CSA S16 Column Design — Compressive Resistance & W250x73 Worked Example

Quick Reference: Compressive resistance Cr = phi _ A _ Fy * (1 + lambda^(2*n))^(-1/n) per Cl. 13.3, with phi = 0.90, n = 1.34. Effective length K per Cl. 14.2. Slenderness ratio KL/r limited to 200 for primary members.

CSA S16 Column Design Philosophy

CSA S16:24 Clause 13.3 governs the design of axially loaded steel compression members. The code uses a single column curve based on the structural steel research by Bjorhovde and the SSRC, adopting the exponent formulation rather than the multiple buckling curves used in EN 1993-1-1. This means all steel columns — regardless of section type — are designed using the same strength curve, unlike Eurocode which uses five buckling curves (a0 through d).

The resistance factor for compression is phi = 0.90 (Cl. 13.1), identical to AISC 360 and AS 4100. The single curve approach simplifies design; you only need the cross-sectional area A, yield strength Fy, elastic modulus E, effective length KL, and radius of gyration r.

Compressive Resistance Formula (Cl. 13.3.1)

The factored compressive resistance of a steel column per CSA S16:24 is:

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

where:

• phi = 0.90 (resistance factor for compression)
• A = gross cross-sectional area (mm^2)
• Fy = specified minimum yield strength (MPa)
• n = 1.34 (empirical exponent for hot-rolled structural steel)
• lambda = non-dimensional slenderness parameter

The slenderness parameter lambda is:

lambda = (KL/r) * sqrt(Fy / (pi^2 * E))

where:

• K = effective length factor
• L = unbraced length (mm)
• r = radius of gyration about the buckling axis (mm), use r_min for the weak axis
• E = 200,000 MPa (elastic modulus of steel)

Understanding the (1 + lambda^(2*n))^(-1/n) Term

This term is the reduction factor for buckling. When lambda = 0 (a stocky column with KL/r = 0), the term equals 1.0 and Cr = phi _ A _ Fy — the full squash load. As lambda increases, the term decreases, reducing Cr below the squash load.

The exponent n = 1.34 controls the shape of the transition from yielding to buckling. A lower n produces a sharper knee (less conservative), while a higher n produces a smoother transition (more conservative for intermediate slenderness). The value n = 1.34 was calibrated against Canadian experimental data.

Section Classification for Compression (Cl. 11)

CSA S16:24 classifies cross-sections under uniform compression using Table 2 limits:

For standard Canadian W-shapes in Grade 350W, most sections through W310 and below are Class 1 or 2 in uniform compression. Only very slender sections (W610x92 and lighter) enter Class 3 or 4 for the web under pure compression, though for beam-columns the classification under combined stress may differ.

Effective Length Factor K (Cl. 14.2)

The effective length factor K accounts for end restraint conditions. CSA S16:24 Clause 14.2 references the alignment chart approach or Appendix D of the CISC Handbook:

For typical building columns in braced frames with simple shear connections to beams, K = 1.0 is the standard conservative assumption. The alignment chart in the CISC Handbook provides more refined values based on the stiffness ratio GA and GB at each column end.

Sway vs Non-Sway Frames

CSA S16:24 Clause 14.2 distinguishes between sway (unbraced) and non-sway (braced) frames. A frame is considered braced if the lateral load resistance is provided entirely by shear walls, braced bays, or other stiffening elements — the columns contribute negligible lateral resistance. In a sway frame, the columns participate in lateral load resistance, and P-delta effects must be included.

For sway frames, the effective length K is always greater than 1.0 because the ends are not prevented from translating laterally. The alignment chart for sway frames typically gives K between 1.0 and infinity, though K > 5.0 indicates the frame is too flexible and needs additional bracing.

Slenderness Limits (Cl. 10.3.3.1)

Columns exceeding KL/r = 200 are not permitted by CSA S16 for primary load-carrying members. Below 200, the limit state is buckling. Below KL/r of about 30, the limit transitions to cross-section yielding, and the full squash load applies.

Worked Example — W250x73 Column, Grade 350W

Problem: Design check for a W250x73 column in a braced frame, Grade G40.21 350W, pin-ended (K = 1.0), unbraced height 4.5 m. The column carries a factored axial compression Cf = 1,200 kN from a 300W plate. Verify the column per CSA S16:24 Clause 13.3.

Section Properties — W250x73 (CSA G40.21 350W)

Step 1 — Section Classification

Flange: b/t = (bf - tw) / (2 _ tf) = (254 - 8.6) / (2 _ 14.2) = 8.64

Class 2 limit for flange in compression: 170 / sqrt(Fy) = 170 / sqrt(350) = 9.09. 8.64 < 9.09 — Class 2.

Web: h = d - 2*tf = 253 - 28.4 = 224.6 mm. h/w = 224.6 / 8.6 = 26.1

Class 2 limit for web in compression: 830 / sqrt(Fy) = 830 / sqrt(350) = 44.4. 26.1 < 44.4 — Class 2.

Section is Class 2 (Compact). Full plastic squash load can be used.

Step 2 — Slenderness Parameter

KL/r = 1.0 * 4,500 / 64.6 = 69.7 (< 200 — OK)

lambda = (KL/r) _ sqrt(Fy / (pi^2 _ E)) = 69.7 _ sqrt(350 / (pi^2 _ 200,000))

= 69.7 _ sqrt(350 / 1,973,920) = 69.7 _ sqrt(1.773e-4) = 69.7 * 0.01332 = 0.928

Step 3 — Compressive Resistance Cr

For n = 1.34, lambda = 0.928:

lambda^(2*n) = 0.928^(2 * 1.34) = 0.928^2.68 ≈ 0.816

1 + lambda^(2*n) = 1 + 0.816 = 1.816

(1 + lambda^(2*n))^(-1/n) = 1.816^(-1/1.34) = 1.816^(-0.746) = 0.647

Cr = phi _ A _ Fy _ 0.647 = 0.90 _ 9,290 _ 350 _ 0.647 / 1,000

= 0.90 _ 3,251,500 _ 0.647 / 1,000 = 0.90 * 2,103.7 / 1.000 = 1,893 kN

Step 4 — Check

Cf = 1,200 kN (factored demand)

Utilisation = Cf / Cr = 1,200 / 1,893 = 0.634 — OK.

The W250x73 column passes with 37% reserve capacity. At 1,200 kN demand, the column has adequate capacity. A lighter W250x58 (Cr ≈ 1,316 kN, utilisation 0.912) might work but would need full re-check and leave minimal margin.

Step 5 — Weak-Axis Restraint Consideration

The weak axis r_min = 64.6 mm governs because ry < rx. If intermediate weak-axis bracing is provided at mid-height (reducing KL to 2,250 mm):

KL/r = 2,250 / 64.6 = 34.8

lambda = 34.8 * 0.01332 = 0.464

lambda^(2*1.34) = 0.464^2.68 ≈ 0.120

Reduction factor = (1 + 0.120)^(-0.746) = 1.120^(-0.746) = 0.918

Cr = 0.90 _ 9,290 _ 350 * 0.918 / 1,000 = 2,685 kN

The mid-height brace increases Cr by 42% (1,893 → 2,685 kN). Intermediate bracing is one of the most cost-effective ways to increase column capacity — a simple kicker or girt line can reduce the effective length by half and nearly double the capacity in the elastic buckling range.

Column Base Plate Bearing

Column bases in Canadian practice are typically designed per the CISC Handbook design tables, which pre-calculate the required base plate area and thickness for standard column sizes. The bearing stress on the concrete footing is:

f_p = Cf / (B * N) <= phi_c * 0.85 * f'c * sqrt(A2/A1) <= phi_c * 1.70 * f'c

where phi_c = 0.65 per CSA A23.3 for concrete bearing, f'c is the concrete cylinder strength (typically 25-35 MPa), and A2/A1 accounts for the confinement effect of the surrounding footing area (limited to a maximum stress increase of 2.0, hence the 1.70 factor).

For a W250x73 base plate with Cf = 1,200 kN on a 400x400 mm plate on 30 MPa concrete:

f_p = 1,200,000 / (400 * 400) = 7.5 MPa

phi*c * 0.85 _ f'c = 0.65 _ 0.85 _ 30 = 16.6 MPa — well above 7.5 MPa. Bearing is not critical for typical base plates.

CSA S16 vs AISC 360 — Column Design Comparison

For practical design, the two codes produce very similar results for stocky and slender columns but differ slightly for intermediate slenderness (KL/r = 60-120) where the CSA S16 curve is 2-5% more conservative. For a W250x73 with KL/r = 70, CSA gives Cr = 1,893 kN vs AISC phi*Pn ≈ 1,940 kN — a 2.4% difference.

Frequently Asked Questions

How do I handle biaxial bending in a CSA S16 column?

CSA S16:24 Clause 13.8 covers beam-columns. For biaxial bending plus compression, the interaction check is:

Cf/Cr + 0.85 _ U1x _ Mfx/Mrx + 0.85 _ U1y _ Mfy/Mry <= 1.0 (cross-section)

Cf/Cr + U1x _ Mfx/Mrx + U1y _ Mfy/Mry <= 1.0 (member stability)

where U1x = omega_1x / (1 - Cf/Cex), U1y = omega_1y / (1 - Cf/Cey), and omega_1 = 0.60 for Class 1-2 sections. The elastic buckling loads Cex and Cey are calculated separately for each axis using the corresponding K, L, and I values.

What is the difference between CSA S16 Class 3 and Class 4 column sections?

Class 3 (non-compact) columns use the gross section properties for Cr calculation, but the resistance is limited to the yield moment — local buckling prevents the full plastic stress distribution. Class 4 (slender) columns require the use of effective section properties (Ae, Se) calculated per CSA S16:24 Clause 11.4. The effective area accounts for local buckling of slender plate elements. For a Class 4 W-shape column, the web in compression may buckle locally before the full squash load is reached, requiring a reduced effective width be = 200tw / sqrt(Fy) * (1 - 0.23 * tw/(bsqrt(Fy/(pi^2*E)))) but limited to the actual width.

When should I use a heavier column section vs adding intermediate bracing?

At KL/r = 70 (W250x73, 4.5 m unbraced), adding a mid-height weak-axis brace reduces KL/r to 35 and increases Cr by 42%. The cost of a horizontal kicker or girt line is typically a fraction of the cost of upsizing the column. For KL/r above 80, bracing provides even more benefit — at KL/r = 120, a mid-height brace can more than double the capacity because the column moves from elastic buckling back into the inelastic transition zone. Below KL/r = 40, bracing provides diminishing returns because the column is already near the squash load.

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Related Pages

• CSA S16 Beam Design — Flexure, LTB & Shear — Detailed beam design per CSA S16
• Canada CSA S16 Steel Design Guide — Full Canadian steel design overview
• CSA S16 Load Combinations — NBCC 2020 — ULS/SLS combos per NBCC
• Canadian Steel Grades — G40.21 — 300W through 480W properties
• Column K Factor Reference — Alignment charts and effective length
• Column Buckling Equations — International Comparison — CSA vs AISC vs EN 1993
• Column Base Plate Design Guide — Anchorage and bearing per CSA S16
• Column Design Guide — Multi-Code Reference — AISC, CSA, EN 1993 comparison

This page is for educational reference. All formulae per CSA S16:24 and CSA G40.21-13. For section properties, refer to the current CISC Handbook of Steel Construction. Results are PRELIMINARY — NOT FOR CONSTRUCTION without independent P.Eng. verification.

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• Column Design Guide — Canadian Practice
• Base Plate Design Worked Example
• Steel Column Design Workflow

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