Steel Column Axial Design

AISC 360 LRFD axial compression design — buckling check per Chapter E. ASCE 7-22 load combinations — P_D, P_L, P_S, P_W. Self-weight automatically applied.

Input Parameters

kip · ft · in

Design Code:

Units:

Steel Grade

Section Selection

Section Type

Section

Column Height L [ft]

Loads

Dead P_D (excl. SW) [kip]

kip

Live P_L [kip]

kip

Roof Live P_Lr [kip]

kip

Snow P_S [kip]

kip

Wind P_W [kip]

kip

⚙

Select a section and enter column height to see results.

📚 Column Axial Compression — Design Theory

Flexural Buckling — AISC 360 §E3

Nominal compressive strength P_n = F_cr × A_g. Design strength φ_cP_n with φ_c = 0.90, E = 29,000 ksi / 200,000 MPa.

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

Elastic — KL/r > 4.71√(E/F_y)F_cr = 0.877 × F_e

Euler stressF_e = π²E / (KL/r)²

LRFD checkP_u ≤ φ_cP_n = 0.90 × F_cr × A_g

F_y	4.71√(E/F_y)
36 ksi / 250 MPa	133.7
50 ksi / 345 MPa	113.4
355 MPa	107.0

ASCE 7-22 §2.3.1 — LRFD Load Combinations

#	Combination
1	1.4D
2	1.2D + 1.6L + 0.5S
3	1.2D + 1.6S + L
4	1.2D + 1.0W + L + 0.5S
5	0.9D + 1.0W

D = Dead (incl. self-weight) | L = Live + Roof Live | S = Snow | W = Wind

Effective Length Factor K — AISC Commentary Table C-A-7.1

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
Both pinned, sway permitted	1.0	1.20
Both fixed, sway permitted	1.0	1.20

Flexural Buckling — EN 1993-1-1 §6.3.1.2

The buckling resistance N_b,Rd uses a reduction factor χ from the Perry-Robertson imperfection model. γ_M1 = 1.00, E = 210,000 MPa.

Non-dimensional slendernessλ̄ = (KL/r) / (π√(E/f_y))

Auxiliary valueΦ = 0.5 [1 + α(λ̄ − 0.2) + λ̄²]

Reduction factorχ = 1 / (Φ + √(Φ² − λ̄²)) ≤ 1.0

Buckling resistanceN_b,Rd = χ · A · f_y / γ_M1

Buckling Curves — EN 1993-1-1 Table 6.2

Section type	Axis	Curve	α
IPE / HE (h/b > 1.2), t_f ≤ 40 mm	y‑y (strong)	a	0.21
IPE / HE (h/b > 1.2), t_f ≤ 40 mm	z‑z (weak)	b	0.34
HEA / HEB (h/b ≤ 1.2), t_f ≤ 100 mm	y‑y (strong)	b	0.34
HEA / HEB (h/b ≤ 1.2), t_f ≤ 100 mm	z‑z (weak)	c	0.49
SHS / RHS (hot-formed)	any	a	0.21
CHS (hot-formed)	any	a	0.21
Welded I, t_f ≤ 40 mm	y‑y	b	0.34
Welded I, t_f ≤ 40 mm	z‑z	c	0.49

EN 1990 §6.4.3 — ULS Load Combinations (Exp. 6.10)

#	Combination
1	1.35 G
2	1.35 G + 1.5 Q
3	1.35 G + 1.5 S + 0.75 Q
4	1.35 G + 1.5 Q + 0.5 S
5	1.35 G + 1.5 W + 0.9 Q
6	1.0 G + 1.5 W

G = Permanent | Q = Imposed (live) | S = Snow | W = Wind. ψ₀ values from EN 1990 Table A1.1; National Annexes may modify γ factors.

Flexural Buckling — TSDS 2016 §5.2

TSDS 2016 adopts the same F_cr formulas as AISC 360 Ch. E in SI units. φ_c = 0.90, E = 200,000 MPa. Slenderness limit: KL/r ≤ 200.

Inelastic — KL/r ≤ 4.71√(E/f_y)F_cr = 0.658^f_y/F_e × f_y

Elastic — KL/r > 4.71√(E/f_y)F_cr = 0.877 × F_e

Euler stress (SI)F_e = π² × 200,000 / (KL/r)² (MPa)

Design strengthφ_cP_n = 0.90 × F_cr × A (kN)

f_y (MPa)	4.71√(E/f_y)
S235 — 235	130.2
S275 — 275	120.4
S355 — 355	106.0

TSDS 2016 — Strength Design Load Combinations

#	Combination
1	1.4 G
2	1.2 G + 1.6 Q + 0.5 S
3	1.2 G + 1.6 S + Q
4	1.2 G + 1.0 W + Q + 0.5 S
5	0.9 G + 1.0 W

G = Dead load | Q = Live load | S = Snow | W = Wind

Flexural Buckling — IS 800:2007 §7.1.2

IS 800 uses the same Perry-Robertson model as EC3 with γ_m0 = 1.10, E = 200,000 MPa. Slenderness limit: KL/r ≤ 180.

Non-dimensional slendernessλ̄ = (KL/r) / (π√(E/f_y))

Auxiliary valueφ = 0.5 [1 + α(λ̄ − 0.2) + λ̄²]

Reduction factorχ = 1 / (φ + √(φ² − λ̄²)) ≤ 1.0

Design strengthP_d = χ · A · f_y / (γ_m0 · 1000) (kN)

Buckling Classes — IS 800:2007 Table 10

Section type	Axis	Class	α
Hot-rolled I (h/b > 1.2), t_f ≤ 40 mm	y‑y (strong)	a	0.21
Hot-rolled I (h/b > 1.2), t_f ≤ 40 mm	z‑z (weak)	b	0.34
Hot-rolled I (h/b ≤ 1.2), t_f ≤ 100 mm	y‑y (strong)	b	0.34
Hot-rolled I (h/b ≤ 1.2), t_f ≤ 100 mm	z‑z (weak)	c	0.49
SHS / RHS (hot-formed)	any	a	0.21
CHS (hot-formed)	any	a	0.21
Welded I, t_f ≤ 40 mm	y‑y	b	0.34
Welded I, t_f ≤ 40 mm	z‑z	c	0.49

IS 800 buckling classes a/b/c/d match EC3 curves a/b/c/d exactly — imperfection factor α values are identical.

IS 800:2007 Table 4 — ULS Load Combinations

#	Combination
1	1.5 (DL + LL)
2	1.5 (DL + SL)
3	1.5 (DL + WL)
4	1.2 (DL + LL + WL)
5	1.2 (DL + LL + SL)
6	0.9 DL + 1.5 WL

DL = Dead Load | LL = Imposed Load | SL = Snow Load | WL = Wind Load. γ_f from IS 875 (Part 5).