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Lateral torsional buckling of an unrestrained beam

Elastic critical moment of a doubly symmetric I-beam under uniform moment and the reduced bending resistance. Reference: EN 1993-1-1 6.3.2.2, Table 6.4.

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# Material
f_y := 355 MPa
gamma_M0 := 1.0
gamma_M1 := 1.0
E_s := 210 GPa
G_s := 81 GPa

# Section IPE 300 (check against your tables)
W_pl.y := 628e3 mm^3
I_z := 604e4 mm^4
I_t := 20.1e4 mm^4
I_w := 126e9 mm^6

# Critical moment
L_LT := 4.0 m
C_1 := 1.0
M_cr := C_1*pi^2*E_s*I_z/L_LT^2*sqrt(I_w/I_z + L_LT^2*G_s*I_t/(pi^2*E_s*I_z)) = kN*m

# Reduction
lambda_LT := sqrt(W_pl.y*f_y/M_cr) =
# Rolled I-section with h/b <= 2: curve a.
alpha_LT := 0.21
Phi_LT := 0.5*(1 + alpha_LT*(lambda_LT - 0.2) + lambda_LT^2) =
chi_LT := min(1/(Phi_LT + sqrt(Phi_LT^2 - lambda_LT^2)), 1) =
M_b.Rd := chi_LT*W_pl.y*f_y/gamma_M1 = kN*m
M_Ed := 100 kN*m
M_Ed <= M_b.Rd =

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