DIN 743 — Calculation of Load Capacity of Shafts and Axles
DIN 743 — Calculation of load capacity of shafts and axles
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DIN 743 is the German standard for the load capacity of shafts and axles. It proves two things for every critical cross-section: safety against fatigue fracture, S_D, and safety against permanent deformation, S_F — each required to reach 1.2. Part 1 sets out the method, Part 2 the form factors and notch factors, Part 3 the material strengths, and Part 4 the equivalent (damage-equivalent) stress amplitude for finite-life and load-spectrum cases.
Its fatigue proof works on nominal stresses at the notch root. The smooth specimen's fatigue strength is reduced to the component's by a technological size factor K1 (hardenability of the bar), a geometric size factor K2, a roughness factor K_F and the notch factor β. The mean stress then lowers the permissible amplitude through the material's mean-stress sensitivity ψ — not through a Goodman line — in one of two load cases, with the yield limit taking over at high mean stress.
The MechanixCalc shaft calculator performs this proof at every shoulder fillet, keyway, retaining-ring groove and at each segment's weakest plain section, for steels without a hard surface layer, on the same bending moment, section torque and axial force as the rest of its calculation — and shows every factor per section. It does not check press-fit seats (bearing and hub fits), splines, cross holes, rounded grooves or threads, hollow or surface-hardened shafts — every result says so — and takes no credit for surface strengthening. It is built on the 2012-12 editions of the three parts; Part 3 is now DIN 743-3:2024-07 (updated material table and strength values), and the proof has not been checked against it or against the 2014 correction to Part 3.
What DIN 743 covers
- Safety against fatigue fracture S_D ≥ 1.2 under combined tension/compression, bending and torsion (DIN 743-1)
- Safety against permanent deformation S_F ≥ 1.2 at the peak loads, with the static support factor K2F and the yield increase γ_F at circumferential notches (DIN 743-1)
- Form factors α for shoulders and grooves, the related stress gradient G′ and support factor n (β = α/n), and measured notch factors for keyways, press fits, splines and retaining-ring grooves (DIN 743-2)
- Material strengths at a reference diameter and the size factors that carry them to the component (DIN 743-3)
- Load case 1 (mean stress constant) and load case 2 (mean-to-amplitude ratio constant)
- Non-welded steel shafts and axles, roughly −40 °C to 150 °C, without dominant transverse-shear stress
Parts of the standard
- DIN 743-1Fundamentals — the fatigue and static proofs
- DIN 743-2Theoretical stress concentration factors and fatigue notch factors
- DIN 743-3Strength of materials
- DIN 743-4Fatigue strength, endurance limit — equivalently damaging stress amplitude
Governing formulas
S_D = 1 / √((σ_zda/σ_zdADK + σ_ba/σ_bADK)² + (τ_ta/τ_tADK)²) ≥ 1.2where σ_zda, σ_ba, τ_ta = nominal stress amplitudes in tension/compression, bending and torsion; σ_ADK, τ_ADK = the component's permissible amplitudes, which carry the size, roughness, notch and mean-stress effects
σ_WK = K1(d_eff) · σ_W(d_B) / K_σ , K_σ = (β_σ / K2(d) + 1/K_Fσ − 1) / K_Vwhere σ_W(d_B) = fully reversed fatigue strength of the smooth specimen; K1 = technological size factor from the heat-treatment diameter d_eff; K2 = geometric size factor; K_F = roughness factor from Rz; K_V = surface-strengthening factor; β = notch factor. Torsion follows the same form with τ.
β = α / n , n = 1 + √(G′·mm) · 10^−(0.33 + σ_S(d) / 712 MPa)where α = form (stress-concentration) factor; n = support factor for steels without a hard surface layer; G′ = related stress gradient at the notch root, which grows as the notch radius shrinks; σ_S(d) = yield strength at the component size
S_F = 1 / √((σ_zdmax/σ_zdFK + σ_bmax/σ_bFK)² + (τ_tmax/τ_tFK)²) ≥ 1.2where σ_max, τ_max = peak nominal stresses; σ_FK, τ_FK = component yield limits, including the static support factor K2F and the yield increase γ_F at circumferential notches
Frequently asked questions
What is DIN 743 used for?
To prove that a steel shaft or axle carries its loads with enough margin against two failures: a fatigue crack growing from a notch under the alternating stresses, and permanent (plastic) deformation under the peak loads. The proof is made at every cross-section change and shaft-hub connection, and at the most-loaded section.
How is DIN 743 different from the Goodman criterion?
Both reduce the permissible stress amplitude as the mean stress rises, but differently. Goodman draws a straight line from the endurance limit to the tensile strength. DIN 743 uses the component's own mean-stress sensitivity ψ, computed from its fatigue limit and tensile strength, and switches to the yield limit when the mean stress is high. It also distinguishes load case 1 (the mean stays constant as the load grows) from load case 2 (mean and amplitude grow together — the more conservative, and the one to choose when in doubt).
How does DIN 743 handle stress concentration at shoulders and keyways?
For shoulders and circumferential grooves DIN 743-2 gives the form factor α from the geometry and turns it into the notch factor through the support factor n, which rewards a STEEP stress gradient — at a sharp notch only a small volume of material sees the peak stress: β = α/n. For keyways, press fits, splines and retaining-ring grooves it gives notch factors measured on test shafts of a reference diameter, which are then scaled to the actual diameter. Threads are outside its scope.
What minimum safety factor does DIN 743 require?
S_min = 1.2, for both the fatigue proof and the static proof. It presumes the loads are known accurately; where they are not, a higher margin is a matter for the designer or the contract.
Does the MechanixCalc shaft calculator perform a DIN 743 proof?
Yes — at every shoulder fillet, keyway, retaining-ring groove and the weakest plain section of each segment of a solid steel shaft without a hard surface layer, with load case 1 or 2 and an application factor K_A for load fluctuation and peak loads. Every factor (K1, K2, K_F, α, n, β, ψ, the component limits and permissible amplitudes) is shown per section and printed in the PDF report. It does not check press-fit seats (bearing and hub fits), splines, cross holes, rounded grooves or threads, hollow or surface-hardened shafts, and takes no credit for surface strengthening (K_V = 1). A section it cannot assess is listed as such and the shaft is then reported as not proven; a seat it never checks is stated on every result.
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