
τT
τS
σx
σø
CC , CL
C1
C2
te
tp
γ, β, β1, β2
Pr
Rm
C1
C2
Kn
Kb
Rm / t
β1 C1/Rm
β2 C2/Rm
VL
VC
Ratio of β1 & β2 β1 / β2
ML 4C2Pr / 3
MC 4C1Pr / 4
13 of 25
For Radial Load
0.91 1.48 1.0031.68 1.2 1.0011.76 0.88 0.9991.2 1.25 1.001
β For Longitudinal Moment
β
β
β
0.89 0.031
0.92 0.031
0.98 0.030
1.05 0.033
β for Circumferential Momentβ
β
β
0.97 0.030
0.94 0.030
1.07 0.032
1.1 0.032
From graph 5-22 through 5-27 finding dimensionless membrane forces & bending moment
Radial Load (Input)from figure 5-22A 12
from figure 5-22B 15
from figure 5-23A 0.1
from figure 5-23B 0.061
Longitudinal Moment (Input)from figure 5-24A 5
from figure 5-24B 1.5
from figure 5-25A 0.06
from figure 5-25B 0.1
Circumferential Moment (Input)from figure 5-26A 1.5
from figure 5-26B 1.7
from figure 5-27A 0.11
from figure 5-27B 0.062.
Radial Load (Results)
membrane forces on the basis of figure 5-22A 752.49 lb/in
membrane forces on the basis of figure 5-22B 940.62 lb/in
membrane Stress on the basis of figure 5-22A 2257.48 psi
membrane forces on the basis of figure 5-22B 2821.85 psi
bending moment on the basis of figure 5-23A 528.00 in-lbs/in
From Table we compute values of β, selecting value of K1 & K2
If β1 / β2 < 1, then , β [1-4/3 (1-c)(1-K2)]√(β1β2)
K1 K2 βNø
Nx
Mø
MX
From Table 5.9 Selecting value of CL & KL & compute value of β
For Nx and Nø3√(β1β2
2)
For Mø KL 3√(β1β2
2)
For Mx KL 3√(β1β2
2)
CL KL βNø
Nx
Mø
MX
For Nx and Nø3√(β1
2β2)
For Mø Kc 3√(β1
2β2)
For Mx Kc 3√(β1
2β2)
CC KC βNø
Nx
Mø
MX
NøRm/Pr
NxRm/Pr
Mø/Pr
Mx/Pr
NøRm2β / ML
NxRm2β / ML
MøRmβ / ML
MxRmβ / ML
NøRm2β / Mc
NxRm2β / Mc
MøRmβ / Mc
MxRmβ / Mc
Nø (NøRm/Pr) x Pr/Rm
Nx (NxRm/Pr) x Pr/Rm
σø KnNø / t
σx KnNx / t
Mø (Mø/Pr) x Pr
14 of 25
bending moment on the basis of figure 5-23B 322.08 in-lbs/in
bending moment on the basis of figure 5-23A 14661.82 psi
bending moment on the basis of figure 5-23B 8943.71 psi
Longitudinal Moments (Results)
membrane forces on the basis of figure 5-24A 392.00 lb/in
membrane forces on the basis of figure 5-24B 121.56 lb/in
membrane Stress on the basis of figure 5-24A 15.00 psi
membrane forces on the basis of figure 5-24B 364.69 psi
bending moment on the basis of figure 5-25A 454.11 in-lbs/in
bending moment on the basis of figure 5-25B 706.40 in-lbs/in
bending moment on the basis of figure 5-25A 12610.07 psi
bending moment on the basis of figure 5-25B 19615.66 psi
Circumferential Moments (Results)
membrane forces on the basis of figure 5-26A 115.47 lb/in
membrane forces on the basis of figure 5-26B 126.82 lb/in
membrane Stress on the basis of figure 5-26A 346.40 psi
membrane forces on the basis of figure 5-26B 380.45 psi
bending moment on the basis of figure 5-27A 686.94 in-lbs/in
bending moment on the basis of figure 5-27B 376.62 in-lbs/in
bending moment on the basis of figure 5-27A 19075.23 psi
bending moment on the basis of figure 5-27B 10458.27 psi
Shear Stress Longitudinal
Shear Stress, Longitudinal 1016.95 psi
Shear Stress Circumferential
Shear Stress, Circumferential 43.48 psi
Mx (Mx/Pr) x Pr
σø 6KbMø / t2
σx 6KbMx / t2
Nø (NøRm2β / ML) x CLML / Rm
2β
Nx (NxRm2β / ML) x CLML / Rm
2β
σø KnNø / t
σx KnNx / t
Mø (MøRmβ / ML) x ML / Rmβ
Mx (MxRmβ / ML) x ML / Rmβ
σø 6KbMø / t2
σx 6KbMx / t2
Nø (NøRm2β / Mc) x CCMC / Rm
2β
Nx (NxRm2β / Mc) x CCMC / Rm
2β
σø KnNø / t
σx KnNx / t
Mø (MøRmβ / Mc) x Mc Rmβ
Mx (MxRmβ / Mc) x Mc Rmβ
σø 6KbMø / t2
σx 6KbMx / t2
τs τs= VL / 4C1t
τc τc= Vc / 4C2t
15 of 25
At 270 degree
NotationRadial load lbinternal design pressure P psi
external longitudinal moment in-lbs
external circumferential moment in-lbsExternal torsional moment in-lbs
Internal Longitudinal moment in-lbs/in
Internal Circumferential Moment in-lbs/in
Longitudinal Shear force lbs
Cicumferential Shear Force lbsRadius of Fillet Weld r in
Mean Radius of Shell in
stress concentration factors
Co-efficients to determine β for rectangular attachments
Longitudinal Membrane Force in Shell lbs/in
Circumferential Membrace Force in Shell lbs/in
Torsional Shear Stress psi
Direct Shear Stress psi
Longitudinal normal stress psi
Circumferential Normal Stress psi
Multiplication Factors for Rectangular Attachments
One-Half Circumferential width of rectangular attachment in
One-Half Longitudinal width of rectangular attachment in
Thickness of Attachment h in
Equivalent Thickness of Shell & re-pad in
Thickness of re-pad in
Thickness of Shell t in
Leg of Fillet Weld w in
Ratios Based on Vessel & Attachment geometry
Inputinternal design pressure P 25 psi
Thickness of Shell t 0.55 in
Leg of Fillet Weld w 0.315 inRadius of Fillet Weld r 0.2 inLoad Pr 220 lbsImpact Factor I 1.2
Radial load (I x Pr) I x Pr 264 lbinternal design pressure P 25 psi
Thickness of Attachment h 0.63 in
Mean Radius of Shell 84.2 in
One-Half Circumferential width of rectangular attachment h+2w+2t 2.36 in
One-Half Longitudinal width of rectangular attachment 2.76 in
Twice the ratio Fillet Weld radius to Thickness of attachment 2r / h 2r / h 0.63
Membrane Stress concentration factor 1.65 From Fig. 5-20
Bending Stress concentration factor 1.40 From Fig. 5-20
Ratios Based on Vessel & Attachment geometry γ 153.09
Ratios Based on Vessel & Attachment geometry 0.03
Ratios Based on Vessel & Attachment geometry 0.03
Longitudinal Shear force, 264.00 lbs
Circumferential Shear Force 13.20 lbs
0.86
External Longitudinal Moment 971.52 in-lbs
External Circumferential Moment 830.72 in-lbs
For Radial Load
STRESSES IN CYLINDERICAL SHELL ON INTERNAL SUPPORTING CLIPS
Pr
ML
Mc
MT
MX
Mø
VL
Vc
Rm
Kn, Kb
Kc, KL, K1, K2
Nx
Nø
τT
τS
σx
σø
CC , CL
C1
C2
te
tp
γ, β, β1, β2
Pr
Rm
C1
C2
Kn
Kb
Rm / t
β1 C1/Rm
β2 C2/Rm
VL
VC
Ratio of β1 & β2 β1 / β2 β1 / β2
ML 4C2Pr / 3
MC 4C1Pr / 4
From Table we compute values of β, selecting value of K1 & K2
If β1 / β2 < 1, then , β [1-4/3 (1-c)(1-K2)]√(β1β2)
16 of 25
0.91 1.48 1.0031.68 1.2 1.0011.76 0.88 0.9991.2 1.25 1.001
β For Longitudinal Moment
β
β
β
0.89 0.031
0.92 0.031
0.98 0.030
1.05 0.033
β for Circumferential Momentβ
β
β
0.97 0.030
0.94 0.030
1.07 0.032
1.1 0.032
From graph 5-22 through 5-27 finding dimensionless membrane forces & bending moment
Radial Load (Input)from figure 5-22A 12
from figure 5-22B 15
from figure 5-23A 0.1
from figure 5-23B 0.061
Longitudinal Moment (Input)from figure 5-24A 5
from figure 5-24B 1.5
from figure 5-25A 0.06
from figure 5-25B 0.1
Circumferential Moment (Input)from figure 5-26A 1.5
from figure 5-26B 1.7
from figure 5-27A 0.11
from figure 5-27B 0.062.
Radial Load (Results)
membrane forces on the basis of figure 5-22A 37.62 lb/in
membrane forces on the basis of figure 5-22B 47.03 lb/in
membrane Stress on the basis of figure 5-22A 112.87 psi
membrane forces on the basis of figure 5-22B 141.09 psi
bending moment on the basis of figure 5-23A 26.40 in-lbs/in
bending moment on the basis of figure 5-23B 16.10 in-lbs/in
bending moment on the basis of figure 5-23A 733.09 psi
bending moment on the basis of figure 5-23B 447.19 psi
Longitudinal Moments (Results)
membrane forces on the basis of figure 5-24A 19.60 lb/in
K1 K2 βNø
Nx
Mø
MX
From Table 5.9 Selecting value of CL & KL & compute value of β
For Nx and Nø3√(β1β2
2)
For Mø KL 3√(β1β2
2)
For Mx KL 3√(β1β2
2)
CL KL βNø
Nx
Mø
MX
For Nx and Nø3√(β1
2β2)
For Mø Kc 3√(β1
2β2)
For Mx Kc 3√(β1
2β2)
CC KC βNø
Nx
Mø
MX
NøRm/Pr
NxRm/Pr
Mø/Pr
Mx/Pr
NøRm2β / ML
NxRm2β / ML
MøRmβ / ML
MxRmβ / ML
NøRm2β / Mc
NxRm2β / Mc
MøRmβ / Mc
MxRmβ / Mc
Nø (NøRm/Pr) x Pr/Rm
Nx (NxRm/Pr) x Pr/Rm
σø KnNø / t
σx KnNx / t
Mø (Mø/Pr) x Pr
Mx (Mx/Pr) x Pr
σø 6KbMø / t2
σx 6KbMx / t2
Nø (NøRm2β / ML) x CLML / Rm
2β
17 of 25
membrane forces on the basis of figure 5-24B 6.08 lb/in
membrane Stress on the basis of figure 5-24A 15.00 psi
membrane forces on the basis of figure 5-24B 18.23 psi
bending moment on the basis of figure 5-25A 22.71 in-lbs/in
bending moment on the basis of figure 5-25B 35.32 in-lbs/in
bending moment on the basis of figure 5-25A 630.50 psi
bending moment on the basis of figure 5-25B 980.78 psi
Circumferential Moments (Results)
membrane forces on the basis of figure 5-26A 5.77 lb/in
membrane forces on the basis of figure 5-26B 6.34 lb/in
membrane Stress on the basis of figure 5-26A 17.32 psi
membrane forces on the basis of figure 5-26B 19.02 psi
bending moment on the basis of figure 5-27A 34.35 in-lbs/in
bending moment on the basis of figure 5-27B 18.83 in-lbs/in
bending moment on the basis of figure 5-27A 953.76 psi
bending moment on the basis of figure 5-27B 522.91 psi
Shear Stress Longitudinal
Shear Stress, Longitudinal 50.85 psi
Shear Stress Circumferential
Shear Stress, Circumferential 2.17 psi
Nx (NxRm2β / ML) x CLML / Rm
2β
σø KnNø / t
σx KnNx / t
Mø (MøRmβ / ML) x ML / Rmβ
Mx (MxRmβ / ML) x ML / Rmβ
σø 6KbMø / t2
σx 6KbMx / t2
Nø (NøRm2β / Mc) x CCMC / Rm
2β
Nx (NxRm2β / Mc) x CCMC / Rm
2β
σø KnNø / t
σx KnNx / t
Mø (MøRmβ / Mc) x Mc Rmβ
Mx (MxRmβ / Mc) x Mc Rmβ
σø 6KbMø / t2
σx 6KbMx / t2
τs τs= VL / 4C1t
τc τc= Vc / 4C2t
Combined Stress TableNote = See Sheets: 0, 90, 180, 270
Stress Due to 0 deg 90 deg 180 deg 270 deg 0 deg 90 deg 180 deg 270 deg
Membrane752.49 37.62 752.49 37.62
940.62 47.03 940.62 47.03
Bending528.00 26.40 528.00 26.40
322.08 16.10 322.08 16.10
Membrane392.00 392.00
121.56 121.56
Bending454.11 454.11
706.40 706.40
Membrane5.77 5.77
6.34 6.34
Bending34.35 34.35
18.83 18.83
Internal Pressure, P
3827.27 3827.27 3827.27 3827.27
1913.64 1913.64 1913.64 1913.64
∑ 4004 2002 4004 2002 5954 3931 5954 3931
σx σø
Radial Load, P ( Sign is (+) for out ward
load & (-) for inward load
NøNxMø
Mx
Longitudinal Moment, ML
NøNxMø
Mx
Circumferential Moment, Mc
NøNxMø
Mx
σø = PRm / t =
σx = PRm / 2t =
Conclusion
Material = SA-516 Gr. 70Shel YP. at room Temp. = 38000 PsiShell YP at 650 F = 26700 PsiShell's allowable Strength = 16020 Psi
Maximum induced Stress = 5954 Psi Maximum of combined stresses(From combined stress table)
Allowable stress = 48060 Psi 3 times shells's allowable
Total Stresses < 3 x Allowable Strength
Design is = SAFE
β
β
NøR
m/P
rN
xRm/P
r
Fig. 5-20 Stress Concentration factor (Ref. Pressure Vessel Manual by Moss)
Fig. 5-22: Membrane force on a cylinder due to radial load on attachment.
β
β
Mø/P
rM
x/P
r
Fig. 5-22: Membrane force on a cylinder due to radial load on attachment.
Fig. 5-23: Bending Moment in a Cylinder due to a radial load on attachment.
β
NøR
m2 β
/ M
LN
xRm
2 β /
ML
β
β
MøR
mβ
/ M
LM
xRmβ
/ M
L
Fig. 5-24: Membrane Force in a cylinder due to radial load on attachment
β
β
NøR
m2 β
/ M
cN
xRm
2 β /
Mc
Fig. 5-25: Bending Moment ina cylinder due to longitudian moment on attachment.
β
β
β
MøR
mβ
/ M
cM
xRmβ
/ M
cFigure: 5-26 Membrane force in a cylinder due to circumferential moment on attachment.
Fig.5-27: Bending Moment in a cylinder due to circumferential moment on attachment.