Jacked RC Pipe Strength & Crack Verification
Ultimate limit state (vertical/side soil pressure, self weight, internal water weight, ground surcharge) and serviceability limit state (crack width ωmax — flexural and large-eccentric-tension) for d2600 / d1800 jacked reinforced-concrete pipes, each with an OK / fail verdict.
kN/m
kN/m
mm
mm
m
kN/m³
°
kN/m²
kN/m³
kN/m³
kN/m²
Outer diameter D1—m
Cover to ground Hs—m
Active soil coeff. Ka—
Influence width Bt—m
Soil pressure coeff. Cj—
Computed cover HS—m
Vertical soil pressure FSV,K3—kN/m
Side soil pressure Fh,k—kN/m
Inner diameter D0—m
Self weight G1k—kN/m
Internal water weight Fw,k—kN/m
Surcharge at crown Qvk—kN/m
Design effect S—kN/m
Design value γ0S—kN/m
Design resistance R—kN/m
Ultimate-state verdict—
Quasi-permanent combination & internal forces
Quasi-permanent combination S—kN/m
Computed radius r0—m
Max design moment M—kN·m/m
Design axial force N—kN/m
Flexural member check
%
mm
mm
N/mm²
N/mm²
Effective depth h0—mm
Tensile steel area AS—mm²
Longitudinal rebar stress σsq—N/mm²
Strain non-uniformity ψ—
Max crack width ωmax—mm—
Large-eccentric-tension check
%
mm
mm
mm
N/mm²
N/mm²
Eccentricity e0—mm
Effective depth h0—mm
Tensile steel area AS—mm²
Coefficient α1—
Coefficient α2—
Longitudinal rebar stress σsq—N/mm²
Strain non-uniformity ψ—
Max crack width ωmax—mm—
D1 = (d+2t)/1000; Hs = H − d/1000 − t/1000; Ka = tan(45−φ/2)²; Bt = D1·(1+tan(45−φ/2)); Cj = (1−exp(−2·Kaμ·Hs/Bt))/(2·Kaμ); HS = Cj·Bt; FSV,K3 = Cj(γs·Bt−2C)D1; Fh,k = ((FSV/D1+γs·D1/2)Ka−2C·√Ka)D1; G1k = γ·π·D0·t/1000; Fw,k = γw·π/4·(d/1000)²; Qvk = qmk·D1. Ultimate: S = Σ(load·内·分项系数), R = 0.318·cracking load + 0.239·G1k, γ0S ≤ R. Cracks: σsq, ψ (clamped 0.4–1), ωmax = 1.8ψ(σsq/ES)(1.5C+0.11d/ρte)(1+α1)ν ≤ 0.2 mm.