MEC-49

Rankine–Gordon strut

Empirical strut between Euler and crush.

Reading speed

MachinesRankine–Gordon strut

Governing equation

P=\frac{f_c A}{1+a(\ell/k)^2}

$\ell/k \in \left[20, 200\right]$

where

f_c: Crush (MPa)
A: Area (mm²)
a: a (—)
\ell/k: Slenderness (—)
P: Load (kN)

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.

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①

Governing law — red

P=\frac{f_c A}{1+a(\ell/k)^2}

$\ell/k \in \left[20, 200\right]$

$\ell/k = 20$ $P = 243.3$

Along the curve

②

Domain of the variable — blue

\ell/k_{\min} = 20,\quad \ell/k_{\max} = 200

$\ell/k \in \left[20, 200\right]$

$\ell/k = 20$ $\ell/k = 20$

Along the curve

③

Response curve — green

P=\frac{f_c A}{1+a(\ell/k)^2}

$\ell/k \in \left[20, 200\right]$

$\ell/k = 20$ $P = 243.3$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}P}{\mathrm{d}\ell/k}

$\ell/k \in \left[20, 200\right]$

$\ell/k = 21.13$ $P^{\prime} = -1.256$

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-49 — Rankine–Gordon strut) is the form associated with Rankine–Gordon strut. Working symbols: $f_c$ , $A$ , $a$ , $\ell/k$ $\rightarrow$ $P$ . Empirical strut between Euler and crush. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

P

from

f_c

A

a

\ell/k

in Mechanical via

P=\frac{f_c A}{1+a(\ell/k)^2}

Empirical strut between Euler and crush. Use it when a real mechanical question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

f_c = 320.000\,\mathrm{MPa}

A = 800.000\,\mathrm{mm^{2}}

a = 1.300e-4\,\mathrm{—}

\ell/k = 80.000\,\mathrm{—}

, the governing relation

P=\frac{f_c A}{1+a(\ell/k)^2}

yields

P = 139.74\,\mathrm{kN}

. One governing identity, SI units, a single sweep on the sheet. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Crush f_c320 MPaArea A800 mm²a a0.00013 —Slenderness \ell/k80 —

Outputs

Load P139.74 kN

Reading speed

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Narration of this film

One governing identity, SI units, a single sweep on the sheet.

Empirical strut between Euler and crush. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube