Australian Combined Loading — AS 4100 Clause 8.4
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Reference for combined axial compression and bending design per AS 4100:2020 Clause 8.4. Covers interaction formulas, moment amplification (δb), and biaxial bending checks.
Interaction Formula — AS 4100 Clause 8.4.2
Mx/φMbx + My/φMby ≤ 1.0**
And separately: N/φNc + Mx/φMsx + My*/φMsy ≤ 1.0**
Where:
- N* = design axial compression
- φNc = design member compression capacity
- Mx*, My* = design moments (including amplification)
- φMbx = design member moment capacity (LTB)
- φMsx = design section moment capacity
Moment Amplification — Clause 8.4.3
M* = δb × M*b + δs × M*s
Where:
- δb = Cm / (1 − N*/φNoc) ≥ 1.0 (braced amplification)
- δs = 1 / (1 − ΣN*/ΣNn) (sway amplification)
- Cm = 1.0 for end moments, 0.6-0.4β for linear variation
- φNoc = elastic buckling capacity (π²EI/Le²)
δb values for common cases:
| N*/φNoc | Cm=1.0 | Cm=0.85 | Cm=0.6 |
|---|---|---|---|
| 0.1 | 1.11 | 0.95 | 0.67 |
| 0.2 | 1.25 | 1.06 | 0.75 |
| 0.3 | 1.43 | 1.21 | 0.86 |
| 0.4 | 1.67 | 1.42 | 1.00 |
| 0.5 | 2.00 | 1.70 | 1.20 |
Biaxial Bending — Clause 8.4.5
For RHS/SHS and symmetric sections: (Mx*/φMsx)^1.4 + (My*/φMsy)^1.4 ≤ 1.0
For I-sections (strong axis bending dominates): Mx*/φMsx + (My*/φMsy)^2 ≤ 1.0 (when N* ≤ φNc)
Simplified (conservative): Mx*/φMsx + My*/φMsy ≤ 1.0
Worked Example
Problem: 310UC137 (φNc=3,200 kN, φMsx=620 kNm). N*=1,200 kN, M*x=280 kNm (including δb=1.15). φNoc=8,000 kN.
Solution:
- N*/φNc = 1,200/3,200 = 0.38 < 1.0 OK
- Check interaction: N*/φNc + Mx*/φMsx = 0.38 + 280/620 = 0.38 + 0.45 = 0.83 ≤ 1.0 OK
- Check second formula: 1,200/3,200 + 280/620 = 0.83 ≤ 1.0 OK
- Moment amplification OK: δb = Cm/(1−1200/8000) = Cm/0.85
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
When is moment amplification important? When N*/φNoc > 0.3, amplification exceeds 1.4. At N*/φNoc = 0.5, amplification is 2.0. Critical for slender columns.
How is Cm determined? Cm = 0.6 - 0.4β for linear moment gradient (β = end moment ratio). Cm = 1.0 for transverse loading between supports.
What is the biaxial bending exponent? 1.4 for RHS/SHS and symmetrical sections, 2.0 for I-section weak axis, per Clause 8.4.5.
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.