What is the polar moment of inertia J?

J is the polar second moment of area: J = πd⁴/32 for a solid shaft, J = π(d_o⁴ − d_i⁴)/32 for a hollow shaft. J measures torsional stiffness.

Where is maximum torsional shear stress?

Maximum shear stress τ_max = Tr_max/J occurs at the outer surface of the shaft (r = d/2). The stress is zero at the center and increases linearly with radius.

What is shear modulus G?

G = E/(2(1+ν)) relates shear stress to shear strain. For steel: G ≈ 80 GPa, aluminum: 27 GPa, brass: 37 GPa. It is always less than Young's modulus E.

Torsion of Circular Shaft Calculator

Calculate torsional shear stress τ = Tr/J (J = πd⁴/32), angle of twist θ = TL/(GJ), and transmitted power P = 2πNT/60. G = shear modulus (steel: 80 GPa, aluminum: 27 GPa).

2D stress state at a point. All stresses in MPa.

σx — Normal Stress X (MPa)

σy — Normal Stress Y (MPa)

τxy — Shear Stress (MPa)

⚙ Mechanical Note: Results are based on standard textbook formulas and ISO/AASHTO references. Always verify critical designs with applicable codes (ISO 898, AASHTO 1993, AISC, Eurocode 3) and a qualified engineer.

How to Use

Enter the values for the patient or scenario you are assessing. Calculate torsional shear stress τ = Tr/J (J = πd⁴/32), angle of twist θ = TL/(GJ), and transmitted power P = 2πNT/60. G = shear modulus (steel: 80 GPa, aluminum: 27 GPa). Use the torsion shaft result to inform your clinical assessment.

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Frequently Asked Questions

What is the polar moment of inertia J?

Where is maximum torsional shear stress?

What is shear modulus G?