Steel Column Compressive Capacity (AISC 360 Ch. E, Flexural Buckling)
The axial load a steel column carries, set by its slenderness not its area.
Example
You enter
- Yield stress Fy (ksi) 50
- Modulus E (ksi) 29000
- Effective-length factor K 1
- Unbraced length L (ft) 14
- Radius of gyration r (in) 2.01
- Gross area Ag (in²) 13.3
You get
- Slenderness KL/r 83.6 (inelastic)
- Critical stress Fcr 30.0 ksi
- Nominal Pn 399 kips
- ASD allowable Pn/Omega 239 kips
- LRFD design phi_c*Pn 359 kips
Details, formula, and sources
KL/r, the elastic buckling stress Fe = pi^2 E / (KL/r)^2, and Fcr from the inelastic 0.658^(Fy/Fe) Fy or the elastic 0.877 Fe branch at the 4.71 sqrt(E/Fy) transition. A 14 ft W10x45 carries 239 kips allowable; stretch it to 24 ft and slenderness alone cuts it to 97 kips. The unbraced length is the number to watch. Flexural buckling only. A design aid, not a substitute for the engineer of record.
KL/r; Fe = pi^2 E / (KL/r)^2; Fcr = 0.658^(Fy/Fe) Fy if KL/r <= 4.71 sqrt(E/Fy) else 0.877 Fe; Pn = Fcr Ag; Pa = Pn / 1.67; phi_c Pn = 0.90 Pn.
AISC 360-22 Chapter E (E3) and §B3.1 / §B3.2, by name; r and Ag are read from the AISC Manual for the actual shape.
The Fe / Fcr flexural-buckling relations and the Omega_c / phi_c factors are stated in AISC 360; r and Ag come from the AISC Manual shape tables.
Estimate. AHJ and licensed professional govern.
Field names used by the API: fy, e_mod, k, l_ft, r_in, ag, slender, fcr, pn, pa, phi_pn
- Governing axis KL/r uses the radius of gyration about the axis that buckles first, usually ry; the smaller r governsAISC 360-22 E3
- Inelastic / elastic branch the transition is at KL/r = 4.71 sqrt(E/Fy) (about 113.4 at Fy = 50 ksi); below it 0.658^(Fy/Fe) Fy, above it 0.877 FeAISC 360-22 E3
- Flexural buckling only no torsional / flexural-torsional buckling or slender-element (Q) reduction; K from the end conditionsAISC 360-22 E3 / E4