Buckling Analysis Supported by "Soft Springs"

Distributed or concentrated forces or a mixed loading? How are -in the second case-positioned on the ring ? Equal angular distances or different ?

Have you had a look on subject via google or any other sources ? Did you have difficulties in founding a pertinent answer ?

Force is evenly distributed, all around ring outer face.

It is considered "float" not supported, because there is no known specific DOF lock anyware on the model. We may asume that the deformation is cylindrically symetric around the ring axis, but the axis is not fixed at all.

We searched google or other sources, but coudn't find any relevant answer.

Thanks

I am surprised that you found nothing on google research. At least you should had a look at Timoscheno's books. I found several texts and equations for the different conditions of "pipe buckling" as you may think a "ring" is a "short pipe" and because it is free the Poisson effect has NOT to be considered.

You should consider that shell/pipe buckling critical load is VERY sensitive to manufacturing imperfections as well roundness as wall thickness so that importnat reserves have to be considered.

For more complex problems you have to consult also von Mises theory.

Basic equation is : P*= (n^2-1)*E*(t/R)^3/12 with

E = Young modulus n= number of waves at buckling t= wall thickness (radial)

R= mean radius of ring section. Valid for small t/R.

Smallest load for n=2

I suspect that the OP must start with the ring bent into a saddle shape, that is the most probable shape, and find out what load then completes the buckling.

For this case, short pipe (or long) is not the way, because this is not a column classic problem as apears in the books...

To demonstrate the problem, take a "weding ring" and make a rope lasso-loop over its center. Now tighten the loop around. This apply radial forces on the outer face of the ring.

Anyhow, we use FEA for this buckling analysis. The issue is that the lasso apply the force on the ring outer face, but do not lock its position in space. Thats why we use "soft springs" to hold the ring in space.

The question was, what is the meaning of the close to nul results of the BLF.

By the way if you fix a small area of the ring, the results become reasonable....but it changes the problem definition.

Thanks

I am not wrong but you are since you look at a pipe for buckling ONLY under axial loads in considered situation loads are RADIAL.

For radial, centripetal, loading a ring is a short pipe and as far as it is not axially constraint (which is here the case) the equation for a pipe is valid for the ring.

At the first buckling the ring will start to build an oval and because the radius grows up the wall will collapse at the critical pressure and build the saddle.

Ask the instructor for help.

You may want to obtain a copy of "Roark's Formulas for Stress and Strain, 8th Edition".

It'll have everything you will need to solve your problem.