Hoop Stress In Short Cylinders

Read this book while hula hooping and you will know more than you do now...maybe

Just ignore it.

Stress in Thick-Walled Tubes or Cylinders

Cylinder Buckling

The buckling stress is for a high external pressure, I do not see it applicable to my cylinder with internal pressure.

With real short cylinders the hoop stress will be lower than the standard hoop stress calculations. How much lower?????? And how short of cylinder?????

I have never seen the "short cylinder with internal pressure - hoop stress" addressed.

Any information is appreciated.

I'll take pity on you. The hoop force is the internal pressure multiplied by the radius. The hoop stress is the force divided by the length of the section and the wall thickness.

The longitudinal force is the pressure multiplied by πR2. The stress is the force divided by the circumference and the wall thickness.

You can work out the magic ratio yourself.

See this interesting file for Hoop_Stress.

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The informations you got are valid as you already noticed ONLY for free end cylinders.

In short cylinders usually the bottom and the tube are made from same piece of material without separation for a more compact design. This changes totally the stress distribution and amplitude.

When the "tube" has a solid end, this plate - due to its radial stiffness - does not allow the tube to deform as "free" thus the stress distribution is modified and ALL equations are different.

There are 2 ways to solve your problem:

1- design with FEA and do not forget the notch factor at the fillet between plate and tube.

2- more complex but effective is the application of the superposition principle. You cut the cylinder from its bottom and introduce the forces and bending moments at tube end and on the plate rim. from those reaction you only know the axial force as force x area of the late. The 2 other -radial force and bending moment - are unknown. If you apply the equations of continuity (angles and displacements are equal at the generated section) you obtain a system with 2 equations whose solutions are the 2 unknown.

All equations for the stresses and deformations under pressure, radial distributed forces and bending moments are available in books (for instance Roark).

When you have the system solved and compute the stress distribution you will see after how many tube wall thicknesses the stress becomes almost equal to the values given by the equations in previous comment. Depending on the geometry it can be a lot higher at the "corner".

If you do not work with high pressures you can use the usual equations since for thick wall due to the lower ratio Di/De equations are quite different.

If you have difficulties ask for help.