Steel Column Compressive Capacity (AISC 360 Ch. E, Flexural Buckling)
The axial load a steel column carries, set by its slenderness not its area: 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.
Formula and source
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.
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