Centroidal Area Moment of a Rectangle
Find the second moment of area about a rectangle’s centroidal bending axis.
Try this formula
Calculate centroidal second moment of area or choose another supported quantity.
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Try this formula
Calculate centroidal second moment of area or choose another supported quantity.
Use decimals or scientific notation, such as 1.2e3. Calculations update as you type.
Centroidal second moment of area
Enter the known values to see the result.
The section is a solid rectangle and the axis passes through its centroid. The cubed dimension is the depth perpendicular to the bending axis. This is an area property in m⁴, not a mass moment in kg·m².
Difficulty
Beginner
Read time
4 min
Prerequisites
Basic algebra, mechanics, and consistent SI units
Source
raymond212 — MECH 260 — Mechanics of MaterialsReference equation: Bending — Second Rectangular Moment of Area. FormuLab wrote new explanations, assumptions, applications, and numerical examples.
Definition
Bending resistance depends strongly on section depth because depth is cubed. Turning a rectangular beam on its side changes its area moment even though the area and material stay the same.
Variables & Units
| Symbol | Meaning | Units |
|---|---|---|
| Centroidal second moment of area | ||
| Width parallel to the bending axis | ||
| Depth perpendicular to the bending axis |
Real-World Applications
Rectangular beams
Calculate a section property for stress or deflection calculations.
Section orientation
Compare the strong and weak bending axes.
Worked Example
Problem
A rectangular section is 0.05 m wide and 0.1 m deep. Find its centroidal area moment.
Given
Solution
Final Answer
Contents
Info
Tools
Source & review
Reference equation: Bending — Second Rectangular Moment of Area. FormuLab wrote new explanations, assumptions, applications, and numerical examples.
Assumptions
- • The section is a solid rectangle and the axis passes through its centroid.
- • The cubed dimension is the depth perpendicular to the bending axis.
- • This is an area property in m⁴, not a mass moment in kg·m².
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