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Two-way slab from moment coefficients

Moments in the short and long spans of a two-way slab from bending moment coefficients and the steel for each. Reference: EN 1992-1-1 5.4, 6.1.

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# Materials
f_ck := 30 MPa
f_yk := 500 MPa
gamma_c := 1.5
gamma_s := 1.15
alpha_cc := 1.0
f_cd := alpha_cc*f_ck/gamma_c =
f_yd := f_yk/gamma_s =

# Slab
l_x := 4.5 m
l_y := 6 m
h := 200 mm
d_x := 170 mm
d_y := 160 mm
b := 1000 mm
n := 1.35*((25 kN/m^3)*h + 1.5 kN/m^2) + 1.5*3 kN/m^2 =
# Coefficients for a simply supported panel with l_y/l_x = 1.33 from the usual tables of coefficients (they are not part of EN 1992).
beta_sx := 0.088
beta_sy := 0.051

# Moments and steel
M_x := beta_sx*n*l_x^2*b = kN*m
M_y := beta_sy*n*l_x^2*b = kN*m
k_1 := 0.8*alpha_cc/gamma_c =
z_x := min(d_x*(0.5 + sqrt(0.25 - 0.4*M_x/(b*d_x^2*f_ck)/k_1)), 0.95*d_x) = mm
A_sx := M_x/(f_yd*z_x) = mm^2
z_y := min(d_y*(0.5 + sqrt(0.25 - 0.4*M_y/(b*d_y^2*f_ck)/k_1)), 0.95*d_y) = mm
A_sy := M_y/(f_yd*z_y) = mm^2

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