MEC-48

Poisson strain

Lateral contraction in uniaxial tension.

Reading speed

MachinesPoisson strain

Governing equation

\varepsilon_y=-\nu\varepsilon_x

$\varepsilon_x \in \left[0, 0.02\right]$

where

\nu: Poisson (—)
\varepsilon_x: Axial (—)
\varepsilon_y: Lateral (—)

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

\varepsilon_y=-\nu\varepsilon_x

$\varepsilon_x \in \left[0, 0.02\right]$

$\varepsilon_x = 0$ $\varepsilon_y = 0$

Along the curve

②

Domain of the variable — blue

\varepsilon_x_{\min} = 0,\quad \varepsilon_x_{\max} = 0.02

$\varepsilon_x \in \left[0, 0.02\right]$

$\varepsilon_x = 0$ $\varepsilon_x = 0$

Along the curve

③

Response curve — green

\varepsilon_y=-\nu\varepsilon_x

$\varepsilon_x \in \left[0, 0.02\right]$

$\varepsilon_x = 0$ $\varepsilon_y = 0$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}\varepsilon_y}{\mathrm{d}\varepsilon_x}

$\varepsilon_x \in \left[0, 0.02\right]$

$\varepsilon_x = 1.26\times 10^{-4}$ $\varepsilon_y^{\prime} = -0.3$

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-48 — Poisson strain) is the form associated with Poisson strain. Working symbols: $\nu$ , $\varepsilon_x$ $\rightarrow$ $\varepsilon_y$ . Lateral contraction in uniaxial tension. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

\varepsilon_y

from

\nu

\varepsilon_x

in Mechanical via

\varepsilon_y=-\nu\varepsilon_x

Lateral contraction in uniaxial tension. Use it when a real mechanical question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

\nu = 0.300\,\mathrm{—}

\varepsilon_x = 0.002\,\mathrm{—}

, the governing relation

\varepsilon_y=-\nu\varepsilon_x

yields

\varepsilon_y = -6.000e-4\,\mathrm{—}

. 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

Poisson \nu0.3 —Axial \varepsilon_x0.002 —

Outputs

Lateral \varepsilon_y-0.00060 —

Reading speed

Watch on YouTube

Free library

Full library

Free PDF / open book

YouTube channels

00:0 / 00:08

Narration of this film

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

Lateral contraction in uniaxial tension. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube