Canadian Column Design — Axial Compression per CSA S16-19 Clause 13.3

Complete reference for column axial compression design per CSA S16-19 Clause 13.3. Covers column buckling curves (Cr vs KL/r), effective length factors, section classification effects, and a step-by-step worked example for a W310x107 column in 350W steel.

Quick access: Effective length factor K → | Combined loading → | Column capacity calculator →

CSA S16 Column Design Philosophy

Per CSA S16-19 Clause 13.3.1, the factored compressive resistance Cr for a steel column is:

Cr = phi × A × Fy × (1 + lambda^(2n))^(-1/n)

Where:

• phi = 0.90 (resistance factor for steel members)
• A = gross cross-sectional area (mm^2)
• Fy = minimum yield strength (MPa, thickness-adjusted)
• lambda = non-dimensional slenderness parameter = (KL/r) × sqrt(Fy/(pi^2 × E))
• E = 200,000 MPa
• n = 1.34 (for W-shapes buckling about the strong axis, or any section about the weak axis with standard residual stress pattern)
• n = 2.24 (for hollow structural sections, cold-formed)
• n = 0.69 (for fabricated sections)

The CSA S16 column curve is based on the SSRC Multiple Column Curve concept, using the parameter n to adjust the curve shape for different section types.

Column Curves — n Factor Selection

Per CSA S16-19 Table 4:

The higher the n value, the more favourable the column curve (higher Cr for the same KL/r). HSS sections with n = 2.24 have significantly higher capacity than W-shapes with n = 1.34 at intermediate slenderness.

Cr Values — W-Shapes (350W, n = 1.34)

KL/r Limits

Per CSA S16-19 Clause 13.3.2:

• Maximum KL/r for main compression members: 200
• Maximum KL/r for secondary members (bracing, etc.): 300
• Minimum KL/r for main tension members (to prevent vibration): 300 (recommended)

For columns where KL/r ≥ 200, the factored resistance becomes very small. In practice, columns are designed with KL/r ≤ 80-100 for economical design.

Effective Length Factor K

Per CSA S16-19 Clause 13.3.3 and the CISC Handbook, the effective length factor K is determined from the alignment chart (Figure 1 of CISC Commentary).

For non-sway frames (braced), K ≤ 1.0. For sway frames (moment frames), K > 1.0 and depends on G factors from the alignment chart.

See the column K factor reference for detailed alignment chart usage.

Section Classification Effects

Per CSA S16 Clause 13.3.1(b), for Class 3 and 4 sections in axial compression:

For Class 3 webs: Use effective area Aeff = b_eff × t where:

• b_eff = width determined from the Class 3 limit
• For webs in axial compression: b_eff = (750/sqrt(Fy)) / (h/w) × h

For Class 4 sections: Use effective width per Clause 13.5.3.

Most W-shapes used as columns in 350W will be Class 1 or 2 in the flange but Class 3 in the web. The effective area reduction typically ranges from 5-20% for light sections.

Worked Example — W310x107 Column Design

Given: W310×107 Grade 350W, length = 5.0 m, pinned at both ends (K = 1.0). Factored axial load Cf = 2200 kN (dead + live from roof + 3 floors).

Section Properties:

• A = 13,600 mm^2
• rx = 136 mm, ry = 77.5 mm
• b/2tf = 6.28, h/w = 24.3

Step 1 — Section Classification: Flange: 6.28 ≤ 7.75 → Class 1 Web (axial): 24.3 ≤ 35.8 → Class 1 Overall: Class 1 — full area effective.

Step 2 — Slenderness: KL/rx = 1.0 × 5000 / 136 = 36.8 (minor axis governs — always check both) KL/ry = 1.0 × 5000 / 77.5 = 64.5 → governs

lambda = (KL/ry) × sqrt(Fy / (pi^2 × E)) = 64.5 × sqrt(350 / (pi^2 × 200,000)) lambda = 64.5 × 0.01332 = 0.859

Step 3 — Cr: Cr = phi × A × Fy × (1 + lambda^(2n))^(-1/n) n = 1.34 (W-shape, weak axis) lambda^2 = 0.738 lambda^(2n) = lambda^(2.68) = 0.738^1.34 = 0.645 Cr = 0.90 × 13,600 × 350 × (1 + 0.645)^(-1/1.34) Cr = 0.90 × 13,600 × 350 × (1.645)^(-0.746) Cr = 4,284,000 × 0.669 = 2,866,000 N = 2866 kN

Step 4 — Check: Cf = 2200 kN ≤ Cr = 2866 kN. Ratio = 0.77. OK.

Alternative: Using the CISC Handbook, the tabulated Cr for KL = 5000 mm (y-y) with W310×107, 350W is approximately 2850 kN — matches closely.

Design for KL/r — Minimum Section Size

A practical approach for column preliminary sizing:

For Cf = 2200 kN, try to maintain Cf/Cr ≤ 0.8:

Required Cr = 2200/0.8 = 2750 kN From Cr curves, for 350W with KL/r ≈ 65: Cr/A ≈ 215 MPa Required A = 2750 × 10^3 / 215 = 12,800 mm^2

Select the lightest section with A ≥ 12,800 mm^2 and ry sufficient for KL/ry ≤ 65:

• ry ≤ 5000/65 = 77 mm
• W310×107 (A = 13,600, ry = 77.5) — adequate

This quick method works well for initial sizing. Always verify with the full Cr calculation.

Base Plate Design

The column base plate must distribute the factored axial load to the foundation without exceeding the concrete bearing resistance. Per CSA S16 Clause 13.14:

Bearing resistance of concrete: Br = phi_c × 0.85 × f'c × A1 × sqrt(A2/A1) ≤ 2 × phi_c × 0.85 × f'c × A1

For a W310×107 with Cf = 2200 kN on 30 MPa concrete with a 400×400 plate: Br = 0.65 × 0.85 × 30 × 400^2 × 1.0 / 1000 = 2652 kN ≥ 2200 kN. OK.

See CSA S16 base plate design for full details.

Frequently Asked Questions

What is the maximum KL/r for columns in CSA S16? CSA S16-19 Clause 13.3.2 limits KL/r to 200 for main compression members and 300 for secondary members. However, economical column design targets KL/r ≤ 80-100. Columns with KL/r > 100 are inefficient (more than 50% capacity reduction from the squash load).

What is the difference between n = 1.34 and n = 2.24 column curves? The n factor adjusts the SSRC column curve shape. W-shapes use n = 1.34 (SSRC curve 2P, representing typical hot-rolled residual stresses). HSS sections use n = 2.24 (SSRC curve 1P, representing lower residual stresses). For KL/r = 60 in 350W: W-shape gives Cr/A ≈ 236 MPa, HSS gives approximately 270 MPa — about 14% higher capacity.

How does section class affect column capacity in CSA S16? Class 1 and 2 sections can use the full gross area A. Class 3 sections use effective area Aeff reduced for the slender web proportion. Class 4 sections use reduced effective widths for all slender elements. For typical W-shape columns in 350W, the web is often Class 3, requiring a 5-20% area reduction depending on slenderness.

When does weak-axis buckling govern for columns? Weak-axis buckling (about the y-y axis) governs for most columns because ry < rx. For example, W310×107 has ry = 77.5 mm vs rx = 136 mm, so KL/ry = 64.5 vs KL/rx = 36.8 for a 5.0 m pinned column. The weak axis determines the capacity unless the column is braced differently in each direction.

Related Pages

• CSA S16 Effective Length Factor K
• CSA S16 Combined Axial + Bending
• Canadian Beam Design
• Canadian Compact Section Limits
• CSA S16 Base Plate Design
• Column Capacity Calculator
• All Canadian References

This page is for educational reference. Column design per CSA S16-19 Clause 13.3. Verify n factor selection and Cr values against CISC Handbook. Results are PRELIMINARY — NOT FOR CONSTRUCTION without independent PE/SE verification.

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