How is the column strength affected by its slenderness?
The column slenderness is defined in terms of its slenderness ratio kLu/r, where the term kLu is called the effective length and the factor k modifies the actual column length to account for end restraints other than pinned. The value of the effective length factor k varies between 0.5 and 2.0, depending of the buckled shape of the column for different end conditions. The parameter r is the radius of gyration of the cross section.
In practice, columns are rarely found as isolated members, but they are part of rigid frames together with other structural members such as beams. When the frame is laterally braced, the joint translation is prevented by shear walls, attachment to adjoining structures, etc, and such a column is called Non-sway, as opposed to a Sway column, where the lateral stability is dependent of the stiffness of the members of the frame.
When a slender column is axially loaded, it tends to buckle, which creates a deflection Δ. This deflection times the axial load produces an additional (secondary) moment, which in turn increases the deflection, which in turn increases the moment, and so on until the system converges. This is called a P-Δ analysis. A material failure will result when a particular combination of load P and moment P(e+Δ) intersects the interaction diagram, as shown in the figure below. Note that the additional moment actually reduces the axial capacity of the column.