Allowable length of hollow shaft under torsion

[WillowEng]

Hi everyone,

I am currently reviewing a simple hollow shaft "extension" design which is basically a pipe with a flange at each end under torsion.

Calculations for shear and angle of deflection are readily available, but I have been unable to find a reference for calculating the allowable length. Any references to allowable angular deflection are per unit length or based on an 'allowable deflection' limited by the equipment rather than potential failure of the shaft. The rotational speed of the device is slow, so amount of angular deflection is unlikely to be an issue in operating the device (within reason).

I have scoured the references available and the internet. I have reviewed sources re: thin shell cylinders under pure torsion, but the sources are either far too mathematical to digest and based entirely on theory, or aren't designed for slender use and yield poor results. What I am after is a relatively simple conservative approach - surely this has all been done before and there is a simple method.

Simplified example:
- DN80 SCH40 pipe (OD 88.9mm, ID 77.92mm, thickness 5.49mm)
- Torque of 3000 Nm

I can calculate the deflection, and allowable shear, but how do I know how long I can make the shaft before it fails by 'buckling'?

WillowEng

 

[GregLocock]

That's an interesting one, not much seen in my experience. The failure mode is called skin or shell buckling, and here's one stab at an analysis:

http://naca.central.cranfield.ac.uk/reports/1935/naca-report-479.pdf

and the Johnny-come-lately's get in on the act

http://shellbuckling.com/papers/classicNASAReports/NASASP-8007.pdf

I hope they help, I haven't looked through them in detail, looks like the NASA one is a design guide.



Cheers

Greg Locock


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[Tmoose]

Any possibility for tension or compression in the shaft?

 

[WillowEng]

Hi Greg, thanks for the response. I have reviewed both of those sources, neither appear to apply as both have some form of "slenderness ratio" for which long (eg 5m) pipes are outside the scope of the paper.

Tmoose, the shaft is able to move axially - I would expect it to fail by buckling along symmetrical curves or by deflecting laterally and failing due to the resulting eccentricity.

WillowEng

 

[gruntguru]

The NACA paper shows a simple formula (Equation 2) for high slenderness ratios.

je suis charlie

 

[jlnsol]

A practical solution to avoid buckling is to add stiffening plates at an interval of 5*D where D is the outer diameter of the pipe.
The risc of buckling reduces drastically when adding stiffening plates (reduction of the shear tension under the critical shear value)
Timoshenko-Greve, Theory of Elastic Stability (1961) documented torsion tests.

 

[zdas04]

Not my part of Oil & Gas, but in this industry we regularly put a drill bit on the end of 20,000 ft of hollow drill pipe and spin it from the top. You might look in Oil & Gas references.

David Simpson, PE
MuleShoe Engineering

In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. Galileo Galilei, Italian Physicist

 

[RolMec]

If i look into Roark it says there that failure mode from twisting would be breaking. It does not say deflection. In my experience the limits derived from allowable stress design are to be checked for instability only in case of compression loads.
If you can accept the deflections coming from a limit stress (allowable = ultimate / safety factor), then you would have a "first" point to stop.
Deflections (e.g. bending of girders or so) usually find a deflection limit coming from other aspects than instability, say for a bridge girder to have less deflection than 1/300 of the span. So if from that point of view you could derive other limits (from tolerances, force application range limits, surface deflection limits, functionally or operationally permitted deflection) you would have another point to stop. Ideal rotationally symmetric profiles don't warp, point is: ideally.
Third is, base to all elastic stress etc. designs is the assumption that cross sections remain planar and parallel. So if you go beyound the limits of that theory due to slenderness, little thickness of the shell, length of your application: you need other tools & input from people familiar with such kind of quest. Call FEA at some reputable company / university.
So, if in the end you come down to the problem of "warping", that is the instability due to torsional loading, then there is an fullscale apparatus of formulae to be applied, and should so. Dare say: imho ;-) Me, I do so, from pure respect of what an instability failure can entangle. Such failure cannot be stopped, or seen developing and stopped.
Pls. don't neglect effects of bending from dead weight or other, tolerances from position, shape or fixation or profile or application of forces.

Good luck!

 

[thaidavid40]

Willow,
If you are looking for some design guidance, have you by chance tried any of the naval architecture references? Some of the larger propeller drive shafts for huge vessels are tubes - as opposed to solid rods - and so there might be some guidance there, based on practical experience.
Dave

Thaidavid

 

[BUGGAR]

I'm into race car design and I searched monocoque (thin shell steel or aluminum) race car chassis like those cigar shaped formula cars. I can't find any numbers (proprietary) but I've seen their torsion test photos and curved body panels can go into a warped buckling shape. It didn't appear to be an even spaced buckling like on stiffened bridge girders but just sort of one section "lets go". Probably no mathematical equation for that. The analysis I've seen indicates that generally fastener strength limit the torsion strength (not stiffness) of these cars.
Your pipe d/t is similar to what ZDAS does everyday so I don't think you are in the buckling realm.
Thaidavid, good idea - Besides the shafts, I found good data relative to torsion loadings on hulls. Anybody ride a container freighter and heard the containers groan as the ship's hull distorts at sea?