Stress analysis in pressurised cylinders
Stress analysis in pressurised cylinders
(OP)
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.





RE: Stress analysis in pressurised cylinders
RE: Stress analysis in pressurised cylinders
RE: Stress analysis in pressurised 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.
RE: Stress analysis in pressurised cylinders
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.
RE: Stress analysis in pressurised cylinders
ht
RE: Stress analysis in pressurised cylinders
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.