Area A
mm²
T 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
01
Choose a shape
03
Diagram
04
Results
Centroid x̄
mm
Centroid ȳ
mm
Second moment Iₓ
mm⁴
Second moment Iᵧ
mm⁴
05Show additional results
Minimum modulus Wₓ,min mm³
Minimum modulus Wᵧ,min mm³
Radius of gyration rₓ mm
Radius of gyration rᵧ mm
Product of inertia Iₓᵧ mm⁴
Principal moment I₁ (max.) mm⁴
Principal moment I₂ (min.) mm⁴
Principal-axis angle θₚ °
Torsion constant J mm⁴
Plastic modulus Wpl,x mm³
Plastic modulus Wpl,y mm³
Shear area Av,x mm²
Shear area Av,y mm²
Wpl is integrated exactly over the geometry. J is shown only where an exact implemented solution applies; code-dependent shear areas remain unavailable.
View calculation detailsFormulas, numerical substitution and resultsOpen ↓Close ↑
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
A
Bt_f + tᵥ(H − t_f)x̄
B / 2ȳ
ΣAᵢyᵢ / AIₓ, Iᵧ
Σ(Iᵢ + Aᵢdᵢ²)Wmin
I / cmax| Symbol | Meaning | Dimension |
|---|---|---|
| B | Flange width B | L |
| H | Overall height H | L |
| tᵥ | Web thickness t_w | L |
| t_f | Flange thickness t_f | L |
| A | Area | L² |
| x̄ | Horizontal centroid | L |
| ȳ | Vertical centroid | L |
| Iₓ, Iᵧ | Centroidal second moments | L⁴ |
| Wmin | Minimum section modulus | L³ |
02Assumptions and limits
Assumptions and limits
- Flange centred on web.
- Sharp corners.
- Fillets ignored.
- x modulus uses the farthest fibre.
This calculation does not check strength, stability or code compliance.
03Calculator validation
Calculator validation
Two non-overlapping rectangles are combined.
- B = 120, H = 180, t_w = 10, t_f = 15 mm give A = 3,450 mm².
- x̄ = 60 mm.
- ȳ = 129.4565 mm.
- Iₓ = 10,750,231.0 mm⁴.
04References
References
- Roark’s Formulas for Stress and Strain, 9th edition, section-property tables.
- Young, Budynas & Sadegh, Roark’s Formulas for Stress and Strain, McGraw-Hill.
- BIPM, The International System of Units (SI), 9th edition.
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 / cChoose the correct shape
Rectangle, circle, tube, I, channel, T and angle sections require different geometries.