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Second order moment by the nominal curvature method

Curvature with the correction factors for axial load and creep, the second order eccentricity and the design moment. Reference: EN 1992-1-1 5.8.8.

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Second order moment by the nominal curvature method: worked example sheet in Equation Pad with typeset equations and results.

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# Inputs
b := 300 mm
h := 300 mm
d := 250 mm
l_0 := 5.4 m
N_Ed := 1100 kN
M_0Ed := 45 kN*m
f_ck := 30 MPa
f_yk := 500 MPa
A_s := 1608 mm^2
phi_ef := 1.0
gamma_c := 1.5
gamma_s := 1.15

# Factors
f_cd := f_ck/gamma_c =
f_yd := f_yk/gamma_s =
n := N_Ed/(b*h*f_cd) =
omega := A_s*f_yd/(b*h*f_cd) =
n_u := 1 + omega =
K_r := min((n_u - n)/(n_u - 0.4), 1) =
lambda := l_0/(h/sqrt(12)) =
beta := 0.35 + f_ck/(200 MPa) - lambda/150 =
K_phi := max(1 + beta*phi_ef, 1) =

# Curvature and moment
epsilon_yd := f_yd/(200 GPa) =
r_inv := K_r*K_phi*epsilon_yd/(0.45*d) =
e_2 := r_inv*l_0^2/10 = mm
M_2 := N_Ed*e_2 = kN*m
M_Ed := M_0Ed + M_2 = kN*m

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