Australian Beam Design — AS 4100 Clause 5 Complete Guide

Comprehensive reference for flexural design of steel beams to AS 4100:2020. Covers section moment capacity, member moment capacity with lateral-torsional buckling, shear capacity with tension field action, web bearing and buckling, deflection serviceability, and combined actions.

Related pages: AS 4100 LTB Reference | Australian Beam Sizes | AS 4100 Deflection Guide | Beam Capacity Calculator

Section Classification — AS 4100 Table 5.2

Before determining moment capacity, classify the section to establish which capacity formula applies. The key ratio for flanges is lambda_e = b/tf; for webs, lambda_e = d1/tw.

For Grade 300 steel, lambda_ep = 9 for flanges with uniform compression (hot-rolled) and lambda_ep = 82 for webs in bending (hot-rolled UB). Most commercial UB sections up to 610UB are compact in both flange and web.

Section Moment Capacity — Clause 5.2.3

For compact sections, the design section moment capacity is the full plastic moment:

phi_Msx = phi x fy x Sx (plastic section modulus)

For non-compact sections, the capacity is interpolated between the yield moment phi_My and the plastic moment phi_Mp: phi_Msx = phi_Mp - (phi_Mp - phi_My) x (lambda - lambda_ep) / (lambda_ey - lambda_ep)

For slender sections, the elastic buckling moment governs, with effective section properties: phi_Msx = phi x fy x Ze

Where Ze is the effective section modulus accounting for the reduced effectiveness of slender elements.

The capacity factor phi = 0.90 for all beam moment checks per AS 4100 Table 3.4.

Member Moment Capacity — Lateral-Torsional Buckling, Clause 5.6

LTB is the dominant limit state for beams with limited lateral restraint to the compression flange:

phi_Mb = phi x alpha_m x alpha_s x Msx <= phi_Msx

Where:

• alpha_m = moment modification factor (Clause 5.6.1.2), accounting for the shape of the bending moment diagram along the segment. A uniform moment (alpha_m = 1.0) is the worst case; a linear gradient from positive to negative (alpha_m = 2.5 to 3.0) significantly increases capacity.
• alpha_s = slenderness reduction factor, a function of lambda_s = sqrt(Msx / Mo), where Mo is the elastic buckling moment.

alpha_s formula: alpha_s = 0.6 x [sqrt(lambda_s^4 + 3) - lambda_s^2]^(0.5)

Elastic buckling moment Mo (doubly symmetric I-section): Mo = sqrt[(pi^2 x E x Iy) / Le^2 x (G x J + pi^2 x E x Iw / Le^2)]

The Mo formula reveals why deep, narrow I-sections are poor in LTB: Iy is small (weak axis), Iw (warping constant) may be moderate, but the controlling term is the effective length Le. Doubling Le approximately quarters the elastic buckling moment.

alpha_m Values — Moment Modification Factor

The Australian approach uses a single alpha_m factor applied to the section capacity, in contrast to AISC 360 which uses a Cb multiplier on the elastic buckling moment. The numerical effect is similar but the Australian alpha_m is applied post-buckling reduction rather than pre-reduction.

The alpha_m values are proportional to the area under the moment diagram relative to the peak moment. A full reversal (double curvature) at end moments gives the highest alpha_m because the moment changes sign, making LTB less likely.

LTB Design Examples — 410UB59.7 Segments

For a 410UB59.7 beam (Grade 300, Msx = 320 kNm):

For a 8 m simply supported UDL beam with midspan restraint (Le = 4.0 m): phi_Mb = 0.90 x 1.13 x 0.85 x 320 = 277 kNm, considerably less than the section capacity of phi x 320 = 288 kNm.

Shear Capacity — Clause 5.9

Unstiffened web shear (Clause 5.9.2): phi_Vu = phi x 0.60 x fy x Aw x kv Where Aw = d x tw (gross web area) and kv = 1.0 for webs without transverse stiffeners.

Stiffened web shear with tension field action (Clause 5.9.4): phi_Vu = phi x 0.60 x fy x Aw x [kv + 0.50 x (1 - kv) x (1 - d1/(82 x tw x sqrt(fy/250)))]

Where kv for stiffened webs depends on the stiffener spacing s: kv = 5.34 + 4.00 / (s/d1)^2 for s/d1 >= 1.0 kv = 4.00 + 5.34 / (s/d1)^2 for s/d1 < 1.0

Tension field action can increase shear capacity by 30-50% for deep girders with close stiffener spacing. However, stiffeners must be designed as compression members per Clause 5.9.5, including a check of the stiffener-plate buckling as a column.

Web Bearing and Buckling — Clause 5.13

Concentrated forces from reactions or point loads on beam flanges must be checked for web bearing (yield) and web buckling:

Web bearing yield (Clause 5.13.3): Rb = phi x 1.25 x bb x tw x fy

Where bb is the bearing width (length of stiff bearing). The factor 1.25 accounts for the spread of force through the flange at 1:2.5 slope.

Web bearing buckling (Clause 5.13.4): Rb_buckle = phi x alpha_c x tw x L_eff x fy

Where L_eff is the effective bearing length (spread through flange + distance to web face) and alpha_c is the column buckling reduction factor based on an effective column of web height d1.

For practical beam design, load-bearing stiffeners are required when:

• The factored reaction exceeds the web bearing capacity
• The unframed end of a beam carries significant concentrated load
• The beam depth exceeds approximately 600 mm with heavy reactions

Deflection Serviceability — Clause 16.4 and AS/NZS 1170.0 Appendix C

The deflection limit that governs most office floor beams is L/500 for live load where partitions are present. For a 10 m span beam, this limits live load deflection to 20 mm. Pre-camber of beams for dead load deflection is common practice for spans exceeding 8 m and should be specified as a note on the fabrication drawing.

Worked Example — 610UB125 Floor Beam

Problem: A simply supported 610UB125 beam spans 12.0 m supporting office floor loads. Dead load = 12.0 kN/m (including self-weight), live load = 16.0 kN/m (office with partitions). Beam is laterally restrained at supports and at 3.0 m centres along the span by the concrete slab. Grade 300 steel.

Section properties — 610UB125: Sx = 3220 x 10^3 mm^3 | Ix = 1030 x 10^6 mm^4 | tw = 11.9 mm | tf = 19.6 mm | d = 611 mm | bf = 229 mm | ry = 48.2 mm

Step 1 — Factored load: wf = 1.2 x 12.0 + 1.5 x 16.0 = 14.4 + 24.0 = 38.4 kN/m

Step 2 — Maximum design actions: M* = wf x L^2 / 8 = 38.4 x 144 / 8 = 691.2 kNm V* = wf x L / 2 = 38.4 x 12.0 / 2 = 230.4 kN

Step 3 — Section classification: Flange: b/2tf = 229 / (2 x 19.6) = 5.84 < 9 (compact) Web: d1/tw = (611 - 2 x 19.6) / 11.9 = 571.8 / 11.9 = 48.1 < 82 (compact) Compact section — full plastic moment applies.

Step 4 — Section moment capacity: phi_Msx = 0.90 x 300 x 3220 x 10^3 / 10^6 = 869.4 kNm > 691.2 kNm. OK (section).

Step 5 — LTB check: Segment length Le = 3.0 m (restrained by slab at 3.0 m centres). lambda_s = sqrt(Msx / Mo). Compute Mo estimated for this section: Iy = 56.1 x 10^6 mm^4, J = 1.87 x 10^6 mm^4, Iw = 2.89 x 10^12 mm^6 Mo = sqrt[(pi^2 x 200000 x 56.1 x 10^6) / 3000^2 x (80000 x 1.87 x 10^6 + pi^2 x 200000 x 2.89 x 10^12 / 3000^2)] = approximately 2,450 kNm

lambda_s = sqrt(966 / 2450) = 0.629 (where Msx = 3220 x 10^3 x 300 / 10^6 = 966 kNm) alpha_s = 0.6 x [sqrt(0.629^4 + 3) - 0.629^2]^0.5 = 0.6 x [sqrt(0.157 + 3) - 0.396]^0.5 = 0.6 x [1.777 - 0.396]^0.5 = 0.6 x 1.175 = 0.705

alpha_m = 1.13 (UDL on restrained segment with end moments from continuity giving partial fixity) Actually, for a simply supported UDL with intermediate restraints, alpha_m varies per segment. For the end segment (length = 3.0 m), the moment diagram is approximately linear from zero to 0.44_M_max, giving alpha_m ~ 1.35. Use 1.13 conservatively.

phi_Mb = 0.90 x 1.13 x 0.705 x 966 = 692 kNm >= 691.2 kNm. Just OK.

Step 6 — Shear: Aw = 611 x 11.9 = 7,271 mm^2 phi_Vu = 0.90 x 0.60 x 300 x 7271 x 1.0 / 1000 = 1,178 kN > 230.4 kN. OK.

Step 7 — Deflection (serviceability live load): w_L = 16.0 kN/m delta = 5 x 16.0 x 12000^4 / (384 x 200000 x 1030 x 10^6) = 21.0 mm L/500 = 24.0 mm (partition limit). 21.0 < 24.0. OK. Consider 10 mm upward camber for dead load deflection (approximately 11.5 mm).

Result: 610UB125 Grade 300 is adequate. LTB governs at the end segments; check midspan segment may be more favourable due to higher alpha_m from moment reversal at adjacent spans.

Practical Design Notes for Steel Beams

Web openings: Penetrations in beam webs for services must be reinforced if the opening diameter exceeds 0.25 x d. The Vierendeel moment across the opening should be checked per industry guidelines (e.g., ASI Design Guide 1).

Flange curling: For beams with slender flanges in compression, flange curling can reduce the effective section. AS 4100 does not explicitly limit curling, but b/2tf > 15 warrants consideration for deep beams.

Lateral restraint from slabs: Composite slabs on steel deck can provide continuous lateral restraint to the top flange provided the shear studs are adequately spaced (typically at 300-450 mm centres) and the deck is positively connected.

Temperature effects: Internal beams in enclosed buildings require no temperature allowance. External beams exposed to sun may experience 40-60 degree differential temperature and should allow for thermal expansion in the connection design.

Frequently Asked Questions

At what span does LTB start governing for a typical UB floor beam? For standard UB sections (410UB59.7, 530UB82, 610UB101) with unsupported top flanges, LTB begins to govern at segment lengths of approximately 3-4 m for light sections and 4-6 m for heavier sections. When the concrete slab provides continuous lateral restraint (composite construction), LTB of the positive moment region is eliminated entirely and only the negative moment region over supports needs checking.

How does the Australian alpha_m differ from AISC Cb? Both modify capacity to account for non-uniform moment. AS 4100 applies alpha_m directly to the section capacity (multiplier on phi_Msx), while AISC 360 applies Cb to the elastic buckling moment (modifies LTB resistance curve). For the same moment diagram, both produce similar results. The key difference is that alpha_m is applied after the buckling reduction, so it provides proportionally more benefit at high slenderness where alpha_s is small.

When are transverse stiffeners required in beams? Transverse stiffeners are required when: (a) the unstiffened web shear capacity is insufficient (d1/tw > 82/sqrt(fy/250) for Grade 300); (b) there are large concentrated loads requiring web bearing stiffeners; or (c) tension field action is needed to increase shear capacity. In practice, stiffeners are common in plate girders (typically d > 800 mm) and rare in hot-rolled UB sections where the web slenderness is usually adequate.

What is the minimum bearing length for a beam end reaction? Per AS 4100 Clause 5.13.3, the minimum bearing length must satisfy: bb >= R* / (phi x 1.25 x tw x fy). For a 410UB59.7 with R* = 150 kN, bb >= 150000 / (0.90 x 1.25 x 7.8 x 300) = 57 mm. In practice, specify a minimum bearing of 75 mm for beams up to 20 kN/m reaction intensity. For crane girders, bearing stiffeners are standard regardless of calculated bearing length due to fatigue considerations.

Should beam design account for construction stage loading? Yes. During construction, the concrete slab is wet (additional 1.5-2.0 kPa) and the beam may lack the full lateral restraint that the hardened slab provides. Check the beam for construction loads with Le = full span length (no slab restraint). Temporary propping or a construction sequence note on drawings can mitigate this if the bare steel capacity is insufficient.

This page is for educational reference. Beam design per AS 4100:2020 Clause 5. Verify section properties and capacities against current ASI design capacity tables. All structural designs must be independently verified by a licensed Professional Engineer or Structural Engineer. Results are PRELIMINARY — NOT FOR CONSTRUCTION.