Circular elastic shaft

Solid-shaft torsion

Inputs

Applied torqueTSteady transmitted torque for the displayed shaft segment.

Shaft diameterDUniform solid circular shaft diameter.

Shaft lengthLUniform torsion length between the stated reference sections.

Shear modulusGElastic shear modulus for the stated material condition.

Rotational speednSteady rotational speed for the power relationship.

Maximum torsional shear stressτ

29.697

Elastic angle of twistφ

0.98459

Transmitted mechanical powerP

37.961

Polar second momentJ

147,324

J = πD⁴/32; τmax = Tc/J; φ = TL/GJ; P = Tω

A first-pass number, not a code check, certification, or approval. Read the method and its limits below. What this is and is not.

Calculation snapshot

Formula version 1.0.0

Maximum torsional shear stress	29.697 MPa
Elastic angle of twist	0.98459 °
Transmitted mechanical power	37.961 kW
Polar second moment	147,324 mm⁴

J = πD⁴/32 · τmax = Tc/J · φ = TL/GJ · P = Tω

Boston University torsion reference: https://www.bu.edu/moss/mechanics-of-materials-torsion/

This printout is a record of displayed inputs and deterministic formula output. It is not an approval, certification, or engineering conclusion.

Method

Screen maximum shear stress, angle of twist, and transmitted power for one uniform solid circular shaft.

J = πD⁴/32; τmax = Tc/J; φ = TL/GJ; P = Tω

When

Don’t

This is a uniform solid circular elastic shaft under steady torque. It excludes stress concentration, combined bending, fatigue, keyways, bearings, critical speed, torsional vibration, material strength limits, and code or safety-factor decisions.