Shaft strength calculation (DIN 743)

A shaft rarely fails on its plain sections. It fails at a shoulder, a keyway, a groove or the edge of a press fit, where the local stress is raised, and usually by fatigue long before its static strength is reached. DIN 743 turns the nominal stresses at such a section into a fatigue safety and a static safety that you compare with a required minimum.

Axomek takes the section forces from its shaft solution, checks every diameter step as a shoulder, each notch you add and the most stressed plain section, and reports both safeties at each point. With a duty cycle the checks take the worst load case.

DIN 743-1:2012
DIN 743-2:2012
DIN 743 Beiblatt 1:2024

Try this example in the app

The shaft module with the drive shaft example open: the DIN 743 strength inputs of the 42CrMo4 shaft beside the stepped shaft with its gear and coupling, and the checks with the fatigue and static safety.

What Axomek calculates

You enter

The shaft: sections, supports and loads (forces, moments, torque), and optionally a duty cycle
Material: a preset steel (C45 +QT to E335) or your own σ_B and σ_S at their reference diameter, and the size-effect class for K₁
Surface roughness R_z, fillet radius at the steps and an optional surface treatment (nitrided, case hardened, deep rolled, shot peened and others)
Notches: keyway, two keyways, groove, retaining-ring groove, V-notch, cross bore, press fit, shoulder radius or plain section, each at its position
Torque amplitude, peak load factor for the static check, rotating or non-rotating bending, and mean stress case 1 or 2
Minimum fatigue and static safety (1.2 by default)

It calculates

Fatigue safety S and static safety at every shoulder, notch and the most stressed plain section
Nominal bending, torsion and axial stresses at each point
Stress concentration factor α, notch factor β, total influence factor K and the component fatigue limits
Amplitude strength σ_ADK after the mean stress, and the material strengths at the effective diameter
The incipient crack safety of a hard surface layer, as part of the static safety
Pass or fail against the minimum safeties, with the governing point and load case

Method and standards

Nominal stresses from the section forces, DIN 743-1, 4.2 and Table 1; on a rotating shaft the bending moment is a fully reversed amplitude
Notch factors β = α/n from the stress gradient for shoulders, round grooves and cross bores (DIN 743-2, 4.3); measured factors for keyways, press fits, V-notches and retaining-ring grooves (4.2), scaled by K₃
Size factors K₁(d_eff) and K₂(d), roughness factor K_F and surface factor K_V from the lower bounds of Table 4 (DIN 743-2, clauses 6 to 8)
Total influence factor K_σ, K_τ and component fatigue limits, DIN 743-1, eqs. (5) to (9)
Mean stress case 1 (constant mean) or case 2 (constant ratio, the default), with the compression zone of Annex A for compressive mean stresses
Fatigue safety by eq. (2), static safety by eq. (25) against the component yield point, and the incipient crack check of 5.1.2 for hard layers
axm verify recomputes the three worked examples of DIN 743 Beiblatt 1

Limits

Splined and serrated shafts (DIN 743-2, 4.2.2) are not among the notch kinds
An endurance-limit check: with a duty cycle the worst load case governs, with no damage accumulation (use the FKM method for that)
DIN 743-3 material tables are not built in beyond the seven preset steels; enter σ_B and σ_S for other steels
Nominal stress approach only; K_V is always the lower bound of the table
Cross bores up to 2r/d = 0.3, V-notches for t/d from 0.05 to 0.2

Worked example

The drive shaft example: a 420 mm 42CrMo4 +QT output shaft (σ_B 1100 MPa, σ_S 900 MPa at Ø16 mm, R_z 6.3 µm, fillet radius 1.6 mm) with a helical gear at x = 197 mm passing 525 N·m to a coupling at x = 40 mm. Keyways, a retaining-ring groove, a press-fit edge and a relief groove are checked with a 10 % torque amplitude, a peak load factor of 2 and a duty cycle of Nominal 60 %, Peak 5 % (loads × 1.6) and Part load 35 % (loads × 0.5).

Result	Value
Fatigue safety, worst load case	6.55
Minimum fatigue safety	1.2
Static safety, worst load case	5.19
Fatigue safety at the gear keyway, nominal load	10.46
Notch factor β_σ at the gear keyway	2.949
σ_B at the effective diameter	916.7 MPa
σ_S at the effective diameter	703.9 MPa

The gear keyway governs fatigue, where the bending moment is largest; the Ø45 mm coupling seat governs the static safety, as the full torque passes through the smallest diameter.

The numbers come from the engine: the same commands, run with the axm command line, give them.

The same with the axm command line

axm new ex.axm.json --template drive-shaft
axm solve ex.axm.json --json

Open the example in the app

Questions

Which load case does the DIN 743 check use with a duty cycle?

The worst one. DIN 743 is applied here as an endurance-limit check without damage accumulation; for finite life and load spectra switch the method to the FKM guideline and give a number of load cycles.

At which diameter are the material strengths taken?

The strengths you enter hold at their reference diameter (16 mm by default). The technological size factor K₁ of DIN 743-2, 6.2, reduces them to the largest diameter of the shaft, and the results note gives the values used.

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