Australian Moment Modification Factor αm — AS 4100 Clause 5.6
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Reference for moment modification factor αm per AS 4100:2020 Clause 5.6 (Table 5.6.1). Used to determine member moment capacity φMb for lateral-torsional buckling. Similar to Cb in AISC.
αm Values — AS 4100 Table 5.6.1
| Moment Diagram | αm |
|---|---|
| Uniform moment (constant) | 1.0 |
| Linear variation, end moment ratio β: | |
| β = +1.0 (double curvature) | 2.0 |
| β = +0.5 | 1.5 |
| β = 0.0 (one end zero) | 1.75 |
| β = -0.5 | 2.3 |
| β = -1.0 (single curvature, equal end moments) | 1.0 |
| Central point load, simply supported | 1.35 |
| Uniformly distributed load, simply supported | 1.13 |
| End moments + UDL (restrained ends) | 1.0 |
| Cantilever, point load at tip | 1.0 |
| Cantilever, UDL | 1.0 |
αm Formula for General Cases
αm = 1.7 × Mmax / sqrt(M²₂ + M²₃ + M²₄)
Where:
- Mmax = maximum moment within segment
- M₂, M₄ = moments at quarter points
- M₃ = moment at mid-length
This formula applies for any moment distribution and satisfies αm ≤ 2.5 for most practical cases.
Application to LTB Design — Clause 5.6.1.1
φMb = φ × αm × αs × Msx ≤ φMsx
Where:
- Msx = section moment capacity (× Sx)
- αs = slenderness reduction factor (based on modified slenderness λs)
- αm = moment modification factor (≥ 1.0)
- φ = 0.90
Worked Example
Problem: Simply supported beam, 8.0 m span, UDL. Determine αm and φMb.
Solution:
- From Table 5.6.1: UDL, simply supported → αm = 1.13
- For a point load at midspan: αm = 1.35
- If αm = 1.0 (uniform moment): φMb = φ × 1.0 × αs × Msx
- With αm = 1.13: φMb increases by 13% over uniform moment case
Design Resources
- [[Australian Steel Grades|/reference/australian-steel-grades/]] | [[Australian Steel Properties|/reference/australian-steel-properties/]] | [[Australian Beam Sizes|/reference/au-beam-sizes/]] | [[Australian Bolt Capacity|/reference/australian-bolt-capacity/]] | [[AS 4100 Beam Design|/reference/as4100-beam-design-example/]] | [[All Australian References|/reference/]]
FAQ
What is the minimum αm value? αm = 1.0 for uniform moment (conservative lower bound). Values range from 1.0 to approximately 2.5.
Why does αm increase capacity? Non-uniform moment diagrams concentrate inelastic behavior over a smaller region, delaying LTB. Higher αm means higher member moment capacity.
When can αm = 2.0 be used? For double curvature bending (β=+1.0) per Table 5.6.1. This provides the highest benefit (doubles the LTB capacity compared to uniform moment).
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.