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I / H 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

I / H section
mm
mm
mm
mm

Identical centred flanges. Centred web. Fillets ignored. t_w < B and 2t_f < H.

Results are up to date.

03

Diagram

BHtᵥt_f
04

Results

Area A
10,600mm²
Centroid x̄
100mm
Centroid ȳ
150mm
Second moment Iₓ
171.713E6mm⁴
Second moment Iᵧ
26.6883E6mm⁴
05Show additional results
Section modulus Wₓ (Sₓ)1.14476E6 mm³
Section modulus Wᵧ (Sᵧ)266,883 mm³
Radius of gyration rₓ127.277 mm
Radius of gyration rᵧ50.1774 mm
Product of inertia Iₓᵧ0 mm⁴
Principal moment I₁ (max.)171.713E6 mm⁴
Principal moment I₂ (min.)26.6883E6 mm⁴
Principal-axis angle θₚ0 °
Torsion constant J1.08401E6 mm⁴
Plastic modulus Wpl,x1.289E6 mm³
Plastic modulus Wpl,y406,500 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

A2Bt_f + tᵥ(H − 2t_f)
x̄, ȳB/2 ; H/2
Iₓ[BH³ − (B − tᵥ)(H − 2t_f)³] / 12
Iᵧ[2t_fB³ + (H − 2t_f)tᵥ³] / 12
Wₓ, Wᵧ2Iₓ/H ; 2Iᵧ/B
SymbolMeaningDimension
BFlange width BL
HOverall height HL
tᵥWeb thickness t_wL
t_fFlange thickness t_fL
AAreaL²
x̄, ȳCentroid by double symmetryL
IₓStrong-axis second momentL⁴
IᵧWeak-axis second momentL⁴
Wₓ, WᵧSection moduliL³
02Assumptions and limits

Assumptions and limits

  • Identical centred flanges.
  • Centred web.
  • Fillets ignored.
  • t_w < B and 2t_f < H.

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

03Calculator validation

Calculator validation

The engine combines three non-overlapping rectangles and checks double symmetry.

  • B = 200, H = 300, t_w = 10, t_f = 20 mm give A = 10,600 mm².
  • x̄ = 100 mm and ȳ = 150 mm.
  • Iₓ = 171,713,333.3 mm⁴.
  • Incompatible thicknesses are rejected.
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.

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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

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

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