Australian Lateral Torsional Buckling (LTB) — AS 4100 Clause 5.6
Comprehensive guide to lateral torsional buckling design per AS 4100:2020 Clause 5.6. LTB occurs when a beam loaded in bending deflects laterally and twists, reducing its moment capacity below the plastic section capacity. Understanding LTB is essential for safe and economical UB design in Australian practice.
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LTB Design Formula — AS 4100 Clause 5.6.1.1
The design member moment capacity is:
phi-Mb = phi x alpham x alphas x Ms <= phi-Ms
Where:
- phi = 0.90 (capacity factor)
- alpham = moment modification factor (Clause 5.6.1.1(a))
- alphas = slenderness reduction factor (Clause 5.6.1.1(c))
- Ms = section moment capacity (kNm)
Moment Modification Factor (alpham) — AS 4100 Table 5.6.1
The alpham factor accounts for the bending moment distribution along the segment:
| Moment Diagram | alpham Value | Condition |
|---|---|---|
| Uniform moment (constant throughout) | 1.00 | Most conservative |
| Parabolic (UDL on simply supported) | 1.13 | Typical floor beam |
| Triangular (point load at midspan) | 1.35 | Concentrated load |
| Linear (ends unequal) | 1.75 - 1.05(beta_m) + 0.3(beta_m)^2 | General case |
| Restrained at both ends (double curvature) | 2.50 | Max for framed beams |
beta_m is the ratio of smaller to larger end moment (positive for double curvature)
Slenderness Reduction Factor (alphas)
The alphas factor is calculated from the modified slenderness (Le/r_y) and design yield stress:
| Section | Le/r_y Range | alphas Formula |
|---|---|---|
| Compact | lambda_s <= 0.786 | 1.0 |
| Compact | 0.786 < lambda_s <= 3.153 | 1.35 - 0.259 x lambda_s + 0.00810 x lambda_s^2 + 0.000348 x lambda_s^3 |
| Compact | lambda_s > 3.153 | 1.0 / (lambda_s^2) |
Where lambda_s = sqrt(fy / 250) x (Le / r_y) / (pi x sqrt(E / G x J / (I_y x d^2 / 4 + I_w))) — approximated for standard UB sections.
Table: Critical LTB Moment (Mo) for Common UB Sections
| Section | ry (mm) | J (x10^3 mm^4) | Iw (x10^9 mm^6) | Mo for L = 4 m (kNm) |
|---|---|---|---|---|
| 250UB25.7 | 32.5 | 51.2 | 6.77 | 112 |
| 310UB40.4 | 38.0 | 96.8 | 13.4 | 171 |
| 410UB59.7 | 47.8 | 131 | 71.3 | 298 |
| 530UB92.4 | 67.5 | 319 | 241 | 594 |
| 610UB125 | 76.0 | 568 | 589 | 893 |
| 700UB173 | 89.0 | 972 | 1,490 | 1,442 |
Worked Example: LTB Assessment
Problem: A 410UB59.7 Grade 300 beam spans 8.0 m with a central point load (factored = 100 kN). The compression flange is laterally restrained at the load point and at supports. Check the member moment capacity of the 4.0 m segment adjacent to the support.
Solution:
- Alpham for point load at midspan (segment with linear moment variation): alpham = 1.35
- Segment length Le = 4.0 m
- From table above for 410UB59.7 with L = 4 m: Mo = 298 kNm
- Modified slenderness: lambda_s = sqrt(fy / 250) x sqrt(Ms / Mo) = sqrt(280/250) x sqrt(288/298) = 1.058 x 0.983 = 1.04
- alphas = 1.35 - 0.259 x 1.04 + 0.00810 x 1.04^2 + 0.000348 x 1.04^3 = 1.089
- phi-Mb = 0.90 x 1.35 x 1.089 x 288 = 381 kNm > phi-Ms = 288 kNm, so phi-Mb = 288 kNm
- Check: M* = PL/4 = 100 x 8 / 4 = 200 kNm <= 288 kNm — OK (69% utilisation)
Design Resources
- Australian Steel Grades | Australian Steel Properties | Australian Beam Sizes | Australian Bolt Capacity | All Australian References
- Australian Beam Design
- Cb Factor for LTB
- Compact Section Limits
Frequently Asked Questions
What is lateral torsional buckling in steel beams? LTB is a limit state where a beam loaded in bending deflects laterally and twists simultaneously, reducing its flexural capacity below the plastic section capacity. It is analogous to column buckling but occurs in bending members.
What is the alpham factor in AS 4100 LTB design? alpham is the moment modification factor (AS 4100 Table 5.6.1) that accounts for the shape of the bending moment diagram. A uniform moment gives alpham = 1.0 (most conservative), while a parabolic distribution gives alpham = 1.13.
How does segment length affect LTB capacity? Longer unbraced segments reduce the member moment capacity (phi-Mb). At Lb near zero, phi-Mb = phi-Ms (no LTB). As Lb increases, phi-Mb drops approximately hyperbolically. Limiting Lb to phi-Mb = 0.80 x phi-Ms is a common economical target.
What bracing prevents lateral torsional buckling? Full lateral restraint prevents both lateral displacement and twist of the compression flange. Effective bracing includes: concrete slabs on the compression flange, secondary beams framing into the compression flange at close spacing, or fly braces attached to the web at the compression flange level.
Can LTB be ignored for beams in concrete slabs? When the compression flange is in direct contact with a concrete slab capable of resisting lateral forces (e.g., composite slab with shear studs), the beam is considered fully laterally restrained and LTB does not apply. The design moment capacity equals phi-Ms.---
Educational reference only. Verify all design values against the current edition of AS 4100:2020 and the project specification. This information does not constitute professional engineering advice. Always consult a qualified structural engineer for design decisions.
Educational Use Only — This reference is for educational and preliminary design purposes only. All structural designs must be independently verified by a licensed Professional Engineer (PE) or Structural Engineer (SE) in accordance with AS 4100:2020 and all applicable Australian Standards. Results are not for construction.