Lab · Structural Mechanics
Torsion Lab
A circular shaft built from prismatic steps, twisted by concentrated torques. The engine cuts it at every section change and every torque, so the internal torque, the outer-surface shear stress and the accumulated twist are exact on each interval rather than averaged over the shaft.
Shaft
Shaft segments
Applied torques
A torque is positive by the right-hand rule about the shaft axis, pointing away from the restrained end. The internal torque on a cut is the sum of every torque beyond it, so it jumps by −T as the cut passes an applied torque.
Largest internal torque |T|
interval 2
Largest surface shear |τ|
interval 2
Total angle of twist φ
0.027446 rad end to end
Internal torque T(x)
Interval results
| # | x range [m] | J | T | |τ| outer | Δφ | φ at end |
|---|---|---|---|---|---|---|
| 1 | 0 – 1 | 1.2723e+6 mm⁴ | 900 N·m | 21.221 MPa | 0.51108° | 0.51108° |
| 2 | 1 – 2 | 1.0210e+6 mm⁴ | 1500 N·m | 44.074 MPa | 1.0615° | 1.5725° |
Summary
| Shaft length L | 2 m |
|---|---|
| Computational intervals | 2 |
| Total angle of twist φ | 1.5725° (0.027446 rad) |
| Reaction torque implied at the restrained end | -900 N·m |
| Largest internal torque |T| | 1500 N·m |
| Largest outer-surface shear |τ| | 44.074 MPa |
The Lab does not solve for supports. It reports the torque the restrained end must supply to hold this torque set in equilibrium — equal and opposite to the sum of the applied torques.
Assumptions
- · Circular prismatic shaft in Saint-Venant torsion: plane sections remain plane and radii remain straight.
- · Linear-elastic, homogeneous material and pure torsion with no warping restraint.
- · The left end is the restrained rotational reference, φ(xStart) = 0; the reaction torque reported there is implied by that reference, not solved from a support model.
What this Lab models
A circular shaft carrying torque about its own axis. It is built from prismatic steps, each solid or hollow with its own diameters and shear modulus, and concentrated torques may sit anywhere along it. The engine cuts the shaft at every section change and every torque, so T, the outer-surface shear stress and the twist rate are constant and exact within each resulting interval.
Model scope
- · Internal torque from the right free body: T(x) is the sum of every applied torque beyond the cut, so T jumps by −T at an applied torque.
- · One restrained reference end at x = 0 with φ = 0; the Lab reports the reaction torque that end must supply and never invents a second support.
- · Circular sections only. For a circular section the torsion constant equals the polar second moment of area; a non-circular section warps and these relations do not apply to it.
- · Linear-elastic, homogeneous material and pure torsion with no warping restraint. No stress concentration at a step, keyway or fillet is included.
- · The shear stress varies linearly with radius, so the value reported is the maximum, at the outer surface.