CSA S16 HSS Design Guide — Clause 13.4.1, Class C Sections & Wall Slenderness

Quick Reference: HSS compression capacity Cr = phi _ Ae _ Fy per Cl. 13.3 with n = 1.34 column curve. Class C sections have reduced effective area due to local buckling. Rectangular HSS wall slenderness limit: b/t <= 670/sqrt(Fy). Round HSS: D/t <= 23,000/Fy. All design per CSA S16:24.

HSS in Canadian Construction

Hollow Structural Sections (HSS) are the most common member type for compression bracing, truss chords, and columns in Canadian steel construction. Their closed shape provides excellent torsional stiffness, equal buckling resistance in both axes (for square/round sections), and a clean architectural appearance without exposed bolt heads or connection hardware.

Canadian HSS are produced to CSA G40.20/G40.21 standards in two strength grades:

• Class C: Fy = 350 MPa, Fu = 450 MPa — standard structural grade
• Class H: Fy = 350 MPa, Fu = 450 MPa — hot-formed, lower residual stress, larger corner radii

ASTM A500 Grade C (Fy = 345 MPa, Fu = 425 MPa) sections are also widely available and accepted under CSA S16 where material equivalence is demonstrated per Cl. 5.1.3.

Wall Slenderness and Section Classification (Cl. 11.3)

HSS walls are flat plates supported along two edges (at the corners). Under compression, the walls can buckle locally before the member reaches its full yield capacity. Section classification determines how this local buckling affects design.

Rectangular HSS (Cl. 11.3, Table 2)

The flat width b is taken as the clear distance between the inside corners, less the outside corner radius: b = B - 3t (approximately, where B is the outer dimension, t is wall thickness)

Class C designation applies to sections where b/t exceeds Class 2 limits but remains within Class 3 or 4. In CSA S16:24, the term "Class C" is a material designation, not a section class. The section class (1-4) is determined independently.

Common Canadian rectangular HSS section classifications:

Note the 6.4 mm wall sections above 200 mm: they rapidly become Class 4 (slender). Always specify minimum 8-10 mm wall thickness for HSS columns larger than 200 mm unless slenderness effects are explicitly calculated.

Round HSS (Cl. 11.3, Table 2)

Round HSS classification uses D/t ratio:

Round HSS are far less susceptible to local buckling than rectangular HSS of comparable size — the circular cross-section provides inherent shell stability. In practice, most standard round HSS are Class 1 or 2.

Compression Resistance (Cl. 13.3)

Standard Column Curve (n = 1.34)

CSA S16:24 uses a single column curve for all structural shapes:

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

where:

• lambda = (K*L/r) * sqrt(Fy/(pi^2_E))
• n = 1.34 for all shapes

This differs from AISC 360 which uses separate curves for HSS (n = 1.6 per modified E3) vs W-shapes (n = 1.0 per E3-2/E3-3). CSA's single curve is slightly more conservative for HSS at intermediate slenderness.

For HSS, the radius of gyration r is similar about both axes (rx ≈ ry for square, rx = ry for round). The buckling direction is therefore governed by the effective length factor K and unbraced length L, not by section geometry.

Effective Area for Class 4 (Slender) Sections

When the section is Class 4 (b/t > 670/sqrt(Fy)), local buckling precedes member buckling. The effective area Ae replaces the gross area:

Cr = phi _ Ae _ Fy _ (1 + lambda_e^(2_n))^(-1/n)

where lambda_e uses the effective section properties.

For each flat wall in a rectangular HSS, the effective width be is: be = 1.91 _ t _ sqrt(E/(Fy _ k)) for uniform compression

where k = 4.0 for simply supported edges (HSS corners provide partial fixity; using k = 4.0 is conservative). For stress gradients (flexure), k varies based on the stress ratio.

The effective area is the sum of (be _ t) for all four walls minus the corner radii. For HSS 254x254x6.4 (b/t = 36.0, Fy = 350 MPa):

• Flat width b = 254 - 3 _ 6.4 = 234.8 mm
• b/t = 234.8/6.4 = 36.7 (using more precise dimensions)
• be = 1.91 _ 6.4 _ sqrt(200,000/(350 _ 4)) = 12.22 _ sqrt(142.9) = 12.22 _ 11.95 = 146.0 mm per wall
• Total effective area: 4 _ 146.0 _ 6.4 = 3,738 mm^2
• Gross area: ≈ 6,050 mm^2
• Reduction: Ae/Ag = 3,738/6,050 = 0.62 — only 62% effective

A thicker wall of 9.5 mm (b/t = 23.0, Class 2) avoids this drastic reduction entirely.

Flexural Resistance of HSS (Cl. 13.5, 13.6)

HSS in flexure exhibit behaviour distinct from W-shapes:

• No lateral-torsional buckling — the closed section has very high torsional stiffness; LTB is not a limit state for HSS
• Plastic moment Mp = Zx _ Fy for Class 1 and 2 sections
• Yield moment My = Sx _ Fy for Class 3 sections
• Effective section modulus Se for Class 4 sections

For rectangular HSS with the moment applied about the strong axis: Mr = phi _ Zx _ Fy (Class 1-2) Mr = phi _ Sx _ Fy (Class 3)

where Zx and Sx are the plastic and elastic section moduli about the axis of bending. The absence of LTB makes HSS particularly efficient for unbraced flexural members like spandrel beams and cantilevers — they achieve full plastic moment regardless of unbraced length.

HSS Flexural Worked Example

Given: HSS 127x127x6.4 Grade 350W, 4 m span, simply supported, full UDL. No intermediate bracing.

Section properties: Sx = 80.9 × 10^3 mm^3, Zx = 96.8 × 10^3 mm^3

Step 1 — Check class: b/t = 16.2, Class 1. OK.

Step 2 — Moment Capacity: Mr = 0.90 × 96,800 × 350 / 1,000,000 = 30.5 kN.m

Step 3 — Check LTB: Not applicable for HSS (Cl. 13.6.5 does not govern closed sections). Maximum moment = Mr regardless of span.

For comparison, an equivalent-weight W-shape (W130x28) with a 4 m unbraced length may require LTB reduction, giving a lower usable moment. This is why HSS excel as unbraced beams in industrial walkways, pipe supports, and equipment platforms.

HSS Connection Design (Cl. 21.4)

HSS connections present unique challenges because access to the inside of the section is impossible after fabrication. Three connection types dominate Canadian practice:

1. Slotted Gusset Plate (Tension/Compression Brace)

The most common HSS bracing connection. A gusset plate passes through slots cut in the HSS walls and is fillet welded on both sides:

• Slot width: plate thickness + 2 mm clearance
• Slot length: determined by weld length required to develop brace force
• Weld: fillet weld both sides, minimum size per Table 25 (typically 6 mm)
• Check: shear lag in the HSS walls adjacent to the slot; net section through the slotted wall
• HSS wall thickness should be >= plate thickness/2 for adequate weld fusion

2. End Plate (Column Base or Beam-to-Column)

The HSS is welded to a base plate or end plate, which is then field-bolted:

• Plate weld: all-around fillet weld (8-10 mm typical for HSS 152+)
• Bolt pattern: symmetric about both axes to avoid prying
• Plate thickness: determined by yield line analysis for the bolt pattern
• Special consideration: the interior of the HSS is inaccessible — the plate only contacts the HSS wall perimeter, not the full footprint

3. HSS-to-HSS Welded Connections (Trusses & Frames)

Direct branch-to-chord welded connections per Cl. 21.4 and CIDECT design guides:

Chord plastification (Cl. 21.4.2): The branch force is limited by the chord wall's ability to resist the transverse component without excessive deformation. For K-joints with gap:

N* <= phi _ Fy _ t0^2 _ (2 _ eta + 4 _ sqrt(1-beta)) _ Qf / sin(theta)

where:

• t0 = chord wall thickness
• beta = branch width/chord width ratio (b1/B0)
• eta = branch height/chord width ratio (h1/B0)
• Qf = chord stress function
• theta = branch-to-chord angle

Punching shear (Cl. 21.4.3): Effective width concept — only the portion of the branch wall directly over the chord flat face is effective in tension.

Worked Example: HSS Column Design

Given: HSS 127x127x6.4 Grade 350W, 3.6 m column height, K = 1.0 (pin-ended). Factored axial load Cf = 350 kN.

Section properties: Ag = 2,930 mm^2, r = 49.5 mm, b/t = 16.2 (Class 1), b = 127 - 3*6.4 = 107.8 mm

Step 1 — Section Class: b/t = 107.8/6.4 = 16.8 (using flat width). Class 1 limit = 420/sqrt(350) = 22.4. 16.8 < 22.4 — Class 1, OK.

Step 2 — Slenderness Parameter: lambda = (K*L/r) * sqrt(Fy/(pi^2 _ E)) = (3,600/49.5) _ sqrt(350/(pi^2*200,000))

= 72.73 _ sqrt(350/1,973,920) = 72.73 _ sqrt(1.773e-4) = 72.73 _ 0.0133 = 0.967

Step 3 — Compressive Resistance: Cr = 0.90 × 2,930 × 350 × (1 + 0.967^(2×1.34))^(-1/1.34) / 1,000

= 923.0 × (1 + 0.967^2.68)^(-0.746) / 1,000

= 923.0 × (1 + 0.914)^(-0.746) / 1,000

= 923.0 × (1.914)^(-0.746) / 1,000

= 923.0 × 0.619 / 1,000

= 571 kN

Step 4 — Utilisation: Cf/Cr = 350/571 = 0.61 — OK. The HSS 127x127x6.4 has 43% reserve capacity at this load and height.

Step 5 — Alternative: Try lighter section HSS 127x127x4.8 Ag = 2,230 mm^2, r = 50.3 mm, b/t = 22.8 (Class 2)

lambda = (3,600/50.3) × 0.0133 = 0.950

Cr = 0.90 × 2,230 × 350 × (1 + 0.950^2.68)^(-0.746) / 1,000 = 702.5 × 0.626 / 1,000 = 440 kN

Utilisation = 350/440 = 0.80 — still OK, more economical.

CSA S16 vs AISC 360 — HSS Comparison

The codes are closely aligned for HSS, with AISC offering slightly more refined treatment of thick-walled and high-strength HSS. The column curve comparison: CSA's n = 1.34 is essentially an average of AISC's W-shape (n ≈ 1.0) and HSS (n = 1.6) curves. For stocky HSS columns (lambda < 0.5), the difference is minimal; for slender HSS (lambda > 1.0), AISC's n = 1.6 gives 5-10% higher capacity.

Try it now: Design HSS columns with our free CA Column Capacity calculator

Related Pages

• CSA S16 Code Overview — Full CSA S16:24 design code reference
• CSA S16 Column Design Guide — W-shape column design per CSA
• HSS Connection Design — AISC 360 — US HSS design comparison
• HSS Properties Quick Reference — Section dimensions and properties
• Canadian Steel Sections Guide — All Canadian section types
• Load Combinations — CSA S16 & NBCC — Loading for HSS member design

This page is for educational reference. All formulae per CSA S16:24. For section properties and dimensions, refer to the current CISC Handbook of Steel Construction. Results are PRELIMINARY — NOT FOR CONSTRUCTION without independent PE/SE verification.

Design Resources

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• Column Capacity Calculator — Multi-Code
• Beam Capacity Calculator — HSS Flexure
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Design guides

• CSA S16 Beam Design — Flexure & LTB
• HSS Section Properties — Complete Tables
• Steel Column Design — Comprehensive Guide
• Lateral-Torsional Buckling Reference

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