Canadian Beam Capacity Calculator — CSA S16:24

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Design per CSA S16:24 Clause 13 and 14

Calculate the flexural and shear capacity of Canadian steel W-shapes per CSA S16:24. The calculator supports W, S, and C shapes in 300W, 350W, and 380W steel grades.

Supported Sections and Grades

• W-shapes — W100× to W1100× series (Canadian metric sections)
• S-shapes — S75× to S310× series
• C-shapes — C75× to C380× series
• Steel grades — 300W (300 MPa yield, most common), 350W, 380W

Design Checks Performed

• Class determination — Class 1, 2, 3, or 4 per CSA S16:24 Clause 11 (flange and web slenderness limits)
• Flexural resistance — Mr = φ × Z × Fy per Clause 13.5 for Class 1 and 2 sections
• Lateral-torsional buckling — Mr = φ × Mu per Clause 13.6 with ω2 moment gradient factor
• Shear resistance — Vr = φ × Aw × Fs per Clause 13.4 where Fs = 0.66Fy
• Shear buckling — Clause 13.4.1.1 web stiffener requirements for slender webs

Worked Example

Problem: Check a W410×60 beam in 350W steel for a 7.0 m simply supported span with a factored UDL of 35 kN/m.

Solution:

• Section: W410×60 (W-shape metric), 350W (Fy = 350 MPa)
• Class 1 (compact flange and web)
• Plastic modulus Zx = 1200 × 10³ mm³
• Design moment: Mf = 35 × 7.0² / 8 = 214 kNm
• Moment resistance: Mr = 0.9 × 1200 × 10³ × 350 = 378 kNm
• Utilisation: 214/378 = 0.57 (57%) — OK
• Shear: Vf = 35 × 7.0 / 2 = 123 kN
• Shear resistance: Vr = 0.9 × 4520 × 0.66 × 350 = 939 kN
• Utilisation: 123/939 = 0.13 (13%) — OK

Result: W410×60 in 350W is adequate. Moment governs at 57% utilisation.

Second Worked Example — Laterally Unrestrained Beam

Problem: Check a W530×82 beam in 350W steel for a 9.0 m unbraced span with a factored UDL of 20 kN/m. No intermediate lateral restraint. Load applied to top flange.

Solution:

1. Section properties: W530×82 in 350W (Fy = 350 MPa) Zx = 2070 × 10³ mm³, Iy = 20.1 × 10⁶ mm⁴, J = 478 × 10³ mm⁴, Cw = 878 × 10⁹ mm⁶
2. Class check: Class 1 (compact — b/t = 6.3 ≤ 145/√Fy = 7.75)
3. Design moment: Mf = 20 × 9.0²/8 = 203 kNm
4. Plastic moment: Mp = 2070 × 10³ × 350 × 10⁻⁶ = 725 kNm
5. Elastic LTB moment Mu (Clause 13.6.1): Mu = ω2 × (π/L) × ÃƒÂ¢Ã‚ÂˆÃ‚Âš[E × Iy × G × J + (πE/L)² × Iy × Cw] With ω2 = 1.0 (uniform moment between restraints for conservative estimate) Mu = (π/9000) × ÃƒÂ¢Ã‚ÂˆÃ‚Âš[200000 × 20.1 × 10⁶ × 77000 × 478 × 10³ + (π × 200000/9000)² × 20.1 × 10⁶ × 878 × 10⁹] × 10⁻⁶ Mu = 412 kNm
6. LTB resistance (Clause 13.6): Since Mu > 0.67Mp, Mr = 1.15 × φ × Mp × [1 - 0.28Mp/Mu] ≤ φMp Mr = 1.15 × 0.9 × 725 × [1 - 0.28 × 725/412] = 750 × [1 - 0.493] = 750 × 0.507 = 380 kNm Check φMp = 0.9 × 725 = 653 kNm → Mr = 380 ≤ 653 → OK
7. Utilisation: 203/380 = 0.53 (53%) — OK

Result: W530×82 in 350W is adequate for the 9.0 m unbraced span. LTB governs at 53% utilisation. If the load were applied to the bottom flange (destabilising), reduce Mr further or provide lateral restraint.

CSA S16:24 Clause Reference

Serviceability and Deflection — Canadian Practice

Per NBCC 2025 and CSA S16:24 Annex D:

• Floor beams: total deflection ≤ L/360, live load ≤ L/480 for floors supporting partitions
• Roof beams: total ≤ L/240 (steel deck), L/180 (standing seam)
• Camber: Pre-camber to 75% of calculated dead load deflection
• Vibration: Fundamental frequency fn ≥ 5 Hz for offices, fn ≥ 8 Hz for gymnasiums per NBCC 2025

For the W410×60 worked example under service loads (unfactored): Δ = 5 × 25 × 7000⁴ / (384 × 200000 × 216 × 10⁶) = 17.8 mm < 7000/360 = 19.4 mm → OK.

Moment Gradient Factor omega2 — Practical Values

The omega2 factor per CSA S16:24 Clause 13.6.1(a) accounts for non-uniform moment along the unbraced length. Higher omega2 values increase the elastic LTB moment Mu and thus the LTB resistance Mr:

Practical use: For a simply-supported beam with UDL (the most common case in Canadian building construction), omega2 = 1.75 increases Mu by 75% compared to the uniform moment case. This is the primary reason why simply-supported beams with UDL can span further without LTB failure than beams with constant moment (e.g., cantilever back-spans, transfer beams with heavy point loads).

Web Crippling and Bearing — CSA S16 Clause 14.3.2

For beams subjected to concentrated loads at supports or from incoming beams, the web bearing resistance Br must be checked:

Br = phi x 1.45 x tw x sqrt(Fy x E) (interior load) Br = phi x 0.60 x tw^2 x sqrt(Fy x E) (end reaction, stiff bearing length >= tw)

For a W410x60 beam (tw = 7.7 mm, Fy = 350 MPa) with an end reaction of 123 kN:

Br_end = 0.80 x 0.60 x 7.7^2 x sqrt(350 x 200,000) / 1000 = 0.80 x 0.60 x 59.3 x 8,367 / 1000 = 238 kN > 123 kN. OK.

If the bearing is insufficient, provide web stiffeners (full-depth or partial-depth) per Clause 14.4, or specify a bearing plate to distribute the reaction over a longer bearing length.

Practical Beam Selection — Canadian Design Office Quick Reference

These are rule-of-thumb starting points for preliminary sizing. Always verify with the calculator using project-specific loads, unbraced lengths, and deflection limits. For beams supporting masonry or brittle partitions, the live load deflection limit of L/480 may govern over strength.

Cold-Formed Steel Beams — CSA S136

For light-gauge cold-formed steel beams (C-sections, Z-sections, track sections), CSA S136 (North American Specification for Cold-Formed Steel Structural Members) applies rather than CSA S16. Key differences:

• Yield strength: Typically 230-550 MPa for cold-formed grades (e.g., 350 MPa is common)
• Buckling modes: Local buckling (plate elements), distortional buckling (intermediate stiffeners), and global buckling (flexural, torsional, or flexural-torsional)
• Effective width method or Direct Strength Method for determining post-buckling capacity
• phi factor: 0.80 for cold-formed members (vs 0.90 for hot-rolled per CSA S16)

The calculator currently supports hot-rolled W, S, and C shapes only. For cold-formed beam design, use a cold-formed steel design tool or refer to the CSSBI (Canadian Sheet Steel Building Institute) design tables.

Related Resources

• Canadian Beam Design Guide
• Canadian Steel Grades Fy/Fu
• Canadian Column Design Guide
• Lateral-Torsional Buckling Guide

FAQ

What is the resistance factor φ for beams in CSA S16? The φ factor for steel beams is 0.9 per CSA S16:24 Clause 13. This applies to both flexure and shear.

How does the calculator handle lateral-torsional buckling? LTB is checked per Clause 13.6 using the unbraced length Lb, the moment gradient factor ω2, and the section classification. The elastic buckling moment Mu is computed and compared to the plastic moment Mp.

What steel grades are supported? 300W (Fy = 300 MPa), 350W (Fy = 350 MPa), and 380W (Fy = 380 MPa) per CSA G40.20-13/G40.21-13.

Can I use imperial W-shapes? The calculator uses metric W-shape designations (e.g., W410×60) common in Canadian practice. For US imperial W-shapes, use the AISC code selection instead.

What is the ω2 moment gradient factor? The ω2 factor per CSA S16:24 Clause 13.6.1 accounts for the variation of bending moment along the unbraced segment. ω2 = 1.0 for uniform moment (double curvature), ω2 = 1.75 for a simply-supported beam with UDL, and ω2 = 2.50 for a cantilever with tip load. Higher ω2 values increase the elastic LTB moment Mu and thus the LTB resistance Mr. The factor is analogous to Cb in AISC 360.

How does the calculator handle Class 4 sections? For sections with flange or web slenderness exceeding Class 3 limits, the calculator determines effective section properties per CSA S16:24 Clause 11.4. The effective width be is calculated from the buckled plate width using the Winter formula. Class 4 sections have reduced moment resistance: Mr = φ × Se × Fy where Se is the effective elastic section modulus.

What is the shear resistance Fs factor? CSA S16:24 uses Fs = 0.66Fy for the shear yield stress per Clause 13.4.1.1. For S16-14 and earlier editions, Fs = 0.66Fy was also standard. Note that AISC 360 uses 0.6Fy — the Canadian 0.66 factor provides slightly higher shear resistance. For shear buckling in slender webs, the post-buckling tension field action is considered per S16:24 Clause 13.4.1.1(c).

What deflection limits apply in Canada? Per NBCC 2025 Commentary L and CSA S16:24 Annex D: floor beams are limited to L/360 total deflection and L/480 incremental live load deflection where partitions may crack. Roofs with steel decking use L/240. The calculator follows these defaults but allows custom limits for specific project requirements.