Free Tool · EN 1994-1-1 §6.2 & §6.6 & §7.3

Composite Beam Calculator

A composite beam is a steel section bonded to a concrete slab with shear studs. The slab carries compression, the steel carries tension, and the studs lock the two together so they behave as a single unit. Enter your beam and slab details below. Get the design moment capacity, utilisation ratio, deflection, and how many studs you need — all backed by EN 1994-1-1. No sign-up, no PDF — just the numbers.

§6.2 Plastic moment §6.6.3 Stud resistance §7.3 Deflection §6.6.1 Degree of shear connection IPE · HEA · HEB C20/25 · C45/55

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Results EN 1994-1-1

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"Calculate" to get M_Rd, deflection and stud count.

Formulas

The Math Behind It

Bending resistance (EN 1994-1-1 §6.2.1):

Fa = Aa · fyd (steel axial force)

Fc = beff · hc · (0.85·fck/γc) (slab force)

PNA found by force equilibrium; lever arm → Mpl,Rd

Stud resistance (EN 1994-1-1 §6.6.3 eq.6.18/6.19):

PRd1 = (0.8 · fu · π·d²/4) / γV   (shank)

PRd2 = (0.29 · α · d² · √(fck·Ecm)) / γV   (concrete)

α = 1.0 for hsc/d ≥ 4, else 0.2(hsc/d + 1)

PRd = min(PRd1, PRd2)  ·  γV = 1.25

Degree of shear connection (EN 1994-1-1 §6.6.1.2):

η = Nc / Nf   where Nf = Fa / PRd

Minimum η from Table 6.1 (e.g. η ≥ 0.4 for L ≤ 5 m, η ≥ 0.55 for L ≥ 15 m)

Deflection (EN 1994-1-1 §7.3.1):

Modular ratio n = Ea / Ecm (transformed section)

Short-term: Ecm = 22000 · ((fck+8)/10)0.3 MPa

Creep: nL = n · (1 + φt) where φt = 2.5 typically

Δ = (5/384) · q · L&sup4; / (E·I)   for simply-supported

Verification — Worked Example

IPE 400, L = 8 m, C30/37, t_slab = 120 mm, b_eff = 2000 mm

Reference result

IPE 400 · L = 8 m · C30/37 slab (f_ck = 30 MPa, E_cm = 32837 MPa) · t_slab = 120 mm · b_eff = 2000 mm · G = 5 kN/m, Q = 10 kN/m

M_Ed = (1.35·5 + 1.5·10) · 8² / 8 = (6.75 + 15) = 21.75 kNm design moment

A_a = 8450 mm² · f_yd = 355 MPa → F_a = 2999 kN

F_c = 2000 · 120 · 0.85·30/1.5 / 1000 = 4080 kN → steel governs PNA

M_pl,Rd = 505.8 kNm (PNA falls in top flange) · Δ = 2.8 mm (L/2857) · studs total (both spans) ≈ 74

Learn More

Deep Dives

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EN 1994-1-1 Composite Design
Full reference for composite beams, columns, and shear connections in FrameAI.
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Office Floor Composite
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Full list of every EN 1993, EN 1994, EN 1992 check FrameAI supports.

FAQ

Common Questions

How does composite beam design work in Eurocode 4? ▾
A composite beam combines a steel section with a concrete slab via headed studs welded to the top flange. The concrete carries compression, the steel carries tension, and the studs transfer horizontal shear at the interface. EN 1994-1-1 §6.2 gives the plastic moment resistance M_pl,Rd — the method used when the steel section is class 1 or 2 and the slab is in uniform compression.
What is the effective slab width b_eff? ▾
EN 1994-1-1 §5.4.1.2 defines b_eff = b_0 + Σ b_ei where b_ei = min(L_e/8, b_i/2). For a simply-supported span, L_e = L. For an interior beam with slab on both sides, b_0 is the stud spacing across the web (typically 0) and b_1, b_2 are the distances from the beam centreline to the slab edges. A wider effective width increases the composite moment capacity.
How many shear studs do I need? ▾
EN 1994-1-1 §6.6.1.2 requires N_f studs minimum where N_f = F_a / P_Rd and F_a = A_a · f_yd (steel section axial force). The degree of shear connection η = N_c / N_f must meet the minimum from §6.6.1.2 Table 6.1 (e.g. for simply supported spans: η ≥ 0.4 for L ≤ 5 m, η ≥ 0.55 for L ≥ 15 m — linear interpolation between). Full shear connection (η = 1.0) gives the maximum moment capacity.
What is the stud spacing requirement? ▾
Studs must be spaced not more than 600 mm longitudinally along the beam. Transverse spacing must be at least 4d (or 5d for high-strength concrete) and not more than 2·h_sc. End studs must be within 300 mm of a concentrated load. For simply-supported beams with uniform loading, studs are typically distributed uniformly over the half-span adjacent to each support.
Why is deflection important for composite beams? ▾
EN 1994-1-1 §7.3.1 checks SLS deflection, usually L/250 for beams and L/300 for cantilevers. The deflection of a composite beam depends on whether the slab is effective (wet stage vs long-term). At construction stage (steel only), use E_a and I_a. In service, use the modular ratio n = E_a / E_cm to transform the concrete to an equivalent steel area, giving the long-term transformed section properties.
IPE 400 composite beam — why ~480 kNm for a typical design? ▾
IPE 400 (A = 8450 mm², f_yd = 355 MPa) gives F_a = 8450 × 355 / 1000 = 2999 kN. With a C30/37 slab (fck = 30 MPa, b_eff = 2000 mm, h_c = 120 mm) the full slab force F_c = 2000 × 120 × 0.85×30/1.5 / 1000 = 4080 kN, so the steel governs. PNA falls in the flange → M_pl,Rd ≈ 480 kNm. The exact value depends on where the PNA lands.
When can I use the plastic analysis method? ▾
EN 1994-1-1 §6.2.1 allows plastic analysis for composite sections when the steel is class 1 or 2, the concrete is in uniform compression, and the shear connection satisfies §6.6.1. For class 3 steel sections, use elastic analysis (§6.4). For continuous beams with moment redistribution, class 1 or 2 is required.

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