Example: Eurocode bending check answered by Structural AI
Question: Check a UB 457x191x67 in S355 for bending - 8 m simply supported span, 47 kN/m at ULS.
Section classification (EN 1993-1-1, Table 5.2)
With tf = 12.7 mm <= 16 mm, S355 gives fy = 355 N/mm2, so eps = sqrt(235/355) = 0.814.
- Flange: cf/tf = 6.34 <= 9 eps = 7.32, so Class 1
- Web: cw/tw = 48 <= 72 eps = 58.6, so Class 1
Design moment
- M_Ed = w L^2 / 8 = 47 x 8^2 / 8 = 376 kNm
Moment resistance (EN 1993-1-1, 6.2.5(2), Eq. 6.13)
Class 1 in bending, so the full plastic modulus may be used.
- M_c,Rd = M_pl,Rd = Wpl,y x fy / gamma_M0 = 1470 x 10^3 x 355 / 1.0 = 521.9 kNm
Verdict
- M_Ed / M_c,Rd = 376 / 521.9 = 0.72, so PASS with 28% spare capacity
This checks cross-section bending only, assuming the compression flange is fully restrained. Without continuous restraint you must also verify lateral-torsional buckling to 6.3.2, which will usually govern an 8 m span.
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