Design Shear Resistance — Clause 6.6.3.1

The design shear resistance of a headed stud is the minimum of:

P_Rd = min(0.8 × f_u × π × d² / 4 / γ_V, 0.29 × α × d² × √(f_ck × E_cm) / γ_V)

Where:

The first term represents stud shank failure. The second term represents concrete cone failure.

Stud Resistance Table

Stud Grade — EN ISO 13918 (f_u = 450 MPa typical)

Stud Diameter h_sc (mm) h_sc/d α Steel Failure Concrete Failure (C30/37) P_Rd (kN)
19 mm 100 5.3 1.0 81.4 kN 69.5 kN 69.5
19 mm 125 6.6 1.0 81.4 kN 69.5 kN 69.5
22 mm 100 4.5 1.0 109.1 kN 93.2 kN 93.2
22 mm 125 5.7 1.0 109.1 kN 93.2 kN 93.2
25 mm 100 4.0 1.0 141.4 kN 120.3 kN 120.3
25 mm 125 5.0 1.0 141.4 kN 120.3 kN 120.3

For h_sc/d ≥ 4, h_sc ≥ 4d, α = 1.0 (applies to all standard studs). The concrete failure mode governs for all C30/37 concrete.

Effect of Concrete Grade (22 mm stud, h_sc = 100 mm)

Concrete Grade f_ck (MPa) E_cm (GPa) P_Rd (kN)
C25/30 25 31.0 80.7
C30/37 30 33.0 93.2
C35/45 35 34.0 104.2
C40/50 40 35.0 114.3
C50/60 50 37.0 133.8

Degree of Shear Connection — Clause 6.6.1.2

The degree of shear connection η is:

η = N_c / N_c,f

Where N_c is the compressive force in the concrete (from the number of shear connectors) and N_c,f is the compressive force at full shear connection (concrete or steel section capacity, whichever is less).

Minimum Degree of Shear Connection

For steel sections with equal flanges and L ≤ 25 m:

Span L Minimum η
L ≤ 5 m 0.40
5 < L ≤ 10 m 0.40 + 0.03 × (L - 5)
10 < L ≤ 25 m 0.55

For L = 8 m: minimum η = 0.40 + 0.03 × 3 = 0.49.

Worked Example — IPE 300 Composite Beam

Parameter Value
Beam IPE 300, S355
Concrete slab 150 mm deep, C30/37
Effective width 1500 mm
Span 8.0 m
Studs 19 mm × 100 mm

Shear Connection Design

Parameter Value
P_Rd (19 mm, C30/37) 69.5 kN
N_c,f (full connection) min(A_a × f_y / γ_M0, b_eff × h_c × 0.85 × f_ck / γ_c)
A_a × f_y / γ_M0 5380 × 355 / 1.00 = 1910 kN
b_eff × h_c × 0.85 f_ck / γ_c 1500 × 100 × 0.85 × 30 / 1.50 = 2550 kN
N_c,f 1910 kN (steel governs)
Studs for full connection 1910 / 69.5 = 27.5 ≈ 28 studs
Minimum η (L = 8 m) 0.49
Minimum studs 0.49 × 28 = 14 studs
Provide 20 studs (2 rows of 10, 200 mm spacing)

Design decision: 20 studs provides η = 20/28 = 71% shear connection, exceeding the minimum 49%. The beam achieves 71% of full composite action, significantly improving stiffness and strength over non-composite design.

Second Worked Example — HE 240A Composite Beam

Parameter Value
Beam HEA 240, S355
Concrete slab 130 mm deep, C30/37
Effective width 1800 mm
Span 10.0 m
Studs 22 mm × 125 mm

Shear Connection Design

Parameter Value
P_Rd (22 mm, C30/37) 93.2 kN
N_c,f (full connection) min(A_a × f_y / γ_M0, b_eff × h_c × 0.85 × f_ck / γ_c)
A_a × f_y / γ_M0 7680 × 355 / 1.00 = 2726 kN
b_eff × h_c × 0.85 f_ck / γ_c 1800 × 80 × 0.85 × 30 / 1.50 = 2448 kN
N_c,f 2448 kN (concrete governs)
Studs for full connection 2448 / 93.2 = 26.3 ≈ 27 studs
Minimum η (L = 10 m) 0.40 + 0.03 × (10 - 5) = 0.55
Minimum studs 0.55 × 27 = 15 studs
Provide 30 studs (2 rows of 15, 300 mm spacing)

Design decision: 30 studs provides η = 30/27 ≈ 111% — essentially full shear connection. The stiffer composite section reduces deflection by approximately 40% compared to the bare steel beam.

Stud Welding and Quality Control

Stud Welding Process per EN 14555

Headed shear studs are attached to the steel beam top flange via drawn-arc stud welding (EN 14555). The process uses a ceramic ferrule to contain the weld pool and form the fillet at the stud base.

Key quality requirements:

Stud Placement Through Steel Decking

When studs are welded through profiled steel decking (common in composite slab construction), P_Rd is reduced per EN 1994-1-1 Clause 6.6.4:

Reduction factor k_t: k_t = (0.7 / √N_r) × (b_o / h_p) × (h_sc / h_p - 1) ≤ 1.0

Where:

For decking parallel to the beam, no reduction if the deck is continuous over the beam. For decking transverse, the reduction typically ranges from 0.7 to 0.9 depending on stud-in-rib positioning.

Important: The maximum reduction for studs through decking is k_t × P_Rd, and k_t ≥ 0.5 is required for the connection to be classified as ductile per Clause 6.6.1.2(5).

Detailing Requirements — Clause 6.6.5

Parameter Requirement
Stud height h_sc h_sc ≥ 4d (≥ 76 mm for 19 mm stud)
Stud spacing long. min 5d, max 6 × slab depth or 800 mm
Stud spacing trans. min 4d, max 600 mm
Cover to stud edge min 20 mm in solid slab
Stud head diameter ≥ 1.5d
Stud head height ≥ 0.4d

Frequently Asked Questions

What is the design shear resistance of a 19 mm headed stud in C30/37 concrete per EN 1994-1-1?

The design resistance of a 19 mm × 100 mm headed stud in C30/37 concrete is P_Rd = 69.5 kN. This is governed by the concrete failure mode (0.29 × α × d² × √(f_ck × E_cm) / γ_V = 69.5 kN) rather than the steel shank failure mode (81.4 kN).

What is the minimum degree of shear connection for composite beams per EN 1994-1-1?

Per Clause 6.6.1.2, the minimum degree of shear connection η depends on the span. For spans ≤ 5 m, η_min = 0.40. For spans > 25 m, η_min = 0.55. Between 5 and 25 m, linear interpolation applies: η = 0.40 + 0.03 × (L - 5). For an 8 m span, η_min = 0.49 (49% of full shear connection).

How does stud height affect the design shear resistance? Per the α correction factor (Clause 6.6.3.1(3)), when h_sc/d ≥ 4, α = 1.0 and stud height has no effect on P_Rd. When 3 ≤ h_sc/d < 4, α = 0.2 × (h_sc/d + 1) ≤ 1.0, reducing the concrete failure term. Stud heights below 3d are not permitted. In practice, standard 100 mm studs with 19 mm diameter (h_sc/d = 5.3) operate in the α = 1.0 range.

What is the difference between ductile and non-ductile shear connectors? Ductile connectors (Clause 6.6.1.2) have sufficient deformation capacity to allow redistribution of longitudinal shear between studs at failure. Headed studs with h_sc/d ≥ 4 and 16 ≤ d ≤ 25 mm are classified as ductile, permitting the use of partial shear connection (η < 1.0). Non-ductile connectors require full shear connection (η = 1.0) or justification by testing.

Can studs be welded to the underside of the top flange? No. Shear studs must be welded to the top surface of the top flange of the steel beam. Welding to the underside is not permitted because the concrete slab bears on the top flange, and the studs must project into the compression zone of the concrete. Welding to the web or bottom flange provides no composite action.

What happens if stud spacing exceeds the maximum limit? Per Clause 6.6.5.7, the maximum longitudinal spacing is 6 × h_c (slab depth) or 800 mm, whichever is smaller. Exceeding this limit can cause slip concentration and premature failure of individual studs. The minimum spacing (5d longitudinally) ensures adequate concrete between studs to develop the bearing stress.

Related Pages

Educational reference only. Design per EN 1994-1-1:2004 Clauses 6.6 and 6.7. γ_V = 1.25. f_u for studs per EN ISO 13918 (typical 450 MPa). Verify stud weld quality per EN 14555. Results are PRELIMINARY — NOT FOR CONSTRUCTION without independent verification.

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