Matrix Formulation of Structural Stability Problems

A stability coefficient matrix is derived for use with the stiffness matrix in the deformation analysis of structures. This matrix allows the easy modification of the conventional beam stiffness matrix to include the effects of axial loads in the members and therefore gives a simple and rapid formulation of stability problems for columns and general frame structures. The matrix presented is approximate and the method gives an upper bound to the critical loading. However, the examples presented indicated excellent agreement with known exact results for both column and rigid frame critical loads, and the accuracy may be improved by a finer subdivision of the structure. The method is ideally suited for computers.