Australian Column Capacity Calculator — AS 4100

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Design per AS 4100:2020

This calculator checks steel column compressive capacity per AS 4100-2020 Clause 6 for Australian UC sections. Select "AS 4100" from the code selector to use Australian capacity factors and slenderness rules.

Section Capacity — Clause 6.2

φNs = φ × kf × An × fy (φ = 0.9)

kf = form factor (Ae/Ag) accounting for local buckling in slender sections. For compact sections, kf = 1.0.

Member Capacity — Clause 6.3

φNc = φ × ÃƒÂŽÃ‚±c × Ns ≤ φNs

αc = member slenderness reduction factor based on the modified slenderness:

λn = (le/r) × ÃƒÂ¢Ã‚ÂˆÃ‚Âš(fy/250)

The αc factor follows the AS 4100 column curve, which uses the Perry-Robertson formulation with αb = 0.5 for hot-rolled UB and UC sections.

Worked Example

Problem: Check a 200UC52.2 column, Grade 300, 4.0 m effective length.

Axial load: N* = 800 kN (factored) | Steel: Grade 300 (fy = 300 MPa)

Solution:

1. Section properties: Ag = 6660 mm², rx = 89.1 mm, ry = 50.8 mm (ry controls)
2. Section capacity: φNs = 0.9 × 1.0 × 6660 × 300 × 10⁻³ = 1798 kN
3. Modified slenderness: λn = (4000/50.8) × ÃƒÂ¢Ã‚ÂˆÃ‚Âš(300/250) = 78.7 × 1.095 = 86.2
4. αc factor: from AS 4100 Table 6.3.3(1), αc ≈ 0.726
5. Member capacity: φNc = 0.726 × 1798 = 1305 kN
6. Check: 800 ≤ 1305 → OK (usage: 61%)

Result: 200UC52.2 is adequate for compression.

Additional Design Considerations

Effective length factor K: Per AS 4100 Clause 4.6.3, K depends on the column's end restraint conditions. For braced frames with pinned ends, K = 1.0. For sway frames, K ≥ 1.2 and must be determined by rational analysis (Clause 4.7.2). The calculator defaults to K = 1.0 for braced frames.

Minimum eccentricity: Per Clause 6.5, columns must be designed for a minimum eccentricity of 0.05D (where D is the section depth). This ensures the column can accommodate incidental moments at connections.

Biaxial bending check: When moments act about both axes, use the interaction formula from Clause 8.3.4: N*/φNc + Mx*/φMsx + My*/φMsiy ≤ 1.0. The minor-axis section moment capacity φMsi uses the full section modulus with an effective modulus Ze accounting for local buckling.

Slender section penalty: For UC webs in uniform compression, λey = 35 for Grade 300 and λey = 32 for Grade 350 per Table 5.2. Sections with slender elements have kf < 1.0, directly reducing φNs per Clause 6.2.4.

Fire design: At elevated temperatures (fire conditions), fy and E degrade per Clause 12. Use the fire-resistance calculator under Combined Actions for fire-rated designs.

Second Worked Example — Slender Column

Problem: Check a 310UC158 column, Grade 350, 8.0 m effective length. N* = 2500 kN.

Solution:

1. Ag = 20100 mm², ry = 78.2 mm
2. φNs = 0.9 × 20100 × 350 × 10⁻³ = 6332 kN
3. λn = (8000/78.2) × ÃƒÂ¢Ã‚ÂˆÃ‚Âš(350/250) = 102.3 × 1.183 = 121.0
4. αc from Table 6.3.3(1): αc ≈ 0.384
5. φNc = 0.384 × 6332 = 2432 kN
6. Check: 2500 > 2432 → FAIL (usage: 103%)

Result: 310UC158 insufficient at 8.0 m. Upsize to 310UC200 (φNc ≈ 2950 kN) or add intermediate bracing to reduce KL.

How to Use

1. Select "AS 4100" from the code selector
2. Choose an Australian UC section
3. Select Grade 300 or Grade 350
4. Enter effective length (KL) in metres
5. Enter the applied factored axial load
6. Review φNs, φNc, and slenderness results

Combined Compression and Bending — AS 4100 Clause 8.3

When a column experiences both axial compression and bending moment, the interaction check per AS 4100 Clause 8.3.4 must be satisfied:

For in-plane bending (Clause 8.3.4): N*/φNc + M*/φMsx ≤ 1.0

For biaxial bending (Clause 8.3.4): N*/φNc + Mx*/φMsx + My*/φMsiy ≤ 1.4 and N*/φNc + Mx*/φMsx + My*/φMsiy ≤ 1.0 (governs for most cases)

Where φMsiy is the minor-axis section moment capacity, calculated using Ze (effective modulus) for slender elements. The major-axis term uses φMsx, and the minor-axis term uses φMsiy.

Moment amplification for sway columns: For columns in sway frames (K > 1.0), the design moments must include second-order (P-Δ) effects per Clause 4.7. The moment amplification factor δ = 1/(1 - N*/Neuler) where Neuler = π²EI/(KL)².

Effective Length Factors — Practical Guide

For sway frames, K must be determined by rational buckling analysis per Clause 4.7.2, not from this table.

AS 4100 Column Curve — alpha_c Table (Selected Values)

The full alpha_c factor per AS 4100 Table 6.3.3(3) is a function of the modified slenderness lambda_n and the section constant alpha_b:

For lambda_n <= 13.5 (the plateau), alpha_c = 1.0. For Australian UC sections in braced frames, typical lambda_n values range from 25-80 for storey-height columns (3.0-5.0 m), giving alpha_c values of 0.978 to 0.706. Columns above lambda_n = 120 are uncommon in multi-storey construction — they indicate insufficient bracing or very slender sections.

Interaction Check — Biaxial Bending (Clause 8.3.4)

For columns with axial load plus moments about both axes, the interaction check per AS 4100 Clause 8.3.4 has two limits:

In-plane (strong-axis bending + axial): N*/(phi Nc) + Mx*/(phi Msx) <= 1.0

Biaxial (both axes + axial): N*/(phi Nc) + Mx*/(phi Msx) + My*/(phi Msiy) <= 1.4 ... AND (N*/(phi Nc))^1.4 + (Mx*/(phi Msx))^1.4 + (My*/(phi Msiy))^1.4 <= 1.0

The second form (exponent 1.4) is typically more conservative for intermediate utilisation levels and should always be checked when My* is significant. The calculator applies both forms and reports the governing utilisation.

Worked Example — Biaxial Loading

Problem: A 200UC52.2 column, Grade 300, effective length 4.0 m, N* = 600 kN, Mx* = 30 kN.m, My* = 15 kN.m (minor axis moment from eccentric connection).

Check 1 — Section capacities:

• phi Nc = 1305 kN (from earlier example)
• phi Msx = 0.9 x 568 x 10^3 x 300 x 10^-6 = 153 kN.m (major axis)
• phi Msiy = 0.9 x 195 x 10^3 x 300 x 10^-6 = 53 kN.m (minor axis)

Check 2 — Linear interaction (Clause 8.3.4 limit 1.4): 600/1305 + 30/153 + 15/53 = 0.460 + 0.196 + 0.283 = 0.939 <= 1.4. OK.

Check 3 — Exponent 1.4 interaction (Clause 8.3.4 governing): (0.460)^1.4 + (0.196)^1.4 + (0.283)^1.4 = 0.335 + 0.112 + 0.184 = 0.631 <= 1.0. OK.

Result: Column is adequate at 63% utilisation. The minor-axis moment from connection eccentricity accounts for 29% of the interaction capacity — always include connection eccentricity in the analysis.

Column Splice Design — AS 4100 Clause 9.4

Column splices in Australian multi-storey construction are typically located 600-1200 mm above the floor level. Per AS 4100 Clause 9.4:

• Bearing splices: Machined ends bearing directly. The splice plates carry 50% of the column capacity in the connected elements. Preferred for shop-welded columns delivered in two-storey lengths.
• Non-bearing splices: Splice plates carry 100% of the axial load plus any moment at the splice location. Used for site-bolted connections where machining is impractical.
• Minimum bolt count: 4 bolts per side per flange for W-shapes; 4 bolts per side for HSS columns.
• Splice plate thickness: Minimum 10 mm or half the column flange thickness, whichever is greater.

For a 200UC52.2 column splice (bearing type), the splice plates must carry 50% x 800 kN = 400 kN. With 8-M20 Grade 8.8/S bolts in double shear: Vf per bolt = 2 x 79.0 = 158 kN. 8 x 158 = 1264 kN > 400 kN. Bolt shear is adequate. Splice plate (200x200x10 mm, S300) bearing check controls the final design.

Related Australian Resources

• Australian Beam Sizes (UB/UC/PFC)
• Australian Steel Grades
• AS 4100 Column Buckling Guide
• Australian Beam Capacity Calculator
• All Australian References

FAQ

What is the form factor kf? The form factor kf = Ae/Ag accounts for local buckling in slender sections per AS 4100 Clause 6.2. For compact sections with λ ≤ λey, kf = 1.0. For slender elements, the effective area Ae is reduced based on the effective width per Clause 6.2.4.

Calculation Tips

• Always use the minor axis (ry) for slenderness — it governs unless bracing restrains the weak axis.
• Grade 350 provides 17% more capacity than Grade 300 for the same section size.
• Adding intermediate bracing at mid-height halves the effective length, increasing φNc significantly.
• For crane columns and columns supporting vibrating equipment, check fatigue per AS 4100 Clause 13.

What is αb for Australian UC sections? Hot-rolled UC, UB, and welded sections with fy ≤ 450 MPa use αb = 0.5 per AS 4100 Table 6.3.3(1). This corresponds to the AISC column curve. Cold-formed sections and very thick sections use different αb values.

How does the effective length factor K affect column capacity? K directly multiplies the effective length in the slenderness calculation: le = K × L. Doubling K doubles λn, which reduces αc significantly. For example, a column with K = 1.0 might have φNc = 1305 kN, while the same column with K = 2.0 (cantilever) would have φNc ≈ 480 kN — a 63% reduction. Proper end restraint characterisation per Clause 4.6.3 is critical for economic design.

What is the full AS 4100 column capacity equation? The Perry-Robertson formulation in AS 4100 Clause 6.3.3 gives αc = ξ × [1 - √(1 - (90/(ξ × ÃƒÂŽÃ‚Â»))²)] where ξ = (λ/90)² + 1 + η and η = αb × (λ - 13.5)/(λ - 15.3 + 2050/αb). For λ ≤ 13.5, αc = 1.0. This formulation accounts for geometric imperfections (αb = 0.5 for hot-rolled sections) and residual stresses.

Can I use UB sections (Universal Beams) as columns? Yes, UB sections can be used as columns. However, UC sections are generally preferred because their more balanced flange width-to-depth ratio provides better minor-axis buckling resistance. When using a UB as a column, always check the minor axis slenderness and consider that UB sections have lower ry/rx ratios than UC sections, making minor axis buckling more critical.

Disclaimer: This content is for educational purposes only. Results must be verified by a licensed professional engineer. Steel Calculator provides preliminary design tools — NOT a substitute for professional engineering judgment.