Investigation of a matrix solution of variable cross-section columns

Abstract

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.