Torsional Rigidity Calculator: worked example
This example is generated from PROFENG's own default input set and the implemented relationship. It is not copied from a cited publication.
Relationship
GJ
This calculator determines torsional rigidity from solid shaft diameter, shear modulus. Use it for first-pass mechanics and machine-design calculations with explicit loads, geometry and material inputs.
Inputs
- Solid shaft diameter (diameter) = 50 mm
- Shear modulus (shearModulus) = 80 GPa
Working
(80)*1e9*(Math.PI*Math.pow((50)/1000,4)/32) = 49,087.385 N·m²
Torsional rigidity: 49,087.385 N·m²
Assumptions and limits
- Loads and geometry are represented by the idealized relationship shown.
- Material behavior is treated according to the simple formula, typically linear-elastic where relevant.
- Units and section properties are consistent with the displayed equation.
- Shaft is solid, circular and uniform.
- Material is linear elastic in shear.
- G and J must use consistent units.
Formula source and acknowledgement
Ferdinand P. Beer, E. Russell Johnston, John T. DeWolf, David F. Mazurek, Mechanics of Materials, 8th, 2020, McGraw Hill. Credit belongs to the cited author(s)/publisher; PROFENG presents its own implementation and does not imply endorsement.
Richard G. Budynas, Keith J. Nisbett, Shigley's Mechanical Engineering Design in SI Units, 11th, 2020, McGraw Hill. Credit belongs to the cited author(s)/publisher; PROFENG presents its own implementation and does not imply endorsement.
Automated verification passed – 30 September 2026 – six numerical cases checked, with dimensional checks and an independent implementation where applicable.
This worked example is for engineering screening and education. Replace defaults with traceable project data and confirm the method, assumptions, standards and equipment information before design, procurement or operation.