Steel Column Compression Capacity
Compute the nominal compressive strength (Pn) and design strength (φcPn) of a wide-flange steel column. Evaluates slenderness ratio KL/r about both major and minor axes to find the governing case. Applies the AISC 360-22 Chapter E flexural buckling equations to determine the critical stress Fcr, then calculates φcPn with φc = 0.90.
What this calculates
Effective slenderness ratios (KL/r)x and (KL/r)y, elastic buckling stress Fe, critical stress Fcr per Section E3, nominal axial strength Pn = Fcr·Ag, and design compressive strength φcPn. Reports the demand-to-capacity ratio Pu/φcPn.
Inputs
Required axial compressive strength from load combinations
Gross cross-sectional area of the W-shape
Radius of gyration about the major (x) axis
Radius of gyration about the minor (y) axis
Unbraced length about the major axis
Unbraced length about the minor axis
Effective length factor about the major axis
Effective length factor about the minor axis
Minimum yield stress (typically 50 ksi for A992)
Modulus of elasticity (29000 ksi)
Outputs
Governing slenderness ratio (larger of both axes)
Euler elastic buckling stress
Nominal critical buckling stress
Available compressive strength with φc = 0.90
Axial demand / design strength — must be ≤ 1.0
Methodology
The governing slenderness ratio is the larger of KxLx/rx and KyLy/ry. If KL/r ≤ 4.71√(E/Fy), inelastic buckling governs and Fcr = [0.658^(Fy/Fe)]·Fy per Equation E3-2. If KL/r > 4.71√(E/Fy), elastic buckling governs and Fcr = 0.877·Fe per Equation E3-3, where Fe = π²E/(KL/r)² per Equation E3-4. The design strength is φcPn = 0.90·Fcr·Ag.
Code References
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