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
Sele Se lect ct "0 "0 deg. deg." " shee sheett fir first. st. All ot other her sh sheet eets s will will be cha chang nged ed by pr
2
Input values in pink cel ellls -------->
3
Res esul ults ts
4
Reference of the calculations in this workbook is P r es es s u r e V es es s e
are ar e sh show own n at "C "Con oncl clus usio ion" n" Sh Shee eett
gram
l Manual by Moss
3 of 22
STRESSES IN CYLINDERICAL SHELL ON INTERNAL SUPPORTING CLIP (Vertical)
Vessel Number: D412
At 0 degree
Fig. Dimensions for clips
Notation Radial load internal design pressure external longitudinal moment
Pr P ML
lb psi in-lbs in-lbs in-lbs
Internal Longitudinal moment
Mc MT MX
Internal Circumferential Moment
Mø
in-lbs/in
Longitudinal Shear force
VL
lbs
Cicumferential Shear Force Radius of Fillet Weld
Vc
lbs in
external circumferential moment External torsional moment
Mean Radius of Shell stress concentration factors
Co-efficients to determine β for rect angular attachments
r Rm
in-lbs/in
in
Kn, Kb Kc, KL, K1, K2
Longitudinal Membrane Force in Shell
Nx
lbs/in
Circumferential Membrace Force in Shell
Nø
lbs/in
Torsional Shear Stress
τT
psi
Direct Shear Stress
τS
psi
Longitudinal normal stress
σx
psi
Circumferential Normal Stress
σø
psi
Multiplication Factors for Rectangular Attachments
CC , CL
One-Half Circumferential width of rectangular attachment
C1
in
One-Half Longitudinal width of rectangular attachment
C2
in
Thickness of Attachment
h
in
Equivalent Thickness of Shell & re-pad
te
in
Thickness of re-pad
tp
in
Thickness of Shell
t
in
w
in
Leg of Fillet Weld Ratios Based on Vessel & Attachment geometry
Input
γ, β, β1, β2
4 of 22 internal design pressure Thickness of Shell Leg of Fillet Weld
P
25 psi 0.55 in 0.315 in
t w
Radius of Fillet Weld
r
0.2 in
Load (on each plate)
Pr
4400 lbs
I
Impact Factor Radial load (I x Pr) internal design pressure Thickness of Attachment
Pr
Mean Radius of Shell One-Half Circumferential width of rectangular attachment
Rm
1.2 I x Pr
P h
C1
h+2w+2t
84.2 in 2.36 in
2r / h
2.76 in 0.63
C2
One-Half Longitudinal width of rectangular attachment Twice the ratio Fillet Weld radius to Thickness of attachment
2r / h
Membrane Stress concentration factor
Kn
Bending Stress concentration factor Ratios Based on Vessel & Attachment geometry
Kb
Ratios Based on Vessel & Attachment geometry
γ β1 β2
Longitudinal Shear force,
VL
Circumferential Shear Force
VC
Ratios Based on Vessel & Attachment geometry
Ratio of β 1 & β2
52 80 l b 25 psi 0.63 in
1.65 From Fig. 5-20 Rm / t C1/Rm C2/Rm
1.40 From Fig. 5-20 153.09 0.03 0.03 5280.00 lbs 264.00 lbs
c
β1 / β2
External Longitudinal Moment
ML
4C2Pr / 3
19430.40 in-lbs
External Circumferential Moment
MC
4C1Pr / 3
16614.40 in-lbs
β
[1-4/3 (1-c)(1-K 2)]√(β1β2)
0.86
For Radial Load From Table we compute values of β, selecting value of K 1 & K2 If β1 / β2 < 1, then ,
K1 Nø
0.91 1.68 1.76 1.2
Nx Mø MX
β
K2 1.48
1.003
1.20
1.001
0.88
0.999
1.25
1.001
β For Longitudinal Moment From Table 5.9 Selecting value of C L & KL & compute value of β For Nx and Nø For Mø For Mx
β β β
3
√(β1β22) (β1β2 ) KL (β1β2 ) KL CL
β
KL
0.89 0.92
Nø Nx
0.031 0.031
0.98 1.05
Mø MX
0.030 0.033
β for Circumferential Moment For Nx and Nø For Mø For Mx
β β β
3
√(β12β2) Kc (β1 β2) Kc (β1 β2) CC
Nø Nx
β
KC
0.97 0.94
Mø MX
0.030 0.030
1.07 1.1
From graph 5-22 through 5-27 finding dimensionless membrane forces & bending moment Radial Load (Input) from figure 5-22A
NøRm/Pr
from figure 5-22B
NxRm/Pr
15
from figure 5-23A
Mø/Pr
0.1
from figure 5-23B
Mx/Pr
0.061
12
0.032 0.032
5 of 22
Longitudinal Moment (Input) 2
NøRm β / ML
from figure 5-24A
5
2
from figure 5-25A
NxRm β / ML MøRmβ / ML
0.06
from figure 5-25B
MxRm β / ML
0.1
from figure 5-24B
1.5
Circumferential Moment (Input) 2
from figure 5-26A
NøRm β / Mc
from figure 5-26B from figure 5-27A
NxRm β / Mc MøRmβ / Mc
0.11
from figure 5-27B
MxRmβ / Mc
0.062
1.5
2
1.7
.
Radial Load (Results) membrane forces on the basis of figure 5-22A
Nø
(NøRm /Pr) x Pr /Rm
752.49 lb/in
membrane forces on the basis of figure 5-22B
Nx
(NxRm /Pr) x Pr /Rm
940.62 lb/in
membrane Stress on the basis of figure 5-22A
σø
K n Nø / t
2257.48 psi
membrane forces on the basis of figure 5-22B
σx
K n Nx / t
2821.85 psi
bending moment on the basis of figure 5-23A
Mø
(Mø/Pr ) x Pr
528.00 in-lbs/in
bending moment on the basis of figure 5-23B
Mx
(Mx/Pr ) x Pr
322.08 in-lbs/in
bending moment on the basis of figure 5-23A
σø
bending moment on the basis of figure 5-23B
2
6K bMø / t
14661.82 psi
2
6K bMx / t
σx
8943.71 psi
Longitudinal Moments (Results) 2
2
2
2
membrane forces on the basis of figure 5-24A
Nø
(NøRm β / ML) x CLML / Rm β
membrane forces on the basis of figure 5-24B
Nx
(NxRm β / ML) x CLML / Rm β
121.56 lb/in
membrane Stress on the basis of figure 5-24A
σø
K n Nø / t
15.00 psi
membrane forces on the basis of figure 5-24B
σx
K n Nx / t
364.69 psi
bending moment on the basis of figure 5-25A
Mø
(MøRm β / ML) x ML / Rmβ
454.11 in-lbs/in
bending moment on the basis of figure 5-25B
Mx
(MxRmβ / ML) x ML / Rmβ
706.40 in-lbs/in
bending moment on the basis of figure 5-25A
σø
bending moment on the basis of figure 5-25B
σx
2
6K bM / t
392.00 lb/in
12610.07 psi
2
6K bMx / t
19615.66 psi
Circumferential Moments (Results) 2
2
2
2
(NøRm β / Mc) x CCMC / Rm β
membrane forces on the basis of figure 5-26A
Nø
membrane forces on the basis of figure 5-26B
Nx
(NxRm β / Mc) x CCMC / Rm β
membrane Stress on the basis of figure 5-26A
σø
K n Nø / t
346.40 psi
membrane forces on the basis of figure 5-26B
σx
K n Nx / t
380.45 psi
bending moment on the basis of figure 5-27A
Mø
(MøRmβ / Mc) x Mc Rmβ
686.94 in-lbs/in
bending moment on the basis of figure 5-27B
Mx
(MxRmβ / Mc) x Mc Rmβ
376.62 in-lbs/in
bending moment on the basis of figure 5-27A
σø
bending moment on the basis of figure 5-27B
σx
2
6K bMø / t
2
6K bMx / t
115.47 lb/in 126.82 lb/in
19075.23 psi 10458.27 psi
Shear Stress Longitudinal Shear Stress, Longitudinal
τs
τs= VL / 4C1t
1016.95 psi
τc
τc= Vc / 4C2t
43.48 psi
Shear Stress Circumferential Shear Stress, Circumferential
6 of 22
STRESSES IN CYLINDERICAL SHELL ON INTERNAL SUPPORTING CLIPS At 90 degree
Notation Pr P ML
lb psi in-lbs in-lbs
Internal Longitudinal moment
Mc MT MX
Internal Circumferential Moment
Mø
in-lbs/in
Longitudinal Shear force
VL
lbs
Cicumferential Shear Force Radius of Fillet Weld
Vc r Rm
lbs in
Radial load internal design pressure external longitudinal moment external circumferential moment External torsional moment
Mean Radius of Shell stress concentration factors
Co-efficients to determine β for rectangular attachments
in-lbs
in-lbs/in
in
Kn, Kb Kc, KL, K1, K2
Longitudinal Membrane Force in Shell
Nx
lbs/in
Circumferential Membrace Force in Shell
Nø
lbs/in
Torsional Shear Stress
τT
psi
Direct Shear Stress
τS
psi
Longitudinal normal stress
σx
psi
Circumferential Normal Stress
σø
psi
Multiplication Factors for Rectangular Attachments
CC , CL
One-Half Circumferential width of rectangular attachment
C1
in
One-Half Longitudinal width of rectangular attachment
C2
in
Thickness of Attachment
h
in
Equivalent Thickness of Shell & re-pad
te
in
Thickness of re-pad
tp
in
Thickness of Shell
t
in
w
in
Leg of Fillet Weld Ratios Based on Vessel & Attachment geometry
γ, β, β1, β2
Input internal design pressure
P
Thickness of Shell
t
0.55 in
Leg of Fillet Weld Radius of Fillet Weld Load Impact Factor
w
0.315 in 0.2 in 220 lbs 1.2
Radial load (I x Pr) internal design pressure Thickness of Attachment
r Pr I Pr P Rm
One-Half Longitudinal width of rectangular attachment
C2
C1 2r / h
Membrane Stress concentration factor
Kn
Bending Stress concentration factor
Kb
Ratios Based on Vessel & Attachment geometry
γ β1 β2
Ratios Based on Vessel & Attachment geometry Ratios Based on Vessel & Attachment geometry Longitudinal Shear force, Circumferential Shear Force
I x Pr
h
Mean Radius of Shell One-Half Circumferential width of rectangular attachment Twice the ratio Fillet Weld radius to Thickness of attachment
25 psi
264 lb 25 psi 0.63 in
h+2w+2t
84.2 in 2.36 in 2.76 in
2r / h
0.63 1.65 From Fig. 5-20 1.40 From Fig. 5-20
Rm / t
153.09
C1/Rm
0.03
C2/Rm
0.03
VL VC
264.00 lbs 13.20 lbs
β1 / β2
β1 / β2
External Longitudinal Moment
ML
4C2Pr / 3
971.52 in-lbs
External Circumferential Moment
MC
4C1Pr / 4
830.72 in-lbs
Ratio of β1 & β2
For Radial Load
From Table we compute values of β, selecting value of K 1 & K2
0.86
7 of 22
If β1 / β2 < 1, then ,
β
[1-4/3 (1-c)(1-K 2)]√(β1β2) K1
K2
Nø
0.91 1.68 1.76 1.2
1.48 1.2 0.88 1.25
β 1.003 1.001 0.999 1.001
KL
β
Nx Mø MX
β For Longitudinal Moment From Table 5.9 Selecting value of C L & KL & compute value of β For Nx and Nø For Mø For Mx
β β β
3
(β1β22) (β1β2 ) KL (β1β2 ) KL
Nø
0.89 0.92
CL Nx
0.031 0.031
0.98 1.05
Mø MX
0.030 0.033
β for Circumferential Moment For Nx and Nø For Mø For Mx
β β β
3
(β12β2) Kc (β1 β2) Kc (β1 β2) CC
Nø Nx
β
KC
0.97 0.94
0.030 0.030
1.07 1.1
Mø MX
0.032 0.032
From graph 5-22 through 5-27 finding dimensionless membrane forces & bending moment Radial Load (Input) from figure 5-22A
NøRm/Pr
from figure 5-22B
NxRm/Pr
15
from figure 5-23A
Mø/Pr
0.1
from figure 5-23B
Mx/Pr
0.061
12
Longitudinal Moment (Input) 2
NøRm β / ML
from figure 5-24A
5
2
from figure 5-25A
NxRm β / ML MøRmβ / ML
0.06
from figure 5-25B
MxRmβ / ML
0.1
from figure 5-24B
1.5
Circumferential Moment (Input) 2
from figure 5-26A
NøRm β / Mc
from figure 5-26B
NxRm β / Mc MøRmβ / Mc
0.11
MxRmβ / Mc
0.062
1.5
2
from figure 5-27A from figure 5-27B
1.7
.
Radial Load (Results) membrane forces on the basis of figure 5-22A
Nø
(NøRm /Pr) x Pr /Rm
37.62 lb/in
membrane forces on the basis of figure 5-22B
Nx
(NxRm /Pr) x Pr /Rm
47.03 lb/in
membrane Stress on the basis of figure 5-22A
σø
K n Nø / t
112.87 psi
membrane forces on the basis of figure 5-22B
σx
K n Nx / t
141.09 psi
bending moment on the basis of figure 5-23A
Mø
(Mø/Pr ) x Pr
26.40 in-lbs/in
bending moment on the basis of figure 5-23B
Mx
(Mx/Pr ) x Pr
16.10 in-lbs/in
bending moment on the basis of figure 5-23A
σø
2
6K bMø / t
733.09 psi
8 of 22
bending moment on the basis of figure 5-23B
2
6K bMx / t
σx
447.19 psi
Longitudinal Moments (Results) membrane forces on the basis of figure 5-24A
Nø
(NøRm2β / ML) x CLML / Rm2β
membrane forces on the basis of figure 5-24B
Nx
(NxRm β / ML) x CLML / Rm β
membrane Stress on the basis of figure 5-24A
σø
K n Nø / t
15.00 psi
membrane forces on the basis of figure 5-24B
σx
K n Nx / t
18.23 psi
bending moment on the basis of figure 5-25A
Mø
(MøRmβ / ML) x ML / Rmβ
22.71 in-lbs/in
bending moment on the basis of figure 5-25B
Mx
(MxRmβ / ML) x ML / Rmβ
35.32 in-lbs/in
bending moment on the basis of figure 5-25A
σø
bending moment on the basis of figure 5-25B
2
2
2
6K bMø / t
6.08 lb/in
630.50 psi
2
6K bMx / t
σx
19.60 lb/in
980.78 psi
Circumferential Moments (Results) 2
2
2
2
membrane forces on the basis of figure 5-26A
Nø
(NøRm β / Mc) x CCMC / Rm β
membrane forces on the basis of figure 5-26B
Nx
(NxRm β / Mc) x CCMC / Rm β
membrane Stress on the basis of figure 5-26A
σø
K n Nø / t
17.32 psi
membrane forces on the basis of figure 5-26B
σx
K n Nx / t
19.02 psi
bending moment on the basis of figure 5-27A
Mø
(MøRmβ / Mc) x Mc Rmβ
34.35 in-lbs/in
bending moment on the basis of figure 5-27B
Mx
(MxRmβ / Mc) x Mc Rmβ
18.83 in-lbs/in
bending moment on the basis of figure 5-27A
σø
bending moment on the basis of figure 5-27B
σx
2
6K bMø / t
2
6K bMx / t
5.77 lb/in 6.34 lb/in
953.76 psi 522.91 psi
Shear Stress Longitudinal Shear Stress, Longitudinal
τs
τs= VL / 4C1t
50.85 psi
τc
τc= Vc / 4C2t
2.17 psi
Shear Stress Circumferential Shear Stress, Circumferential
9 of 22
STRESSES IN CYLINDERICAL SHELL ON INTERNAL SUPPORTING CLIPS At 180 degree
Notation Pr P ML
lb psi in-lbs in-lbs
Internal Longitudinal moment
Mc MT MX
Internal Circumferential Moment
Mø
in-lbs/in
Longitudinal Shear force
VL
lbs
Cicumferential Shear Force Radius of Fillet Weld
Vc r Rm
lbs in
Radial load internal design pressure external longitudinal moment external circumferential moment External torsional moment
Mean Radius of Shell stress concentration factors
Co-efficients to determine β for rectangular attachments
in-lbs
in-lbs/in
in
Kn, Kb Kc, KL, K1, K2
Longitudinal Membrane Force in Shell
Nx
lbs/in
Circumferential Membrace Force in Shell
Nø
lbs/in
Torsional Shear Stress
τT
psi
Direct Shear Stress
τS
psi
Longitudinal normal stress
σx
psi
σø
psi
Circumferential Normal Stress Multiplication Factors for Rectangular Attachments
CC , CL
One-Half Circumferential width of rectangular attachment
C1
in
One-Half Longitudinal width of rectangular attachment
C2
in
Thickness of Attachment
h
in
Equivalent Thickness of Shell & re-pad
te
in
Thickness of re-pad
tp
in
Thickness of Shell
t
in
Leg of Fillet Weld
w
in
Ratios Based on Vessel & Attachment geometry
γ, β, β 1, β2
Input internal design pressure
P
Thickness of Shell
t
Leg of Fillet Weld
w
Radius of Fillet Weld
r
0.2 in
Load (on each plate)
Pr
4400 lbs
Impact Factor Radial load (I x Pr) internal design pressure Thickness of Attachment Mean Radius of Shell One-Half Circumferential width of rectangular attachment One-Half Longitudinal width of rectangular attachment Twice the ratio Fillet Weld radius to Thickness of attachment
h C1
Bending Stress concentration factor Ratios Based on Vessel & Attachment geometry
γ β1 β2
Circumferential Shear Force
5280 lb 25 psi 0.63 in
h+2w+2t
C2 2r / h
Kn
Longitudinal Shear force,
1.2 I x Pr
Rm
Kb
Ratios Based on Vessel & Attachment geometry
0.315 in
I Pr P
Membrane Stress concentration factor
Ratios Based on Vessel & Attachment geometry
25 psi 0.55 in
84.2 in 2.36 in 2.76 in
2r / h
0.634921 1.65 From Fig. 5-20 1.4 From Fig. 5-20
Rm / t
153.0909
C1/Rm
0.028029
C2/Rm
0.032779
VL VC
5280 lbs 264 lbs
c
β1 / β2
External Longitudinal Moment
ML
4C2Pr / 3
19430.4 in-lbs
External Circumferential Moment
MC
4C1Pr / 4
16614.4 in-lbs
Ratio of β 1 & β2
For Radial Load
0.855072
10 of 22
From Table we compute values of β, selecting value of K 1 & K2
β
If β1 / β2 < 1, then ,
[1-4/3 (1-c)(1-K 2)]√(β1β2)
Nø Nx Mø MX
K1
K2
0.91 1.68 1.76 1.2
1.48 1.2 0.88 1.25
β 1.003 1.001 0.999 1.001
KL
β
β For Longitudinal Moment From Table 5.9 Selecting value of C L & KL & compute value of β For Nx and Nø For Mø For Mx
β β β
(β1β2 ) (β1β2 ) (β1β2 ) KL KL
CL
0.89 0.92
Nø Nx
0.031 0.031
0.98 1.05
Mø MX
0.030 0.033
β for Circumferential Moment For Nx and Nø For Mø For Mx
β β β
(β1 β2) (β1 β2) Kc (β1 β2) Kc
CC Nø Nx
β
KC
0.97 0.94
0.030 0.030
1.07 1.1
Mø MX
0.032 0.032
From graph 5-22 through 5-27 finding dimensionless membrane forces & bending moment Radial Load (Input) from figure 5-22A
NøRm/Pr
from figure 5-22B
NxRm /Pr
15
from figure 5-23A
Mø/Pr
0.1
from figure 5-23B
Mx/Pr
0.061
12
Longitudinal Moment (Input) 2
NøRm β / ML
from figure 5-24A
5
2
from figure 5-25A
NxRm β / ML MøRmβ / ML
0.06
from figure 5-25B
MxRmβ / ML
0.1
from figure 5-24B
1.5
Circumferential Moment (Input) 2
NøRm β / Mc
from figure 5-26A
1.5
2
from figure 5-26B from figure 5-27A from figure 5-27B
NxRm β / Mc MøRmβ / Mc
0.11
MxRmβ / Mc
0.062
1.7
.
Radial Load (Results) membrane forces on the basis of figure 5-22A
Nø
(NøRm/Pr) x Pr /Rm
752.49 lb/in
membrane forces on the basis of figure 5-22B
Nx
(NxRm/Pr) x Pr /Rm
940.62 lb/in
membrane Stress on the basis of figure 5-22A
σø
K n Nø / t
2257.48 psi
membrane forces on the basis of figure 5-22B
σx
K n Nx / t
2821.85 psi
bending moment on the basis of figure 5-23A
Mø
(Mø/Pr ) x Pr
528.00 in-lbs/in
bending moment on the basis of figure 5-23B
Mx
(Mx/Pr ) x Pr
322.08 in-lbs/in
11 of 22
2
bending moment on the basis of figure 5-23A
σø
6K bMø / t
bending moment on the basis of figure 5-23B
σx
6K bMx / t
14661.82 psi
2
8943.71 psi
Longitudinal Moments (Results) membrane forces on the basis of figure 5-24A
Nø
(NøRm2β / ML) x CLML / Rm2β
membrane forces on the basis of figure 5-24B
Nx
(NxRm β / ML) x CLML / Rm β
121.56 lb/in
membrane Stress on the basis of figure 5-24A
σø
K n Nø / t
15.00 psi
membrane forces on the basis of figure 5-24B
σx
K n Nx / t
364.69 psi
bending moment on the basis of figure 5-25A
Mø
(MøRmβ / ML) x ML / Rmβ
454.11 in-lbs/in
bending moment on the basis of figure 5-25B
Mx
(MxRmβ / ML) x ML / Rmβ
706.40 in-lbs/in
bending moment on the basis of figure 5-25A
σø
bending moment on the basis of figure 5-25B
σx
2
2
2
6K bM / t
392.00 lb/in
12610.07 psi
2
6K bMx / t
19615.66 psi
Circumferential Moments (Results) membrane forces on the basis of figure 5-26A
Nø
(NøRm2β / Mc) x CCMC / Rm2β 2
2
115.47 lb/in
membrane forces on the basis of figure 5-26B
Nx
(NxRm β / Mc) x CCMC / Rm β
126.82 lb/in
membrane Stress on the basis of figure 5-26A
σø
K n Nø / t
346.40 psi
membrane forces on the basis of figure 5-26B
σx
K n Nx / t
380.45 psi
bending moment on the basis of figure 5-27A
Mø
(MøRmβ / Mc) x Mc Rmβ
686.94 in-lbs/in
bending moment on the basis of figure 5-27B
Mx
(MxRmβ / Mc) x Mc Rmβ
376.62 in-lbs/in
bending moment on the basis of figure 5-27A
σø
6K bMø / t
bending moment on the basis of figure 5-27B
σx
6K bMx / t
2 2
19075.23 psi 10458.27 psi
Shear Stress Longitudinal Shear Stress, Longitudinal
τs
τs= VL / 4C1t
1016.95 psi
τc
τc= Vc / 4C2t
43.48 psi
Shear Stress Circumferential Shear Stress, Circumferential
12 of 22
STRESSES IN CYLINDERICAL SHELL ON INTERNAL SUPPORTING CLIPS At 270 degree
Notation Radial load internal design pressure external longitudinal moment
Pr
lb psi
P ML
in-lbs in-lbs in-lbs
Internal Longitudinal moment
Mc MT MX
Internal Circumferential Moment
Mø
in-lbs/in
Longitudinal Shear force
VL
lbs
Cicumferential Shear Force Radius of Fillet Weld
Vc
lbs in
external circumferential moment External torsional moment
Mean Radius of Shell stress concentration factors
Co-efficients to determine β for rectangular attachments
in-lbs/in
r Rm
in
Kn, Kb K c , K L, K 1, K 2
Longitudinal Membrane Force in Shell
Nx
lbs/in
Circumferential Membrace Force in Shell
Nø
lbs/in
Torsional Shear Stress
τT
psi
Direct Shear Stress
τS
psi
Longitudinal normal stress
σx
psi
σø
psi
Circumferential Normal Stress Multiplication Factors for Rectangular Attachments
C C , CL
One-Half Circumferential width of rectangular attachment
C1
in
One-Half Longitudinal width of rectangular attachment
C2
in
Thickness of Attachment
h
in
Equivalent Thickness of Shell & re-pad
te
in
Thickness of re-pad
tp
in
Thickness of Shell
t
in
w
in
Leg of Fillet Weld Ratios Based on Vessel & Attachment geometry
γ, β, β 1, β2
Input internal design pressure
P
Thickness of Shell
t
0.55 in
Leg of Fillet Weld Radius of Fillet Weld Load Impact Factor
w
0.315 in 0.2 in 220 lbs 1.2
Radial load (I x Pr) internal design pressure Thickness of Attachment
r Pr I Pr
I x Pr
P h
Mean Radius of Shell
Rm
One-Half Circumferential width of rectangular attachment
C1
One-Half Longitudinal width of rectangular attachment
C2
Twice the ratio Fillet Weld radius to Thickness of attachment
25 psi
2r / h
264 lb 25 psi 0.63 in 84.2 in
h+2w+2t
2.36 in 2.76 in
2r / h
0.63
Membrane Stress concentration factor
Kn
1.65 From Fig. 5-20
Bending Stress concentration factor
Kb
1.40 From Fig. 5-20
Ratios Based on Vessel & Attachment geometry
γ β1 β2
Ratios Based on Vessel & Attachment geometry Ratios Based on Vessel & Attachment geometry Longitudinal Shear force, Circumferential Shear Force
Rm / t
153.09
C1/Rm
0.03
C2/Rm
0.03
VL VC
264.00 lbs 13.20 lbs
β1 / β2
β1 / β2
External Longitudinal Moment
ML
4C2Pr / 3
971.52 in-lbs
External Circumferential Moment
MC
4C1Pr / 4
830.72 in-lbs
β
[1-4/3 (1-c)(1-K 2)]√(β1β2)
Ratio of β1 & β2
For Radial Load
From Table we compute values of β, selecting value of K 1 & K2 If β1 / β2 < 1, then ,
0.86
13 of 22
K1
K2
MX
0.91 1.68 1.76 1.2
1.48 1.2 0.88 1.25
β 1.003 1.001 0.999 1.001
β β β
(β1β2 ) (β1β2 ) KL (β1β2 ) KL KL
β
Nø Nx Mø
β For Longitudinal Moment From Table 5.9 Selecting value of C L & KL & compute value of β For Nx and Nø For Mø For Mx
CL
0.89 0.92
Nø Nx
0.031 0.031
0.98 1.05
Mø MX
0.030 0.033
β for Circumferential Moment For Nx and Nø For Mø For Mx
β β β
3
√(β12β2) 3 2 Kc √(β1 β2) 3 2 Kc √(β1 β2)
Nø
0.97 0.94
CC Nx
β
KC
0.030 0.030
1.07 1.1
Mø MX
0.032 0.032
From graph 5-22 through 5-27 finding dimensionless membrane forces & bending moment Radial Load (Input) from figure 5-22A
NøRm/Pr
12
from figure 5-22B
NxRm/Pr
15
from figure 5-23A
Mø/Pr
0.1
from figure 5-23B
Mx/Pr
0.061
Longitudinal Moment (Input) 2
from figure 5-24A
NøRm β / ML
from figure 5-24B
2
5
from figure 5-25A
NxRm β / ML MøRmβ / ML
0.06
from figure 5-25B
MxRmβ / ML
0.1
1.5
Circumferential Moment (Input) 2
NøRm β / Mc
from figure 5-26A
1.5
2
from figure 5-26B from figure 5-27A from figure 5-27B
NxRm β / Mc MøRmβ / Mc
0.11
MxRmβ / Mc
0.062
1.7
.
Radial Load (Results) membrane forces on the basis of figure 5-22A
Nø
(NøRm/Pr) x Pr /Rm
37.62 lb/in
membrane forces on the basis of figure 5-22B
Nx
(NxRm/Pr) x Pr /Rm
47.03 lb/in
membrane Stress on the basis of fi gure 5-22A
σø
K n Nø / t
112.87 psi
membrane forces on the basis of figure 5-22B
σx
K n Nx / t
141.09 psi
bending moment on the basis of figure 5-23A
Mø
(Mø/Pr ) x Pr
26.40 in-lbs/in
bending moment on the basis of figure 5-23B
Mx
(Mx/Pr ) x Pr
16.10 in-lbs/in
bending moment on the basis of figure 5-23A
σø
bending moment on the basis of figure 5-23B
σx
6K bMø / t 6K bMx / t
2
733.09 psi
2
447.19 psi
Longitudinal Moments (Results) 2
2
2
2
membrane forces on the basis of figure 5-24A
Nø
(NøRm β / ML) x CLML / Rm β
membrane forces on the basis of figure 5-24B
Nx
(NxRm β / ML) x CLML / Rm β
19.60 lb/in 6.08 lb/in
14 of 22 membrane Stress on the basis of figure 5-24A
σø
K n Nø / t
15.00 psi
membrane forces on the basis of figure 5-24B
σx
K n Nx / t
18.23 psi
bending moment on the basis of figure 5-25A
Mø
(MøRmβ / ML) x M L / Rmβ
22.71 in-lbs/in
bending moment on the basis of figure 5-25B
Mx
(MxRmβ / ML) x M L / Rmβ
35.32 in-lbs/in
bending moment on the basis of figure 5-25A
σø
6K bMø / t
bending moment on the basis of figure 5-25B
σx
6K bMx / t
2
630.50 psi
2
980.78 psi
Circumferential Moments (Results) Nø
(NøRm β / Mc) x CCMC / Rm β
2
2
5.77 lb/in
membrane forces on the basis of figure 5-26B
Nx
2 (NxRm
2
6.34 lb/in
membrane Stress on the basis of figure 5-26A
σø
K n Nø / t
17.32 psi
membrane forces on the basis of figure 5-26B
σx
K n Nx / t
19.02 psi
bending moment on the basis of figure 5-27A
Mø
(MøRmβ / Mc) x M c Rmβ
34.35 in-lbs/in
bending moment on the basis of figure 5-27B
Mx
(MxRmβ / Mc) x M c Rmβ
18.83 in-lbs/in
bending moment on the basis of figure 5-27A
σø
bending moment on the basis of figure 5-27B
σx
membrane forces on the basis of figure 5-26A
β / Mc) x CCMC / Rm β
6K bMø / t 6K bMx / t
2 2
953.76 psi 522.91 psi
Shear Stress Longitudinal Shear Stress, Longitudinal
τs
τs= VL / 4C1t
50.85 psi
τc
τc= Vc / 4C2t
2.17 psi
Shear Stress Circumferential Shear Stress, Circumferential
Combined Stress Table Note = See Sheets: 0, 90, 180, 270
σx
Stress Due to 0 deg Radial Load, P ( Sign is (+) for out ward load & (-) for inward load
Longitudinal Moment, ML
Membrane
Bending
Membrane
Bending
Membrane Circumferential Moment, Mc
Bending
90 deg
σø 180 deg
270 deg
Nø Nx
940.62
47.03
940.62
322.08
16.10
322.08
121.56
121.56
706.40
706.40
Mø Mx
180 deg
270 deg
37.62
752.49
37.62
528.00
26.40
528.00
26.40
16.10
Nø Nx
90 deg
47.03
Mø Mx
0 deg 752.49
392.00
392.00
454.11
454.11
Nø Nx
6.34
6.34
18.83
18.83
Mø Mx
σø = PRm / t =
5.77
5.77
34.35
34.35
3827.27
3827.27
3827.27
3827.27
5954
3931
5954
3931
Internal Pressure, P σx = PRm / 2t =
∑
1913.64
1913.64
1913.64
1913.64
4004
2002
4004
2002
Conclusion
Material Shel YP. at room Temp. Shell YP at 650 F Shell's allowable Strength
= = = =
SA-516 Gr. 70 38000 Psi 26700 Psi 16020 Psi
Maximum induced Stress
=
5954 Psi
=
48060 Psi
Allowable stress
Total Stresses
<
Maximum of combined stresses (From combined stress table) 3 times shells's allowable 3 x Allowable Strength
Design is =
SAFE
Conclusion
Material Shel YP. at room Temp. Shell YP at 650 F Shell's allowable Strength
= = = =
SA-516 Gr. 70 38000 Psi 26700 Psi 16020 Psi
Maximum induced Stress
=
5954 Psi
=
48060 Psi
Allowable stress
Total Stresses
<
Maximum of combined stresses (From combined stress table) 3 times shells's allowable 3 x Allowable Strength
Design is =
SAFE
Fig. 5-20 Stress Concentration factor (Ref. Pressure Vessel Manual by Moss)
r
P /
m
R ø N
β
r
P /
m
R x N
β Fig. 5-22: Membrane force on a cylinder due to radial load on attachment.
r
P / ø
M
β
r
P / x M
β
Fig. 5-23: Bending Moment in a Cylinder due to a radial load on attachment.
L
M / β
2 m
R ø N
β
L
M / β
2 m
R x N
β Fig. 5-24: Membrane Force in a cylinder due to radial load on attachment
L
M / β
m
R ø
M
β
L
M / β
m
R x M
β Fig. 5-25: Bending Moment ina cylinder due to longitudian moment on attachment.
c
M / β
2 m
R ø N
β
c
M / β
2 m
R x N
β Figure: 5-26 Membrane force in a cylinder due to circumferential moment on attachment.
c
M / β
m
R ø
M
β
c
M / β
m
R x M
β Fig.5-27: Bending Moment in a cylinder due to circumferential moment on attachment.
