Solid rectangle
Wₓ = b·h²/6Width b and height h
Open calculatorGeometric properties · Bending
Section modulus calculators by shape
Choose a geometry to calculate its area, second moment of area and elastic section modulus about the centroidal axes.
Created v1.0
By Thibaut Grzelak, Mechanical Analysis Engineer
Definition
What is section modulus W used for?
Elastic section modulus relates second moment I to the distance c between the neutral axis and the extreme fibre. It gives maximum bending stress directly through σ = M/W.
W = I / cσmax = |M| / WGeometry selection
Open the calculator for your section
Solid circle
W = π·D³/32Diameter d
Open calculatorCircular tube
W = π(D⁴−d⁴)/(32D)Diameter D and thickness t
Open calculatorRectangular tube
W = I/cB, H and thickness t
Open calculatorI / H section
Wₓ = Iₓ/(h/2)B, H, web t_w and flange t_f
Open calculatorChannel section
W = I/cB, H, web t_w and flanges t_f
Open calculatorT section
Wtop = I/ȳB, H, web t_w and flange t_f
Open calculatorAngle section
W = I/cWidth B, height H, thickness t
Open calculatorElastic and plastic section modulus
The calculators above provide elastic section modulus W used for first yield in elastic bending. Plastic modulus Zp describes full stress redistribution and must not be confused with W.
IPE beam: a complete worked example
Major axis: 22.8 MPa and 1.81 mm. Minor axis: 156 MPa and 24.8 mm. These are model results, not an approval of the beam.
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.