MEC-21

Soderberg fatigue line

1/n = σm/Sy + σa/Se. The conservative mean–amplitude line through yield.

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FatigueSoderberg 1930

Governing equation

\dfrac{1}{n}=\dfrac{\sigma_m}{S_y}+\dfrac{\sigma_a}{S_e}

where

\sigma_m: Mean stress (MPa)
\sigma_a: Alternating stress (MPa)
S_y: Yield strength (MPa)
S_e: Endurance limit (MPa)
n: Factor of safety (—)

Lecture brief

Historical brief

Machine design grew from Coulomb torsion and Hertz contact (1881) through Soderberg fatigue and the heat-engine cycle. The lab writes shaft, bearing, contact and thermodynamic limits in SI. This sheet (MEC-21 — Soderberg fatigue line) is the form associated with Soderberg 1930. Working symbols: $\sigma_m$ , $\sigma_a$ , $S_y$ , $S_e$ $\rightarrow$ $n$ . Soderberg joins Sy on the mean axis to Se on the amplitude axis so yield is never crossed under a static load.

Purpose

Purpose: compute

n

from

\sigma_m

\sigma_a

S_y

S_e

in Mechanical via

\dfrac{1}{n}=\dfrac{\sigma_m}{S_y}+\dfrac{\sigma_a}{S_e}

1/n = σm/Sy + σa/Se. The conservative mean–amplitude line through yield. Use it when a real mechanical question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

\sigma_m = 80.000\,\mathrm{MPa}

\sigma_a = 60.000\,\mathrm{MPa}

S_y = 350.000\,\mathrm{MPa}

S_e = 180.000\,\mathrm{MPa}

, the governing relation

\dfrac{1}{n}=\dfrac{\sigma_m}{S_y}+\dfrac{\sigma_a}{S_e}

yields

n = 1.780\,\mathrm{—}

. A Haigh plot, a Soderberg line, a safety tick. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Mean stress \sigma_m80 MPaAlternating stress \sigma_a60 MPaYield strength S_y350 MPaEndurance limit S_e180 MPa

Outputs

Factor of safety n1.780 —

Reading speed

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Narration of this film

A Haigh plot, a Soderberg line, a safety tick.

Soderberg joins Sy on the mean axis to Se on the amplitude axis so yield is never crossed under a static load.

Reading speed

Watch on YouTube