## Elastic Buckling

## Elastic Buckling

(OP)

This seems like an elementary question, but I've always wondered about it and have scoured the internet to no avail. Perhaps it is too simple for Mech of materials books to explain.

My question is how does a compression member buckle with a purely axial load. Is this due to inherent initial out of straightness, which means the load actually isn't purely axial and does have eccentricity and moment, or is this due to poissons effect where the axial load creates a lateral stress?

My question is how does a compression member buckle with a purely axial load. Is this due to inherent initial out of straightness, which means the load actually isn't purely axial and does have eccentricity and moment, or is this due to poissons effect where the axial load creates a lateral stress?

## RE: Elastic Buckling

## RE: Elastic Buckling

Cheers

Greg Locock

New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?

## RE: Elastic Buckling

## RE: Elastic Buckling

## RE: Elastic Buckling

Cheers

Greg Locock

New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?

## RE: Elastic Buckling

stocky column material plastic failure

https://www.youtube.com/watch?v=jNwvub87l8o

slender column elastic failure

https://www.youtube.com/watch?v=wrdO8hPJGyg

A column's critical load is often "first mode" lateral eigenvalue solved by FEA programs.

## RE: Elastic Buckling

Dik

## RE: Elastic Buckling

There are many many sources of information out there (BTW it's "scoured" the internet not "scowered"). you just need to use the right terms. It's also quite complex given the variance of issues not there is no simple rule, whereas Euler buckling on a long thin member is pretty basic stuff. Essentially in my mind the higher the axial force essentially reduces the initial deformity to the point where it becomes practically impossible not to have such deformation. However there are limits and the L/d ratio is one of them as well as the stiffness.

E.g.

https://www.sciencedirect.com/science/article/pii/...

~And if you search for "elephants foot tube buckling", you find things like the pictures below.

If the conditions are right then a tube especially will fail in a compressive circular bulge or bulges. For a simple example think of a Coke can crushed under your foot. Get it right and it simply collapses vertically into a squashed flat, but wrinkled mass.

Buried pipelines and pipes heavily guided on occasion fail in compression like that, sometimes called a mash buckle or in columns they call it elephants foot.

If you have a solid rod e.g. inside a sleeve, but leave a certain short section able to expand sideways but not buckle, it will in the end simply yield sideways in a uniform "bulge"

Remember - More details = better answers

Also: If you get a response it's polite to respond to it.

## RE: Elastic Buckling

another day in paradise, or is paradise one day closer ?

## RE: Elastic Buckling

## RE: Elastic Buckling

from wiki ...

Mathematical Derivation - Pin Ended Column[edit]

The following model applies to columns simply supported at each end.

Firstly, we will put attention to the fact there are no (lateral) reactions in the hinged ends, so we also have no shear force in any cross-section of the column. The reason for no reactions can be obtained from symmetry (so the reactions should be in the same direction) and from moment equilibrium (so the reactions should be in opposite directions).

Using the free body diagram in the right side of figure 3, and making a summation of moments about point A:

Sigma M=0 ... M(x)+Pw=0

where w is the lateral deflection.

According to Euler–Bernoulli beam theory, the deflection of a beam is related with its bending moment by:

M=-EI{d^2w/dx^2}

The column is perfectly straight until the critical load is reached and it fails instantly. This is in the ideal mathematical world, the real world is full of imperfections.

another day in paradise, or is paradise one day closer ?

## RE: Elastic Buckling

Remember - More details = better answers

Also: If you get a response it's polite to respond to it.

## RE: Elastic Buckling

## RE: Elastic Buckling

another day in paradise, or is paradise one day closer ?

## RE: Elastic Buckling

This is a very good video that shows how I affects Euler.

The problem (as I see it) is K. It is a made-up number.

It's all well and good to say that it is 1 for a pinned-pinned column and a lower number for other situations. What is the lower number? You make it up.

Torsion is well defined because it is repeatable and predictable.

Tension is well defined because it is repeatable and predictable.

Compression is defined using a fudge factor.

You can get pretty close to the correct answer, but you will never be exact. You can see why when you look at the images in LittleInches's post. No two failures were the same. When you get to Point A on his graph almost anything can happen, but that is discussing failure.

Elastic region is defined by the gradient of his graph. The gradient is a factor of how "pinned" the ends are.

If you are compressing the strut using pure axial loading (almost impossible), will the strut bend upwards, downwards, or compress as shown in L/D=2 and L/D=4.

## RE: Elastic Buckling

another day in paradise, or is paradise one day closer ?

## RE: Elastic Buckling

Cheers

Greg Locock

New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?

## RE: Elastic Buckling

have a look at his link

http://www.idc-online.com/technical_references/pdf...

“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein

## RE: Elastic Buckling

Dik

## RE: Elastic Buckling