How to determine how much torque a hollow cylinder can take?

[Maxxon]

I'd like to calculate how much torque a hollow cylinder along its axis can take before it will start to buckle. The cylinder is held at one end, and the torque is applied equally in discrete intervals along the length of the cylinder.

In the example image above, the hollow cylinder is mounted on a slab which is immovable.

I'm guessing I need to know the tensile strength of the material the hollow cylinder is made of, the thickness of the cylinder wall and the diameter of the cylinder. Is that correct?

Is there a formula that I can use to calculate this information?

 

[Dr. Courtney]

Is this a homework problem?

https://www.physicsforums.com/threads/guidelines-for-students-and-helpers.686781/

 

[jack action]

Torsion of Shafts
Shear strength of different materials

 

[SteamKing]

I'd like to calculate how much torque a hollow cylinder along its axis can take before it will start to buckle. The cylinder is held at one end, and the torque is applied equally in discrete intervals along the length of the cylinder.

In the example image above, the hollow cylinder is mounted on a slab which is immovable.

I'm guessing I need to know the tensile strength of the material the hollow cylinder is made of, the thickness of the cylinder wall and the diameter of the cylinder. Is that correct?

That's a start. You'll also need to know E, G, or Poisson's ratio for the material, as well, for starters.

Is there a formula that I can use to calculate this information?

Are you talking about the amount of torque required to cause buckling?

If so, based on the history of this problem given in this paper:

http://www.tech.plym.ac.uk/sme/fpcm/FPCM06\FPCM-6_14.PDF

I doubt there is a simple formula which is also accurate, even for shafts which can be considered "thin wall", i.e., where the shear stress distribution across the thickness of the wall can be treated as constant.

More likely than not, you will have to analyze this shaft using finite element techniques, and then keep your fingers crossed, unless you have a way to do some experiments on an actual shaft and compare these empirical results with the results of a numerical analysis.

 

[Nidum]

Thin tubes buckle in torsion in a way similar in concept to the way that stressed thin flat plates buckle when subject to edge shear .

Doesn't help much to know that though - the actual calculations are horrendous even for simple cases .

Also quite small imperfections in tube or quite minor distortions in applied loads can make calculated failure condition meaningless .

Far safer to use an alternative design that can be analysed easier or which is intrinsically more stable anyway if requirement is a critical one ..

 

[Nidum]

Just a thought though - do you actually mean failure by buckling or do you really mean just simple failure of a thicker tube by overstressing ??

 

[jack action]

I answered too fast about a subject I doesn't master. Done some research about and I found out it is called «shell buckling». There is a very interesting website about it. On a link from the website (Buckling of Shells—Pitfall for Designers), I found what I think is the closest to what you are looking for:

The graph originally comes from Buckling of Bars, Plates, and Shells (see section 4.3.2.5, p. 504).

 

[Maxxon]

Is this a homework problem?

https://www.physicsforums.com/threads/guidelines-for-students-and-helpers.686781/

No, my own interest.

 

[Maxxon]

That's a start. You'll also need to know E, G, or Poisson's ratio for the material, as well, for starters.Are you talking about the amount of torque required to cause buckling?

If so, based on the history of this problem given in this paper:

http://www.tech.plym.ac.uk/sme/fpcm/FPCM06\FPCM-6_14.PDF

I doubt there is a simple formula which is also accurate, even for shafts which can be considered "thin wall", i.e., where the shear stress distribution across the thickness of the wall can be treated as constant.

More likely than not, you will have to analyze this shaft using finite element techniques, and then keep your fingers crossed, unless you have a way to do some experiments on an actual shaft and compare these empirical results with the results of a numerical analysis.

Thanks. I'm not an engineer (I'm a programmer), but I'll look up these terms and see what I can learn.

 

[Maxxon]

Just a thought though - do you actually mean failure by buckling or do you really mean just simple failure of a thicker tube by overstressing ??

Buckling or any deformation. I've been reading up on ultrasonic motors and wish to rotate a shaft (probably a hollow cylinder as it has a better weight to strength ratio) using a bunch in parallel to increase the torque on it.

 

[Nidum]

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