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Column under axial load and biaxial bending

Interaction check for biaxial bending with the exponent depending on the axial load ratio. Reference: IS 456:2000 Cl. 39.6.

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# Data
b := 400 mm
D := 600 mm
f_ck := 25 MPa
f_y := 415 MPa
A_sc := 3770 mm^2
P_u := 1800 kN
M_ux := 180 kN*m
M_uy := 90 kN*m
# M_ux1 and M_uy1 are the uniaxial capacities at P_u, read from the interaction diagrams of the design aid.
M_ux1 := 320 kN*m
M_uy1 := 200 kN*m

# Exponent
P_uz := 0.45*f_ck*(b*D - A_sc) + 0.75*f_y*A_sc = kN
r := P_u/P_uz =
alpha_n := interp(r, [0, 0.2, 0.8, 1], [1, 1, 2, 2]) =

# Check
U := (M_ux/M_ux1)^alpha_n + (M_uy/M_uy1)^alpha_n =
U <= 1 =

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