Moment of Inertia of a Channel Section
Iₓ, Iₖ, Centroid Offset & Section Modulus • C-Sections
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Moment of Inertia of a Channel Section — Formula and Worked Example
A channel is symmetric about the horizontal axis only. That single missing symmetry is the whole story: the centroid shifts toward the web, and Iₖ must be found about that shifted axis rather than about mid-width.
Formulas
| Quantity | Expression |
|---|---|
| Area | A = t₷H + 2(B − t₷)tₜ |
| Centroid from web face | xᶜ = Σ(Aᵢxᵢ) / ΣAᵢ |
| Second moment about x | Iₓ = Σ[Iᶜₓ + Aᵢ(yᵢ − yᶜ)²] |
| Second moment about y | Iₖ = Σ[Iᶜₖ + Aᵢ(xᵢ − xᶜ)²] |
| Section modulus | Sₓ = 2Iₓ / H |
The horizontal axis is still an axis of symmetry, so yᶜ = H/2 and Iₓ behaves much like an I-beam. Iₖ does not: you must locate xᶜ first, then apply the parallel-axis transfer to every component. Note also that the shear centre lies outside the section, so a load applied through the centroid will twist a channel.
Worked Example — A 75 × 150 mm channel with a 7 mm web and 10 mm flanges
| Quantity | Value |
|---|---|
| B (flange width) | 75 mm |
| H (depth) | 150 mm |
| t₷ (web) | 7 mm |
| tₜ (flange) | 10 mm |
| A | 2,410 mm² |
| xᶜ from web face | 24.7 mm |
| Iₓ | 8.64 × 10⁶ mm⁴ |
| Iₖ | 1.362 × 10⁶ mm⁴ |
| Sₓ | 115.3 × 10³ mm³ |
Values computed by the calculator above. Change any dimension and every property updates live.
Where is the centroid of a channel section?
It lies on the horizontal axis of symmetry at mid-height, but is offset horizontally toward the web. Find it with xᶜ = Σ(Aᵢxᵢ)/ΣAᵢ, treating the web and the two flanges as rectangles. For a 75 × 150 × 7 × 10 channel the centroid sits about 24.7 mm from the outer face of the web.
Why is Iy so much smaller than Ix for a channel?
Almost all of the material is close to the vertical centroidal axis, so the Ad² transfer terms that dominate Ix are tiny for Iy. In the worked example Ix is roughly six times Iy, which is why channels are used as beams rather than as columns loaded about the weak axis.
Does a channel twist under load?
Yes, if the load is applied through the centroid. A channel's shear centre lies outside the section, on the opposite side of the web from the flanges, so a load through the centroid produces a torque. Load through the shear centre, or restrain the member, to avoid twist.
Other Cross-Sections
The same calculator handles all eight standard sections:
- I-Beam
- Channel (this page)
- Angle
- T-Section
- Rectangle
- Circle
- Hollow Circle
- Hollow Rect
For the full section-property reference and the parallel-axis theorem, see the Moment of Inertia Calculator hub.