Free Tool · EN 1994-1-1 §6.2 §7.3

Composite Beam Design Calculator

Design a steel–concrete composite beam to EN 1994-1-1. Computes effective slab width beff (§5.4.1.2), plastic moment resistance Mpl,Rd (§6.2.1) with PNA location, shear resistance Vpl,Rd (§6.2.2), minimum degree of shear connection η (§6.6.1.2), and deflection check against L/250 (§7.3.1).

Inputs

Section & material
Geometry
Loading
Design options
Effective width
1500
b_eff mm
Moment resistance
783.48 PASS
M_pl,Rd kNm
Shear resistance
657.5 PASS
V_pl,Rd kN
Deflection
3.54 PASS
Deflection δ mm

Section diagram — composite cross-section

1. Effective slab width b_eff — §5.4.1.2 ▼
EN 1994-1-1 §5.4.1.2
b_e = min(L_e/8, b_i/2)
b_eff = b_0 + b_e1 + b_e2

b_eff = 1500 mm
2. Plastic moment resistance M_pl,Rd — §6.2.1 ▼
EN 1994-1-1 §6.2.1
N_pl,a = A_a · f_yd = 2999.8 kN
N_c,f = b_eff · h_c · 0.85·f_cd = 3060 kN
N_c = η · min(N_pl,a, N_c,f) = 2999.8 kN
PNA: slab

M_pl,Rd = 783.48 kNm
M_Ed = 270 kNm
M_Ed/M_pl,Rd = 0.345 PASS
3. Shear resistance V_pl,Rd — §6.2.2 ▼
EN 1994-1-1 §6.2.2
A_v = (h − 2·t_f) · t_w
V_pl,Rd = A_v · f_yd / √3

V_pl,Rd = 657.5 kN
V_Ed = 135 kN
V_Ed/V_pl,Rd = 0.205 PASS
4. Degree of shear connection η — §6.6.1.2 ▼
EN 1994-1-1 §6.6.1.2
η_min = 1 − (355/f_y)·(0.75 − 0.03·L) ≥ 0.4

η_min = 0.49
η provided = 1 PASS

N_c = 2999.8 kN → use shear stud tool for stud sizing
Total studs needed (19mm ∅): 74
5. Deflection check — §7.3.1 ▼
EN 1994-1-1 §7.3.1
n_0 = E_a / E_cm = 6.4
n_L = n_0 · (1 + 1.1·φ) (φ = 2.5, indoor)

δ_total = 3.54 mm
Limit L/250 = 32 mm
L/δ = 2257 PASS

Summary checks

Check Design Resistance Ratio Result
Bending M_Ed/M_pl,Rd (§6.2.1) 270 kNm 783.48 kNm 0.345 ✓ PASS
Shear V_Ed/V_pl,Rd (§6.2.2) 135 kN 657.5 kN 0.205 ✓ PASS
Shear connection η ≥ η_min (§6.6.1.2) η = 1 η_min = 0.49 — ✓ PASS
Deflection δ ≤ L/250 (§7.3.1) 3.54 mm 32 mm L/2257 ✓ PASS

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Related tools

→ Shear stud design (EN 1994-1-1 §6.6) → Endplate moment connection (EN 1993-1-8 §6.2) → Lateral torsional buckling (EN 1993-1-1 §6.3.2)

FAQ

How is the effective slab width b_eff calculated to EN 1994-1-1? ▼
Per §5.4.1.2, b_eff = b_0 + Σb_ei where b_ei = min(L_e/8, b_i/2). L_e is the equivalent span (= span for simply supported). b_0 is the distance between stud centrelines (0 for a single stud row). b_1 and b_2 are distances from the stud row to the slab edges. For an interior beam with s=3m and L=8m: b_e = min(8000/8, 1500/2) = min(1000, 750) = 750mm each side → b_eff = 1500mm.
How is M_pl,Rd determined — what are the three PNA cases? ▼
EN 1994-1-1 §6.2.1 uses plastic theory. The plastic neutral axis (PNA) is found by force equilibrium: F_a = A_a·f_yd (steel tension) vs F_c = b_eff·h_c·0.85·f_cd (concrete compression). Case 1 — PNA in slab: compression block depth a = N_c/(b_eff·f_cd) < h_c. Case 2 — PNA in steel top flange: slab fully in compression, small zone of steel top flange in compression. Case 3 — PNA in web: both flanges and part of the web used. M_pl,Rd is summed as N_c × lever arm to resultant.
What is the minimum degree of shear connection η_min? ▼
Per §6.6.1.2 for simply supported beams: η_min = 1 − (355/f_y)·(0.75 − 0.03·L) ≥ 0.4 for L ≤ 25m; η_min = 1.0 for L > 25m. For S355 and L=8m: η_min = 1 − 1.0·(0.75 − 0.24) = 0.51. This means at least 51% of full shear connection studs are required.
How is deflection checked for a composite beam to EN 1994-1-1 §7.3.1? ▼
Deflection uses elastic composite section stiffness EI. Modular ratio n_0 = E_a/E_cm for short-term (live Q); long-term n_L = n_0·(1 + 1.1·φ_t) for permanent G with creep (φ_t ≈ 2.5). Composite second moment I_comp is calculated for both, then δ = 5wL⁴/(384EI). Total δ_total = δ_G + δ_Q + δ_shrink ≤ L/250 per EN 1990 recommended limit.