Columns

Vertical members whose ratio of length to lateral dimensions is large, and are carrying axial loads are called columns. Large columns fail by buckling. Difference between buckling and critical load is stated. Classical column theory proposed by Euler is used to find the critical load for axially loaded columns with different support conditions at the ends. The theory is based on equilibrium of the system in the displaced shape. The differential equations of equilibrium form an eigenvalue problem. The solution of the eigenvalue problem gives the critical load and the mode shapes. The columns are also analyzed by higher order governing differential equation. Continuous columns, columns with intermediate compressive force, non‐ prismatic columns, and columns supported on elastic supports are studied. Eccentrically loaded and geometrically imperfect columns are covered. Large deflection theory is used to study the post‐buckling behavior, and load versus deformation graphs are plotted. The concept of effective length of columns is given to find the critical compressive force. Rayleigh – Ritz and Galerkin methods are introduced to find critical load in columns by energy method. Elastic column behavior is considered in this chapter. There are nine practice problems and ten references at the end of the chapter.