What is the section modulus (Sx / Zx) and why does it matter?
Steel Profiles
The section modulus measures how efficiently a cross-section resists bending moment. Sx (elastic section modulus, Wel) is used for elastic design — maximum bending stress = M/Sx. Zx (plastic section modulus, Wpl) is used for plastic design — plastic moment = Zx × fy. For a given steel grade, a profile with higher Sx/Zx can resist more bending with less material. For example, an IPE 300 has Zx ≈ 628 cm³ giving plastic moment Mpl ≈ 157 kN·m in S250 steel. When choosing a beam profile, you compare required Z (from Mreq/fy) to available Z in the catalog, then pick the lightest profile. CalcSteel shows Sx, Zx, Iy, Iz and all section properties on each profile page.
Key takeaways
- The elastic modulus is <strong>S = I / c</strong> (moment of inertia over distance to the extreme fiber); the plastic modulus <strong>Z</strong> sums the first moments of the two half-areas about the plastic (equal-area) neutral axis.
- Their ratio is the <strong>shape factor</strong> Z/S = Mp/My; for a rectangle it is exactly 1.5, while real wide-flange I-shapes fall in roughly <strong>1.10-1.18</strong> (about 1.12 is typical).
- Notation is regional: North America uses <strong>S and Z</strong>, while Eurocode 3 writes <strong>Wel and Wpl</strong> for the same quantities.
- Tabulated section properties trace back over a century - AISC shape data reaches back to <em>Iron and Steel Beams 1873 to 1952</em> and the first AISC Manual of 1927.
Full guide
Section Modulus (Sx, Zx): Formula & Meaning
Step-by-step with figures and sources — 9 min read
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