Section Modulus⚠ unverified
Mechanical / Beams · Elastic section modulus
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| I | I | m^4 | 1e-05 | Second moment of area |
| y_max | ymax | m | 0.05 | Max distance from neutral axis |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| S | S | m^3 | Section modulus |
The science & history
Understanding the Parameters
- $I$ — larger $I$ → larger $S$.
- $c$ — deeper sections have larger $c$, which reduces $S$ relative to $I$ alone.
- $S$ — tabulated for standard beams; $\sigma_{\max} = M c / I = M/S$.
Derivation (Approaching a Proof)
From elastic flexure formula $\sigma = My/I$, the maximum is at $y = c$: $\sigma_{\max} = Mc/I$. Defining $S = I/c$ gives $\sigma_{\max} = M/S$.
History
Section modulus is the everyday beam-selection number in structural and machine design.
Related Concepts: Moment Of Inertia Disk, Shear Stress, Von Mises Stress, Euler Buckling Load
Notes: Registry calculator section-modulus (unverified). Elastic $S$, not plastic modulus $Z$.