Several steel design codes require the bimoment B in the strength interaction check for open thin-walled members, yet none specify how B is obtained from the applied loading. One long-standing remedy approximates the bimoment diagram directly from the bending-moment diagram; a recent tabulated form of this bending–bimoment analogy, validated against nine classical schemes, reports a maximum error of 4.6%, but only for cold-formed sections with flexural-torsional parameter k ~ 10⁻⁴–10⁻³ cm⁻¹. The novelty of this study is to re-examine the analogy's applicability range with an independently verified toolchain closed-form Vlasov solutions for four schemes, cross-checked against a purpose-built two-node torsion finite element and to show that the analogy's relative error is a universal function of the single dimensionless parameter k·L, independent of section geometry, material or load, so that one applicability chart serves any open thin-walled section and scheme. Applied to a hot-rolled channel (k ≈ 0.02 cm⁻¹), the analogy exceeds a 5% tolerance beyond k·L ≈ 1.5–3, reaching 20–55% at k·L = 8–15, typical of hot-rolled spans. For a comparable cold-formed channel, three of the four schemes remain accurate at ordinary purlin spans, but the cantilever scheme already exceeds tolerance there, a scheme-dependent sensitivity not previously reported. A representative strength check shows that neglecting the bimoment altogether overestimates the allowable load by up to 24.2% at the reference section, and by as much as 227% for other schemes, showing that the practical risk of omitting B outweighs the accuracy question addressed by the analogy itself.