Combined Fatigue Loading (Von Mises Alternating and Mean)
A shaft that bends and twists at once needs one alternating and one mean stress for the Goodman check.
Example
You enter
- Bending alternating stress (psi) 10000
- Bending mean stress (psi) 0
- Axial alternating stress (psi) 0
- Axial mean stress (psi) 0
- Torsional alternating stress (psi) 0
- Torsional mean stress (psi) 5000
- Kf, bending (1 if no notch) 2
- Kf, axial (1 if no notch) 1
- Kfs, torsion (1 if no notch) 1.5
You get
- Von Mises alternating stress 20000
- Von Mises mean stress 12990 psi (sigma_m)
- Peak von Mises (first-cycle yield) 23848
No published worked example is on file for this calculation. It is checked against a hand-worked derivation of its method and an independent reference test.
Details, formula, and sources
ScopeApply each mode's notch factor, combine the alternating parts and the mean parts by von Mises, and divide the axial alternating stress by 0.85 so a bending endurance limit fits. 10,000 psi reversed bending with Kf 2 and a steady 5,000 psi torsion with Kfs 1.5 gives 20,000 psi alternating and 12,990 psi mean, plus a 23,848 psi peak for the yield check. In-phase loading. A design aid; test data govern.
Formula or tablesigma'a = sqrt((Kf_b sa_b + Kf_ax sa_ax/0.85)^2 + 3 (Kfs ta)^2); sigma'm = sqrt((Kf_b sm_b + Kf_ax sm_ax)^2 + 3 (Kfs tm)^2); sigma'max = sqrt((Kf_b (sa_b + sm_b) + Kf_ax (sa_ax + sm_ax))^2 + 3 (Kfs (ta + tm))^2).
Source and editionCombinations of loading modes for fatigue (Shigley, Mischke and Budynas, Mechanical Engineering Design, Ch. 6), by name: von Mises combination of the notch-corrected alternating and mean components, with the axial alternating stress divided by the axial load factor 0.85 so a rotating-bending endurance limit applies.
Free accessStandard published fatigue relations; the stress components and notch factors are the user's inputs.
What governsEstimate. AHJ and licensed professional govern.
API field namesbending_alt_psi, bending_mean_psi, axial_alt_psi, axial_mean_psi, torsion_alt_psi, torsion_mean_psi, kf_bending, kf_axial, kfs_torsion, vm_alt_psi, vm_mean_psi, vm_max_psi
- Combination von Mises on the alternating and the mean components separatelyShigley Ch. 6, combinations of loading modes
- Axial load factor axial alternating stress divided by 0.85 (kc) so the bending Se appliesShigley Ch. 6
- Phase all modes in phase at one frequencyscope of this tile