Is there a solution for compression of cylinder?

[Mugged]

Hello,

for some reason I can't seem to be able to find this.

Suppose you have a elastic cylinder, a full cylindrical bar (not hollow), and you want to compress the two end faces (axial compression) together and find the stress in the axial direction...or strain.

I can't seem to be able to find this problem posed anywhere in a google search and it seems easy enough for there to be a textbook analytical expression.

anyone know of any references?

Thank you

 

[Mech_Engineer]

It's just column compression, cross-section doesn't really matter other than from an area standpoint. In fact, circular makes it easier because it's an axisymmetric cross-section.

http://www.efunda.com/formulae/solid_mechanics/columns/intro.cfm

 

[Chestermiller]

Hello,

for some reason I can't seem to be able to find this.

Suppose you have a elastic cylinder, a full cylindrical bar (not hollow), and you want to compress the two end faces (axial compression) together and find the stress in the axial direction...or strain.

I can't seem to be able to find this problem posed anywhere in a google search and it seems easy enough for there to be a textbook analytical expression.

anyone know of any references?

Thank you

This is the same problem of a bar in tension, except that the imposed tension stress is negative. The compressive strain is just the compressive stress divided by Young's modulus.

 

[Aero51]

If its elastic than you probably won't find an analytical expression that doesn't require a supercomputer to solve.

 

[Studiot]

Mugged, what is special about your cylinder or axial loading that makes this problem difficult?

The answer by Mech_Engineer is one of the first things in any mechanics of materials book.

However this assumes several things.

Firstly that the cylinder axis is long compared to its diameter

Secondly that the applied force is (sensibly) normal to the end faces

Thirdly that the applied force is applied via a large stiff plate, larger than the diameter of the cylinder

Fourthly that the cylinder is not restrained from expansion along its curved surfaces

Fifthly that the material is isotropic

Please note one more thing about Mech_eng link.
The link refers to failure, where stresses are different.
I presume you are asking about a non destructive load?

The problem is still tractable however, Aero51 is over the top with his suggestion.