Bending moment resistance
Design resistance of the cross-section to bending per EN 1993-1-1 §6.2.5
Tool information
What this calculator checks
The calculator determines the design bending resistance of the cross-section, \(M_{c,Rd}\), about the major axis y-y, according to EN 1993-1-1 §6.2.5, and compares it with the design moment \(M_{Ed}\):
\(\frac{M_{Ed}}{M_{c,Rd}} \le 1.0\)
The section modulus used depends on the cross-section class — this is where classification matters most visibly:
| Class | Expression | Modulus |
|---|---|---|
| 1 and 2 | (6.13) | \(M_{c,Rd} = W_{pl,y} \cdot f_y / \gamma_{M0}\) |
| 3 | (6.14) | \(M_{c,Rd} = W_{el,y} \cdot f_y / \gamma_{M0}\) |
| 4 | (6.15) | \(M_{c,Rd} = W_{eff,y} \cdot f_y / \gamma_{M0}\) |
The difference is not formal. Class 1 and 2 sections can develop the plastic moment — the whole section reaches yield. Class 3 stops at the elastic moment, that is, at the first fibre to yield. For a typical IPE, \(W_{pl}\) is some 10–15% larger than \(W_{el}\), so dropping from Class 2 to Class 3 costs exactly that much capacity.
Important: cross-section resistance is not the full check
As with every cross-section check, the calculation assumes the beam does not lose stability. In a laterally unrestrained beam, failure by lateral-torsional buckling generally occurs before \(M_{c,Rd}\) is reached, and the governing resistance becomes \(M_{b,Rd}\), which is lower.
The assumption holds only when the compression flange is restrained along its full length — by a connected concrete slab or closely spaced purlins, for instance. Otherwise, continue with lateral-torsional buckling.
Likewise, if a large shear force acts on the same section, the reduction of §6.2.8 applies — see bending and shear.
Input data
- \(M_{Ed}\) — the design bending moment, in kNm, at Ultimate Limit State.
- Profile and section — \(W_{pl,y}\) and \(W_{el,y}\) are taken automatically from the European profile catalogue.
- Steel grade — \(f_y\) per EN 1993-1-1 Table 3.1, as a function of the governing thickness.
- Cross-section class — determined automatically from Table 5.2 for I and H profiles. Note that classification in bending differs from classification in compression, because the stress distribution in the web is different. See the cross-section classification calculator.
- \(W_{eff,y}\) — entered manually for Class 4; determined according to EN 1993-1-5.
- \(\gamma_{M0}\) — the recommended value is 1.0, but the National Annex takes precedence.
Assumptions and limitations
- Bending about the major axis (y-y). Minor-axis and biaxial bending are not covered.
- Loss of stability by lateral-torsional buckling is not included.
- Interaction with axial force is not treated — see bending and axial force.
- The reduction due to large shear force (§6.2.8) is not treated.
- Fastener holes in the tension flange are not considered (§6.2.5(4)–(5)).
Related calculations
- Lateral-torsional buckling — the governing check for laterally unrestrained beams
- Bending and shear — \(M\)–\(V\) interaction
- Bending and axial force — \(M\)–\(N\) interaction
- Shear force — \(V_{pl,Rd}\) and web buckling
- Cross-section class — it decides which modulus applies