Section Modulus
Section property relating bending moment to extreme-fibre bending stress
Section modulus Z (mm³) links the bending moment to the maximum bending stress: σ = M / Z, where Z = I / y and y is the distance from the neutral axis to the extreme fibre. It is the single most useful number for sizing a flexural member — given an allowable stress, the required Z = M / σallow.
Steel design distinguishes the elastic section modulus Ze (first yield at the extreme fibre) from the plastic section modulus Zp (full plastic hinge, entire section yielded). The shape factor Zp/Ze is 1.5 for a rectangle and ≈1.12-1.15 for rolled I-sections. IS 800 limit-state design uses Zp for plastic + compact sections and Ze for semi-compact sections, with the design bending strength Md = βb·Zp·fy/γm0.
- Selecting steel beams from IS 808 (required Z = M/σ)
- Limit-state moment capacity of steel sections (IS 800 Cl. 8.2)
- Crane-girder + purlin design
- Quick beam sizing before detailed analysis
- Comparing efficiency of alternative section shapes