Simplified Approach to the Analysis and Design of Columns with Imperfections

The design of columns makes an extensive use of the column curves. A column curve is a plot of the strength of the column (in stress or load form) vs. its slenderness ratio. The column curve for a perfectly straight column in the elastic or inelastic range can easily be derived using the eigenvalue approach. However, columns in actual building frames are rarely straight. The derivation of the column curve for an initially crooked column is very complex, with recourse to laborious numerical technique often necessary. The intent of this paper is to present a simple method to assess the strength of columns with initial out-of-straightness. A beam-column approach is used in the method. And the validity of the approach is determined by comparing it with existing column design formulas and with more elaborate computer models. A computer program is also written to help the designer use the proposed approach. In this paper, the fundamental theories of perfectly straight and initially crooked columns will first be reviewed. The derivation of the proposed column equation will then follow.