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Crack width calculation
Cracked elastic section, steel stress, mean strain difference, maximum crack spacing and the crack width. Reference: EN 1992-1-1 7.3.4.
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# Inputs
b := 300 mm
h := 600 mm
d := 545 mm
A_s := 1473 mm^2
phi := 25 mm
c := 40 mm
M_qp := 170 kN*m
f_ck := 30 MPa
E_s := 200 GPa
E_cm := 33 GPa
phi_cr := 2.0
k_t := 0.4
# Cracked section
E_ceff := E_cm/(1 + phi_cr) = GPa
alpha_e := E_s/E_ceff =
x := (-alpha_e*A_s + sqrt((alpha_e*A_s)^2 + 2*b*alpha_e*A_s*d))/b = mm
sigma_s := M_qp/(A_s*(d - x/3)) = MPa
# Effective tension area
h_ceff := min(2.5*(h - d), (h - x)/3, h/2) = mm
rho_peff := A_s/(b*h_ceff) =
f_cteff := 0.30*(f_ck/(1 MPa))^(2/3)*1 MPa =
# Crack width
Delta_eps := max((sigma_s - k_t*f_cteff/rho_peff*(1 + alpha_e*rho_peff))/E_s, 0.6*sigma_s/E_s) =
s_rmax := 3.4*c + 0.425*0.8*0.5*phi/rho_peff = mm
w_k := s_rmax*Delta_eps = mm
w_k <= 0.3 mm =How to use this example
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More Eurocode 2 sheets on serviceability
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- Maximum bar spacing for crack control
- Stress limits at the serviceability limit state
- Stresses in a cracked rectangular section
- Cracking moment of a rectangular section
- Deflection by interpolation between uncracked and cracked states