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

Composite Beam Design Calculator

Design steel + concrete composite beams to EN 1994-1-1. Computes effective slab width (§5.4.1.2), plastic moment resistance Mpl,Rd (§6.2.1.2), shear connector resistance PRd (§6.6.3), degree of shear connection η (§6.6.1.2), and SLS deflection (§7.3.1).

Free composite beam design cheatsheet — 4-page A4 PDF
Concrete slab (h_c) b_eff h_a studs PNA
Beam Parameters
Results
491.35
Mpl,Rd (kNm)
1500
beff (mm)
Utilisation M_Ed / M_pl,Rd: 57.4% PASS
PNA location PNA in slab
Stud resistance P_Rd 81.66 kN
Shear connection η 0.572
η_min (§6.6.1.2) 0.49 OK
Studs required (total) 74
SLS deflection δ_total 3.64 mm
Limit L/250 32 mm PASS
1. Effective slab width b_eff (§5.4.1.2)
be1 = min(Le/8, bi/2) = min(8.0m/8, 1.500m) = 750 mm
be2 = 750 mm
beff = b0 + be1 + be2 = 0 + 750 + 750 = 1500 mm
2. Shear connector resistance P_Rd (§6.6.3)
d = 19mm, hsc = 100mm, hsc/d = 5.26
α = 1 (≥4.0 → α=1.0)
PRd1 = 0.8·fu·π·d²/4 / γV = 81.66 kN (shank)
PRd2 = 0.29·α·d²·√(fck·Ecm) / γV = 83.13 kN (concrete)
PRd = min(PRd1, PRd2) = 81.66 kN [governs: shank (eq.6.18)]
3. Plastic moment resistance M_pl,Rd (§6.2.1.2)
Fa = Aa·fyd = 2999.8 kN
Fc,full = 0.85·fck/γc·beff·hc = 3060 kN
Nc,full = min(Fa, Fc,full) = 2999.8 kN
PNA: PNA in slab
Mpl,Rd (full, η=1) = 783.48 kNm
4. Degree of shear connection η (§6.6.1.2)
Nf per half-span = Nc,full/PRd = 36.7
N studs per half = 37 → total = 74
η actual = 0.572 (ηmin = 0.49) → OK
Mpl,Rd (η=0.572) = 491.35 kNm
5. SLS deflection (§7.3.1)
n0 = Ea/Ecm = 210000/32837 = 6.4
nL = n0·(1+1.1·φt) = 6.4·(1+1.1·2.5) = 23.98
δG (long-term) = 1.47 mm
δQ (live) = 0.91 mm
δshrink = 1.25 mm
δtotal = 3.64 mm
Limit L/250 = 32 mm → PASS
Email calculation report
Enter your email to receive a formatted composite beam design report with clause references.
Run composite checks on every beam in your drawing set
FrameAI Pro extracts all members from your PDF and runs EN 1994-1-1 checks — M_pl,Rd, η, and deflection — in 90 seconds.
See Pro plans →
Related tools
Steel beam moment capacity (§6.2.5) Deflection check (§7.2) Section classification (Table 5.2) Lateral-torsional buckling (§6.3.2) 📄 Composite beam cheatsheet (PDF) EN 1994-1-1 Composite (simple)

FAQ

What is the effective slab width b_eff and how is it calculated?

Per EN 1994-1-1 §5.4.1.2, b_eff = b_0 + Σb_ei where b_ei = min(L_e/8, b_i/2) for each side. For a simply-supported beam L_e = span. b_0 is the distance between shear connector rows (= 0 for a single row). b_1, b_2 are the half-spacings to adjacent beams. A wider effective width increases the composite bending resistance.

What are the three PNA cases in EN 1994-1-1 §6.2.1.2?

The plastic neutral axis (PNA) location depends on the balance of forces. Case A: PNA in slab — concrete stress block depth a = N_pl,a / (0.85·f_cd·b_eff) < h_c, slab fully controls. Case B: PNA in steel top flange — concrete slab at full depth, top flange partially in compression. Case C: PNA in steel web — top flange fully compressed plus part of the web. In all cases the moment is computed by taking moments about the PNA.

What is the degree of shear connection η and what is the minimum?

η = N_c / N_c,f is the ratio of actual shear force transferred to the maximum possible. Full shear connection (η = 1.0) gives M_pl,Rd at maximum. For simply-supported beams EN 1994-1-1 §6.6.1.2 sets η_min = max(0.4, 1 − (355/f_y)(0.75 − 0.03L)) where L ≤ 25m. With partial shear connection the moment resistance is interpolated linearly between M_a,pl,Rd (steel alone) and M_pl,Rd (full interaction).

How is stud resistance P_Rd calculated?

Per EN 1994-1-1 §6.6.3: P_Rd = min(P_Rd1, P_Rd2). Shank failure: P_Rd1 = 0.8·f_u·π·d²/4 / γ_V. Concrete failure: P_Rd2 = 0.29·α·d²·√(f_ck·E_cm) / γ_V. α = 1.0 when h_sc/d ≥ 4, else α = 0.2(h_sc/d + 1). γ_V = 1.25 (EN recommended). f_u = 450 MPa for standard S-SD headed studs.

What modular ratios are used for deflection?

EN 1994-1-1 §7.3.1 / Table 5.2: short-term (live load) n_0 = E_a/E_cm ≈ 6–10. Long-term (creep, permanent G): n_L = n_0(1 + 1.1·φ_t) where φ_t ≈ 2.5 for indoor offices. Shrinkage: n_s = n_0(1 + 0.55·φ_t). The composite second moment of area I_comp is computed using the transformed slab area A_slab = b_eff·h_c/n. Total deflection = δ_G (long-term) + δ_Q (short-term) + δ_shrink.