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Rectangular tube — 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

Rectangular tube
mm
mm
mm

Uniform thickness. Ideal sharp corners. B > 2t and H > 2t.

Results are up to date.

03

Diagram

BHt
04

Results

Area A
2,900mm²
Centroid x̄
50mm
Centroid ȳ
100mm
Second moment Iₓ
15.2242E6mm⁴
Second moment Iᵧ
5.12417E6mm⁴
05Show additional results
Section modulus Wₓ (Sₓ)152,242 mm³
Section modulus Wᵧ (Sᵧ)102,483 mm³
Radius of gyration rₓ72.4549 mm
Radius of gyration rᵧ42.0352 mm
Product of inertia Iₓᵧ0 mm⁴
Principal moment I₁ (max.)15.2242E6 mm⁴
Principal moment I₂ (min.)5.12417E6 mm⁴
Principal-axis angle θₚ0 °
Torsion constant JNot available
Plastic modulus Wpl,x187,750 mm³
Plastic modulus Wpl,y115,250 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

b, hB − 2t ; H − 2t
ABH − bh
Iₓ(BH³ − bh³) / 12
Iᵧ(HB³ − hb³) / 12
Wₓ, WᵧIₓ/(H/2) ; Iᵧ/(B/2)
SymbolMeaningDimension
BOuter width BL
HOuter height HL
tThickness tL
b, hInner dimensionsL
AMaterial areaL²
IₓSecond moment about xL⁴
IᵧSecond moment about yL⁴
Wₓ, WᵧSection moduliL³
02Assumptions and limits

Assumptions and limits

  • Uniform thickness.
  • Ideal sharp corners.
  • B > 2t and H > 2t.

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

03Calculator validation

Calculator validation

The inner void is subtracted from the outer rectangle.

  • B = 100, H = 200 and t = 5 mm give A = 2,900 mm².
  • A square tube satisfies Iₓ = Iᵧ.
  • B ≤ 2t or H ≤ 2t is rejected.
  • Scaling laws are tested.
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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