Torsional Resistance Of Solid Bar Or Tube

[pgp001]

Does anyone know if a 30mm dia solid bar will have more or less torsional resistance than a thick walled tube of the same outside diameter.
I may need to use it for the main spindle on an indexing table machine I am designing, I need to minimise the "whip" as it comes to rest on each station.
If the tube has a better performance, does anyone know of suppliers in the UK.
Ideally the wall thickness needs to be enough to allow keyways to be milled in it for the taper lock couplings.
Thanks
Phil

[Ian B]

Phil,

All else being equal (material specs etc), the tube will have less torsional resistance than solid bar of the same od.

If a tube were to be picked having the same weight as solid bar, the tube would come out better (the outer fibres do the most work when it comes to transmitting torque).

The difference between solid bar and tube in your case may not be that much.

Ian

[Evan]

Think of it this way. Say you have a 30mm tube with 5mm walls. It has X torsional resistance (torsional moment of inertia). This leaves an ID of 20mm. Then you have a solid bar of 20mm OD. It has Y torsional resistance. If you have a solid bar of 30mm it has X plus Y torsional resistance.

[hitnmiss]

The tube will have less inertia which will help the "whip" problem you mentioned.

[Forrest Addy]

It's all down in the "Strength of materials formulas.

The question asked "[Does a] 30mm dia solid bar ... have more or less torsional resistance than a thick walled tube of the same outside diameter?"

Ian has it right: the answer is "more" within the limits he states.

A tube of the same weight could transmit more torque but that means you've exceeded the 30mm diameter.

The tortional moment of intertia is a D^4 function and that of a tube is (D^4 - d^4). In the specific case of a shaft and a tube of the same diameter, the solid shaft will deliver more torque at the same fiber stress whereas a hollow shaft's capacity is reduced by the missing material.

Thus the popular aphorism "A hollow shaft transmits more power than a solid shaft..." HAS to include the words "...of the same weight" to be true.

[pgp001]

Thankyou all for confirming what I already knew to be true.
One of the directors at work tried to be clever today and started quoting college boy maths formula's at me, he insisted that a tube of the same diameter as a solid would be torsionally stiffer.
I will show him your replies on Monday and see what his reaction is.
Thanks again
Phil

[Michael Moore]

Hi pgp001,

What you need to do is to go to

http://www.tonyfoale.com

and download

http://www.tonyfoale.com/progs/Sections.zip from his free software section.

This is a solid and tube properties calculator I badgered him into writing, and if you want to be able to compare different sizes/wall thickness of tubes (either rectangular or round) you'll find it invaluable.

cheers,
Michael

[This message has been edited by Michael Moore (edited 06-18-2004).]

[Dave Opincarne]

I'm confused, are you asking about inertia or stiffness?

[Evan]

Dave,

The rotational moment of inertia is the "stiffness" or the resistance to being twisted. It is a different use of the term inertia than when inertia means the resistance of an object at rest to being set in motion and has nothing to do directly with Newtons laws of motion.