UK C1 Factor — Moment Gradient Correction for LTB per EN 1993-1-1 + UK NA
The C1 factor (equivalent uniform moment factor) accounts for the shape of the bending moment diagram in lateral-torsional buckling calculations per EN 1993-1-1 Clause 6.3.2. Reference tables of C1 values for common loading and restraint conditions, including UK National Annex guidance for the calculation of Mcr in UK steel beam design.
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The C1 Factor in LTB Design
The elastic critical moment Mcr for LTB includes the C1 factor to account for the beneficial effect of non-uniform moment distributions:
Mcr = C1 × π²EIz / (kzL)² × √[(kz/kw)² × Iw/Iz + (kzL)² × GIt / (π²EIz)]
C1 = 1.00 for uniform bending moment (worst case — no stress gradient benefit).
C1 > 1.00 for all other moment diagrams, reflecting the reduced LTB susceptibility when the moment varies along the beam.
C1 Values for Simply Supported Beams (kz = kw = 1.0)
| Loading & Moment Diagram | ψ (end moment ratio) | C1 |
|---|---|---|
| Uniform moment | 1.0 | 1.00 |
| Triangular (single point load at midspan) | — | 1.35 |
| UDL (parabolic) | — | 1.13 |
| End moment + UDL (max at midspan) | — | 1.05-1.13* |
| End moment (ψ = 0) | 0.0 | 1.77 |
| End moment (ψ = −1, double curvature) | −1.0 | 2.55 |
C1 for General End Moment Ratio ψ
For a beam subject to end moments only (no transverse loads), with ψ = Msmall/Mlarge (ratio of smaller to larger end moment, sign considered):
| ψ | C1 | ψ | C1 |
|---|---|---|---|
| 1.00 | 1.00 | −0.25 | 2.05 |
| 0.75 | 1.14 | −0.50 | 2.26 |
| 0.50 | 1.31 | −0.75 | 2.42 |
| 0.25 | 1.52 | −1.00 | 2.55 |
| 0.00 | 1.77 | — | — |
Formula: C1 = 1.77 − 1.04ψ + 0.27ψ² (for −1 ≤ ψ ≤ 1, end moments only)
C1 for Transverse Loading (UK NA Approach)
For simply supported beams with transverse loads and end moments, use NCCI SN003:
| Load case | C1 |
|---|---|
| UDL, simply supported | 1.13 |
| UDL, both ends partially fixed | 1.17 |
| UDL, both ends fully fixed | 1.36 |
| Point load at midspan | 1.35 |
| Two point loads at third points | 1.11 |
| Three point loads at quarter points | 1.05 |
UK National Annex Guidance
The UK NA to BS EN 1993-1-1 does not provide specific C1 values but refers to the general method in Clause 6.3.2.2 and NCCI SN003. In UK practice:
- Conservative approach: Use C1 = 1.0 for all cases (simplest but penalises non-uniform moment)
- Standard approach: Use NCCI SN003 tables (most common in UK design offices)
- The C1 factor is NOT modified by the UK NA — the recommended values in NCCI SN003 apply
C1 and kz Interaction
C1 values above depend on the end rotation factor kz. For kz < 1.0 (partial end fixity), C1 reduces because the end restraint already provides some LTB benefit. For design to UK NA:
- kz = 1.0 (pinned): Use the standard C1 tables above
- kz = 0.7 (partially restrained bending): C1 is approximately 90 % of the kz = 1.0 value
- kz = 0.5 (fixed ends): C1 is approximately 80 % of the kz = 1.0 value
For practical UK design, most beams are assumed pinned at supports (kz = 1.0) unless the connection detail explicitly provides rotational restraint to the beam end.
Design Resources
- UK Steel Grades Reference — EN 10025-2 grade selection for UK projects
- UK Steel Mechanical Properties — fy, fu, and elongation tables
- UK Universal Beam and Column Sizes — UB/UC section dimensions and properties
- UK Bolt Capacity Tables — Class 8.8 and 10.9 bolt resistance
- UK Beam Design Guide — EN 1993-1-1 flexure, shear, and LTB
- UK Connection Design Guide — EN 1993-1-8 bolted and welded joints
- All UK Steel Design References — complete library
Frequently Asked Questions
What C1 factor should I use for a simply supported UB with UDL?
For a simply supported beam under UDL with kz = 1.0 (pinned ends), use C1 = 1.13. This is the standard value from NCCI SN003 and is used in UK design practice. Using C1 = 1.0 is conservative (13 % reduction in Mcr). The C1 = 1.13 accounts for the parabolic moment diagram being less severe for LTB than uniform moment.
How does the UK NA modify C1 values for LTB design?
The UK NA does not modify C1 values. It adopts the general LTB framework from Clause 6.3.2 and references NCCI SN003 for Mcr calculation including C1 factors. UK practice commonly uses the NCCI SN003 tables or the formulae: C1 = 1.77 − 1.04ψ + 0.27ψ² (end moments) or the specific values for transverse loading cases.
Can I use C1 = 1.0 conservatively for all beams?
Yes, C1 = 1.0 is always conservative for simply supported beams because it corresponds to the worst-case uniform moment distribution. However, this can be unnecessarily penalising. For a beam with no transverse loads and ψ = 0 (triangular moment), using C1 = 1.0 rather than the correct 1.77 underestimates Mcr by 77 %. This results in a higher λLT,bar and lower χLT, potentially requiring a heavier section. For design optimisation, use the correct C1 value.
Does C1 apply to cantilever beams?
EN 1993-1-1 covers cantilever LTB in Clause 6.3.2.4 with specific rules. For cantilevers, the C1 values differ from simply supported cases and depend on the tip loading condition and root fixity. For a cantilever with a point load at the tip acting through the shear centre, C1 ≈ 0.9 (less than 1.0 because the moment distribution is more severe than uniform moment for LTB). The UK NA to Clause 6.3.2.4 provides specific guidance for cantilever beams.
Related Pages
- EN 1993 Steel Design Overview
- European Steel Properties
- EN 1993 Beam Design Guide
- EN 1993 Column Buckling
- EN 1990 Load Combinations
- UK Steel Chemical Composition
- UK Steel Charpy Values
Educational reference only. All design values are per BS EN 1993-1-1:2005 + UK National Annex and BS EN 10025-2:2019. Verify all values against the current editions of the standards and the applicable National Annex for your project jurisdiction. Designs must be independently verified by a Chartered Structural Engineer registered with the Institution of Structural Engineers (IStructE) or the Institution of Civil Engineers (ICE). Results are PRELIMINARY — NOT FOR CONSTRUCTION without independent professional verification.