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Anonymous Poster #1

# Principle Stresses for Thick Walled Cylinder

02/10/2018 2:06 AM

Hi, I trying to calculate principle stresses for pressure vessel (thick walled) which is pressurized from inside. I calculated all 3 stresses radial, hoop and axial and I am looking for what formula to use to calculate principle stresses.
thanks

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Guru

Join Date: Jul 2005
Location: Stoke-on-Trent, UK
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#1

### Re: Principle Stresses for thick walled cylinder

02/10/2018 3:48 AM

If you have calculated the stresses you presumably already have formulas.

Radial stress is usually negligible compared with the other two.

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Guru

Join Date: Apr 2010
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#2

### Re: Principle Stresses for thick walled cylinder

02/10/2018 9:34 AM

The principal stresses are in the direction where there is no shear stress. (Maximum shear stress occurs at 45 degrees to these directions.) For a pressurized cylinder, the principal stresses would be in the radial and tangential directions, so I suspect you already have those numbers.

http://classes.mst.edu/civeng120/lessons/pressure/manual_thick/index.html

Anonymous Poster #1
#5

### Re: Principle Stresses for thick walled cylinder

02/10/2018 1:45 PM

Yes I have calculated all 3 stresses (axial, radial and hoop), but I thought I have use following equations to calculate principle stresses, but I guess shear stresses are zero at the wall for thick walled cylinder (is it right) which makes following equation no change in what I allready calculated (as shear is zero in the normal stress calculation below).

2
Guru

Join Date: Apr 2010
Posts: 6204
#6

### Re: Principle Stresses for thick walled cylinder

02/10/2018 2:27 PM

If you cut an object with stress, the direction of the cut determines the type of stress. As you rotate the direction of the "cutting plane" through 90 degrees, the stress changes from compressive (principal stress, zero shear) to maximum shear (and compressive) at 45 degrees back to principal stress again.

A good way to visualize this is Mohr's circle, where shear stress is plotted on the vertical axis and compressive stress on the horizontal axis. Rotating the cutting plane through the object through angle θ rotates the line through Mohr's circle by 2θ. The direction corresponding to principal stress is the angle where the circle diameter lies on the x-axis (σ1 σ2)

Here is a good description of Mohr's circle:

Guru

Join Date: Jul 2005
Location: Stoke-on-Trent, UK
Posts: 4006
#8

### Re: Principle Stresses for thick walled cylinder

02/12/2018 4:19 AM

May I ask why you want to know? Is it an academic exercise (eg homework) or something practical?

If the latter, you only need to know the hoop stress. Design codes for cylindrical pressure vessels calculate thickness using design stress and diameter, based on the hoop stress formula. That's the limiting case, the axial stress is (approx) 1/2 the hoop stress.

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Guru

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#3

### Principal Stresses for thick walled cylinder

02/10/2018 11:33 AM
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Guru

Join Date: Oct 2008
Posts: 40866
#4

### Re: Principle Stresses for Thick Walled Cylinder

02/10/2018 12:31 PM

Don't get it wrong.

Off Topic (Score 4)
Guru

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#7

### Re: Principle Stresses for Thick Walled Cylinder

02/10/2018 6:04 PM

Blurp

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Anonymous Poster #2
#9

### Re: Principle Stresses for Thick Walled Cylinder

02/13/2018 4:19 AM

principle principal

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