Box Culvert Design Calculations Eurocode 2021 • Complete & Real

Load combination (example ULS per EN 1990):

Combination for SLS: characteristic or quasi-permanent factors (ψ factors) per EN 1990/EN 1991.

  • Shear at supports Vmax = qd·L/2 = 195 * 2.10 / 2 = 204.75 ≈ 205 kN.

    • Key formulae (compact):

  • Provide practical reinforcement: use 4Ø12 bars (area per bar Ø12 = 113 mm² → 4×113 = 452 mm²) — too small. Use 6Ø16 bars: area Ø16 = 201 mm² → 6×201 = 1206 mm² (close). Use 7Ø16 = 1407 mm² — choose 7Ø16 per meter run (arrange as distributed mesh or two layers). Alternatively provide top reinforcement for negative moment at supports as 3Ø12 per support. Note: distribute as per detailing rules.

    • For hydraulic structures, crack widths ≤ 0.2 mm (for watertightness) are typical in 2021 designs.

    Additionally, ensure minimum reinforcement for crack control at all tension zones: A_s,min = k_c × k × f_ct,eff × A_ct / σ_s. box culvert design calculations eurocode 2021

    Model: 2D rigid frame with fixed supports at base (or pinned – but soil-structure interaction often simplified to fixed for small culverts).
    Software or manual using moment distribution/coefficients.

    Load cases:

    Envelope moments (kNm/m):

    From analysis (typical for 3×2 box with 0.25m thickness): Load combination (example ULS per EN 1990):

    | Location | M_max (kNm/m) | M_min (kNm/m) | |----------|--------------|---------------| | Top slab – midspan | +45 (sagging) | - | | Top slab – support | -35 (hogging) | - | | Wall – top end | -35 | +? | | Wall – mid-height | +/- 12 | - | | Bottom slab – midspan | +38 | - |

    Use M_Ed = 45 kNm/m for top slab reinforcement design (sagging). Shear at supports Vmax = qd·L/2 = 195 * 2

  • VRd,c ≈ 199 kN < VEd 205 kN → shear reinforcement required. Provide stirrups: design shear reinforcement VRd,s = (Asw/s)·z·fyw·cotθ, choose θ = 45° (cotθ=1), fyw = 500 N/mm², z≈0.9d = 189 mm. Required Asw/s = (VEd - VRd,c)/(z·fyw·cotθ) = (205e3 - 199e3)/(189*500) = 6e3 / 94,500 ≈ 0.0635 mm²/mm = 63.5 mm² per 1000 mm → per meter Asw = 63.5 mm². For stirrups Ø8 single leg area Asw per stirrup leg = 50.3 mm² (Ø8 area = 50.3). If two-legged stirrup provides 100.6 mm² per stirrup spaced s = (100.6 / 63.5)*1000 ≈ 1584 mm (too wide). Use single Ø8 stirrups @ 150 mm c/c (Asw/s = 50.3/150 = 0.335 mm²/mm = 335 mm²/m > required) — conservative but OK. So provide Ø8 @150 mm c/c.