Torsion bar (hollow, round)
Polar moment of inertia, shear stress, angular deflection and torsional stiffness of a hollow round torsion bar.
Polar moment of inertia, I_p1.47 10⁻¹² m⁴
Section modulus, S = I_p/e1.47 10⁻⁹ m³
Shear stress, τ339.53 10⁶ Pa
Deflection, φ0.43 rad
Deflection, φ24.53 deg
Torsional stiffness, k = dT/dφ1.17 Nm/rad
Torsional stiffness, k = dT/dφ0.02 Nm/deg
Method & references
- Hollow round torsion bar — polar moment of inertia, shear stress and angular deflection.
- The legacy page this was ported from shares its exact page title with four other spring calculators (disc/Belleville washer; torsion bar, solid; cantilever leaf spring; tension bar/rod spring) that are, despite the shared title, genuinely different spring types.
- Disc (Belleville washer) spring (shares this calculator's legacy page title, but a distinct spring type)
- Torsion bar, solid round (same torsion-bar family, solid section)
- Cantilever leaf spring (shares this calculator's legacy page title, but a distinct spring type)
- Tension bar / rod spring (shares this calculator's legacy page title, but a distinct spring type)
The computation is a literal port of the original client-side JavaScript from /calculators/t14_8.htm. Results are verified equal to the original by an automated golden-master test. No formula has been re-derived or “improved”.