Compression members

A steel column rarely fails by crushing. Long before the average stress reaches yield, it usually bows sideways and buckles. Euler showed that a perfectly straight, pin-ended elastic strut buckles at π² E I / L². Real members are not perfect: they have initial crookedness, eccentric loading and residual stresses from rolling and welding, all of which lower the strength, especially at intermediate slenderness.

Modern codes, including IS 800, use column buckling curves. The key parameter is the non-dimensional slenderness λ, the square root of yield load over Euler load. For stocky members λ is small and strength approaches the squash load. For slender members strength approaches the Euler load. In between, an imperfection factor α chosen by section type, buckling axis and plate thickness sets which curve (a, b, c or d) applies. Hot-rolled I-sections buckling about the major axis usually use a better curve than welded or thick sections about the minor axis.

Effective length captures end restraint: a column fixed at both ends behaves like a much shorter pinned one, while a cantilever column behaves like one twice its length. Slenderness KL/r should be kept within code limits. Plate elements must be stocky enough not to buckle locally before the member reaches its capacity, which is why sections are classified as plastic, compact, semi-compact or slender. Built-up columns need lacing or battens to act as one.