CIV-29

Radius of gyration

r = √(I/A). The distance at which the area would sit as a thin ring of equal I.

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StabilityRadius of gyration

Governing equation

r=\sqrt{I/A}

where

I: Second moment (cm^4)
A: Area (cm^2)
r: Radius of gyration (cm)

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-29 — Radius of gyration) is the form associated with Radius of gyration. Working symbols: $I$ , $A$ $\rightarrow$ $r$ . Slenderness λ = KL/r uses this r. The weak-axis r governs a pin-ended strut.

Purpose

Purpose: compute

r

from

I

A

in Structural & civil via

r=\sqrt{I/A}

r = √(I/A). The distance at which the area would sit as a thin ring of equal I. 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

I = 800.000\,\mathrm{cm^4}

A = 40.000\,\mathrm{cm^2}

, the governing relation

r=\sqrt{I/A}

yields

r = 4.47\,\mathrm{cm}

. A section, an I, a shrinking radius. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Second moment I800 cm^4Area A40 cm^2

Outputs

Radius of gyration r4.47 cm

Reading speed

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Narration of this film

A section, an I, a shrinking radius.

Slenderness λ = KL/r uses this r. The weak-axis r governs a pin-ended strut.

Reading speed

Watch on YouTube