CSA S16 Composite Beam Design — Shear Studs, Clause 17 & Effective Width

Quick Reference: Composite action couples the steel beam with the concrete slab via shear studs. Moment resistance in full composite: plastic neutral axis in slab (Qr = AsFy <= 0.85f'cbetc) or in steel section. Shear stud capacity per Cl. 17.7: qr = 0.5phi_scA_scsqrt(f'cEc). All design per CSA S16:24.

Why Composite Construction?

Composite steel-concrete construction exploits the best properties of both materials: steel resists tension efficiently, concrete resists compression economically. A composite beam achieves 30-50% more moment capacity than the bare steel section alone, reduces beam depth by 2-3 size increments, and increases floor stiffness by a factor of 2-4. In Canadian practice, composite beams are the default for multi-storey steel-framed buildings — the cost premium for shear studs (approximately $8-15/stud installed) is recovered through lighter steel tonnage and reduced floor-to-floor heights.

The composite system comprises:

1. Steel beam (typically W-shape, G40.21 350W): resists tension, provides construction-stage strength
2. Concrete slab (20-25 MPa normal-weight, 130-200 mm total thickness): resists compression
3. Shear studs (19 mm dia, CSA-compliant, welded through deck): transfers horizontal shear
4. Steel deck (38-76 mm profile, 0.76-1.22 mm base metal thickness): permanent formwork, may contribute to composite action
5. Welded wire mesh (152x152 MW18.7/MW18.7): crack control and temperature steel

Effective Concrete Slab Width (Cl. 17.4.1)

CSA S16:24 limits the effective slab width acting compositely with each steel beam. The slab stress distribution is non-uniform — maximum directly over the beam, diminishing with transverse distance due to shear lag. The effective width concept compresses the real 3D stress field into an equivalent 2D design:

Interior Beams

be = min(span/4, centre-to-centre spacing)

For a typical office building with 3.0 m beam spacing on a 9.0 m span:

• Span/4 = 9,000/4 = 2,250 mm
• Beam spacing = 3,000 mm
• be = 2,250 mm

Edge Beams (Spandrel Beams)

be = min(span/8 + edge_dist, spacing/2 + edge_dist, actual width)

For the same 9.0 m span with 750 mm from beam centreline to slab edge:

• Span/8 + 750 = 1,125 + 750 = 1,875 mm
• Spacing/2 + 750 = 3,000/2 + 750 = 2,250 mm
• be = 1,875 mm

Beams Parallel to Slab Edge

For beams with slab on one side only (e.g., perimeter beams with cantilever slab):

• be = min(span/8, actual slab width on that side)

Rib Width Deduction for Metal Deck

When the slab is cast on formed steel deck with ribs perpendicular to the beam, the effective concrete area in compression must account for the deck profile. The concrete within ribs below the top of the deck is ignored for compression capacity unless the ribs are filled with concrete and the deck is properly anchored. The effective slab depth for compression is taken as the concrete thickness above the deck ribs (tc), typically 65-90 mm for common Canadian deck profiles.

Shear Stud Design (Cl. 17.7)

Shear studs are the mechanical connectors that transfer horizontal shear across the steel-concrete interface. Without them, the two materials slide past each other and composite action is lost.

Stud Capacity (Cl. 17.7.1)

The factored shear resistance per stud is the lesser of concrete crushing and stud yielding:

qr = 0.5 _ phi_sc _ Asc * sqrt(f'c _ Ec) <= phi_sc _ Asc * Fu

where:

• phi_sc = 0.80 (stud connector resistance factor)
• A_sc = pi * d^2 / 4 (stud cross-sectional area, mm^2)
• f'c = specified concrete compressive strength (MPa)
• Ec = 4,500 * sqrt(f'c) for normal-density concrete (MPa) — NBCC/CSA A23.3
• Fu = specified minimum tensile strength of stud material (typically 450 MPa)

Capacity Table — 19 mm Diameter Shear Studs

For the most common Canadian specification (25 MPa concrete, 19 mm studs): qr = 80.0 kN.

Metal Deck Reduction (Cl. 17.7.2)

When shear studs are welded through metal deck with ribs perpendicular to the beam, a reduction factor is applied:

Rr = 0.85 _ (wr / hr) _ ((Hs / hr) - 1.0) <= 1.0

where:

• wr = average width of concrete rib (mm)
• hr = nominal rib height (mm)
• Hs = length of stud after welding, but <= hr + 75 mm

Common Canadian deck profiles:

For 38 mm deck profiles where Hs/hr > 2.0, the reduction factor caps at 1.0 — no reduction. For 76 mm deep deck, the reduction to 66% substantially increases the number of studs required and is often the factor that pushes designers toward partial composite action.

Stud Placement Requirements

CSA S16:24 Clause 17.7.3 specifies:

• Minimum stud height above deck: 40 mm (measured from top of deck rib)
• Maximum stud spacing: 900 mm or 4 × slab thickness (Cl. 17.7.3.1)
• Minimum stud spacing: 6 × stud diameter, 114 mm for 19 mm studs
• Minimum transverse clear spacing: 4 × stud diameter, 76 mm for 19 mm studs
• Minimum edge distance: 25 mm from stud to edge of steel flange
• Stud diameter limit: stud diameter <= 2.5 × flange thickness (for weld quality)

For 76 mm deck with 125 mm studs: Hs - hr = 125 - 76 = 49 mm >= 40 mm — OK.

Full Composite Action — Plastic Moment Capacity

The plastic moment capacity of a composite section depends on the location of the plastic neutral axis (PNA).

Case 1: PNA in Concrete Slab

This occurs when the concrete compression capacity exceeds the steel tension capacity:

0.85 _ phi_c _ f'c _ be _ a = phi _ As _ Fy

where a = depth of compression block in concrete. If a <= tc (slab thickness above deck):

Mr = phi _ As _ Fy _ (d/2 + hs + tc - a/2)

where d = steel beam depth, hs = deck rib height (ignored for compression), tc = concrete above deck.

Case 2: PNA in Steel Section (Top Flange or Web)

When As*Fy exceeds the concrete capacity (a > tc), the PNA drops into the steel section. The tension and compression forces in the steel must balance the concrete compression force. The calculation becomes:

C = 0.85 _ phi_c _ f'c _ be _ tc (maximum concrete compression)

T = phi _ (As _ Fy - C) / 2 (force in steel tension region)

The moment capacity is then calculated by summing moments of these forces about any convenient point.

Partial Composite Action (Cl. 17.8)

When full composite action would require an impractical number of shear studs (common with deep deck, short spans, or heavy beams), CSA S16 permits partial composite design:

Minimum degree of composite action: 25%

The reduced moment capacity Mr_pc is interpolated between:

• Mr_s = bare steel moment capacity (0% composite)
• Mr_fc = full composite moment capacity (100% composite)

For degrees of composite action > 50%, linear interpolation is permitted: Mr*pc = Mr_s + (SC - 0) * (Mr_fc - Mr_s) / (1 - 0) No — more accurately: Mr*pc = Mr_s + (degree%) * (Mr_fc - Mr_s) / 100

where degree% = (sum of stud capacities provided) / (horizontal shear force at full composite).

For degrees between 25% and 50%, additional deflection checks are required per Cl. 17.8.2. The reduced shear connection results in larger interface slip, increasing deflections by 10-30%.

Worked Example: Composite Beam with 75 mm Deck

Given:

• W410x46 (W16x31), Grade 350W: As = 5,890 mm^2, d = 403 mm, Zx = 885 × 10^3 mm^3, Ix = 176 × 10^6 mm^4
• Beam span = 9,000 mm, spacing = 3,000 mm, interior beam
• 75 mm deep deck (hr = 75 mm), 65 mm concrete topping (tc = 65 mm, total = 140 mm)
• f'c = 25 MPa, normal-density concrete (Ec = 22,500 MPa)
• 19 mm dia shear studs, Fu = 450 MPa, Hs = 125 mm
• Factored load (after construction): w = 22 kN/m (includes dead + live per NBCC)

Step 1 — Effective Width (Cl. 17.4.1): be = min(9,000/4, 3,000) = min(2,250, 3,000) = 2,250 mm

Step 2 — Bare Steel Moment Capacity (Construction Stage): Construction load: w_const = 1.25 × 2.5 (steel weight) + 1.25 × 2.0 (wet concrete) + 1.5 × 1.0 (construction live) = 3.125 + 2.5 + 1.5 = 7.125 kN/m

M_const = 7.125 × 9.0^2 / 8 = 72.1 kN.m

Mr_steel = 0.90 × 885,000 × 350 / 1,000,000 = 278.8 kN.m — OK for construction.

Step 3 — Concrete Compression Capacity: C_conc = 0.85 × 0.65 × 25 × 2,250 × 65 / 1,000 = 1,991 kN (phi_c = 0.65 per CSA A23.3 for concrete in compression)

Step 4 — Steel Tension Capacity: T_steel = 0.90 × 5,890 × 350 / 1,000 = 1,855 kN

Since T_steel (1,855) < C_conc (1,991), PNA is in the slab — Case 1.

Step 5 — Compression Block Depth: a = T_steel / (0.85 × phi_c × f'c × be) = 1,855,000 / (0.85 × 0.65 × 25 × 2,250) = 1,855,000 / 31,113 = 59.6 mm

a = 59.6 mm < tc = 65 mm — PNA in slab, as assumed. OK.

Step 6 — Full Composite Moment Capacity: Lever arm: d/2 + hs + tc - a/2 = 403/2 + 75 + 65 - 59.6/2 = 201.5 + 75 + 65 - 29.8 = 311.7 mm

Mr_fc = T_steel × lever_arm = 1,855 × 0.312 / 1,000 = 578.3 kN.m

Compare to bare steel moment (Mp = 278.8 kN.m): composite action increases capacity by 107% — the beam carries more than double the moment.

Step 7 — Number of Shear Studs Required (Full Composite): Total horizontal shear = T_steel = 1,855 kN

Stud capacity (with deck reduction): Wr = 150 mm, hr = 75 mm, Hs = 125 mm Rr = 0.85 × (150/75) × ((125/75) - 1.0) = 0.85 × 2.0 × 0.667 = 1.13 — capped at 1.0.

Wait — that's > 1.0. Let me recalculate: for this deck, the ribs are relatively wide. Rr = 1.13 > 1.0, so Rr = 1.0 (no reduction).

qr_effective = 80.0 kN (from the 25 MPa table above)

Number of studs for full composite = 1,855 / 80.0 = 23.2 → 24 studs, placed in pairs (12 pairs staggered at approximately 600 mm spacing)

Total of 24 studs over 9 m span: spacing = 9,000/(12+1) = 692 mm — less than the 900 mm maximum. Check minimum: 6 × 19 = 114 mm — OK.

Step 8 — Check Partial Composite Option: If 50% composite action (12 studs): Mr_50% = 278.8 + 0.50 × (578.3 - 278.8) = 278.8 + 149.8 = 428.6 kN.m

Applied moment Mf = 22 × 9.0^2 / 8 = 222.8 kN.m

Utilisation = 222.8 / 428.6 = 0.52 — OK.

Partial composite at 50% provides adequate capacity with half the studs. This is often the economical choice for typical office loading (3.6 kPa live, 1.0 kPa superimposed dead).

Step 9 — Deflection Check (Unfactored Live Load): Live load component: w_LL = 3.6 kPa × 3.0 m = 10.8 kN/m (unfactored)

Composite transformed moment of inertia (Cl. 17.5): n = Es/Ec = 200,000/22,500 = 8.89 Transformed slab width = be/n = 2,250/8.89 = 253 mm

The transformed section includes the steel beam plus the equivalent concrete area. For full composite, I_tr ≈ 450 × 10^6 mm^4 (from transformed section analysis).

Deflection = 5 × 10.8 × 9,000^4 / (384 × 200,000 × 450 × 10^6) = 5 × 10.8 × 6.561e15 / 3.456e16 = 10.3 mm

Limit = L/360 = 9,000/360 = 25 mm. 10.3 < 25 — OK.

For partial composite at 50%, interface slip increases deflection. Multiply by 1.15: 10.3 × 1.15 = 11.8 mm — still OK at L/763.

Construction Stage Considerations

The steel beam must support the wet concrete weight and construction live load without composite action. This is often the governing condition for beam size selection. Canadian practice typically uses:

Unshored Construction (Cl. 17.3.1): The steel beam alone resists dead load of wet concrete + deck + self-weight + construction live load (1.0 kPa). After concrete curing, the composite section resists superimposed dead and live loads. Most economical — no temporary shoring.

Shored Construction: Temporary shores support the wet concrete until curing. The composite section resists all loads. Economically justified only for long spans or heavy loading where a smaller steel section is feasible with shoring.

Construction Stage Check — W410x46:

Factored construction load: w = 1.25 × (0.46 + 2.4) + 1.5 × 1.0 = 3.575 + 1.5 = 5.075 kN/m M = 5.075 × 9.0^2 / 8 = 51.4 kN.m Mr (bare steel) = 0.90 × Zx × Fy = 0.90 × 885,000 × 350 / 1,000,000 = 278.8 kN.m Utilisation = 51.4/278.8 = 0.18 — generous, the beam is oversized for construction.

For a lighter section like W310x28 (W12x19), the construction check would be tighter and might govern.

Vibration and Serviceability

Composite floors are typically stiffer than bare steel, but the reduced mass (compared to reinforced concrete flat slab) makes them more sensitive to footfall vibration. CSA S16:24 Clause 17.9 requires:

• Natural frequency > 5 Hz for rhythmic activities (dance floors, gymnasia)
• Natural frequency > 3 Hz for office/residential walking excitation
• Peak acceleration < 0.5% g for office floors (ISO 10137 or AISC Design Guide 11)

For the worked example: estimated natural frequency f = pi/(2×L^2) × sqrt(E×I_tr/m) ≈ 4.8 Hz. Just below the 5 Hz threshold for rhythmic occupancy but adequate for office use.

CSA S16 vs AISC 360 — Composite Beam Comparison

The significant differences are:

1. phi factor: CSA's 0.80 is significantly higher than AISC's 0.65, resulting in 23% more shear stud capacity for identical geometry — Canadian composite beams need fewer studs
2. f'c limit: CSA caps the stud formula at 40 MPa concrete, while AISC permits up to 70 MPa (reflecting prevalence of high-strength concrete in US construction)
3. Deck reduction: CSA uses a single equation; AISC uses tabulated Rg and Rp values. For common profiles, results are within 10%

Try it now: Check your composite beam design with our free CA Beam Capacity tool

Related Pages

• CSA S16 Code Overview — Full CSA S16:24 design code reference
• CSA S16 Beam Design — Flexure & LTB — Bare steel beam design per CSA
• Composite Beam Design Guide — General Principles — Multi-code comparison
• Shear Stud Design — CSA S16 & AISC — Stud capacity across codes
• Steel Deck Types & Selection — Canadian deck profiles and gauges
• Steel Connection Design — CSA S16 — Welding for composite beams

This page is for educational reference. All formulae per CSA S16:24. Deck profiles are representative — confirm with manufacturer data. Results are PRELIMINARY — NOT FOR CONSTRUCTION without independent PE/SE verification.

Design Resources

Calculator tools

• Beam Bending and Shear Calculator
• Beam Deflection Calculator
• Beam Optimizer — Find Most Efficient Section
• Column Capacity Calculator
• Load Combinations — CSA S16 & NBCC

Design guides

• Composite Beam Design — Full Worked Example
• Composite Slab on Metal Deck — Design Guide
• Concrete on Steel Deck — Technical Reference
• Canadian Steel Beam Sizes
• Canadian Steel Grades — G40.21 Reference

Disclaimer: This content is for educational purposes only. Results must be verified by a licensed professional engineer. Steel Calculator provides preliminary design tools — NOT a substitute for professional engineering judgment.