Eurocode 5 (EN 1995-1-1) Verification Suite:

• Design Bending Strength: Calculates f_{m,d} = k_{mod} * (f_{m,k} / gamma_M) with default partial safety factor gamma_M = 1.25 and load duration factor k_{mod} = 0.9.
• Curvature Vector: Evaluates spatial differential curvature kappa = |r'(t) x r''(t)| / |r'(t)|^3 to derive active bending moments M(t) = E * I * kappa.
• Biaxial Torsion & Twist: Monitors cross-sectional shear stress tau_d against characteristic shear strength f_{v,k}.
• Global Buckling Criterion: Computes the critical buckling load index using the continuous shell equivalence parameter q_{cr} = C * sqrt(E_u * E_v * (t / R)^2).