Convert solid shaft to hollow shaft

  • #1
I have a "bending stress" question, which is causing me "actual stress"...
I have a solid 30m Aluminium shaft, which I need to replace with an equivalent hollow shaft, but I am having difficulty in calculating the internal and external diameters.

The solid shaft diameter is 0.118m, and all I know about the hollow shaft is that the external diameter should be 2.5 times greater than the internal diameter.

I worked out the second moment of area for the solid shaft (9.5*10^-6), but can't seem to find the right way of using this to find the hollow shaft dimensions.

Any help with this would be much appreciated.
 

Answers and Replies

  • #2
CWatters
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Been a long time since I did anything like this so I might be wrong but..

Have you got equations for the bending stress (F) developed in terms of applied bending moment(M) for both hollow and solid?
Presumably the ratio of F/M for both needs to be the same so equate.
See what cancels.
Substitute ID = OD/2.5

Something like that anyway.
 
  • #3
rock.freak667
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Sounds like you'd just be inevitably conserving the second moment of area for the shaft such that Isolid = Ihollow and for a shaft I = πD4/4
 
  • #4
CWatters
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I found..

For solid
FS = 32M/(pi * Ds3)
and for hollow
FH = 32MOD/(Pi(OD4 - ID4)

where
F = bending stress
M = bending moment
Ds = diameter of solid
OD = Outside Diamater of hollow shaft
ID = Inside Diamater of hollow shaft

If you rearrange these to give the ratio F/M for both and equate it simplifies to :

OD = (OD4 - ID4) / Ds3

Can then substitute for ID = OD / 2.5 to give an equation for the OD of the hollow shaft in terms of the diameter for the solid.

but as I said it's been a long time since I did this. Does it even make sense to preserve the ratio of F/M ?

Edit: Oops I'd better check my working as it looks like the OD of the hollow shaft gets smaller as the solid one gets bigger.
 
  • #5
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0
What was the final relationship between solid shaft dia.and hollow shaft outside dia
 

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