Compression members, primarily columns but also compression truss chords and bracing struts, are structural elements subjected to axial compressive forces. Unlike tension members, which generally fail by yielding or rupture, the strength of compression members is almost always governed by stability, specifically buckling failure.

Buckling is a sudden loss of stability where a member deflects laterally under compressive load before the material itself reaches its yield stress. The critical load depends primarily on the member's flexural stiffness ($EI$), length ($L$), and end support conditions ($K$).

Real columns rarely have perfect pin-pin ends. The effective length factor ($K$) adjusts the actual length ($L$) to the length of an equivalent pinned-end column ($KL$) that has the same buckling strength. $KL$ represents the distance between points of zero moment (inflection points) on the buckled shape.

The critical buckling axis is the one with the highest slenderness ratio $KL/r$. For standard W-shapes, this is almost always the weak y-axis ($I_y \ll I_x$), unless the y-axis is braced at intermediate points.

The theoretical Euler buckling formula assumes a mathematically perfect, perfectly straight column loaded exactly at its centroid. Real structural steel columns deviate from this ideal in two critical ways:

When a compressive load is applied to a column that is already slightly bent, the initial curvature acts as an eccentricity. This immediately induces bending moments (a $P-\delta$ effect) from the very start of loading, accelerating the onset of buckling. The empirical AISC column curves specifically account for both residual stresses and a maximum allowable initial out-of-straightness of $L/1500$ in their derivation.

The Euler formula assumes a perfectly straight, perfectly elastic column. Real columns have initial crookedness and residual stresses from uneven cooling during manufacturing. These imperfections cause the column to yield prematurely, reducing its strength below the theoretical Euler load. The AISC Specification uses two equations based on the slenderness ratio to account for this inelastic behavior.

While flexural (Euler) bending buckling is the primary mode for closed shapes (HSS) and doubly symmetric open shapes (W-shapes), other buckling modes can govern, especially for asymmetric shapes.

When these modes govern, the elastic buckling stress $F_e$ in the AISC equations must be calculated using complex formulas (AISC Section E4) that account for the torsional constant ($J$) and warping constant ($C_w$) of the section, rather than just the weak-axis $KL/r$.

The cross-section itself is composed of plate elements (flanges and webs). These individual elements can buckle locally (wrinkle) under compression before the entire member buckles globally.

AISC Table B4.1a provides limiting width-to-thickness ratios ($\lambda_r$) to classify sections. For example, a W-shape flange is checked using $b_f/2t_f \le 0.56\sqrt{E/F_y}$.

When standard rolled shapes are insufficient, two or more shapes can be connected together (e.g., two channels back-to-back, or four angles in a box).

Use the simulation below to observe how the critical buckling stress ($F_{cr}$) transitions from inelastic yielding (plateau) to elastic buckling (Euler hyperbola) as the slenderness ratio ($KL/r$) increases. Note how the inelastic curve lies significantly below the theoretical Euler curve due to residual stresses.