Stability of plane Frames Omitting Axial Strains

Abstract

The number of degrees of freedom for the stability analysis of plane frames may be considerably reduced by introducing axial constraints. Determination of the rank and basis of the constraint matrix by Gauss-Jordan elimination with pivoting leads to automatic selection of the best set of dependent and independent joint translations. Then a transformation of the buckling equations produces a reduced set of equations, that may be solved for the buckling loads of frames. This technique can be applied in conjunction with the elimination of joint rotations, thereby accomplishing a double reduction without significant loss of accuracy. The procedure described has been programmed on a digital computer.