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Channel section — Geometric properties

Calculate area, centroid, second moments of area, section moduli and radii of gyration with clearly defined dimensions.

Created v1.0

By Thibaut Grzelak, Mechanical Analysis Engineer

8 profiles available
01

Choose a shape

02

Calculation inputs

Channel section
mm
mm
mm
mm

Opening faces right. Constant thicknesses. Fillets ignored. Displayed modulus uses the farthest extreme fibre.

Results are up to date.

03

Diagram

BHtᵥt_f
04

Results

Area A
3,808mm²
Centroid x̄
32.9916mm
Centroid ȳ
100mm
Second moment Iₓ
24.8697E6mm⁴
Second moment Iᵧ
3.88524E6mm⁴
05Show additional results
Minimum modulus Wₓ,min248,697 mm³
Minimum modulus Wᵧ,min57,981.3 mm³
Radius of gyration rₓ80.8141 mm
Radius of gyration rᵧ31.9419 mm
Product of inertia Iₓᵧ0 mm⁴
Principal moment I₁ (max.)24.8697E6 mm⁴
Principal moment I₂ (min.)3.88524E6 mm⁴
Principal-axis angle θₚ0 °
Torsion constant JNot available
Plastic modulus Wpl,x287,552 mm³
Plastic modulus Wpl,y104,117 mm³
Shear area Av,xNot available
Shear area Av,yNot available

Wpl is integrated exactly over the geometry. J is shown only where an exact implemented solution applies; code-dependent shear areas remain unavailable.

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Calculation note

Full calculation details

Show additional results

Wpl,x
∫A |y − yp| dA
Wpl,y
∫A |x − xp| dA
J
Not available
Av,x / Av,y
Not available

Wpl is integrated exactly over the geometry. J is shown only where an exact implemented solution applies; code-dependent shear areas remain unavailable.

01Equations and symbols

Formulas used

AtᵥH + 2(B − tᵥ)t_f
ȳH / 2
x̄ΣAᵢxᵢ / A
Iₓ, IᵧΣ(Iᵢ + Aᵢdᵢ²)
WminI / cmax
SymbolMeaningDimension
BOverall width BL
HOverall height HL
tᵥWeb thickness t_wL
t_fFlange thickness t_fL
AAreaL²
ȳVertical centroidL
x̄Horizontal centroidL
Iₓ, IᵧParallel-axis theoremL⁴
WminMinimum modulus at extreme fibreL³
02Assumptions and limits

Assumptions and limits

  • Opening faces right.
  • Constant thicknesses.
  • Fillets ignored.
  • Displayed modulus uses the farthest extreme fibre.

This calculation does not check strength, stability or code compliance.

03Calculator validation

Calculator validation

Three non-overlapping rectangles are combined using the parallel-axis theorem.

  • B = 100, H = 200, t_w = 8, t_f = 12 mm give A = 3,808 mm².
  • ȳ = 100 mm by symmetry.
  • x̄ = 32.9916 mm.
  • Iₓ = 24,869,717.3 mm⁴.
04References

References

  1. Roark’s Formulas for Stress and Strain, 9th edition, section-property tables.
  2. Young, Budynas & Sadegh, Roark’s Formulas for Stress and Strain, McGraw-Hill.
  3. BIPM, The International System of Units (SI), 9th edition.

Calculation path and sources

Section properties can be reused for linear mass, bending and buckling checks.

Reuse the results

Continue with a mechanical calculation

Geometric properties become inputs for mass, stress, deformation and stability checks.

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External technical sources

Geometric properties

Second moment of area and section modulus: which value to use?

I describes material distribution and W connects geometry to bending stress. Values change with the x or y axis.

Second moment of area I

Also called area moment of inertia, I is used in deflection and buckling.

I [mm⁴, cm⁴, m⁴, in⁴]

Elastic section modulus W

W uses distance c to the extreme fibre. For an unsymmetrical section, check both sides.

W = I / c

Choose the correct shape

Rectangle, circle, tube, I, channel, T and angle sections require different geometries.

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