Shaft Torsion & Angle of Twist Simulator
Apply a motor torque to a solid or hollow shaft and watch it visibly twist, with live shear stress, angle of twist, power transmitted and a pass/fail safety check.
Choose a solid or hollow shaft, pick the material and dimensions, then apply a torque at the motor end against the load at the other end. Watch the shaft visibly twist, check the shear-stress-vs-radius diagram, and see whether the design stays inside the allowable stress.
| Outer diameter | Cross-section (rel.) | Shear stress τ | Factor of safety | Verdict |
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About the Shaft Torsion & Angle of Twist Simulator
Free shaft torsion & angle of twist simulator. Apply a motor torque to a solid or hollow shaft and watch it visibly twist, with live shear stress, angle of twist, power transmitted and a pass/fail safety check. Drag, change the sliders and see the result live. No sign-up, works on phone and computer. Built for engineering, the shaft torsion & angle of twist simulator runs instantly in your browser: change a setting or drag an object and the result updates at once, so you learn by trying things out rather than only reading about them.
Apply a motor torque to a solid or hollow shaft and watch it visibly twist, with live shear stress, angle of twist, power transmitted and a pass/fail safety check. Use it to explore engineering ideas at your own pace, then check what you found against the key ideas further down this page.
How to use the Shaft Torsion & Angle of Twist Simulator
- Use the controls to change Shaft type, Material, Shaft length, Outer diameter, Inner diameter (hollow only), and more. The simulation reacts instantly.
- Pick an option such as Solid, Hollow, Steel, Aluminum to switch modes or load an example.
- Press "Overload it!", "Reset", "Compare 3 diameters" to start, reset or change what is happening.
- Where you see a glowing handle, object, weight or atom, drag it with your mouse or finger. Everything responds in real time.
- Watch the readouts and graphs update as you experiment, and compare what you see with the key ideas below.
Things to try
- Switch from solid to hollow with the same outer diameter and see how much the maximum shear stress and angle of twist change.
- Keep the torque fixed and swap between steel, aluminum, brass and titanium — which one twists least for the same size?
- Try the design challenge: find the smallest-diameter steel shaft that can still transmit 5 kW at 1500 RPM safely.
- Press "Overload it!" and watch the shear-stress-vs-radius diagram cross the green allowable line.
Key ideas you can learn
- Torsion twists a shaft about its own axis; the polar moment of inertia J measures how well the cross-section resists that twist, larger for a bigger or hollower-but-thicker-walled section.
- Shear stress from torsion is zero at the center and rises linearly to a maximum at the outer surface (τ = T·c / J), which is why hollow shafts use material efficiently — they remove low-stressed material near the center.
- The angle of twist θ = T·L / (J·G) grows with a longer shaft or a softer material (lower shear modulus G), and shrinks with a stiffer cross-section.
- Power transmitted by a rotating shaft is P = T·ω, so the same power can be delivered by a high torque at low RPM or a low torque at high RPM — this is exactly why gearboxes trade torque for speed.
- A safe shaft design keeps the maximum shear stress below an allowable limit (here approximated as half the material's tensile yield strength) with some margin, not exactly at the limit.
Polar moment of inertia: solid J = π·d⁴/32, hollow J = π·(do⁴ − di⁴)/32
Max shear stress: τmax = T·c / J, where c is the outer radius
Angle of twist: θ = T·L / (J·G), G is the material's shear modulus
Power transmitted: P = T·ω = T·(2π·N / 60), N in RPM
Simplified safety check: allowable shear stress ≈ 0.5 × the material's tensile yield strength (Tresca-style approximation)
Factor of safety: FOS = τallow / τmax — how many times over the shaft could take before yielding (FOS ≥ 1 is required, real designs usually target 1.5–3+)
Diameter comparison: for the same torque and material, a bigger diameter needs far more material (cross-section grows with d²) but stress drops fast (τ shrinks roughly with d³ for a solid shaft) — the "Compare 3 diameters" button shows this material-vs-safety trade-off directly.
Where this is used in the real world
Power transmission shafts in cars, ships, wind turbines and industrial gearboxes, drill strings in oil and gas drilling, robot and machine-tool spindles, and aircraft engine shafts are all sized using this exact torsion analysis.
Who is this simulation for?
Engineering and technology students, makers, robotics clubs and teachers of design and technology. It gives a hands-on feel for how machines behave before you build a real one.
For teachers: project it on the board, let students predict what will happen, then run it together. For students: change one thing at a time and write down what changes.
Frequently asked questions
Why do hollow shafts transmit torque more efficiently than solid shafts of the same weight?
Shear stress is lowest near the center of a shaft, so that material barely contributes to resisting torque. A hollow shaft removes that underused material and puts more material near the outer radius where the stress — and therefore the resistance to twisting — is highest, giving a better strength-to-weight ratio.
What is the difference between shear stress and shear strain in torsion?
Shear stress (τ) is the internal force per unit area resisting the twist, and it's what you compare against the material's strength. Shear strain (γ) is the geometric distortion angle at a point, related to stress by γ = τ / G. The angle of twist θ you see the whole shaft rotate by is the accumulated effect of that strain along the shaft's length.
Why does angle of twist matter if the shaft is not overstressed?
Excess twist (angular deflection) can misalign gears, couplings or timing components even when the stress is well within the material's strength. Many real shaft designs are limited by an allowable twist per unit length rather than by stress alone.
Is the Shaft Torsion & Angle of Twist Simulator free to use?
Yes. It is completely free, with no signup, no download and no ads inside the simulation. It runs in your web browser.
Does the Shaft Torsion & Angle of Twist Simulator work on a phone or tablet?
Yes. It uses touch as well as the mouse, so you can drag objects with your finger. A larger screen makes the controls easier to see.