Section E3/Flexural Buckling of Members Without Slender Elements
AISC 360-22 Section E3 covers the compressive strength of columns without slender elements, using the slenderness ratio KL/r to determine the critical stress for inelastic or elastic buckling.
The nominal compressive strength for columns without slender elements (compact or noncompact sections per Table B4.1a) is Pn = Fcr x Ag, where Fcr is the critical stress and Ag is the gross cross-sectional area. The critical stress depends on the slenderness parameter KL/r, where K is the effective length factor, L is the unbraced length, and r is the radius of gyration about the governing axis. The column must be checked about both axes, with the higher KL/r (weaker axis) typically governing. When KL/r is less than or equal to 4.71 x sqrt(E/Fy) (approximately 134 for Fy = 50 ksi), inelastic buckling governs and Fcr = (0.658^(Fy/Fe)) x Fy, where Fe is the elastic buckling stress (pi^2 x E / (KL/r)^2). When KL/r exceeds 4.71 x sqrt(E/Fy), elastic buckling governs and Fcr = 0.877 x Fe. The resistance factor phi is 0.90 for LRFD and the safety factor omega is 1.67 for ASD. The effective length factor K depends on end conditions: K = 1.0 for pinned-pinned, K = 0.65 for fixed-fixed (theoretical 0.5, practical 0.65), K = 0.80 for fixed-pinned, and K = 2.0 for fixed-free (cantilever). For frames with sidesway, K exceeds 1.0 and must be determined from the alignment chart in Commentary Figure C-A-7.2.
Why this section exists
Columns fail by buckling rather than by material yielding when the slenderness ratio is high. The Euler elastic buckling formula predicts the theoretical buckling load for a perfectly straight, perfectly loaded column, but real columns have residual stresses from manufacturing, initial bow, and load eccentricity that reduce the actual buckling capacity. The AISC column curve accounts for these imperfections: at low slenderness (stocky columns), the capacity approaches the squash load Fy x Ag; at high slenderness (slender columns), the capacity approaches the Euler load; and in between, the inelastic buckling curve provides a smooth transition. The effective length factor K captures the influence of end restraint on the column buckling mode. For beam-columns (combined axial and bending), the compression capacity from Section E3 is used in the interaction equations of Chapter H.
What plan reviewers look for
Plan reviewers check the column schedule for member sizes, unbraced lengths, and effective length factors. They verify KL/r is calculated for both axes and the weaker axis governs. They check the K factor against the actual end conditions and framing connections. For braced frames, they verify K is 1.0 or less. For moment frames with sidesway, they verify K is determined from an analysis or the alignment chart and exceeds 1.0. They check that the column is not slender (if slender elements exist, Section E7 applies instead). They verify the tension capacity is also checked for members that experience load reversal.