DIN 743 — Calculation of Load Capacity of Shafts and Axles
DIN 743 — Calculation of load capacity of shafts and axles
DIN 743 is the German standard for calculating the load-carrying capacity of rotating shafts and non-rotating axles. It defines the method for determining the fatigue safety factor under combined alternating and mean bending and torsional stresses, accounting for the material endurance limit, the notch effect (fatigue stress-concentration factor Kf), the size influence factor, and the surface factor. DIN 743:2012 is the current edition, structured in four parts, and is the standard cited in German and European drivetrain and machinery design.
MechanixCalc does not currently perform a DIN 743 proof. The MechanixCalc shaft calculator covers the same design questions using the classical textbook methods — modified-Goodman fatigue with a Marin-corrected endurance limit, Peterson/Pilkey notch factors, von Mises static yield, and a Timoshenko beam-FEM deflection and critical-speed solve — which will give a comparable but not identical answer. Use it as an engineering calculation and design-review aid; a DIN 743 submission needs the standard's own endurance values, size factors and support-figure notch factors.
Calculators that implement DIN 743
What DIN 743 covers
- Fatigue safety factor under cyclic bending and torsion with Goodman mean-stress correction (DIN 743-1)
- Notch effects — fatigue stress-concentration factor Kf for shoulder fillets, keyways, grooves and threads (DIN 743-2)
- Material fatigue properties: endurance limit, ultimate strength, size and surface influence factors (DIN 743-3)
- Static safety factor against yielding under combined bending and torsional stress (von Mises criterion) (DIN 743-1)
- Multi-segment stepped shafts — critical-section identification across the full shaft geometry
- Assessment of both load-controlled (R = -1) and mean-stress-shifted (R ≠ -1) fatigue conditions
Parts of the standard
- DIN 743-1Calculation procedure
- DIN 743-2Theoretical stress concentration factors and fatigue notch factors
- DIN 743-3Material properties
- DIN 743-4Calculation of equivalent mean and amplitude stresses, supplementary rules
Governing formulas
σ_a / S_e + σ_m / S_u = 1 / SF_fatwhere σ_a = local alternating stress amplitude including Kf; σ_m = local mean stress; S_e = corrected endurance limit; S_u = ultimate tensile strength. DIN 743-1 §5.4 does NOT use a Goodman line — it builds the amplitude limit σ_ADK from the mean-stress sensitivity ψ_σK and compares against it, then takes S = 1/√((σ_a/σ_ADK)² + (τ_a/τ_ADK)²) ≥ 1.2. This is the Goodman form the MechanixCalc calculator uses instead.
σ_vM = √( (σ_b + σ_ax)² + 3·τ² ) ; SF_stat = S_y / σ_vMwhere σ_b = bending stress at the critical section; σ_ax = axial direct stress (F_ax / A); τ = torsional shear stress; S_y = material yield strength; SF_stat = static safety factor against yielding
n_c = 945.81 · √(1 / δ) [rpm, with δ in mm]where n_c = first lateral critical speed (rpm); δ = maximum static bending deflection under self-weight and attached masses (mm). The constant 945.81 = (60 / 2π) · √9810, for g = 9810 mm/s². A healthy design keeps the operating speed at least 20–25 % away from n_c.
Frequently asked questions
What is DIN 743 used for?
DIN 743 is used to verify that a rotating shaft or non-rotating axle has adequate fatigue strength under combined cyclic bending and torsional loading. It calculates the fatigue safety factor — accounting for notch effects (Kf), the size influence factor and the surface factor — so the designer knows how much margin exists against a fatigue crack initiating at a stress-raising feature such as a shoulder fillet, keyway or groove.
What is the difference between DIN 743 and the Goodman criterion?
DIN 743 uses the Goodman mean-stress line as its core fatigue relationship, but adds a structured framework on top: it defines how to compute the component endurance limit S_e from the material limit by applying Kf (fatigue notch factor from DIN 743-2), the size factor K_d and the surface factor K_R (from DIN 743-3). The Goodman line itself is then applied to the locally corrected S_e, so a notched shaft is never assigned the smooth-specimen endurance limit.
How does DIN 743 handle stress concentration at keyways and shoulder fillets?
Part 2 (DIN 743-2) provides theoretical stress-concentration factors Kt and the fatigue notch factor Kf for the common features: shoulder fillets (as a function of D/d and r/d), keyways, circlip grooves and threads. Kf is applied to the alternating-stress component so the fatigue safety factor reflects the weakening effect of each notch. The MechanixCalc shaft calculator handles notches too, but takes Kt from the Peterson/Pilkey charts rather than DIN 743-2 — a comparable engineering approach, not the standard's own method.
What safety factor does DIN 743 recommend?
DIN 743-1 does not mandate a single universal value; the required minimum depends on the application, load-data uncertainty and consequence of failure. Typical industry practice for power-transmission shafts is SF ≥ 1.5 for fatigue and SF ≥ 1.2 for static yield, with higher margins (≥ 2.0 fatigue) where load data are uncertain or failure is safety-critical. DIN 743-1 §6 itself specifies S_min = 1.2. The MechanixCalc shaft calculator flags warning and fail states at its own default thresholds — which are MechanixCalc's, not the standard's — and shows the raw margin so you can apply your own requirement.
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Related standards
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