Thick+Thin Press Vess
Transcript of Thick+Thin Press Vess
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Determination of Stresses in Radially Loaded
Cylindrical Members
by Kevin Hausen F'04
Inputs: outer diameter of cylinder = 1.00 inches
cylinder thickness = 0.25 inches
internal pressure = 1000.00 psi
material yield strength = 30000.00 psi
minimum safety factor 2.00
type 1 if cylinder ends are
constrained or type 0 if the
ends are open
1
Outputs:
Other Measures: inside diameter = 0.50 inches
average diameter = 0.75 inches
inside radius = 0.25 inches
outside radius = 0.50 inches
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Thick-Wall Thin-Wall
Theory Theory
Max Tang Stress (hoop) 1666.7 psi 1500.0 psi
Max Axial Stress (a) 750.0 psi 750.0 psi
Max Radial Stress (r) -1000.0 psi -1000.0 psi
Max Safety Factor 18.00 Safe 20.00 Safe
Maximum
factor is no
z
Max Tau Safety Factor 18.00 Safe 20.00 Safe
Max D.E. Safety Factor 12.78 Safe 13.50 Safe
The graphs will not be accurate when the axial stress is not zero
-Syp
-40
-30
-20
-10
0
10
20
30
40
-40 -20
Sigma
2
Kpsi
Sig
Ductile Failure Env
-Syp
Syp
Syp
-Syp
-40
-30
-20
-10
0
10
20
30
40
-40 -20 0 20 40
Sigma
A
Kpsi
Sigma B
Kpsi
Ductile Failure Envelope For Thick-Wall Theory
Max Normal Stress
Max Shear Stress
Distortion Energy
Load Line
Stress Location
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Shear Stress safety
t correct for three non-
ro stresses!
-Syp
Syp
Syp
0 20 40
a 1
Kpsi
lopes For Thin-Wall Theory
Max Normal Stress
Max Shear Stress
Distortion Energy
Load Line
Stress Location
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Determination of Stresses in
Radially Loaded, Thick-walled Cylindrical Members
For nonrotating cylinder, internal pressure only, neglecting end effects.
Variables Defined: Input: Units:
internal press pi 1000.00 psi
inner radius ri 0.25 inches
outer radius ro 0.50 inches
At Inner Radius Outputs: At Outer Radius
Tangential Str s t 1666.67 psi Tangential Str s t 666.667Radial Stress s r -1000 psi Radial Stress s r 0Axial Stress a 750.00 Axial Stress a 750.00
Max Shear Tau max 1333.33 Max Shear Tau max 333.333
von Mises eq 2346.69 von Mises eq 712
-1500
-1000
-500
0
500
1000
1500
2000
0.2 0.3 0.4 0.5
stress
radius
Stress in Thick-walled Cylinder
Sigma TSigma RSigma AMax ShearRi
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Sigma Eq inside and outside
Greater of
Greater of
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Calculate Ri and Ro lines for Graph
Ri 0.25 1833.333 Ro 0.5 1833.333
0.25 -1100 0.5 -1100
R range s t s r Sigma a (axial)0 0.5 666.667 0 750 333.3333
1 0.4875 683.98 -17.3132 750 350.64652 0.475 702.678 -36.0111 750 369.34443 0.4625 722.912 -56.2454 750 389.57884 0.45 744.856 -78.1893 750 411.5226
5 0.4375 768.707 -102.041 750 435.3741
6 0.425 794.694 -128.028 750 461.361
7 0.4125 823.079 -156.413 750 489.7459
8 0.4 854.167 -187.5 750 520.8333
9 0.3875 888.311 -221.644 750 554.9775
10 0.375 925.926 -259.259 750 592.5926
11 0.3625 967.499 -300.832 750 634.165712 0.35 1013.61 -346.939 750 680.272113 0.3375 1064.93 -398.262 750 731.595814 0.325 1122.29 -455.621 750 788.954615 0.3125 1186.67 -520 750 853.333316 0.3 1259.26 -592.593 750 925.925917 0.2875 1341.52 -674.858 750 1008.19218 0.275 1435.26 -768.595 750 1101.92819 0.2625 1542.71 -876.039 750 1209.37320 0.25 1666.67 -1000 750 1333.333
Max Shear
Inside Outside
SigmaT - (SigmaR or SigmaA) 1333.333 333.3333
above or SigmaR-SigmaA 1333.333 375
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Max Shear
375
383.657
393.006
403.123
414.095
435.374
461.361
489.746
520.833
554.977
592.593
634.166
680.272
731.596
788.955
853.333
925.926
1008.19
1101.93
1209.37
1333.33
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Ductile Failure Using Thin-Wall Theory
Yeild Strength (Syp): 30000 Load Line: 0 0 Graph Lines:
0 0 Max. Normal StressPrincipal Stresses: Sig1= 1500
Sig2= 750 Graph will n Stress Locatio 0 0
Sig3= -1000
Minimum Safety Factor: 2
Max. Shear Stress
Maximum Normal Stress
Safety Factor: 20 Safe
Maximum Shear Stress safety factor is not correct for three non-zero stresses!
Maximum Shear Stress
Safety Factor: 20 Safe
Distortion EnergyMaximum Distortion Energy
Safety Factor: 13.5011 Safe
-Syp
Syp
Syp
-Syp
-30000
-20000
-10000
0
10000
20000
30000
40000
-40000 -20000 0 20000 40000SigmaA
Ductile Failure Envelopes
Max Normal Stress
Max Shear Stress
Distortion Energy
Load Line
Stress Location
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-40000
Sigma B
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X Y
30000 -3000030000 30000
-30000 30000
-30000 -30000
30000 -30000
0 -30000
30000 0
0 30000
-30000 0
slope
30000 0 033282 8320.5 0.25
34641 17320.5 0.5
33282 24961.5 0.75
30000 30000 1
24962 33282 1.333333
17321 34641 2
8320.5 33282 4
0 30000
-6546.5 26186.1 -4
-11339 22677.9 -2
-14796 19727.9 -1.33333
-17321 17320.5 -1
-19728 14795.9 -0.75
-22678 11338.9 -0.5
-26186 6546.54 -0.25
-30000 0
-33282 -8320.5 0.25
-34641 -17321 0.5
-33282 -24962 0.75
-30000 -30000 1
-24962 -33282 1.333333
-17321 -34641 2
-8320.5 -33282 4
0 -30000
6546.5 -26186 -411339 -22678 -2
14796 -19728 -1.33333
17321 -17321 -1
19728 -14796 -0.75
22678 -11339 -0.5
26186 -6546.5 -0.25
30000 0
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0
0
0
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95688250.xls.ms_office
e Using Thick-Wall Theory
Yeild Strength (Syp): 30000 Load Line: 0 0 Graph Lines: X
0 0 Max. Normal Stre 30000cipal Stresses: Sig1= 1666.67 30000
Sig2= 750 Graph will n Stress Locatio 0 0 -30000
Sig3= -1000 -30000
30000
Minimum Safety Factor: 2
Max. Shear Stres 0
Maximum Normal Stress 30000
Safety Factor: 18 Safe
Maximum Shear Stress safety factor is not correct for three non-zero stresses! 0
Maximum Shear Stress -30000
Safety Factor: 18 Safe
Distortion Energy 30000Maximum Distortion Energy 33282
Safety Factor: 12.784 Safe 34641
33282
30000
24962
17321
8320.5
0
-6546.5
-11339
-14796
-17321
-19728
-22678
-26186
-30000
-33282
-34641
-33282
-30000
-24962
-17321
-8320.5
0
6546.511339
14796
17321
19728
22678
26186
30000-Syp
Syp
Syp
-Syp
-30
-20
-10
0
10
20
30
40
-40 -20 0 20 40SigmaA
Kpsi
Kpsi
Ductile Failure Envelopes
Max Normal Stress
Max Shear Stress
Distortion Energy
Load Line
Stress Location
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inside outside
Y von Mises:
-3000030000
30000
-30000
-30000
-30000
0
30000
0
slope
0 08320.5 0.25
17320.5 0.5
24961.5 0.75
30000 1
33282 1.333333
34641 2
33282 4
30000
26186.1 -4
22677.9 -2
19727.9 -1.33333
17320.5 -1
14795.9 -0.75
11338.9 -0.5
6546.54 -0.25
0
-8320.5 0.25
-17321 0.5
-24962 0.75
-30000 1
-33282 1.333333
-34641 2
-33282 4
-30000
-26186 -4-22678 -2
-19728 -1.33333
-17321 -1
-14796 -0.75
-11339 -0.5
-6546.5 -0.25
0
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