Statics › Section J · Moments of inertia › Topic J.3
The parallel axis theorem
Tables give moments of inertia about a shape's own centroid, but real problems need them about some other axis. The parallel axis theorem makes that shift with one extra term, and it also explains why the material far from the axis matters most.
In this topic
- The problem of the moving axis
- Where the theorem comes from
- Using the theorem
- Worked example: a triangle's centroidal value
- Worked example: an offset tube
- Semicircles and quarter circles
- A table of centroidal values
- Worked example: between two off-centre axes
- Why the flanges carry a beam
- Common mistakes to avoid
- Key takeaways
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