Lessons · Engineering · A shaft in torsion
A shaft twisting under load
A shaft transmitting torque carries shear stress that is zero at the centre and highest at the surface. That is why a hollow shaft is nearly as strong as a solid one of the same outside diameter: the material near the axis was barely working.
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In beta. This lesson was written for Hone and has not yet been checked by a licensed engineer. Practice material, not professional advice. What that means.
What it is for
It explains why drive shafts are tubes. Removing the middle third of the material costs very little strength and saves considerable weight, and weight on a rotating part costs twice.
How to think about it
Remember that resistance to twist grows with the fourth power of diameter while stress depends on the third. A small increase in diameter is worth far more than a large increase in material elsewhere, which is why shafts get thicker rather than longer.
Worked example
Shear stress is zero on the axis, maximum at the surface.The middle contributes least.
A hollow shaft loses little strength for much weight.Why drive shafts are tubes.
Polar second moment grows with the fourth power of diameter.Doubling diameter multiplies stiffness by sixteen.
Stress falls with the cube of diameter.Doubling diameter divides stress by eight.
Your turn
Doubling a solid shaft's diameter divides the peak shear stress by what factor?
Stress falls with the cube, so doubling diameter divides stress by
Solve one, graded on the server
The trap
Adding length to stiffen a shaft. Length makes twist worse, not better; diameter is the lever and it is a very strong one.