AS 4100 Moment Capacity Guide — am, as, Ms, Compact, Non-Compact, Slender
The bending capacity of a steel beam is governed by two distinct failure modes: the section can yield or locally buckle (controlled by Ms), and the member can laterally-torsionally buckle (controlled by Mb = am x as x Ms). AS 4100 Section 5 organises these checks through three key parameters. This guide explains each one, walks through section classification, and provides a full worked example on a 310UB40.4 beam.
PRELIMINARY — NOT FOR CONSTRUCTION. This is an educational reference. All designs must be independently verified by a licensed Professional Engineer before use in any project.
The AS 4100 Bending Capacity Framework
- Section moment capacity (Ms) — Clauses 5.1 and 5.2: Cross-section strength before member buckling. Depends on section classification.
- Member moment capacity (Mb) — Clause 5.6: Beam strength considering lateral-torsional buckling over the unbraced length. Mb = am x as x Ms (cannot exceed Ms).
Section Classification — Table 5.2
AS 4100 defines three categories based on plate element slenderness:
| Category | Flange slenderness limit | Web slenderness limit | Plastic capacity? |
|---|---|---|---|
| Compact | lambda-e <= 9 | lambda-e <= 82 | Yes (Ms = fy x S, capped at 1.5 x fy x Z) |
| Non-compact | 9 < lambda-e <= 16 | 82 < lambda-e <= 115 | Partial (interpolated) |
| Slender | lambda-e > 16 | lambda-e > 115 | No (effective width method) |
For hot-rolled I-sections in Grade 300PLUS (fy = 300 MPa): flange slenderness = (bf - tw)/(2 x tf) x sqrt(300/250), web slenderness = (d1/tw) x sqrt(300/250).
Section Moment Capacity Ms — Worked Example (310UB40.4)
A 310UB40.4 in Grade 300PLUS (fy = 300 MPa):
Section properties: d = 304 mm, bf = 165 mm, tf = 10.2 mm, tw = 6.1 mm
Zx = 633 x 10^3 mm3, Sx = 722 x 10^3 mm3
Iy = 7.64 x 10^6 mm4, ry = 39.6 mm, J = 133 x 10^3 mm4, Cw = 101 x 10^9 mm6
Classify the section:
d1 = 304 - 2 x 10.2 = 283.6 mm
Flange lambda-e = (165 - 6.1)/(2 x 10.2) x 1.095 = 7.79 x 1.095 = 8.53 <= 9 --> Compact
Web lambda-e = (283.6/6.1) x 1.095 = 46.5 x 1.095 = 50.9 <= 82 --> Compact
Both elements compact --> Section is COMPACT.
Calculate Ms:
Ze = min(S, 1.5 x Z) = min(722,000, 949,500) = 722,000 mm3
Ms = fy x Ze = 300 x 722,000 = 216.6 kNm
Design Ms = 0.90 x 216.6 = 194.9 kNm
Member Moment Capacity Mb — Lateral-Torsional Buckling
The member capacity is: Mb = am x as x Ms <= Ms
The Slenderness Reduction Factor as
as is calculated from the elastic buckling moment Moa:
Moa = sqrt[(pi^2 x E x Iy / Le^2) x (G x J + pi^2 x E x Cw / Le^2)]
For the 310UB40.4 at Le = 4,000 mm:
E = 200,000 MPa, G = 80,000 MPa
First term (Euler): pi^2 x 200,000 x 7.64e6 / 16e6 = 942,486 N
Torsional term: 80,000 x 133,000 = 10.64e9 Nmm2
Warping term: pi^2 x 200,000 x 101e9 / 16e6 = 12.45e9 Nmm2
Combined = (10.64 + 12.45)e9 = 23.09e9 Nmm2
Moa = sqrt(942,486 x 23.09e9) = 46.7 kNm
as = 0.6 x [sqrt((216.6/46.7)^2 + 3) - (216.6/46.7)]
= 0.6 x [sqrt(4.64^2 + 3) - 4.64]
= 0.6 x [sqrt(24.53) - 4.64] = 0.6 x [4.953 - 4.64] = 0.188
At Le = 4,000 mm, as = 0.188. Compare with Le = 2,000 mm:
Moa(Le=2000) = 477 kNm
as = 0.6 x [sqrt((216.6/477)^2 + 3) - (216.6/477)]
= 0.6 x [sqrt(0.454^2 + 3) - 0.454] = 0.6 x [1.768 - 0.454] = 0.802
The Moment Modification Factor am
am adjusts for non-uniform moment distribution:
| Loading Condition | am |
|---|---|
| Uniform moment (conservative) | 1.00 |
| Central point load, simply supported | 1.35 |
| UDL, simply supported | 1.13 |
| End moments M and -M (double curvature) | 2.27 |
| Propped cantilever with UDL | 1.75 |
Member Capacity Results
| Condition | Le (mm) | am | as | Mb (kNm) | Design Mb (kNm) |
|---|---|---|---|---|---|
| Le = 2000, UDL | 2,000 | 1.13 | 0.802 | 216.6* | 194.9 |
| Le = 4000, UDL | 4,000 | 1.13 | 0.188 | 46.0 | 41.4 |
| Le = 6000, UDL | 6,000 | 1.13 | 0.085 | 20.8 | 18.7 |
*At Le = 2,000 mm, Mb would be 196.3 kNm but is capped at Ms = 216.6 kNm — section capacity governs.
The 310UB40.4 has relatively narrow flanges (bf = 165 mm), giving low minor-axis stiffness (Iy = 7.64e6 mm4), making it susceptible to LTB at longer unbraced lengths.
Frequently Asked Questions
When can I take am > 1.0?
am > 1.0 applies whenever the moment diagram is non-uniform. A simply-supported beam with UDL gets am = 1.13. A beam with central point load gets am = 1.35. A cantilever with tip load gets am = 1.28. End moments producing double curvature can achieve am = 2.27, more than doubling member capacity compared to uniform moment.
Do I need to check LTB for a beam with continuous slab restraint?
No — if the top flange is continuously restrained by a composite slab (through shear studs) or by precast plank bearing, LTB cannot occur in the final condition. However, LTB must be checked for the construction condition before the slab is in place, which often means providing temporary fly braces at 2,000-3,000 mm centres.
What is the most effective way to increase LTB capacity?
In decreasing order: (1) reduce unbraced length (closer fly braces) — increases as exponentially; (2) select a section with wider flanges (higher Iy) — increases Moa linearly; (3) utilise moment gradient (higher am). Adding flange width is more effective than adding depth for LTB.
How does AS 4100 moment capacity compare with AISC 360?
Key differences: AS 4100 uses three classification categories (compact/non-compact/slender) vs AISC's two (compact/non-compact and slender); AS 4100 uses am x as with separate factors vs AISC's Cb x Fcr; AS 4100 caps the shape factor at 1.5 while AISC allows higher plastic capacity for certain sections; both use capacity factor 0.90 for bending.
This reference is for educational purposes only. Verify all section properties, material grades, and code clauses against the current editions of AS 4100 and AS/NZS 3679.1 before use in any project. All designs must be independently checked and certified by a licensed Professional Engineer.