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Deflection by interpolation between uncracked and cracked states
Long-term deflection of a simply supported beam by the distribution coefficient zeta. Reference: EN 1992-1-1 7.4.3.
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# Inputs
L := 6 m
b := 300 mm
h := 600 mm
d := 545 mm
A_s := 1473 mm^2
M := 140 kN*m
f_ck := 30 MPa
E_cm := 33 GPa
phi_cr := 2.0
E_s := 200 GPa
beta := 0.5
# Section properties
E_ceff := E_cm/(1 + phi_cr) = GPa
alpha_e := E_s/E_ceff =
I_I := b*h^3/12 = mm^4
x := (-alpha_e*A_s + sqrt((alpha_e*A_s)^2 + 2*b*alpha_e*A_s*d))/b = mm
I_II := b*x^3/3 + alpha_e*A_s*(d - x)^2 = mm^4
# Distribution coefficient
f_ctm := 0.30*(f_ck/(1 MPa))^(2/3)*1 MPa =
M_cr := f_ctm*I_I/(h/2) = kN*m
zeta := M > M_cr ? 1 - beta*(M_cr/M)^2 : 0 =
# Deflection
delta_I := 5*M*L^2/(48*E_ceff*I_I) = mm
delta_II := 5*M*L^2/(48*E_ceff*I_II) = mm
delta := zeta*delta_II + (1 - zeta)*delta_I = mm
delta <= L/250 =How to use this example
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More Eurocode 2 sheets on serviceability
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- Crack width calculation
- 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