Question 1

Where does maximum shear stress occur in torsion?

Accepted Answer

For a circular cross-section under torsion, shear stress is zero at the center and maximum at the outer surface (r = D/2). The maximum shear stress is given by τ_max = T·r/J, where r is the outer radius and J is the polar moment of inertia (πD⁴/32 for solid, π(D⁴-d⁴)/32 for hollow).

Question 2

Why is a hollow shaft more efficient than a solid shaft?

Accepted Answer

Material near the center contributes little to torsional resistance because shear stress is near zero there. Removing it reduces weight significantly while barely reducing stiffness. For the same outer diameter and material volume, a hollow shaft achieves a larger polar moment of inertia J, carrying more torque at the same stress level.

Question 3

How is the angle of twist calculated?

Accepted Answer

The angle of twist is φ = TL/(GJ), where T is applied torque [N·m], L is shaft length [m], G is the shear modulus [Pa] (≈80 GPa for steel, ≈27 GPa for aluminum), and J is the polar moment of inertia [m⁴]. The result is in radians; multiply by 180/π for degrees.

Question 4

What engineering applications use this torsion calculator?

Accepted Answer

Common uses include: preliminary design of drive shafts and propeller shafts, bolt-tightening torque analysis, gear shaft fatigue life assessment, coupling and keyway design, and pre-FEM hand-calculation verification. Compare τ_max against the material's yield shear strength (≈0.577·σ_y for Von Mises) to evaluate the safety factor.

Shaft Torsion & Shear Stress Calculator

Theory