Stress analysis in pressurised cylinders 1

[Raymie]

Up to now I have used the hoop sress formula, PD/2t, to calculate the bursting pressure of pressure vessels. But how can longitudinal forces be accounted for? For example a hydraulic cylinder which has 200 bar hydraulic pressure, and is creating a force of 4 tonnes between fixing pins.

 

[codeeng]

For pure pressure in a cylinder the longitudinal stress is half the hoop stress (PD/4t).

 

[Raymie]

Thank you for your response. The pure Longitudinal stress is PD/4t, but if there are other longitudinal pressures/stresses induced on the tube how can I account for these? I need to know this, in case it becomes larger than the circumfrential stress, and will therefore be the failure mode.

 

[JStephen]

First off, for something like a hydraulic cylinder, the PD/2t probably isn't a real good approach. Check Formulas for Stress and Strain for thick-walled cylinders.

You find the longitudinal stress in a cylinder by isolating a freebody and summing forces on it. I assume you know the force on the piston rod, I assume you know the pressures on either side of the piston, so that leaves the longitudinal force in the cylinder wall itself as the only unknown.

 

[JohnBreen]

Hello,

Look at the high pressure chapter of B31.3. It gives you an equation based upon Mises failure theory. The equation that you cite is just the hoop (circumferential) stress. This must be combined with the longitudinal stresses due to internal pressure and the radial pressure stress. The radial stress can be very significant with very high pressure and wall thicknesses greater than D/t = about 6.

If you can find (out of print) David Burgreen's excellent book, ".......Power Plant Structures" you will see a particularly lucid description of the issues you are addressing.

Regards, John.

 

[unclesyd]

Here is a good approach to designing a pressure vessel.

http://www-training.llnl.gov/wbt/hc/5060/Design.html

 

[TGS4]

It seems to me like the original question was rreally looking for a failure criterion for multi-axial stresses.

If that is indeed the case (eg, longitudinal stress equals hoop stress due to an externally applied traction to the cyliner), then may I propose that the "allowable stress", which is usually simply a uniaxial allowable stress, be compared to the multi-axial stress state using one of the following failure theories:
a) Maximum stress (what is currently used in Div. 1)
b) Tresca (what is currently used in Div. 2)
c) von Mises (what the new Div. 2 is moving towards and a much better failure theory for ductile materials).

You can find a decent description of these failure theories in any good Mechanics of Materials textbook.