Section Modulus and Bending Stress
Section Modulus and Bending Stress
The section modulus links a bending moment to the extreme-fibre stress, so it is the property used to size beams in bending.
For a rectangle S = bh²/6 and the bending stress is σ = M/S. where b is the breadth, h the depth, M the applied moment and S the elastic section modulus.
Inputs
b := 150 mm=150 mm
h := 300 mm=300 mm
M := 45 kN·m=45000 Nm
The elastic section modulus of a solid rectangle about its strong axis.
S := b·h^2/6=2.25e-03 m^3
The extreme-fibre bending stress is the moment divided by the section modulus.
sigma := M/S=20 MPa
Results
The bending stress must stay below the material’s design strength. Because S grows with the square of depth, adding depth is far more effective than adding width.
Assumptions & limitations
- Symmetric solid rectangular section.
- Elastic bending, plane sections remain plane.
- No lateral-torsional buckling or shear interaction.