Max torque a bar can be expected to support based on its tensile strength

[Charon99]

I’m trying to calculate the max torque a bar can be expected to support based on its tensile strength.
Is the following correct:-

Radius of Bar (mm)= r
Moment of inertia =I=pi*r^4/4
Section modulus =z= I/r= (pi*r^4/4)/r= pi*r^3/4
Torque (Nmm)= T
Tensile Strength (N/mm^2)=S
T=S*z

 

[GregLocock]

No it isn't. Amongst any other errors why are you treating a tensile stress as if it was a shear stress?

Cheers

Greg Locock


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[racookpe1978]

Look at what you labeled "section modulus"....

pi*r^4/4 then divide by r doesn't give you pi* r^3/4 - except in badly written equations ...
If you put that into a calculator you will get a wrong answer.

use (r^3)/4

 

[GregLocock]

Also you are assuming that you have a material that fails at yield. In practice normal materials will sustain some post yield strengthm and the fully developed plastic torque is greater than the onset of yield and is calculated from first principles.

Cheers

Greg Locock


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[Charon99]

Racookpe1978,

pi*r^3/4 = (pi*(r^3))/4 and not ((pi*r)^3)/4. If I was to write (pi*(r^3))/4 on paper I would not use the brackets or the times. If r=2.5 then pi*r^3/4 =12.27.

 

[Charon99]

Yes.
The problem is I’m comparing apples to pears.
I’m trying to calculate the torque that can be expected based on a specific tensile load.

Or if I have a Bar with a yield strength of “S”n/mm^2 what torque would I expect to be able to apply before yield.

So can you help me?

 

[GregLocock]

how do you expect to determine the yield stress in shear from the (?ultimate) tensile stress?





Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376

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[Charon99]

I wish I knew. I need help.

If I was to measure the yield torque and yield tensile load on a range are bars with differing tensile yield strengths I expect to find a correlation between tensile load and torque measured. How do I calculate this correlation?

 

[GregLocock]

If you give more details of the material in question then somebody may be able to idenify a stress strain curve

Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376

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[Charon99]

Medium carbon steel with a tensile strength of 800n/mm^2
Different diameters of the steel would support different torques.
What torque could I expect a 5mm dia Bar to support before any permanent deformation.

Then I’d like to be able to calculate with different tensile strengths and bar diameters.

Is what I’m trying to achieve not possible?

 

[Engdoitbetter]

Charon 99,

Didn't you hear of failure theories?

Failure theories try to relate any stress state to the ultimate tensile/yield stress found in tensile test.
This means, in your case, that the yield shear stress can be related to yield tensile stress, keeping in mind that every theory is an approximation which works only for some kinds of material.

In case of ductile materials,

For maximum shear stress theory (Tresca-Guest), tau_max=0.5*sigma_max, from Mohr's circle for pure tensile stress.

For Von Mises theory, tau_max = 0.577*sigma_max.

The best way in your case would be to measure the actual yield shear stress, but, as a first approximation, you may rely on Tresca criterion which is slightly more conservative.

Anyway, you should study at least the basics of theory of elasticity before dealing with this kind of problems. Engineering is not a straightforward formula.

Regards,

Stefano