Steel Column Design — Combined Axial + Biaxial Bending

AISC 360 LRFD combined axial compression + biaxial bending — interaction check per Chapter H. Axial per Ch. E, flexural per Ch. F2 / F6.

Input Parameters

kip · ft · in

Design Code:

Units:

Steel Grade

Section

Section Type

Section

Column height L [ft]

Factored Design Forces

P_u — factored axial compression [kip]

kip

M_ux — factored moment x‑x [kip·ft]

kip·ft

M_uy — factored moment y‑y [kip·ft]

kip·ft

⚙

Select a section and enter column height to see results.

📚 Steel Column Design — Theory Reference

Interaction — AISC 360 §H1-1

P_u/φP_n ≥ 0.2 (H1-1a)P_u/(φ_cP_n) + (8/9)[M_ux/(φ_bM_nx) + M_uy/(φ_bM_ny)] ≤ 1.0

P_u/φP_n < 0.2 (H1-1b)P_u/(2φ_cP_n) + M_ux/(φ_bM_nx) + M_uy/(φ_bM_ny) ≤ 1.0

φ_c = φ_b = 0.90. C_b = 1.0 (uniform moment). L_b = weak-axis unbraced length.

Axial — §E3

KL/r ≤ 4.71√(E/F_y)F_cr = 0.658^F_y/F_e × F_y

KL/r > 4.71√(E/F_y)F_cr = 0.877 × F_e where F_e = π²E/(KL/r)²

Strong-Axis Flexure — §F2

L_b ≤ L_pM_nx = M_p = F_yZ_x

L_p < L_b ≤ L_rM_nx = M_p − (M_p − 0.7F_yS_x)(L_b−L_p)/(L_r−L_p) ≤ M_p

L_b > L_rM_nx = F_cr,LTB × S_x ≤ M_p

Weak-Axis Flexure — §F6

§F6M_ny = min(F_yZ_y, 1.6F_yS_y)

TSDS 2016 uses the same interaction equations in SI units (E = 200,000 MPa).

Axial Buckling — EN 1993-1-1 §6.3.1

N_b,Rd = χ × A × f_y / γ_M1. Imperfection factor α from buckling curve (Table 6.2): h/b > 1.2 → curves a/b; h/b ≤ 1.2 → curves b/c.

Slendernessλ̄ = √(A·f_y / N_cr) N_cr = π²EI/(KL)²

Reduction factorχ = 1 / [φ + √(φ² − λ̄²)] ≤ 1.0 φ = 0.5[1 + α(λ̄ − 0.2) + λ̄²]

LTB — §6.3.2.3 (Rolled Sections)

M_crM_cr = (π/L_b) √(EI_z·GJ) × √(1 + π²EI_w/(GJL_b²))

λ̄_LT√(W_y,pl·f_y / M_cr). Curves: h/b ≤ 2 → b (α_LT=0.34); h/b > 2 → c (α_LT=0.49)

χ_LTλ̄_LT,0 = 0.4, β = 0.75. If λ̄_LT ≤ 0.4: χ_LT=1.0; else χ_LT = 1/[φ_LT+√(φ_LT²−βλ̄_LT²)] ≤ 1/λ̄_LT²

Interaction — §6.3.3 Method 2 (Annex B, C_my=C_mz=1.0)

Eq. 6.61N_Ed/(χ_yN_Rk/γ_M1) + k_yyM_y,Ed/(χ_LTM_y,Rk/γ_M1) + k_yzM_z,Ed/(M_z,Rk/γ_M0) ≤ 1.0

Eq. 6.62N_Ed/(χ_zN_Rk/γ_M1) + k_zyM_y,Ed/(χ_LTM_y,Rk/γ_M1) + k_zzM_z,Ed/(M_z,Rk/γ_M0) ≤ 1.0

n_y=N_Ed/(χ_yN_Rk), n_z=N_Ed/(χ_zN_Rk). k_yy=1+min(λ̄_y−0.2, 0.8)n_y; k_zz=1+min(2λ̄_z−0.6, 1.4)n_z; k_yz=0.6k_zz; k_zy=1−min(0.133λ̄_z, 0.133)n_z.

Axial Compression — IS 800:2007 §7

P_d = A × f_cd. Buckling classes from Table 7: strong axis → class b (α=0.34); weak axis → class c (α=0.49). E = 200,000 MPa, G = 77,000 MPa, γ_m0 = 1.10.

Non-dimensional slendernessλ̄ = √(Af_y/N_cr). Same χ formula as EC3.

Design compressive stressf_cd = χ × f_y / γ_m0. Governing axis: min(f_cd,x, f_cd,y).

Bending Capacity — IS 800:2007 §8.2

LTB curve from Table 6b (rolled sections): h/b ≤ 2 → curve a (α_LT=0.21); h/b > 2 → curve b (α_LT=0.34).

M_crSame formula as EC3 (E=200,000, G=77,000 MPa)

M_dxχ_LT × Z_pl,x × f_y / γ_m0 M_dz = Z_pl,z × f_y / γ_m0

Interaction — IS 800:2007 §9.3.2.2

§9.3.2.2P/P_d + M_x/M_dx + M_y/M_dz ≤ 1.0

Effective Length Factor K

End Condition	K (theoretical)	K (recommended)
Both ends pinned	1.0	1.00
One pinned, one fixed (no sway)	0.7	0.80
Both ends fixed (no sway)	0.5	0.65
One fixed, one free (cantilever)	2.0	2.10

K_x governs strong-axis buckling; K_y governs weak-axis buckling. L_b (LTB unbraced length) = L_b,y × L (weak-axis unbraced fraction).