-------------- | -------------------------------------------- | ------------------------------------------------ | | Resistance factor | phic = 0.90 (compression) | phi_c = 0.90 (compression) | | Column curve method | alpha_c (Perry-Robertson) | Fcr (SSRC curve — tangent modulus + Euler) | | Section constant | alpha_b (form factor for buckling) | None (implicit in Fy via Table B4.1a) | | Modified slenderness | lambdan = (Le/r) _ sqrt(kf) _ sqrt(Fy/250) | KL/r directly; Fy transition at 4.71*sqrt(E/Fy) | | Section capacity | Ns = kf _ An _ Fy | Pn = Fy * Ag (compact sections) | | Member capacity | Nc = alpha_c * Ns | Pn = Fcr * Ag (flexural buckling) | | Key reference | Section 6 | Chapter E |

The resistance factor phi_c = 0.90 is identical in both codes, but the similarity ends there. AS 4100 applies a form factor kf to account for local buckling in the cross-section before the column curve is applied, while AISC addresses local buckling through the section classification table (compact / noncompact / slender) and the Qs/Qa reduction factors in Chapter E7.

The Column Curve: alpha_c vs Fcr

This is the core difference between the two codes and where most design capacity divergence originates.

AS 4100 — Perry-Robertson (alpha_c)

AS 4100 uses the Perry-Robertson formulation, which models the column as an initially imperfect strut. The member slenderness reduction factor alpha_c is:

alpha_c = xi * [1 - sqrt(1 - (90 / (xi * lambda))^2)]

where:
  xi = (lambda / 90)^2 + 1 + eta
  eta = alpha_b * (lambda / 90)^2
  lambda = lambda_n = (Le/r) * sqrt(kf) * sqrt(Fy/250)

• alpha_b is the section constant: +0.50 for lightly welded H-sections (category b), 0.00 for hot-rolled UB/UC (category c), -0.50 for heavily welded box sections
• lambda = 0 gives alpha_c = 1.0 (no reduction for zero slenderness)
• The parameter (90/lambda)^2 inside the sqrt limits alpha_c as slenderness increases

AISC 360 — SSRC Curve (Fcr)

AISC uses the Structural Stability Research Council (SSRC) column curve with two regimes:

Inelastic buckling (KL/r ≤ 4.71 * sqrt(E/Fy)):
  Fe = pi^2 * E / (KL/r)^2
  Fcr = [0.658^(Fy/Fe)] * Fy

Elastic buckling (KL/r > 4.71 * sqrt(E/Fy)):
  Fcr = 0.877 * Fe

The transition slenderness for Fy = 50 ksi (345 MPa) is KL/r = 4.71 * sqrt(29000/50) = 113.4. Below this, the column buckles inelastically and the 0.658 exponent captures the tangent-modulus effect. Above this, elastic Euler buckling controls with a 0.877 imperfection factor.

Curve Comparison: Fy = 350 MPa (50 ksi equivalent)

For hot-rolled I-sections (UB/UC, W-shapes), AS 4100 with alpha_b = 0.0 gives slightly higher capacities at intermediate slenderness (KL/r 60–100) and converges with AISC at very low and very high slenderness. For welded sections with alpha_b = +0.50, AS 4100 is even more favourable at intermediate slenderness.

Section Classification and Form Factor

AS 4100 evaluates the section form factor kf from the effective widths of slender plate elements and applies it to the section capacity Ns = kf _ An _ Fy. AISC reduces the critical stress via the Q factor: Fcr is computed with Q*Fy substituted for Fy in the inelastic/exponential formula. The two approaches are mathematically equivalent for the same slenderness reductions but differ in the specific plate bucking coefficients.

Effective Length Factors

Both codes use the effective length concept k * L, but the determination of k differs:

AS 4100 provides explicit ke values in Clause 4.6.3.3 (braced members) and 4.6.3.4 (sway members) based on the end restraint coefficients gamma_1 and gamma_2. AISC provides the alignment chart (nomograph) in Commentary Figure C-A-7.1 and C-A-7.2 but recommends the Direct Analysis Method (Appendix 7) over effective length methods for sway frames.

For typical braced-frame columns in multi-storey buildings, both codes commonly use ke ≈ 0.8–0.9 (bottom storey, pinned base) and ke ≈ 0.7–0.8 (upper storeys). The differences arise at the extremes: AISC allows K = 0.5 for truly fixed-fixed conditions while AS 4100 caps ke at 0.7 for braced members with full end fixity.

Worked Example: W250x73 / 250UC89.5 Column

Problem: A 4 m (13.1 ft) pin-ended steel column carries a factored axial load of N* = 1500 kN (337 kip). Compare the design capacity under AS 4100 and AISC 360.

Section: 250UC89.5 (AS 4100) / W250x73 (AISC)

• A = 11,400 mm^2 (17.7 in^2)
• rx = 111 mm (4.37 in.), ry = 64.6 mm (2.54 in.)
• Fy = 350 MPa (50 ksi), Fu = 450 MPa (65 ksi)
• Flange: bf = 256 mm, tf = 17.3 mm
• Web: d1 = 203 mm (between flanges), tw = 10.5 mm

Section classification check:

AS 4100 Table 5.2:

• Flange: lambda_ef = (bf-tw)/(2tf) * sqrt(Fy/250) = (256-10.5)/(217.3) * sqrt(350/250) = 7.09 * 1.183 = 8.39
  • lambda_ep = 8 (hot-rolled) → Not compact for AS 4100 (8.39 > 8). However, lambda_ey = 14 (yield limit) → Non-compact. kf from effective width applies.
  • For simplicity in this example, assume kf ≈ 0.98

AISC Table B4.1a:

• Flange: bf/2tf = 256/(2*17.3) = 7.40
  • Limit = 0.38 _ sqrt(E/Fy) = 0.38 _ sqrt(200,000/350) = 0.38 * 23.9 = 9.08 → Compact ✓
• Web: h/tw = 203/10.5 = 19.3
  • Limit = 3.76 _ sqrt(E/Fy) = 3.76 _ 23.9 = 89.9 → Compact ✓
• Section is compact per AISC 360

AS 4100 Calculation:

N* = 1500 kN, Le = ke * L = 1.0 * 4000 = 4000 mm

• Ns = kf _ An _ Fy = 0.98 _ 11,400 _ 350 / 1000 = 3910 kN
  • (phi*Ns = 0.90 * 3910 = 3519 kN)
• lambda*n = (Le/r_min) * sqrt(kf) _ sqrt(Fy/250) = (4000/64.6) _ sqrt(0.98) _ sqrt(350/250) = 61.92 _ 0.990 _ 1.183 = 72.5
• alpha_b = 0.0 (hot-rolled UB)
• eta = alphab * (lambdan/90)^2 = 0.0 * (72.5/90)^2 = 0.0
• xi = (lambda_n/90)^2 + 1 + eta = (72.5/90)^2 + 1 + 0 = 0.649 + 1.0 = 1.649
• alphac = xi * [1 - sqrt(1 - (90/(xilambda_n))^2)] = 1.649 * [1 - sqrt(1 - (90/(1.649*72.5))^2)] = 1.649 * [1 - sqrt(1 - (90/119.6)^2)] = 1.649 _ [1 - sqrt(1 - 0.566)] = 1.649 _ [1 - sqrt(0.434)] = 1.649 _ [1 - 0.659] = 1.649 * 0.341 = 0.562
• Nc = alpha*c * Ns = 0.562 _ 3910 = 2198 kN
• phi*Nc = 0.90 * 2198 = 1978 kN
• Utilization: 1500 / 1978 = 0.758 ✓ OK

AISC 360 Calculation:

Pu = 337 kip, Lc = 13.1 ft

• Ag = 17.7 in^2, r_min = ry = 2.54 in.
• KL/r = 1.0 _ 13.1 _ 12 / 2.54 = 61.9
• Fe = pi^2 _ E / (KL/r)^2 = pi^2 _ 29000 / (61.9)^2 = 286,479 / 3832 = 74.8 ksi
• KL/r = 61.9 ≤ 113.4 (transition limit) → inelastic buckling
• Fcr = [0.658^(Fy/Fe)] _ Fy = [0.658^(50/74.8)] _ 50 = [0.658^0.668] _ 50 = 0.758 _ 50 = 37.9 ksi
• Pn = Fcr _ Ag = 37.9 _ 17.7 = 671 kip = 2985 kN
• phi*Pn = 0.90 * 671 = 604 kip = 2687 kN
• Utilization: 337 / 604 = 0.558 ✓ OK

Comparison Summary:

For this particular column (250UC89.5, 4 m, pin-ended), AS 4100 is about 26% more conservative than AISC 360. This divergence is driven by:

1. The Perry-Robertson curve with alpha_b = 0.0 producing lower alpha_c at lambda = 72.5
2. The kf = 0.98 form factor reducing the section capacity before the column curve
3. The Fy/250 scaling in the AS 4100 slenderness parameter

When Does AS 4100 Give Higher Capacity?

The conservatism is not one-directional. AS 4100 can produce higher capacities than AISC at:

• Very low slenderness (lambda_n < ~30): alpha_c ≈ 1.0 while AISC transition begins reducing Fcr
• Welded I-sections with alpha_b = +0.50: higher eta produces higher xi and higher alpha_c
• Very slender sections (lambda_n > 160): AS 4100 Perry curve converges more slowly to the Euler asymptote

The typical practical range for building columns (KL/r = 40–90) is where AS 4100 is most conservative, which has implications for Australian engineers checking US designs or vice versa.

Material Grade Mapping

Australian structural steel most commonly specifies Grade 350 (equivalent to A572 Gr 50 in the US). Grade 300 is used for lighter sections and Grade 250 for non-structural elements.

Frequently Asked Questions

Why is AS 4100 generally more conservative for compact hot-rolled columns? The Perry-Robertson column curve with alpha_b = 0.0 for hot-rolled UB/UC sections inherently produces lower alpha_c values than the AISC SSRC curve at intermediate slenderness (lambda_n = 50–100). The effective imperfection parameter in AS 4100 is primarily driven by alpha_b; for hot-rolled sections, the design imperfection (delta = L/1000) is a more severe assumption than the 0.877 factor built into the AISC elastic range.

Can I use AISC column tables for an AS 4100 design? Not without conversion. The column curves differ, the effective length factors diverge at certain boundary conditions, and the section constants kf are not directly expressed in AISC tables. For preliminary sizing only, you may reduce AISC table capacities by approximately 20–25% for an AS 4100 conservative estimate, but final design must follow AS 4100 Section 6.

How does the AS 4100 alpha_b affect the result? alpha_b is the most impactful parameter in the AS 4100 column curve. An alpha_b shift from 0.0 (hot-rolled) to +0.50 (lightly welded I-section) can increase alpha_c by 10–20% at intermediate slenderness because the enhanced eta increases xi and shifts the column curve upward. This is the opposite of what many engineers expect — a higher alpha_b value produces a HIGHER alpha_c, meaning the column is predicted to be less sensitive to imperfections.

Does the Direct Analysis Method in AISC have an AS 4100 equivalent? Yes, AS 4100 permits second-order analysis via Clause 4.4.2.3, which allows the moment amplification factor delta*b or a rigorous second-order P-Delta analysis. The Australian approach uses the moment amplification method rather than notional loads. AS 4100 Clause 4.4.2.3 requires a second-order analysis when lambda_ms (the member slenderness in the sway direction) exceeds 1.4. AISC Appendix 7 requires notional loads of 0.002 * alpha _ Yi applied at each level with stiffness reductions.

What effective length should I use for a portal frame column under AS 4100 vs AISC? For the in-plane direction, AS 4100 Clause 4.6.3.4 provides a sway-member chart based on gamma_1 and gamma_2 ratios. For a typical pinned-base portal frame column, ke is typically 2.0–2.5 in-plane (sway mode). AISC produces similar values from the sidesway-uninhibited alignment chart. For the out-of-plane direction, both codes use ke = 1.0 for pinned-pinned girts/rails providing lateral restraint.

Try it now: Check your column design with our free AU Steel Column Capacity calculator →

See Also

• Column Buckling Equations Reference
• Column Effective Length (K-Factor) Guide
• Column Design Guide
• Column Curve Comparison
• EN 1993 Column Buckling
• International Steel Standards Overview
• Steel Design Codes Compared
• Brace Connection Design
• Frame Analysis Reference
• How to Verify Calculations

Disclaimer

This page is for educational and reference use only. It does not constitute professional engineering advice. All design values must be independently verified against the applicable building code and project specifications by a licensed Professional Engineer (PE) or Structural Engineer (SE) before use in construction. The site operator disclaims liability for any loss arising from the use of this information. Results are PRELIMINARY -- NOT FOR CONSTRUCTION.