# Cylindre buckling under axial load

• Enthalpy
In summary: No, your contribution was helpful. In summary, this book discusses how buckling can occur in thin cylinders. The stress caused by an axial load can cause the cylinder to buckle, and this can be different than what is predicted by the elastic theory. Experiments usually yield results that are not as accurate as those predicted by the theory, and there is a correction factor that depends on the specific situation. It is important to design things that can be analyzed before construction begins, as buckling can have global consequences.
Enthalpy
Hello everybody, and a happy new year!

Found in Dubbel (Taschenbuch für den Maschinenbau) page C47 7.3.2 the axial load that buckles a thin cylindre. This is not Euler's buckling of a long compressed beam, but probably from Timoshenko's theory for shell buckling applied to a thin cylinder.

The book gives:
σ = e/R*E/(3(1-μ2))0.5 where σ is the stress,
and taking Poisson's coefficient μ as 0.33 I obtain
σ/E = 0,612*e/R
and
F = 3,845*e2*E.

As I mistrust buckling computations, I stepped on a soda can over bathroom scales and got instead
F = 0,68*e2*E
far less...

I use this lower value now for my computations, but maybe I botched the experiment? I measured the thickness properly with a micrometer at several positions, tried to step slowly and vertically...

Do you have more experimental values, or different formulas from a theory?

And if someone steps on a can, please mind your ankle, I hurt mine.

Thank you!

1 person
Enthalpy said:
Do you have more experimental values, or different formulas from a theory?

"...experiments usualy give only 15 to 50% of that predicted theoretically; moreover, the observed buckle pattern is different from that predicted by the theory..."
http://www.dtic.mil/dtic/tr/fulltext/u2/a801283.pdf

Your 0.68/3.845 = 18% is between 15 and 50%, so your experiment was OK

1 person
Enthalpy
σ = e/R*E/(3(1-μ2))0.5

Have you seen the derivation of this formula?

It is for a long tube of dimensions where axial length > 10√(eR/2)

It was presented by Prescott in 1924, but he does not claim originality for it.

Thank you!

Meanwhile I've also seen
http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19690013955_1969013955.pdf
http://shellbuckling.com/papers/classicNASAReports/1969NASA-TN-D-5561-Peterson.pdf
http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19930084510_1993084510.pdf

Which tell in essence the same picture:
- Elastic theory is b**cks for cylinder buckling
- Experiments are not reproducible, even for plain metal
- Introduce an experimental corrective factor much smaller than 1
- This factor depends on everything

Imagine for a cylinder with stiffeners, or of composite...
Build it first, measure, and only then make predictions?

A few considerations:
- My book isn't as good as I had thought...
- We have no theory for that in 2013! Shame.
- Once again, models are necessarily right - when Nature wants to conforms to them.
- Nasa and Naca documents from pre-computer era, when people made measurements, are a treasure. Fabulous to have them online.

OK, I have the necessary information to go further, thanks!

Enthalpy said:
We have no theory for that in 2013! Shame.

There's nothing wrong with the theory. The "only" difficulty is that this (and other related problems in continuum mechanics) are VERY sensitive to initial conditions and geometric imperfections. For thin cylinders, St Venant's principle often doesn't apply, therefore "local" deviations from a mathematically perfect structure have "global" consequences.

The solution is the same as for any other engineering problem: never "design" things that you can't analyse.

Imagine for a cylinder with stiffeners, or of composite...
Build it first, measure, and only then make predictions?
Stiffeners make the problem a lot simpler. One way to proceed is design a frame structure that carries the loads without buckling, and then cover it with a (non load carrying) thin cylinder.

Stepping on a soda can placed on a bathroom scale is not exactly the ne plus ultra of experimental procedure.

enthalpy
Which tell in essence the same picture:
- Elastic theory is b**cks for cylinder buckling
- Experiments are not reproducible, even for plain metal
- Introduce an experimental corrective factor much smaller than 1
- This factor depends on everything

I was disappointed to see this tantrum in response(?) to my civil question about the derivation of a formula that you yourself posted.

I got The Theory of Elastic Stability down from the shelf this morning.

There is a whole chapter devoted to this subject including a derivation of your formula (referenced to a 1910 paper in German) and a considerably more advanced analysis.

The authors also offer considerable experimental material, including test results on a variety of materials from steel to brass to rubber. There is also discussion of these results and comparison with theory.

Is there any point in my further contribution to this thread?

## 1. What is cylindre buckling under axial load?

Cylindre buckling under axial load is a phenomenon that occurs when a cylindrical structure, such as a column or beam, is subjected to an axial load (force along its central axis) that exceeds its critical buckling load. This causes the structure to suddenly and catastrophically fail by bending or buckling.

## 2. What factors contribute to cylindre buckling under axial load?

There are several factors that can contribute to cylindre buckling under axial load. These include the material properties of the cylindre, its geometrical dimensions and shape, the type and magnitude of the applied load, and the boundary conditions of the structure.

## 3. How can cylindre buckling under axial load be prevented?

Cylindre buckling under axial load can be prevented by designing the structure with sufficient strength and stiffness to resist the applied load. This can be achieved through proper selection of materials, appropriate cross-sectional shape and dimensions, and proper reinforcement or bracing.

## 4. What is the difference between cylindre buckling and bending?

Cylindre buckling and bending are both forms of structural failure, but they occur through different mechanisms. Buckling is a sudden, catastrophic failure caused by compressive forces in the structure exceeding its critical buckling load, while bending is a gradual failure caused by tensile or compressive forces that exceed the strength or stiffness of the structure.

## 5. What are the real-life applications of understanding cylindre buckling under axial load?

Understanding cylindre buckling under axial load is important in many engineering and construction applications, such as designing and building tall buildings, bridges, and other structures that are subjected to axial loads. It is also important in the design of machinery and equipment that use cylindrical components, such as engines and hydraulic systems.