Elements of Matrix and Stability Analysis of Structures: For Engineering Students Selvam, V.K. Manicka.

As of previous edition, the spirit of the present text is also one of dissemination of knowledge and consideration of human welfare. Therefore, beginning with the first edition, successive editions have been supplemented with new materials. In the text, more information on "stability" has been furnished. For non-prismatic Euler columns, exact solution for the critical load is impossible to obtain in the majority of cases. As a result, approximate methods are being resorted to. The Slope and Deflection Comparison Procedure and the Newmark Method are accurate analytical tools. However, their application is restricted to only cantilever (or two-hinged) columns.

The finite difference method and the finite element method are computer-oriented techniques. In finite difference method, the fourth order differential equation is replaced by a difference equation and with the help of a software and computer, the eigenvalues are extracted. This method is of practical use rather than curricular interest. As is well-known, the FEM is not a right choice for every problem. It is so with the finding of critical load of non-prismatic columns also. In such a situation, the only choice then falls on Timoshenko's energy method. It is a neat and versatile procedure suitable for all Euler columns.