CIV-34

Rectangle second moment

I = b h³ / 12 about the centroidal axis parallel to b.

Reading speed

GeometryI rectangle

Governing equation

I=bh^3/12

where

b: Width (mm)
h: Depth (mm)
I: Second moment (cm^4)

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-34 — Rectangle second moment) is the form associated with I rectangle. Working symbols: $b$ , $h$ $\rightarrow$ $I$ . ∫ y² dA for a rectangle of height h. Parallel-axis shifts I by A d².

Purpose

Purpose: compute

I

from

b

h

in Structural & civil via

I=bh^3/12

I = b h³ / 12 about the centroidal axis parallel to b. 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

b = 200.000\,\mathrm{mm}

h = 400.000\,\mathrm{mm}

, the governing relation

I=bh^3/12

yields

I = 106666.7\,\mathrm{cm^4}

. A rectangle, a centroidal axis, an I. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Width b200 mmDepth h400 mm

Outputs

Second moment I106666.7 cm^4

Reading speed

Watch on YouTube

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Narration of this film

A rectangle, a centroidal axis, an I.

∫ y² dA for a rectangle of height h. Parallel-axis shifts I by A d².

Reading speed

Watch on YouTube