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 S = I / c (moment of inertia over distance to the extreme fiber); the plastic modulus Z sums the first moments of the two half-areas about the plastic (equal-area) neutral axis.
- Their ratio is the shape factor Z/S = Mp/My; for a rectangle it is exactly 1.5, while real wide-flange I-shapes fall in roughly 1.10-1.18 (about 1.12 is typical).
- Notation is regional: North America uses S and Z, while Eurocode 3 writes Wel and Wpl for the same quantities.
- Tabulated section properties trace back over a century - AISC shape data reaches back to Iron and Steel Beams 1873 to 1952 and the first AISC Manual of 1927.
- The numbers are axis-dependent: bent the weak way a wide-flange has a shape factor near 1.5 (vs about 1.13 the strong way), and for a singly-symmetric section (a tee, an unequal-flange girder) the plastic neutral axis is the equal-area line, which does not coincide with the elastic centroid.
Full guide
Section Modulus (Sx, Zx): Formula & Meaning
Step-by-step with figures and sources — 12 min read
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