Combined bending and axial compression check per EN 1993-1-1 §6.3.3 Equations 6.61 and 6.62. Computes χy/χz (flexural buckling §6.3.1), χLT (LTB §6.3.2), Annex B interaction factors kyy/kzy/kyz/kzz, and both interaction utilisations. HEA, HEB, HEM, IPE, UC, UB. S235–S460.
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EN 1993-1-1 §6.3.3 provides two interaction equations (6.61 and 6.62) for members subject to combined bending and axial compression. Eq. 6.61 checks the member against y-y buckling with major-axis bending; Eq. 6.62 checks against z-z buckling with biaxial bending. Both must be satisfied simultaneously. The most common situation is Eq. 6.62 governing, because the z-z buckling reduction factor χ_z is typically lower and k_zz amplifies minor-axis moments.
Annex B (simplified method) provides conservative closed-form formulas for k_yy, k_zy, k_yz and k_zz based on slenderness and moment distribution factors C_my/C_mz/C_mLT. It is easier to apply and safe for typical members. Annex A (general method) gives more accurate — often less conservative — k-factors, requiring C_yy/C_zz/C_yz/C_zy auxiliary terms and plastic modulus ratios. Most national codes accept either; Annex B is the default used here.
The equivalent uniform moment factors C_my and C_mz account for the shape of the bending moment diagram along the member. For linear (end-moment) loading: C_m = 0.6 + 0.4ψ ≥ 0.4, where ψ = M₂/M₁ is the ratio of the smaller to larger moment. Uniform moment (ψ = 1) gives C_m = 1.0 (worst case). For parabolic UDL diagrams C_m ≈ 0.4 and for triangular (point load at midspan) C_m ≈ 0.6. Annex B Table B.3 gives the full table.
L_y and L_z are effective buckling lengths for flexural buckling about the major (y-y) and minor (z-z) axes, respectively. L_LT is the unrestrained length for lateral-torsional buckling. For most columns in a non-sway frame: L_y = L_z = L_LT = full height. For columns in a sway frame: L_y = L_z ≈ 2L. Bracing or intermediate restraints shorten L_z and L_LT independently.
Yes. γM1 divides all resistances (N_Rk, M_y,Rk, M_z,Rk) in the denominator of each term. For EN/NL/BE: γM1 = 1.0. For DE (DIN EN 1993-1-1/NA): γM1 = 1.1, which reduces all design resistances by ~9% and makes the check more conservative. Switch the National Annex dropdown to see the effect.