This Shaft Design spreadsheet from 3D-LABS follows ASME standards and gives instant, checkable results for practising engineers — no manual derivation required.
This spreadsheet calculates shaft diameter for combined bending and torsion loading using the Soderberg and modified Goodman fatigue criteria per Shigley’s Machine Design (10th Ed.) and ASME B106.1M. It covers solid and hollow shafts under fully-reversed bending and mean torsion — the standard loading case for motor shafts, pump shafts, and gearbox input/output shafts.
What standard does this calculation follow?
Modified Goodman criterion: σa/Se + σm/Sut = 1/n; Soderberg criterion: σa/Se + σm/Sy = 1/n. Per ASME B106.1M-1985 (Design of Transmission Shafting) and Shigley’s Mechanical Engineering Design, 10th Edition, Sections 6-12 through 6-14.
What formula is used?
ASME DE-Goodman criterion for combined loading: (1/n)² = (16/πd³)² × [(2MaKf)² + (3TmKfs)²] / Se² + [(2Mm Kf)² + (3Tm Kfs)²] / Sut², where Ma = alternating moment, Tm = mean torque, Kf = fatigue stress concentration factor, Se = endurance limit.
Frequently Asked Questions
What is the difference between Soderberg and Goodman shaft design criteria?
Soderberg uses the yield strength (Sy) as the mean stress limit: σa/Se + σm/Sy = 1/n. Modified Goodman uses ultimate tensile strength (Sut): σa/Se + σm/Sut = 1/n. Soderberg is more conservative (smaller shaft) and is preferred for ductile materials under repeated loading. Goodman is standard in ASME B106.1M.
What is the endurance limit Se for a steel shaft?
For wrought steel (Su ≤ 1,400 MPa), the rotary-beam endurance limit Se’ ≈ 0.5 Su. After applying surface factor ka, size factor kb, load factor kc, temperature factor kd, and reliability factor ke: Se = ka × kb × kc × kd × ke × Se’. For a 50mm ground shaft in SAE 1045 (Su = 620 MPa): Se’ = 310 MPa, Se ≈ 0.90 × 0.83 × 1.0 × 1.0 × 0.87 × 310 ≈ 200 MPa.
Does this spreadsheet calculate stress concentration factors Kf?
Yes. Kf = 1 + q(Kt – 1), where q = notch sensitivity (from Peterson’s charts as function of notch radius and Su) and Kt = theoretical stress concentration factor. The spreadsheet includes lookup tables for keyways (Kt = 1.6–2.0 per ASME B106.1M), shoulder fillets, holes, and press-fit interfaces.
What’s Included
An instant Excel download with the complete formula set, a worked numerical example, and reference to the governing standard — ready to adapt to your own project inputs.
