--------------- | --- | --- | ----------------- | ------------------ | | 100 | 5.3 | 1.0 | 82.5 | 66.0 | | 125 | 6.6 | 1.0 | 82.5 | 66.0 | | 150 | 7.9 | 1.0 | 82.5 | 66.0 |

In troughs of profiled sheeting, the stud resistance is reduced by factor kt (typically 0.8 for ribs perpendicular to beam).

Degree of Shear Connection

Actual degree of shear connection: ( N / N_f ) where N = number of studs provided, Nf = number for full shear connection.

Minimum degree of shear connection per EN 1994-1-1 Clause 6.6.1.2:

• For beams with span ≤ 25 m: ( N/N_f \geq \min(1.0, 1.0 - 0.04L) ) where L is span in metres
• For L = 8 m: minimum = 1.0 - 0.04 × 8 = 0.68

Worked Example — 533×210 UB 92 Composite Beam

Given:

• Span: 8000 mm, simply supported
• Beam spacing: 4000 mm
• Slab: 130 mm deep C30/37 (fck = 30 MPa), on 60 mm profiled metal decking
• Total slab depth: 190 mm (60 deck + 130 concrete above flute)
• Steel: S355 (fy = 355 MPa)
• Studs: 19 mm × 100 mm, in pairs per trough
• Loading: dead 4.5 kN/m², imposed 3.5 kN/m²

Step 1 — Effective width: beff = 2 × min(8000/8, 4000/2) = 2 × 1000 = 2000 mm

Step 2 — Design loads for sagging (simply supported): Dead load: 4.5 kN/m² → 4.5 × 4.0 = 18.0 kN/m (beam self-weight + slab + finishes) Imposed: 3.5 kN/m² → 3.5 × 4.0 = 14.0 kN/m Ultimate: qEd = 1.35 × 18.0 + 1.5 × 14.0 = 45.3 kN/m MEd = 45.3 × 8.0² / 8 = 362.4 kNm

Step 3 — Steel beam data (533×210 UB 92): Aa = 11700 mm², Wpl,y = 2616 cm³, h = 533.1 mm

Step 4 — Determine PNA position: Plastic compression capacity of concrete: Nc,f = 0.85 fcd × beff × hc (hc = 130 mm) fcd = αcc fck / γc = 0.85 × 30 / 1.5 = 17.0 N/mm² Nc,f = 0.85 × 17.0 × 2000 × 130 × 10⁻³ = 3757 kN

Plastic tension capacity of steel: Na = 11700 × 355 / 1.0 × 10⁻³ = 4154 kN

Since Na > Nc,f, the PNA lies in the steel flange. Full shear connection requires Nc = Na.

Step 5 — Sagging moment resistance (simplified plastic method): Mpl,Rd = Na × h/2 + Nc,f × (hc/2 + hp) - Nc,f²/(4 b tf fy/γM0) × (tf)

Using the standard lever arm approach: For full shear connection: Mpl,Rd ≈ 2616 × 355/1.0 × 10⁻³ + 3757 × (0.130/2 + 0.060) ≈ 929 + 470 = 1399 kNm

This is a simplification. The exact value depends on PNA position. Conservatively: Mpl,Rd > 362 kNm → UT ≈ 0.26 — Satisfactory (composite action provides substantial extra capacity)

Step 6 — Shear connector design: Number of studs for full shear connection: Nf = Na / PRd PRd = min(0.8 × 450 × π × 19²/4, 0.29 × 1.0 × 19² × √(30 × 33000)) / 1.25 × 10⁻³ = min(102.1 kN, 83.1 kN) / 1.25 × 10⁻³ = 66.5 kN per stud (in solid slab)

In decking: PRd × kt = 66.5 × 0.8 = 53.2 kN per stud

Nf = 4154 / 53.2 = 78 studs (total for half-span) Number per trough (300 mm centres): 78 / (8000/2 / 300) = 78 / 13.3 = 6 → use 2 per trough = 26 studs total over half-span Actual N = 26 × 2 (both directions) = 52 total for full span

Step 7 — Check degree of shear connection: N/Nf = 52 / (78 × 2) = 0.33 (too low — minimum 0.68)

Increase to 3 studs per trough → 78 / (8000/600 × 3) = 78/40 = needs ~40, use 2 per trough in more locations

Design Resources

• UK Beam Design — Steel beam design
• UK Steel Properties — Material data
• UK Steel Beam Sizes — Section dimensions
• UK Deflection — Serviceability limits
• UK Framing Systems — Structural stability
• UK Vibration — Floor vibration design
• All UK References

Frequently Asked Questions

How does EN 1994-1-1 address composite beam design?

EN 1994-1-1 provides design rules for steel-concrete composite beams. Sagging moment resistance uses plastic theory with a rectangular stress block for concrete (0.85 fcd at 0.8× depth). UK NA modifies the stress block parameters: uses αcc = 0.85 for concrete in compression (and confirms γc = 1.50). The effective width is taken as beff = b0 + Σ be1 where bei = Le/8 (Clause 5.4.1.2). For continuous beams, 15% moment redistribution is allowed at internal supports for Class 1 sections.

What shear connector types are used in UK composite construction?

Headed stud connectors per EN 1994-1-1 Clause 6.6: typically 19 mm diametre × 100 mm or 125 mm long. UK NA specifies partial safety factor γV = 1.25 for stud connectors. Studs are welded through the profiled metal decking using a drawn-arc stud welding process. Standard spacing: minimum 5d longitudinally (95 mm for 19 mm studs), maximum 600 mm. Stud height after welding must be ≥ 75 mm for 19 mm studs.

What is partial shear interaction in composite beams?

Partial shear interaction occurs when fewer shear connectors are provided than required for full composite action. This reduces the sagging moment capacity because the steel and concrete cannot fully develop their plastic resistance. EN 1994-1-1 Clause 6.2.1.3 gives the moment resistance for partial shear connection using an interaction formula that depends on the ratio N/Nf. The minimum degree of shear connection per Clause 6.6.1.2 depends on span: for an 8 m span, minimum = 0.68 (i.e., at least 68% of full connection is required).

How is longitudinal shear checked in composite slabs?

Longitudinal shear in the concrete slab is checked per EN 1994-1-1 Clause 6.7. The design shear flow at the steel-concrete interface is VEd × S / I, where S is the first moment of area of the concrete flange. The shear resistance is provided by: (a) the headed stud connectors themselves, and (b) transverse reinforcement in the slab (typically A142 or A193 mesh for UK construction). The reinforcement ratio for longitudinal shear: Asf/sf ≥ 0.002 × heff × spacing.

What deflection criteria apply to composite beams?

Composite beam deflection must account for: (a) the non-composite construction stage (steel beam alone supports wet concrete self-weight), (b) the composite stage under imposed loads, and (c) creep and shrinkage of the concrete slab. The UK NA to EN 1994-1-1 recommends: δmax ≤ L/300 for total deflection, δ2 ≤ L/350 for imposed (live) deflection under characteristic combination. Camber is typically provided equal to the deflection under self-weight + 50% of imposed load to achieve a level finished floor.

Reference only. Verify all values against the current edition of EN 1994-1-1:2004 and UK NA. This information does not constitute professional engineering advice.