How to use the steel column compressive strength calculator
A steel column almost never reaches its yield capacity, because buckling takes over first as the member gets more slender. Enter the unbraced length, end condition, weak axis radius of gyration, gross area, and steel grade to get the critical stress Fcr along with both LRFD and ASD capacities.
The tool follows AISC 360 Chapter E. It computes KL/r, compares it with the limit 4.71√(E/Fy) using E = 29,000 ksi, and then applies the inelastic branch Fcr = 0.658^(Fy/Fe)Fy below the limit or the elastic branch Fcr = 0.877Fe above it, where Fe = π²E/(KL/r)². Nominal strength is Pn = FcrAg.
LRFD design strength multiplies Pn by the resistance factor 0.90, while ASD allowable strength divides Pn by the safety factor 1.67. Results match the tabulated values in AISC Manual Table 4-22: for Fy = 50 ksi and KL/r = 80, Fcr works out to about 31.3 ksi, giving roughly 28.2 ksi for LRFD and 18.7 ksi for ASD.
This calculation covers flexural buckling of a doubly symmetric member with a compact section. Torsional and flexural-torsional buckling, slender element local buckling, and combined axial plus flexural demands all need separate checks, so treat this as a preliminary sizing tool and have a licensed structural engineer verify the final member.
Frequently asked questions
When KL/r is at or below 4.71 times the square root of E over Fy, AISC 360 Chapter E uses Fcr = 0.658 raised to (Fy/Fe) times Fy. Above that limit, Fcr = 0.877 Fe, the elastic buckling branch.
LRFD design strength multiplies the nominal capacity FcrAg by the resistance factor 0.90. ASD allowable strength divides the same nominal capacity by the safety factor 1.67. Use whichever method the project follows.
Not for slender columns. Once elastic buckling governs, Fcr depends on stiffness rather than yield strength, so upgrading the grade only pays off on short, stocky columns with low KL/r.