Stressing of split circular shaft with constrained ends

[grovedes]

Firstly imagine a short circular hollow shaft, then split it in two on a plane passing through its axis. Now constrain the ends (not the cut faces) so that they cannot warp out of their initial plane. Now apply torque about axis. Now stress it.

This is much trickier than I imagined. Any pointers would be appreciated.

Thanks

Austin

 

[CPM]

You'll find this in Timoshenko: Torsion on Thin Walled open Sections
however, does the plane go right through the tube, ie produces two parts of 'C' Section, or only passes through one side of the tube and produce a single 'C' Section. In both cases the maximum shear stress is equal to

Txtmax/J

where J is an integral of (t^3)/3 using polar coordinates and is summed for the arc transcribed.

where T is the maximum torque.

where t is the thickness of the tube.

as the same torque is applied to each part.

If it is one piece the formula is similar, but the integral is summed about the split circle, which means the stresses are generally lower.

When you say, then you stress it, do you mean in bending, because then combined stresses come in to effect where the bending stresses need to be calculate dependant on the postion of the split, only when you have calculated these by general bending theory, can they be combined, generally by St Venants theory to determine the critical stress which can then be compared to the maximum stresses applicable to your particular shaft.

If you could help further by being a bit more specific in terms of dimensions, loads etc, and answer the above queries I could probably be a bit more helpful.


Chris

 

[grovedes]

Thanks so much for kicking this off Chris, this is my first posting and to receive help so quickly is really heartening.

It is two C shapes. When I said "stress it" I only meant to refer to the process of analysing it. It is only subjected to torque. I don't know dimensions and loads yet.

The first complication arises due to it being constrained at its ends. The normal analysis (not that I'm familiar with it) of a thin walled open section allows warping of sections out of their original plane, if the ends are constrained (as if welded to a massive block) this is prevented. Roark proposes modifications to allow for this constraint but they do not apply to short torsion members (the second complication).

The plot thickens.

Austin

 

[EnglishMuffin]

Why not either :
1. Treat your shaft as two superposed C shapes, and find the properties of a single end constrained C shape using the methods given in Roark 5ed or 6ed - tables 21 and 22 in the torsion section ?
or
2. Do an FEA ?

 

[grovedes]

Mr Muffin,

Thank you.

1. Good idea and it's exactly what I'd try if it weren't for the torsion member being short - table 22 in Roark does not apply in this situation since "transverse shear deformations of the beam action are neglected" (p365 6ed). Do you know how to correct for this?

2. Yes I will do an FEA in any case but I'd like to back this up with some theory that I have confidence in.

Thanks again.

Austin

 

[EnglishMuffin]

Oh - its short - didn't notice that!
How short exactly, in terms of L/D ?

 

[grovedes]

I potentially have a family of these to work on, but guess that L/D will be around 0.4 (very short) for them all.

 

[EnglishMuffin]

Thats short all right. It's not clear, at least to me, what effect this will have in your case, from the data given in Roark - I think you'd have to go back to the original source. Because the shapes are circular, the effect of transverse shear may be minimal, but I could be wrong. For increasingly shorter slit round tubes with constrained ends, I think the behavior converges more and more to that of a non slit tube.
You are smart to compare your FEA with a closed form solution -its a pity more people don't do this.