thick+thin press vess

8/2/2019 Thick+Thin Press Vess

1/15

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


2/15

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


3/15

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


4/15

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


5/15

Sigma Eq inside and outside

Greater of

Greater of


6/15

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


7/15

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


8/15

95688250.xls.ms_office

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


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

Page 8


9/15


-40000

Sigma B

Page 9


10/15


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

Page 10


11/15


0

0

0

Page 11


12/15


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


Maximum Shear Stress safety factor is not correct for three non-zero stresses! 0

Maximum Shear Stress -30000


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

Page 12


13/15


14/15


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

Page 14


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