Corrected Endurance Limit (Shigley Marin Factors)
The corrected endurance limit Se from Shigley's Marin equation Se = ka kb kc kd ke Se'.
Example
You enter
- Ultimate strength Sut (psi) 105000
- Surface finish machined
- Diameter d (in) 1
- Load type bending
- Reliability 99
- Temperature factor kd 1
You get
- Corrected endurance limit Se 27365.6
- Marin factors 0.7285
Checked against published worked examples from: McGraw-Hill (Shigley's MED 11th ed. solutions, via Oakland University).
Details, formula, and sources
ScopeWhich turns the ultimate strength into the real fatigue strength. Se' = 0.5 Sut (steel, Sut <= 200 ksi); ka corrects for surface finish (ground/machined/hot-rolled/as-forged, a Sut^b), kb for size (0.879 d^-0.107 rotating, 1 axial), kc for load (1 bending, 0.85 axial, 0.59 torsion), kd for temperature, ke for reliability (0.897 at 90%, 0.814 at 99%). Sut 105 ksi steel, machined, 1 in, rotating bending, 99% reliability gives ka 0.73 (Shigley 11th ed.), kb 0.88, ke 0.81 and Se 27,400 psi - a 48% cut from the raw 52,500 psi, the reason a part sized on Se' alone can be fatigue-unsafe. Feed Se into a fatigue safety-factor check for the full stress-life workflow. Steel; the finite-life S-N line and notch Kf have their own solvers. A design aid; Shigley and the engineer of record govern.
Formula or tableSe = ka kb kc kd ke Se'; Se' = 0.5 Sut (steel, Sut<=200 ksi, else 100 ksi); ka = a Sut_ksi^b (Shigley 11th ed. Table 6-2: ground 1.21/-0.067, machined 2.00/-0.217, hot-rolled 11.0/-0.650, forged 12.7/-0.758; the 10th-edition constants read up to ~8% high); kb = 0.879 d^-0.107 (0.11-2 in) / 0.91 d^-0.157 (2-10 in) bending, 1 axial; kc = 1/0.85/0.59; ke = 0.897/0.868/0.814/0.753 at 90/95/99/99.9%.
Source and editionThe Marin modification factors and the rotating-beam endurance limit Se' = 0.5 Sut (Shigley, Mechanical Engineering Design, 11th ed., Ch. 6 -- Marin surface, size, load, temperature, and reliability factors), by name; feeds the fatigue-safety-factor tile.
Free accessThe Marin equation and its factor tables are standard published machine-design results; the ultimate strength, diameter, finish, load type, and reliability are the designer's inputs.
What governsEstimate. AHJ and licensed professional govern.
API field namesultimate_strength_psi, surface_finish, diameter_in, load_type, reliability_pct, temperature_factor_kd, endurance_limit_psi, ka
- Rotating-beam limit Se' = 0.5 Sut for steel, Sut <= 200 ksi (else 100 ksi)Shigley Ch. 6
- Marin factors ka surface, kb size, kc load, kd temperature, ke reliabilityShigley Tables 6-2/6-4/6-5
- Scope steel; notch Kf and finite-life S-N are separate; feeds fatigue-safety-factorscope of this tile