MEC-02

Soderberg fatigue line

1/n = σm/Sy + σa/Se, a conservative Goodman variant.

Reading speed

FatigueSoderberg 1930Shigley

Governing equation

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

$\sigma_a \in \left[1, 400\right]$

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 (—)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

00:0 / 00:08

①

Governing law — red

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

$\sigma_a \in \left[1, 400\right]$

$\sigma_a = 1$ $n = 4.271$

Along the curve

②

Domain of the variable — blue

\sigma_a_{\min} = 1,\quad \sigma_a_{\max} = 400

$\sigma_a \in \left[1, 400\right]$

$\sigma_a = 1$ $\sigma_a = 1$

Along the curve

③

Response curve — green

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

$\sigma_a \in \left[1, 400\right]$

$\sigma_a = 1$ $n = 4.271$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}n}{\mathrm{d}\sigma_a}

$\sigma_a \in \left[1, 400\right]$

$\sigma_a = 3.509$ $n^{\prime} = -0.091$

Along the curve

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-02 — Soderberg fatigue line) is the form associated with Soderberg 1930 · Shigley. Working symbols: $\sigma_m$ , $\sigma_a$ , $S_y$ , $S_e$ $\rightarrow$ $n$ . Soderberg draws the allowable mean–amplitude line from Sy on the mean axis to Se on the amplitude axis, guaranteeing yield and fatigue.

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, a conservative Goodman variant. 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{—}

. Uniaxial fully reversed plus mean, no stress concentration. 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

Watch on YouTube

Free library

Full library

Free PDF / open book

YouTube channels

00:0 / 00:08

Narration of this film

Uniaxial fully reversed plus mean, no stress concentration.

Soderberg draws the allowable mean–amplitude line from Sy on the mean axis to Se on the amplitude axis, guaranteeing yield and fatigue.

Reading speed

Watch on YouTube