CIV-11

Hooke axial stiffness

δ = P L /(A E) and σ = E ε for a prismatic bar.

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ElasticityHooke 1678ISO 6892

Governing equation

\delta = \dfrac{P L}{A E},\quad \sigma = E\varepsilon

$P \in \left[1, 2000\right]$

where

P: Axial load (kN)
L: Length (m)
A: Area (cm²)
E: Modulus (GPa)
\delta: Elongation (mm)
\sigma: Stress (MPa)
\varepsilon: Strain (—)

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

\delta = \dfrac{P L}{A E},\quad \sigma = E\varepsilon

$P \in \left[1, 2000\right]$

$P = 1$ $\delta = 0.006$

Along the curve

②

Domain of the variable — blue

P_{\min} = 1,\quad P_{\max} = 2000

$P \in \left[1, 2000\right]$

$P = 1$ $P = 1$

Along the curve

③

Response curve — green

\delta = \dfrac{P L}{A E},\quad \sigma = E\varepsilon

$P \in \left[1, 2000\right]$

$P = 1$ $\delta = 0.006$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}\delta}{\mathrm{d}P}

$P \in \left[1, 2000\right]$

$P = 13.57$ $\delta^{\prime} = 0.006$

Along the curve

Lecture brief

Historical brief

From Euler’s 1744 elastica and Navier’s beam theory to Mohr’s circle and transformed-section RC, structural mechanics grew as a closed-form craft before finite elements. The lab keeps those governing lines for buckling, flexure, joints and influence. This sheet (CIV-11 — Hooke axial stiffness) is the form associated with Hooke 1678 · ISO 6892. Working symbols: $P$ , $L$ , $A$ , $E$ $\rightarrow$ $\delta$ , $\sigma$ , $\varepsilon$ . Hooke's linear spring, written σ = E ε, integrates to the engineering displacement of a uniform bar.

Purpose

Purpose: compute

\delta

\sigma

\varepsilon

from

P

L

A

E

in Structural & civil via

\delta = \dfrac{P L}{A E},\quad \sigma = E\varepsilon

δ = P L /(A E) and σ = E ε for a prismatic bar. Use it when a real structural & civil question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

P = 200.000\,\mathrm{kN}

L = 3.000\,\mathrm{m}

A = 25.000\,\mathrm{cm^{2}}

E = 200.000\,\mathrm{GPa}

, the governing relation

\delta = \dfrac{P L}{A E},\quad \sigma = E\varepsilon

yields

\delta = 1.200\,\mathrm{mm}

\sigma = 80.000\,\mathrm{MPa}

\varepsilon = 4.000e-4\,\mathrm{—}

. Uniform tension member, small strain. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Axial load P200 kNLength L3 mArea A25 cm²Modulus E200 GPa

Outputs

Elongation \delta1.200 mm
Stress \sigma80.000 MPa
Strain \varepsilon0.000400 —

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Narration of this film

Uniform tension member, small strain.

Hooke's linear spring, written σ = E ε, integrates to the engineering displacement of a uniform bar.

Reading speed

Watch on YouTube