Torsion: What Happens Inside a Twisting Shaft

Grab a wet towel and wring it out. Your two hands turn in opposite directions, the towel twists into a tight rope, and water drips out. You just did something engineers call torsion — twisting a long object around its own line. The same twisting happens inside the spinning parts of cars, drills, and ships, except those parts are made of solid steel and they must not wring out like a towel.

The everyday version: twisting a licorice stick

Imagine holding a long, soft licorice stick. You keep your left hand still and slowly turn your right hand. The stick twists. The end you turn moves a lot, but the end you are holding does not move at all. Somewhere in the middle, the candy is half-twisted.

Now look very closely. A straight line drawn down the side of the licorice has become a gentle spiral. Nothing got longer or shorter, but every bit of the candy got nudged sideways compared to the bit next to it. That sideways nudge is the secret of torsion. Engineers call a spinning or twisting rod a shaft, and almost every machine has one.

The real engineering idea

When you twist a shaft, you apply a turning effort called torque. Torque is simply a force multiplied by how far it acts from the center — like pushing on the end of a long wrench. A small push on a long wrench gives a big torque.

That torque has to travel through the metal from the hand that twists to the end that is held. As it travels, it makes the layers of metal try to slide past one another. This sliding effort is called shear stress — "shear" means a sliding, scissor-like push rather than a pull. The whole rod also rotates a little from one end to the other, and that small rotation is the angle of twist.

Here is the surprising part. The shear stress is not the same everywhere inside the shaft. Right at the center line, the metal barely slides at all, so the stress there is almost zero. As you move outward toward the skin of the shaft, the sliding gets bigger and bigger. The biggest shear stress sits at the outer surface.

Think about a merry-go-round. A child standing on the very center hardly moves, while a child on the outer rim whizzes around fast. Torsion works the same way: the outside does the hard work, the middle does almost nothing.

The amount of sliding at any spot has a name too: shear strain. Strain just means "how much something has been pushed out of shape." At the center the shear strain is nearly nothing, and at the surface it is largest — which is exactly why the stress follows the same pattern. Stress and strain are partners: where one is big, so is the other. This is why, when a shaft is twisted too hard, the very first cracks almost always begin at the outer skin and never in the middle.

A tiny worked example

Let's twist a real shaft and put numbers on it. Suppose we have a solid steel rod that is 20 mm across (so its radius, the distance from center to skin, is 10 mm) and 500 mm long.

Step 1 — find the torque. We turn it with a wrench. We push with a force of 50 newtons (about the weight of a small bag of potatoes) on a wrench that is 0.4 metres long.

Torque = force × length = 50 N × 0.4 m = 20 N·m

To keep our units tidy, 20 newton-metres is the same as 20,000 newton-millimetres.

Step 2 — meet the "fatness number." How well a round shaft resists twisting depends on how wide it is. Engineers wrap that into one number for the cross-section called the polar moment of area (you can think of it as a "fatness number"). For our 20 mm rod that number works out to about 15,700 (in units of mm to the fourth power). The fatter the shaft, the bigger this number grows — very fast.

Step 3 — find the biggest stress. The largest shear stress, out at the skin, is the torque times the radius, divided by the fatness number:

Stress = (20,000 N·mm × 10 mm) ÷ 15,700 = 200,000 ÷ 15,700 ≈ 13 N/mm²

A stress of 13 newtons per square millimetre (also called 13 megapascals) is gentle for steel, which can safely handle well over 100 in shear. So our rod is comfortably strong — it will twist a tiny bit and spring right back.

Step 4 — how much does it twist? Doing the same kind of multiply-and-divide with the rod's length and how stiff steel is, the whole 500 mm rod turns by only about half a degree from end to end. You would barely see it, but it is there.

Why hollow shafts are a clever trick

Remember that the center of the shaft hardly carries any load. So engineers ask a sneaky question: why carry around heavy metal in the middle that is doing almost nothing? The answer is often to drill it out and use a hollow shaft — a tube instead of a solid bar.

A tube keeps the metal where it matters (out at the surface) and throws away the lazy metal in the middle. The result is a part that is nearly as strong against twisting but much lighter. That is why bicycle frames, car drive shafts, and aircraft parts are so often tubes rather than solid rods.

Where you see torsion in real life

Once you know what to look for, twisting shafts are everywhere:

• Car drive shaft: the long tube under a car carries the engine's twist to the wheels, turning many times every second.
• Screwdriver and power drill: the metal shaft twists as you push the tip into a tight screw.
• Bicycle pedals and cranks: every time you stand up to climb a hill, you are twisting the crank axle.
• A door key: turn a stiff lock and you can feel the thin key twisting in your fingers — sometimes keys snap from too much torsion.
• Wind turbines: the giant shaft behind the blades carries an enormous steady twist to the generator.
• Springs and torsion bars: some cars use a long steel bar that twists to soften bumps instead of a coil spring.

Why engineers care

Torsion matters because a shaft that twists too far, or feels too much shear stress at its surface, can fail — and shafts usually sit at the heart of a machine where a failure is expensive or dangerous. If a car's drive shaft snapped while turning thousands of times a minute, the broken ends could whip around and cause real harm.

So engineers do exactly what we did above: they work out the torque, find the shear stress at the surface, and check it stays safely below what the material can take. They also check the angle of twist, because a shaft that winds up too much can throw delicate timing out of step, even if it never breaks. Getting torsion right is the difference between a machine that runs quietly for years and one that shakes itself apart.

Want to keep exploring how engineers size and tighten the parts that hold machines together? Try the tools and other beginner guides at enggtools.in/articles.