Calculating Max Torque on a Ø140mm x 936mm Shaft

[pegghead]

I have a stainless steel shaft that is Ø140mm x 936mm long.

I need to calculate what the maximum torque is that I can apply to this shaft. I have looked around for formulas and have just got myself confused. Could someone tell me what the formula is that i need to work this out.

 

[CFDFEAGURU]

What is the maximum torsional stress allowed for the shaft material? You will need this for the equation. Also, you need to calculate the polar moment of inertia, J, of the shaft and calculate the shafts section modulus, Z. The equation for Z is Z=J/c and c=outer diameter/2.

 

[pegghead]

The figure i have for the material is 77,000N/mm^2

 

[CFDFEAGURU]

Ok now you can run the equation. Do you know how to calculate J?

 

[pegghead]

Sorry no i don't know how to calculate J.

 

[CFDFEAGURU]

Do you have a book on strenght of materials?

 

[pegghead]

I don't have a strength of material book.

Could yoou tell me the equations that i need.

Like T = ? ? ? ? ?

and

J = ? ? ? ? ?

 

[CFDFEAGURU]

Well,

T = Z*(allowable stress) where Z = J/c

J = PI/2(r^4) if the shaft is solid. Is the shaft solid?

r = c = Outside Diameter/2

Think you can handle the rest?

 

[CFDFEAGURU]

Lastly, be sure to check and make sure all of the units are correct. You should end up with N-mm

Thanks

 

[pegghead]

I have calculated the torque using the formulas given and i get 3.5E-5 Nmm of torque that a Ø140mm shaft can transmit when material allowable stress is 77,000N/mm^2.

I think somewhere i have miscaculated, i have checked a couple of times and got the same result.

O/D = 140mm
R = 70mm
Allowable stress = 77,000N/mm^2

The amount of Torque transmittable seems very low.

 

[CFDFEAGURU]

Check your math.

I have 4.15x10^7 N-m

That is a lot of torque.

 

[pegghead]

the figure i am getting for J is around 6.5E-8

 

[Q_Goest]

Check the allowable stress. It's about 2 orders of magnitude higher than a strong grade of steel.

 

[pegghead]

The allowable stress figure that i have is 77KN/mm^2.

 

[CFDFEAGURU]

For J,

J = PI/2(r^4) = 3.141592/2*(70^4) = 1.570796*(24010000)=37714811.96 mm^4

 

[CFDFEAGURU]

Are you using all the correct units?

 

[pegghead]

I know where i was having problems it was in the formula, i was dividing Pi by 2x(r^4) and not Pi/2 x (r^4).

I get a result of 26534.37mm^3 for Z.

However when i now multiply this by the 77,000N/mm^2 i get 2043146490Nmm. Not the 4.15x10^7 that you got.