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What is Torsional Stiffness?

Bobby R. Goldsmith
Bobby R. Goldsmith

Torsional stiffness is the measure of the amount of torque that a radial shaft can sustain during its rotation in a mechanical system. The concept is central to basic mechanics and engineering, and torsional stiffness is one of the key forces of measure for any mechanical system that rotates on a fixed axis. This force exists in machines as small as a pocket watch and as large as heavy industrial equipment. It is vital to understanding the amount of stress that a rotating shaft can endure while transmitting force through the rest of the mechanical system.

There are two kinds of stiffness in a rotating mechanical system that is driven by a shaft — torsional stiffness and flexural stiffness. Another, more accurate way to describe these forces is to call them the torsional and flexural strength of a shaft. Both flexural and torsional stiffness are measured in pounds per inch or newtons per meter against the surface area of the shaft.

Man with a drill
Man with a drill

The rate of torsional stiffness is stronger along the tighten outer layer (TOL) of the shaft, and weaker along the loosen outer layer (LOL) of the shaft. When the force of the torque winds in the same direction as the movement of the shaft, the transfer of energy is far more efficient because the torsional force compresses the TOL, allowing less energy to be dissipated through heat and friction. A higher rate of torsional stiffness along the TOL is generally desirable in a rotating mechanical system.

When the torsional force turns against the direction in which the shaft is turning, more energy is applied along the LOL of the shaft. This can cause an extreme loss of efficiency in the transfer of energy from the radial shaft to the rest of the mechanical system. The decompression of the shaft, as the layer loosens and expands, allows more of the energy to dissipate out of the mechanical system, meaning that less force is applied.

Generally, all else being equal, a rotating mechanical system operates best when the force applied to the system is transferred through the radial shaft in the same direction that the shaft spins to transfer the energy out of the system. This fact does limit the variety and complexity of mechanical systems that can be constructed, but with harmonic dampers and balancers, counterforce rotating systems can be constructed that are relatively efficient when torsional stiffness levels are high along the LOL of the shaft.

Discussion Comments


@KoiwiGal - I don't think you give people enough credit. The kind of mathematics they were doing thousands of years ago was certainly advanced enough to calculate torsional stiffness.

Think about what the Chinese, for example, accomplished centuries before Western civilizations.

They had advanced hydraulics and mechanical systems. Those would have certainly needed the torsional stiffness formula in order to get past a certain point.

People always underestimate what their ancestors were capable of.


@pleonasm - Sometimes I wonder though, if they actually knew the calculation, or if they simply knew that if they made it this thick, it could turn this amount of weight- any thinner and it would break. That's the kind of thing you could come up with through trial and error, and of course, we only ever see the designs that made it through. They might not have actually had a calculation that worked out torsional shear stress points.

I'm not sure, but I think this is the kind of calculation that would work in proportion. So, if a designer back then made a small model, to test, before making the final piece, they could just try over and over until it all worked, rather than working it out before hand.

I'm not sure if that's how they did it, but it's certainly possible.


I find it so incredible that people hundreds of years ago could recognize this concept and build intricate clockwork mechanisms that take advantage of it.

I recently read an article about clockwork "robots", or moving human figures made with clockwork mechanisms that allowed them to do things like play a small piano, or make movements similar to prayer.

Some of them were several hundred or even a thousand years old and yet the people who built them must have understood the torsional stiffness calculation, something even I don't really claim to understand and most people now wouldn't even know.

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    • Man with a drill
      Man with a drill