In 1949, W. T. Thompson proposed a procedure for the solution of an n-section column using the matrix calculus. Since the matrix method was rather long and unfamiliar to most engineers, it was felt that a further investigation was warranted in the hope that 2 further development of the Thompson method would result in a simplified procedure not involving matrices, thus placing a worthwhile tool in the hands of the practicing structural engineer. From the theoretical point of view, at least, the investigation proved successful. However, the resulting equations could net be simplified as much as was originally hoped which meant that the practical value of the method was limited from the point of view of time required for the solution of a typical problem. In an attempt to circumvent this difficulty, to some degree, a secondary investigation was undertaken. Two common types of columns were analyzed in detail and the results presented in graphical form in such a manner that the critical design load could be found, for the column types investigated, in a matter of minutes. A bibliography of the more important column papers, dealing essentially with variable section columns, is included in the thesis to provide a convenient ready reference source of column information for future investigators.

Columns with three spans separated by elastic braces are analyzed. The influences of translational and rotational resistance at the braces, various end conditions, and the bracing locations for the perfect columns with equal and unequal spans subjected to uniform and nonuniform axial load are investigated. For imperfect columns with equal or unequal spans subjected to uniform compression, the effects of various end conditions at the top and various initial deflections are studied. "Ideal stiffness" and "full bracing" only exist for these columns with equal spans and translational restraints with identical spring stiffness at the braces. Rotational restraints at the braces or at the ends improve the load-carrying capacity of the column. For the imperfect column, three types of initial deflection on the columns with equal and unequal spans and various end conditions at the top are analyzed. Based on a linear elastic analysis, the bracing force induced by a cubic initial deflection for a three-span column often exceeds 20/0 of the axial load. The violation of this rule of thumb in practice is readily revealed. Design curves for the effect of the bracing stiffness on the deflection ratio and bracing force percentage are created for the determination of bracing requirements. / Master of Science