Australian Column Design — AS 4100 Clause 6 Compression and Buckling

Complete reference for steel column design to AS 4100:2020 Clause 6. Covers section capacity, member buckling capacity with the Australian buckling curves, effective length determination using alignment charts, biaxial bending interaction, and practical column sizing.

Related pages: Effective Length (K Factor) | Combined Loading | UC Section Properties | Column Capacity Calculator

Compression Design Flow — AS 4100 Clause 6

The design of a steel column under axial compression proceeds through three sequential capacity checks:

1. Section capacity (Clause 6.2): phi_Ns = phi x kf x An x fy — the squash load, checking that the cross-section itself can carry the load without local buckling or yielding.
2. Member capacity (Clause 6.3): phi_Nc = phi x alpha_c x Ns — accounting for overall column buckling.
3. Combined actions (Clause 8.3): Check interaction of axial compression with bending moments when present.

The form factor kf accounts for local buckling of slender elements and equals 1.0 for compact sections (most hot-rolled UC sections). For slender sections, kf < 1.0 reduces the effective area.

Australian Buckling Curves — Clauses 6.3.2 and 6.3.3

AS 4100 defines alpha_c through a two-stage process that is unique among international codes. First, a modified slenderness lambda_n is computed, then a section factor alpha_b selects the appropriate column curve. This is more nuanced than the single-curve approach of some codes.

Modified slenderness: lambda_n = (Le / r) x sqrt(kf x fy / 250)

The reference slenderness is normalised to 250 MPa yield, giving lambda_n a consistent physical meaning across all steel grades. A Grade 300 section at Le/r = 60 has lambda_n = 60 x sqrt(300/250) = 65.7.

Section constant alpha_b (Table 6.2.3) selects the column curve:

The alpha_b values reflect the magnitude and distribution of residual stresses. Hot-rolled UC sections (alpha_b = 0.0) correspond to the classic AISC curve. The SHC curve (alpha_b = 0.5) is reserved for hot-rolled UB sections buckling about the major axis with relatively wide flanges, where residual stresses are less penalising.

alpha_c from lambda_n and alpha_b (Table 6.2.4):

The difference between curves is largest at moderate slenderness (lambda_n = 60-100), where the choice of alpha_b can alter capacity by 20-40%. At very low slenderness (lambda_n < 20), all curves converge to unity (squash load governs). At very high slenderness (lambda_n > 200), all curves converge to the Euler buckling load.

Effective Length Factor k_e — Clause 6.3.2

The effective length Le = k_e x L accounts for the rotational and translational restraint at column ends. The classic alignment chart (Jackson & Moreland nomograph) provides k_e values based on the stiffness ratio G = sum(I_c/L_c) / sum(I_g/L_g) at each end.

For braced frames (non-sway): 0.50 <= k_e <= 1.00 For sway frames: 1.00 <= k_e <= infinity (practically <= 3.0)

The design k_e values include an allowance for imperfect fixity at connections (0.65 vs 0.50 for fixed-fixed) since true full fixity is impossible to achieve in bolted or welded connections that rotate slightly under load.

UC Section Capacity Tables — Grade 300

Values computed with alpha_b = 0.0 (AISC curve), k_e = 1.0 (pin-ended), Grade 300 steel. For intermediate effective lengths, interpolate linearly. These tabulated values agree with the ASI Design Capacity Tables within 2%.

Biaxial Bending Interaction — Clause 8.3

When a column carries both axial load and bending moments about both axes, the interaction formula governs:

For compact sections (Clause 8.3.2): N*/phi_Nc + Mx*/phi_Msx + My*/phi_Msy <= 1.0 (conservative linear interaction)

For the more accurate section capacity check (Clause 8.3.4): (N*/phi_Ns)^1.4 + (Mx*/phi_Msx)^1.4 + (My*/phi_Msy)^1.4 <= 1.0

The exponent 1.4 (rather than 2.0 in some codes) is based on Australian calibration studies for I-sections. It produces less conservative results than the linear interaction while maintaining adequate safety margins.

Worked Example — 310UC137 Interior Column

Problem: Design an interior column for a 4-storey office building. Storey height = 4.0 m. Axial load N* = 2,650 kN (dead + live from tributary area at all levels). Minor axis moment My* = 45 kNm from beam end fixity. Braced frame in both directions, assume k_e = 1.0. Grade 300 steel.

Section properties — 310UC137: Ag = 17,500 mm^2 | ry = 77.5 mm | Zy = 1,060 x 10^3 mm^3 (minor axis plastic modulus)

Step 1 — Section capacity (axial): phi_Ns = 0.90 x 1.0 x 17,500 x 300 / 1000 = 4,725 kN >> 2,650 kN. OK.

Step 2 — Member buckling capacity: Le/r_min = 1.0 x 4000 / 77.5 = 51.6

lambda_n = 51.6 x sqrt(1.0 x 300 / 250) = 51.6 x 1.095 = 56.5

alpha_b = 0.0 (UC section). Interpolating from alpha_c table: at lambda_n = 50, alpha_c = 0.877; at lambda_n = 60, alpha_c = 0.818. By linear interpolation: alpha_c = 0.877 - (6.5/10) x (0.877 - 0.818) = 0.877 - 0.038 = 0.839.

phi_Nc = 0.90 x 0.839 x 17,500 x 300 / 1000 = 3,964 kN > 2,650 kN. OK.

Step 3 — Moment capacity (minor axis): phi_Msy = 0.90 x 300 x 1,060 x 10^3 / 10^6 = 286.2 kNm > 45 kNm. OK.

Step 4 — Interaction check (Clause 8.3.4): (N*/phi_Ns)^1.4 + (My*/phi_Msy)^1.4 = (2650/4725)^1.4 + (45/286.2)^1.4 = (0.561)^1.4 + (0.157)^1.4 = 0.445 + 0.085 = 0.530 <= 1.0. OK.

The column is conservatively sized at a demand/capacity ratio of 0.53. Consider 250UC89 (phi_Nc ~ 2,510 kN) for the upper storeys where axial load reduces.

Alternative approach — try 250UC89 for a typical upper floor column: Le/r_min = 4000/67.0 = 59.7. lambda_n = 59.7 x 1.095 = 65.4. alpha_c ~ 0.78 (interpolated). phi_Nc = 0.90 x 0.78 x 11,400 x 300 / 1000 = 2,400 kN. At top floor: N* ~ 700 kN. N*/phi_Nc = 700/2400 = 0.29. Clearly adequate. At second floor: N* ~ 1,300 kN. Ratio = 0.54. Still OK.

Mixing sections by floor level (heavier at base, lighter at top) is standard Australian practice and reduces total steel tonnage by 8-15%.

Residual Stresses and Initial Imperfections

AS 4100 accounts for both residual stresses and geometric imperfections implicitly through the alpha_b column curves, rather than through explicit notional loads or geometric imperfections (as in EN 1993-1-1). This means:

• The buckling curves are calibrated to test data for Australian-manufactured sections with typical residual stress patterns from the hot-rolling process.
• The 0.0 alpha_b curve (AISC) represents sections with a typical as-rolled residual stress peak of about 0.3 x fy in the flange tips.
• For sections with severe residual stresses (welded built-up sections), the -0.5 alpha_b curve applies, which is approximately 15-25% lower capacity than the hot-rolled curve at moderate slenderness.

Column Base Connections

The column-to-base plate connection at the foundation level is a critical interface. Pinned bases (typical for braced frames) are modelled as simple bearing connections with nominal holding-down bolts. The base plate must distribute the column load to the foundation per AS 4100 Clause 9 and AS 3600. For columns with uplift, the anchor bolts transfer tension to the foundation and must be designed per Clause 9.3.

Frequently Asked Questions

Why do UC sections use a different buckling curve from CHS sections? The buckling curve depends on the manufacturing process and resulting residual stress pattern. UC sections are hot-rolled and air-cooled, producing a moderate residual stress pattern (alpha_b = 0.0). CHS sections are cold-formed from strip, producing higher residual stresses (alpha_b = -0.5), which reduces the column capacity at intermediate slenderness by about 10-15%. Welded box sections have the highest residual stresses due to the welding process and get the least favourable curve.

How do I determine the effective length for a column in a braced frame? For a column in a rigid-jointed braced frame, use the alignment chart with G = sum(Ic/Lc) / sum(Ig/Lg) at top and bottom joints. For typical multi-storey construction: k_e = 0.75-0.85 for interior columns with continuous beams framing in; k_e = 0.85-0.95 for exterior columns with beams on one side only; k_e = 1.0 for pinned base conditions (standard in Australian practice). The conservative simplification k_e = 1.0 is always acceptable.

At what slenderness does column buckling begin to significantly reduce capacity? The reduction becomes noticeable at lambda_n ~ 30-40, where alpha_c drops to 0.90-0.95. At lambda_n = 60 (the typical upper bound for efficient UC columns), alpha_c is approximately 0.82, representing an 18% reduction from the squash load. Beyond lambda_n = 120 (Le/r ~ 110 for Grade 300), the capacity drops below 50% of squash load and columns become uneconomical.

What is the slenderness limit for secondary members? AS 4100 Clause 6.1 limits Le/r to 200 for primary compression members and 300 for secondary members (bracing, struts). However, economical design targets Le/r <= 80-100. Members with Le/r > 150 have very low alpha_c (< 0.25) and require disproportionately large sections relative to the axial load.

This page is for educational reference. Column design per AS 4100:2020 Clause 6. Verify effective length factors and buckling curves 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.