Parallel-Axis Theorem for Area
Transfer an area moment from a centroidal axis to a parallel axis.
Try this formula
Calculate area moment about the shifted axis or choose another supported quantity.
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Try this formula
Calculate area moment about the shifted axis or choose another supported quantity.
Use decimals or scientific notation, such as 1.2e3. Calculations update as you type.
Area moment about the shifted axis
Enter the known values to see the result.
The two axes are parallel, and the reference axis passes through the area centroid. Use area A in m² here; the mass-inertia form uses mass instead. Use a consistent axis and distance for each part when constructing a composite section.
Difficulty
Intermediate
Read time
5 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. Uses area A in the area-moment theorem; the mass form is not used.
Definition
Shifting a bending axis away from the centroid increases the area moment by area times offset squared. The extra term accounts for the whole section being farther from the new axis.
Variables & Units
| Symbol | Meaning | Units |
|---|---|---|
| Area moment about the shifted axis | ||
| Area moment about the parallel centroidal axis | ||
| Section area | ||
| Perpendicular distance between the axes |
Real-World Applications
Built-up sections
Combine centroidal properties of component rectangles.
Offset axes
Find area moments about a known parallel axis.
Worked Example
Problem
A component has Ic = 0.000002 m⁴, area 0.002 m², and axis offset 0.05 m. Find the shifted 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. Uses area A in the area-moment theorem; the mass form is not used.
Assumptions
- • The two axes are parallel, and the reference axis passes through the area centroid.
- • Use area A in m² here; the mass-inertia form uses mass instead.
- • Use a consistent axis and distance for each part when constructing a composite section.
Languages
FormuLab is a study reference. Verify formulas, units, assumptions, and course-specific conventions before relying on them.