Torsion of Sections — validation & limitations
What this calculator checks and the method behind each result, the independent reference cases its engine is tested against, and what it does not check. Use it to decide how far you can rely on a result.
Open the Torsion of SectionsWhat it calculates
Standard / method: Classical torsion theory (Saint-Venant / Bredt-Batho)
Saint-Venant / Timoshenko / Roark torsion for solid sections · Bredt-Batho shear-flow for closed thin-walled sections · Soderberg and Modified Goodman torsional fatigue (Shigley). No international standard governs the torsion of general prismatic sections; these are textbook methods, not code checks.
Engineering estimate — this tool uses an accepted simplified model rather than one citable governing standard. Use it for preliminary sizing and verify the final design against manufacturer data or a qualified engineer.
- Torsional shear stress and angle of twist for 7 cross-section types (Saint-Venant / Timoshenko / Roark)
- Torsion constant J and torsional section modulus Wt, named for the method that produced them
- Shear-yield safety factor via the Von Mises or Tresca criterion, with an absolute floor at 1.0
- Bredt-Batho shear-flow theory for closed thin-walled boxes, an exact annulus for thin-walled round tubes, and a closed-vs-open comparison panel (box, tube, open channel) — each with an explicit warning when the wall is too thick for the method
- Mohr's circle for the full combined stress state under bending, torsion and axial load
- Minimum solid-round diameter at the ASME shafting-code shear allowable (the historical, withdrawn ASME shaft code as reproduced in Shigley), and a second one that includes the axial force
- Torsional fatigue against Soderberg, Modified Goodman and Sines in shear space (Shigley) plus a first-cycle yield check, from a Marin-corrected endurance limit — surface finish, size and reliability are applied and shown
Validation evidence — independent reference cases (1)
Each case runs the tool's engine on a worked example whose values come from a published source or a hand derivation from the cited equations, and an automated regression test asserts the engine against those values within the stated tolerance. "Conservative" means the engine is known to sit on the safe side of the reference and the test asserts that side. Sources are cited; their text is not reproduced.
Hollow shaft shear-yield safety with Kt and Tresca, twist angle
AgreesSource: Gere & Goodno, Mechanics of Materials, torsion of circular tubes; Shigley 10th ed. eq. 3-37/3-40, §3-13, §5-4 eq. 5-3; Peterson's Stress Concentration Factors
Inputs: Do 60, Di 40 mm, T 2000 N·m, L 1500 mm, G 80 GPa, Sy 350, Sus 260 MPa, Kt 1.5, Tresca, SF 2.0
Quantity Reference value Tolerance tau_peak (MPa) 88.14735 1e-6 relative S_sy Tresca (MPa) 175 1e-6 relative SF_yield 1.985312 1e-6 relative twist angle (deg) 2.104363 1e-6 relative tests/golden/REF-torsion-hollow-kt-tresca.golden.test.ts
Limitations
Not checked by this tool
- Restrained-warping (non-uniform) torsion of open sections — Saint-Venant torsion only; compute warping stresses (bimoment) for restrained I- or C-sections
- Shear buckling of thin-walled tubes under torsion — Not checked; check thin tubes against the torsional buckling stress (Roark / EN 1993-1-6)
- Load spectrum and cumulative fatigue damage — Fatigue uses one mean and amplitude; use /fatigue (Miner panel) or /shaft for a spectrum
- Shaft-hub connection (keys, splines, press fits) — Check with /keys or /pressfit
- Elevated temperature (strength derating) — No temperature factor; derate the material for hot service
Results are engineering calculations for qualified users — see the disclaimer. Other tools: all validation pages · standards reference · symbols glossary.