Canadian Column Design — CSA S16-19 Clause 13.3 Axial Compression
Comprehensive reference for steel column design per CSA S16-19. Covers the SSRC multiple column curve system (n-factors for W-shapes, HSS, and fabricated sections), effective length factors for braced and sway frames, section classification effects on Cr, and biaxial bending interaction.
Related pages: CSA Effective Length (K Factor) | CSA Combined Loading | CSA Compact Section Limits | Column Capacity Calculator
The CSA S16 Column Formula — SSRC Multiple Column Curves
CSA S16-19 uses the Structural Stability Research Council (SSRC) multiple column curve approach, which is fundamentally different from the single-curve approach of some other codes. The factored axial compressive resistance is:
Cr = phi x A x Fy x (1 + lambda^(2n))^(-1/n)
Where:
- phi = 0.90
- A = gross cross-sectional area (mm^2), or effective area for Class 3/4 sections
- Fy = minimum specified yield strength, thickness-adjusted (MPa)
- lambda = non-dimensional slenderness parameter = (KL/r) x sqrt(Fy / (pi^2 x E))
- E = 200,000 MPa
- n = curve-shape parameter depending on section type and manufacturing process
The parameter n controls the shape of the column curve in the transition region between squash (lambda = 0) and Euler buckling (lambda > 2). Higher n values produce a more favourable curve with higher capacity at intermediate slenderness because the section has lower residual stresses.
n-Factor Selection — CSA S16 Table 4
| Section Type | Manufacturing | n | Curve | Residual Stress Level |
|---|---|---|---|---|
| W-shapes (hot-rolled) | Hot-rolled + air | 1.34 | SSRC 2P | Moderate (0.3 Fy) |
| HSS — round or square (hot-formed) | Hot-formed + air | 2.24 | SSRC 1P | Low (0.15 Fy) |
| HSS — cold-formed | Cold-formed | 2.24 | SSRC 1P | Low (0.15 Fy) |
| Double angles, back-to-back | Hot-rolled | 0.69 | SSRC 3P | High (0.5 Fy) |
| Welded built-up I-section (deep fillet welds) | Fabricated | 1.34 | SSRC 2P | Moderate-High |
| Pipe (API 5L) | Seam-welded | 2.24 | SSRC 1P | Low |
| Welded box sections | Fabricated | 0.69 | SSRC 3P | High |
| Heavy welded H-sections (flame-cut) | Fabricated | 0.69 | SSRC 3P | Very High (0.5 Fy) |
The profound effect of n on column capacity is most visible at intermediate slenderness (KL/r = 60-100). At KL/r = 60 in 350W:
- HSS (n = 2.24): Cr/A ~ 265 MPa (76% of Fy)
- W-shape (n = 1.34): Cr/A ~ 236 MPa (67% of Fy)
- Fabricated box (n = 0.69): Cr/A ~ 205 MPa (59% of Fy)
The 30% capacity difference between an HSS and a fabricated box section at the same KL/r is entirely due to the residual stress pattern — the geometric properties (area, radius of gyration) are identical.
Cr Values — W-Shapes (350W, n = 1.34)
| KL/r | lambda | Cr/A (MPa) | Cr for A = 15,000 mm^2 |
|---|---|---|---|
| 20 | 0.216 | 334 | 4,507 kN |
| 40 | 0.431 | 293 | 3,956 kN |
| 60 | 0.647 | 236 | 3,186 kN |
| 80 | 0.862 | 179 | 2,417 kN |
| 100 | 1.078 | 134 | 1,809 kN |
| 120 | 1.294 | 99 | 1,337 kN |
| 150 | 1.617 | 68 | 918 kN |
| 200 | 2.156 | 39 | 527 kN |
KL/r = 200 represents the maximum slenderness for main compression members (Clause 13.3.2). At this slenderness, the column retains only approximately 11% of its squash load capacity.
Effective Length Factor K — Clause 13.3.3
The effective length factor K accounts for the rotational and translational restraint at the column ends. For typical Canadian building columns:
Braced frame (non-sway): 0.50 <= K <= 1.00 **Sway frame (unbraced):** K >= 1.00, determined from alignment charts (Jackson & Moreland nomograph)
For a braced frame, K is determined by the stiffness ratio G = sum(Ic/Lc) / sum(Ig/Lg) at each end of the column:
| End Conditions | Theoretical K | Design K | Typical Application |
|---|---|---|---|
| Both ends fixed | 0.50 | 0.65 | Column with deep beams both sides |
| Fixed-pinned | 0.70 | 0.80 | Interior column, pinned base |
| Both ends pinned | 1.00 | 1.00 | Lean-on column in braced frame |
| Fixed-free | 2.00 | 2.10 | Cantilever column (flagpole) |
The "design K" values include an allowance for the fact that connections are never perfectly rigid. A nominally "fixed" connection provides approximately 90% rotational restraint, which translates to a K of 0.65 rather than the ideal 0.50.
Section Classification Effect on Column Capacity
For Class 3 sections (slender elements in compression), CSA S16 Clause 13.3.1(b) requires using an effective area Aeff rather than the gross area A:
For Class 3 webs in axial compression: The web effective width: b_eff = (750 / sqrt(Fy)) / (h/w) x h (mm)
For a W310x39 in 350W under axial compression: h/w = 44.0, Fy = 350 MPa. 750/sqrt(350) = 40.1. b_eff = (40.1/44.0) x h = 0.911 x h (about 9% of web is ineffective).
The effective area reduction for Class 3 sections ranges from 5-15% for lighter W-shapes. For columns, the web is typically the governing element for Class 3, even when the flange remains Class 1 or 2.
Biaxial Bending Interaction — Clause 13.8
For columns subject to both axial compression and bending about both axes, CSA S16 Clause 13.8.2 provides:
Cf/Cr + 0.85 x Mfx/Mrx + 0.60 x Mfy/Mry <= 1.0 (for Class 1 and 2 sections)
The 0.85 and 0.60 coefficients reflect the lower probability of simultaneous peak loading for secondary bending moments. For Class 3 sections under combined loads, the coefficients are 0.85 for both axes.
More rigorous interaction (Cross-section strength, Clause 13.8.3): Cf/Cr + (Mfx^2 + Mfy^2)^0.5 / Mr <= 1.0
This is appropriate when bending moments are comparable in magnitude about both axes and derive from the same load source (e.g., a corner column loaded by beams in two directions).
Worked Example — W310x107 Interior Column
Problem: An interior column W310x107 (CSA G40.21 350W) at the ground floor of a 6-storey office building. Unbraced length L = 4.2 m. Kx = 1.0 (pinned-pinned in major axis), Ky = 1.0 (pinned-pinned in minor axis — braced by slab in that direction but conservatively assumed). Factored axial load Cf = 2,800 kN. Minor-axis bending from unequal beam spans: Mfy = 60 kNm.
Section properties — W310x107: A = 13,600 mm^2 | rx = 136 mm | ry = 77.5 mm | Zy = 450 x 10^3 mm^3 (minor axis plastic modulus)
Step 1 — Section classification: Flange: b/2tf = (191/2)/13.0 = 7.35 <= 7.75 (Class 1 for 350W) Web (compression): h/w = (311-2x13)/10.5 = 285/10.5 = 27.1 <= 40.1 (Class 1 for axial) Section is Class 1 — full area effective.
Step 2 — Slenderness: KL/rx = 1.0 x 4200 / 136 = 30.9 (major axis — apparently more favourable) KL/ry = 1.0 x 4200 / 77.5 = 54.2 (minor axis governs — always check both)
Weak axis governs for virtually all W-shape columns unless the column is braced differently in each direction.
Step 3 — Cr (axial): lambda = 54.2 x sqrt(350 / (pi^2 x 200000)) = 54.2 x sqrt(350/1,973,921) = 54.2 x 0.01333 = 0.722
n = 1.34 (W-shape) lambda^(2n) = lambda^(2.68) = 0.722^2.68 = 0.722^2.68
0.722^2 = 0.521. 0.521^1.34 = 0.521^(1.34) = exp(1.34 x ln(0.521)) = exp(1.34 x (-0.652)) = exp(-0.874) = 0.417.
Cr = 0.90 x 13,600 x 350 x (1 + 0.417)^(-1/1.34) = 4,284,000 x 1.417^(-0.746) = 4,284,000 x 0.759 = 3,252,000 N = 3,252 kN > 2,800 kN. OK.
Step 4 — Moment resistance (minor axis): Mry = phi x Zy x Fy = 0.90 x 450 x 10^3 x 350 / 10^6 = 141.8 kNm > 60 kNm. OK.
Step 5 — Interaction (Clause 13.8.2): Cf/Cr + 0.85 x Mfx/Mrx + 0.60 x Mfy/Mry <= 1.0
2800/3252 + 0.85 x 0 + 0.60 x 60/141.8 = 0.861 + 0 + 0.254 = 1.115 > 1.0. FAILS.
The column fails the interaction check due to the combined axial and bending. Solutions:
- Check the more rigorous cross-section strength interaction (Clause 13.8.3)
- Increase to W310x118 (A = 15,000 mm^2, ry = 77.8, Cr ~ 3,600 kN, ratio 2800/3600 + 0.60 x 60/156 = 0.778 + 0.231 = 1.009 — marginal)
- Increase to W310x129 (ry = 78.2, Cr ~ 3,900 kN, ratio = 0.718 + 0.22 = 0.938 — OK)
Alternatively, refine the K factor: If the column is part of a braced frame with feasible beam stiffnesses (W460 or larger framing into the strong axis), Kx may reduce to 0.80. The weak axis Ky remains at 1.0 (pinned base + simple beam connection in weak axis). The strong-axis KL/rx reduction does not change the weak-axis governing KL/ry.
Better approach: Re-evaluate Ky. If the floor slab provides some rotational restraint in the minor axis direction (common in Canadian construction where slabs bear onto the column web through shear studs): Ky = 0.85.
KL/ry = 0.85 x 4200 / 77.5 = 46.0. lambda = 46.0 x 0.01333 = 0.613. lambda^2.68 = 0.613^2.68 = 0.613^2 x 0.613^0.68 = 0.376 x 0.707 = 0.266. Cr = 4,284,000 x 1.266^(-0.746) = 4,284,000 x 0.838 = 3,590 kN. Cf/Cr = 2800/3590 = 0.780. Interaction: 0.780 + 0.254 = 1.034 — still marginal.
Final specification: W310x129, 350W, or provide a more refined capacity-design analysis.
Practical Canadian Column Notes
Storey-height column stepping: Canadian practice strongly favours stepping columns at 2-3 storey intervals (e.g., W310x158 at ground-2, W310x107 at 3-4, W310x74 at 5-6). This saves 8-15% of column tonnage and matches the load profile. Splicing at 1.2 m above finished floor is standard for erection access.
Column orientation: Orient W-shape columns with the web parallel to the strong-axis bending direction. In Canadian buildings, this typically means the web runs in the E-W direction of the structural grid, with beams framing into the flanges N-S and into the web E-W.
Base fixity: Canadian practice typically assumes pinned column bases (K = 1.0 at foundation) unless the base plate, anchor bolts, and foundation are specifically designed for moment transfer. Achieving meaningful base fixity requires anchor bolts outside the column footprint and a base plate designed as a moment connection — this is expensive and is avoided where possible.
Frequently Asked Questions
What is the maximum KL/r for columns in CSA S16? Clause 13.3.2 limits KL/r to 200 for main compression members and 300 for secondary members (bracing, struts in light framing). However, economical column design targets KL/r <= 80-100. Columns exceeding KL/r = 120 lose more than 60% of their squash load capacity and become uneconomical. For HSS columns, KL/r up to 120 is still reasonable because the n = 2.24 curve provides higher capacity at intermediate slenderness.
What n-factor should I use for a welded built-up I-section column? Per CSA S16 Table 4, a welded I-section with flame-cut flange plates and fillet-welded web-to-flange connections uses n = 1.34 if the residual stress level is moderate (typically, preheat and controlled cooling produce lower residual stresses). If the section uses submerged arc welded (SAW) heavy fillets without post-weld heat treatment, residual stresses can reach 0.4-0.5 Fy, and n = 0.69 applies. The fabricator should be consulted on the welding procedure to determine which n-factor is appropriate.
When does biaxial bending govern over uniaxial + axial? Biaxial bending governs for corner columns (beams framing in from two orthogonal directions) and for columns in the perimeter frame subject to major-axis bending from the frame action plus minor-axis bending from cladding eccentricity. The 0.60 coefficient on the minor axis in the Clause 13.8.2 interaction makes biaxial bending less penalising than might be expected — a 30% minor-axis utilisation only consumes 18% of the interaction equation capacity.
This page is for educational reference. Column design per CSA S16-19 Clause 13.3. Verify effective length factors, section classification, and n-factors against the CISC Handbook. All structural designs must be independently verified by a licensed Professional Engineer. Results are PRELIMINARY — NOT FOR CONSTRUCTION.