EN 1994-1-1 Composite Beam Design — Steel-Concrete with Headed Stud Connectors

Complete reference for EN 1994-1-1:2004 composite steel-concrete beam design. Covers the effective width of concrete flange (Clause 5.4.1.2), headed stud shear connector design (Clause 6.6), degree of shear connection (Clause 6.6.1.2), partial interaction theory, plastic moment resistance Mpl,Rd (Clause 6.2.1), elastic section properties for serviceability, and transverse reinforcement requirements (Clause 6.6.6). Includes a fully worked composite beam example with a UKB section and profiled steel decking.

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Composite Beam Design — Overview

Composite construction combines a steel beam acting compositely with a reinforced concrete slab through shear connectors (typically headed studs). EN 1994-1-1 governs the design of composite steel-concrete structures. For building floors, the most common form is a downstand steel beam (UKB or UKC) supporting a composite slab on profiled steel decking (e.g., ComFlor, Kingspan Multideck, SMD) with through-deck welded headed studs.

Key advantages of composite design over non-composite steel beams:

The design must consider two stages: (1) the construction stage where the steel beam alone supports the wet concrete and construction loads, and (2) the composite stage where the hardened concrete slab acts compositely with the steel beam for superimposed dead loads and imposed loads.

Material Properties

Concrete (EN 1992-1-1)

For UK building practice, C30/37 is typical for composite slabs on profiled decking. The concrete density for normal-weight concrete is 2,400 kg/m^3 (dry) to 2,500 kg/m^3 (wet). Lightweight concrete is also permitted under EN 1994-1-1 with modified connector resistances.

Structural Steel (EN 10025-2)

For composite beams, S355 is the standard grade. S460 is permitted but requires more shear connectors because the higher strength steel can develop a larger compression force in the concrete flange.

Headed Stud Connectors (EN ISO 13918)

Standard shear stud dimensions and material:

Effective Width of Concrete Flange (Clause 5.4.1.2)

The effective width beff of the concrete flange for a composite T-beam:

beff = b0 + sum(bei)

Where:

• b0 = distance between centres of the outstand shear connectors (0 for single-sided beam with one row of studs; b0 = 0 for the central beam in multi-beam systems)
• bei = min(Le/8, bi) for each side of the beam web
• Le = distance between points of zero bending moment (~ 0.7L to 0.85L for interior spans)
• bi = the actual geometric flange width on each side

Typical values for office floor grids:

For secondary beams at 3.0 m centres in a 9.0 m x 9.0 m grid: b1 = b2 = 1,500 mm, Le = 0.7 * 9.0 = 6.3 m, bei = min(6,300/8 = 788, 1,500) = 788 mm, beff = 0 + 788 + 788 = 1,576 mm. The effective concrete flange depth hc is the depth of concrete above the profiled deck ribs.

Headed Stud Shear Connector Resistance (Clause 6.6.3)

The design shear resistance of a headed stud with diameter d (19 mm standard):

PRd = min(0.8 * fu * pi * d^2 / (4 * gamma_V),          -- stud steel failure
           0.29 * alpha * d^2 * sqrt(fck * Ecm) / gamma_V) -- concrete cone failure

Where:

• fu = specified ultimate tensile strength of the stud material (max 450 MPa to EN ISO 13918, but 500 MPa may be used)
• gamma_V = 1.25 (UK NA)
• alpha = 0.2 * (hsc/d + 1) for 3 <= hsc/d <= 4; alpha = 1.0 for hsc/d > 4

For a 19 mm diameter stud, hsc = 100 mm (hsc/d = 5.26 > 4, alpha = 1.0), C30/37 concrete (fck = 30 MPa, Ecm = 33,000 MPa):

Stud steel: PRd,1 = 0.8 _ 450 _ pi _ 19^2 / (4 _ 1.25) = 0.8 _ 450 _ 283.5 / 1.25 = 102,060 / 1.25 = 81.6 kN Concrete cone: PRd,2 = 0.29 _ 1.0 _ 19^2 _ sqrt(30 _ 33,000) / 1.25 = 0.29 _ 361 _ sqrt(990,000) / 1.25 = 104.7 * 995 / 1.25 = 83.3 kN PRd = min(81.6, 83.3) = 81.6 kN (stud steel governs)

Reduction Factors for Profiled Steel Decking (Clause 6.6.4)

For decking ribs perpendicular to the beam (the most common case):

kt = (0.7 / sqrt(Nr)) * (b0 / hp) * (hsc / hp - 1)

Where:

• Nr = number of stud connectors in one rib (1 or 2)
• b0 = average rib width (mm)
• hp = overall depth of the profiled steel sheet (mm)
• hsc = stud height (mm), > hp + 2d

For ComFlor 60 (common UK trapezoidal deck): hp = 60 mm, b0 = 152 mm With Nr = 1 stud per rib, hsc = 100 mm: kt = (0.7 / sqrt(1)) _ (152 / 60) _ (100/60 - 1) = 0.7 _ 2.533 _ 0.667 = 1.183

But kt <= 1.0 (for Nr = 1), and kt <= kt,max = 0.85 for trapezoidal deck with Nr = 1. So kt = 0.85.

Reduced stud resistance: PRd,red = kt _ PRd = 0.85 _ 81.6 = 69.4 kN per stud.

Degree of Shear Connection — Partial Interaction (Clause 6.6.1.2)

Full shear connection means enough studs are provided so that the design moment resistance is limited by the bending capacity, not by the connector capacity. Partial shear connection means fewer studs are used and the moment resistance is reduced.

The degree of shear connection eta:

eta = n / nf

Where n is the number of studs provided and nf is the number for full shear connection.

For ductile connectors (all standard headed studs qualify), the minimum degree of shear connection is:

• For steel flanges of equal area in tension and compression: eta_min = 1 - (355/fy) * (0.75 - 0.03*Le) but eta_min >= 0.4
• For Le <= 25 m: eta_min = 1 - (355/fy) * (0.75 - 0.03*Le) >= 0.4

For S355 steel, Le = 9.0 m: eta_min = 1 - 1.0 * (0.75 - 0.27) = 1 - 0.48 = 0.52

The reduced moment resistance with partial interaction can be linearly interpolated between the steel-only moment resistance Mpl,a,Rd and the full-composite moment resistance Mpl,Rd:

M_Rd(eta) = Mpl,a,Rd + eta * (Mpl,Rd - Mpl,a,Rd)

This linear interpolation is permitted for ductile connectors and sections with equal flanges.

Plastic Moment Resistance Mpl,Rd (Clause 6.2.1)

The plastic moment resistance of a composite section depends on the position of the plastic neutral axis (PNA):

Case 1 — PNA in concrete flange (most common for typical UK floors): The concrete flange carries the full compression. The tension capacity of the steel section equals the compression capacity of the concrete:

Nc,f = 0.85 * fck * beff * hc / gamma_C  (compression in concrete)
Npl,a = Aa * fy / gamma_M0               (tension in steel)

If Nc,f >= Npl,a, the PNA is in the concrete flange (Case 1, most common). The moment resistance:

Mpl,Rd = Npl,a * (ha/2 + hc - Npl,a / (2 * 0.85 * fck * beff / gamma_C))

Where ha is the steel section depth, hc is the concrete flange depth above deck.

Case 2 — PNA in steel top flange or web: If Nc,f < Npl,a, the PNA is in the steel section. This occurs with shallow slabs or deep steel sections.

Worked Example — UKB 457x191x67, S355, C30/37

Beam: UKB 457x191x67 (Aa = 8,550 mm^2, ha = 453.6 mm, Wpl,y = 1,470 cm^3) Slab: C30/37, hc = 80 mm (above ComFlor 60 deck), beff = 1,576 mm gamma_C = 1.50 (concrete partial factor) gamma_M0 = 1.00

Concrete compression capacity: Nc,f = 0.85 _ 30 _ 1,576 _ 80 / 1.50 = 0.85 _ 30 * 126,080 / 1.50 = 3,215,040 / 1.50 = 2,143,360 N = 2,143 kN

Steel tension capacity: Npl,a = 8,550 * 355 / 1.00 = 3,035,250 N = 3,035 kN

Nc,f = 2,143 kN < Npl,a = 3,035 kN. The PNA is in the steel top flange (Case 2 region).

The compression flange + part of the web provides the balance of compression: Nac = (Npl,a - Nc,f) / 2 = (3,035 - 2,143) / 2 = 446 kN in the steel compression zone.

The additional steel compression balances the remaining tension. For a UKB with equal flanges:

Mpl,Rd ~ Npl,a _ ha/2 + Nc,f _ (ha/2 + hc/2) - (Npl,a - Nc,f)^2 / (4 _ tw _ fy / gamma_M0)

Using approximate values: Mpl,Rd ~ 3,035 _ 0.227 + 2,143 _ (0.227 + 0.040) - (892)^2 / (4 _ 8.5 _ 355) ~ 689 + 572 - 795,000 / 12,070 ~ 689 + 572 - 66 ~ 1,195 kN.m

This is 2.3x the non-composite Mc,Rd = 522 kN.m, demonstrating the significant advantage of composite construction.

Worked Example — Full Composite Beam Design

Problem: Design a composite secondary beam for an office floor. Beam span 9.0 m, beams at 3.0 m centres. Slab: 130 mm overall, ComFlor 60 deck (hp = 60 mm), hc = 70 mm above deck ribs. Concrete: C30/37, normal weight. Steel: S355. The beam supports:

• Construction stage: steel deck + wet concrete = 3.0 kN/m^2, construction live load 0.75 kN/m^2
• Composite stage: raised floor + services + ceilings = 1.5 kN/m^2 dead, imposed load 4.0 kN/m^2

Beam self-weight initially estimated: 0.70 kN/m (UKB 457x191x67).

Step 1 — Construction Stage (Steel Beam Alone)

Ultimate load: w*Ed,c = 1.35 * (3.0 _ 3.0 + 0.70) + 1.5 _ (0.75 _ 3.0) = 1.35 _ 9.70 + 1.5 _ 2.25 = 13.10 + 3.38 = 16.48 kN/m

M_Ed,c = 16.48 * 9.0^2 / 8 = 166.9 kN.m Utilisation (UKB 457x191x67): Mc,Rd = 522 kN.m → 166.9/522 = 0.32 — OK at construction stage.

Step 2 — Composite Stage Loading

Superimposed: w*Ed = 1.35 * (1.5 _ 3.0) + 1.5 _ (4.0 _ 3.0) = 1.35 _ 4.50 + 1.5 _ 12.0 = 6.08 + 18.0 = 24.08 kN/m

M_Ed = 24.08 * 9.0^2 / 8 + 166.9 (construction) = 243.8 + 166.9 = 410.7 kN.m Note: The construction moment remains on the steel section alone because at that stage the concrete had not hardened.

Step 3 — Effective Width

Le = 0.7 * 9.0 = 6.3 m bei = min(6,300/8, 1,500) = 788 mm beff = 0 + 788 + 788 = 1,576 mm

Step 4 — Plastic Moment Resistance

From earlier calculation: Mpl,Rd ~ 1,195 kN.m (approximate — use software for exact value with PNA iteration).

Utilisation: 410.7 / 1,195 = 0.344 — OK, significantly under-utilised. A lighter section UKB 406x178x54 (Mc,Rd = 264 kN.m, but Wpl,y = 927 cm^3) could be considered. Composite Mpl,Rd would be correspondingly lower.

Step 5 — Shear Connector Design

Number of studs for full shear connection: nf = Nc,f / PRd,red = 2,143 / 69.4 = 30.9 → rounds to 31 studs each side of midspan → 62 studs total.

With ribs at 300 mm centres over 9.0 m: n_available = 9,000 / 300 = 30 ribs. One stud per rib each side gives 30 per half-span = 30 < 31 required.

Option 1: Use 2 studs per rib (Nr = 2), kt = (0.7/sqrt(2)) _ (152/60) _ (100/60 - 1) = 0.495 _ 2.533 _ 0.667 = 0.837, but kt,max = 0.70 for Nr = 2. PRd,red = 0.70 _ 81.6 = 57.1 kN. nf = 2,143 / 57.1 = 37.5 → 38 studs per half-span. 30 ribs _ 2 = 60 available > 38 required — OK.

Option 2: Use partial shear connection with eta = 0.75, which satisfies the minimum eta*min = 0.52. MRd(0.75) = 264 + 0.75 * (1,195 - 264) = 264 + 698 = 962 kN.m > 410.7 — OK. Studs needed: 0.75 _ 31 = 23.3 → 24 studs per half-span. 30 ribs with 1 stud each: 30 > 24 — OK.

Step 6 — Deflection (Serviceability)

Composite second moment of area Ic (short-term, uncracked concrete) must be calculated using transformed section analysis:

n0 = Ea / Ecm = 210,000 / 33,000 = 6.36

The concrete area is divided by n0 to give an equivalent steel area. Ic for this beam is typically 3-5x Iy,steel alone:

delta = 5 _ w_SLS _ L^4 / (384 _ Ea _ Ic) w*SLS,n = 4.0 * 3.0 = 12.0 kN/m (imposed only, unfactored) Ic ~ 4.0 _ 29,400 = 117,600 cm^4 (approximate, 4x steel Iy)

delta = 5 _ 12.0 _ 9,000^4 / (384 _ 210,000 _ 117,600e4) = 5 _ 12.0 _ 6.561e15 / (384 _ 210,000 _ 1.176e9) = 3.937e17 / 9.489e15 = 41.5 mm

Limit L/360 = 9,000/360 = 25.0 mm — this exceeds the limit. Pre-camber or a deeper section is required.

Pre-camber of 20 mm (L/450) would reduce the net deflection to 21.5 mm < 25.0 mm — OK.

Conclusion: UKB 457x191x67 with 30 ribs * 1 stud per rib per half-span (partial shear connection eta ~ 0.97) is adequate for strength. Pre-camber 20 mm for deflection. A more economic solution might use UKB 406x178x74 with full shear connection and no camber — a cost comparison should be made.

Frequently Asked Questions

What is the difference between full and partial shear connection in composite beams?

Full shear connection means the number of studs n >= nf such that Mpl,Rd is governed by section bending capacity, not by stud capacity. Partial shear connection (eta = n/nf < 1.0) uses fewer studs, and the moment resistance is reduced by M_Rd = Mpl,a,Rd + eta * (Mpl,Rd - Mpl,a,Rd). EN 1994-1-1 permits partial interaction for ductile connectors (all standard headed studs) provided eta >= eta_min where eta_min depends on the steel grade and span. For S355 beams with Le up to 25 m, eta_min ranges from 0.4 to 0.52. Partial interaction is economical when the full composite capacity is not needed.

How do profiled steel decking ribs affect shear connector design?

Decking ribs perpendicular to the beam reduce stud capacity through the factor kt per EN 1994-1-1 Clause 6.6.4. For trapezoidal decking (standard UK practice, ComFlor, Kingspan Multideck), kt depends on the number of studs per rib Nr, the rib width b0, and deck depth hp. For one stud per rib: kt = 0.85 (maximum). For two studs per rib: kt = 0.70. The stud must project at least 2d (38 mm for 19 mm studs) above the top of the deck rib.

What is the effective width of the concrete flange and why is it limited?

The effective width beff = b0 + Le/8 each side (capped by geometric width) accounts for shear lag — the concrete flange remote from the beam web experiences less longitudinal stress due to in-plane shear flexibility. EN 1994-1-1 Clause 5.4.1.2 limits the effective width so that a uniform stress block assumption is valid for section analysis. The equivalent span Le depends on the moment diagram: Le = 0.85L for simply supported beams under UDL, 0.70L at interior supports in continuous beams, and 0.25(L1+L2) for cantilevers.

How is the construction stage checked for composite beams?

The steel beam alone must resist the construction loads (wet concrete weight, deck weight, self-weight, construction live load 0.75-1.5 kN/m^2) as a non-composite section per EN 1993-1-1. The beam may require temporary propping if the construction stage utilisation exceeds 1.0. Unpropped construction is preferred for speed and cost, so the steel section must be adequate for the construction moment M_Ed,c. For long spans, propping at midspan or third points can halve the construction moment, allowing a lighter steel section with lower embodied carbon.

Can EN 1994-1-1 composite design be used with lightweight concrete?

Yes. EN 1994-1-1 permits lightweight aggregate concrete (LWAC) with density classes LC1.8 to LC2.0. The stud resistance formulae are modified: PRd for concrete cone failure uses a factor eta_E = (rho/2200)^2, and the effective modulus Ecm is reduced per EN 1992-1-1 Clause 11.3.2. For LWAC with rho = 1,800 kg/m^3: eta_E = (1,800/2,200)^2 = 0.669, reducing the concrete cone resistance by 33%. Stud capacity is typically governed by concrete cone rather than stud steel for LWAC.

Related Pages

• EN 1993-1-1 Beam Design — Flexure, Shear & LTB
• EN 1993-1-8 Connection Design — Bolts, Welds & Fin Plates
• EN 1993 Steel Grades — S235, S275, S355, S460
• EN 1993 Column Buckling — Curves a0-d
• EN 1993 Cold-Formed Steel Design
• Beam Capacity Calculator — Free Online Tool
• Column Capacity Calculator — Free EN 1993 Tool

Educational reference only. Verify all design values against the current EN 1994-1-1, the applicable National Annex, and the SCI/BCSA design guides (SCI P300 — Composite Slabs and Beams Using Steel Decking). Composite design is project-specific — always check the published design tables for the specific decking product. Results are PRELIMINARY — NOT FOR CONSTRUCTION without independent verification by a qualified structural engineer.