Long-Wave Extensional Buckling of Large Regular Frames

In very high and slender frames with very stiff members, the safety against long-wave buckling modes involving axial extensions requires investigation. The problem is solved exactly for a planar regular rectangular frame of rectangular boundary, compressed between two sliding rigid half spaces. The problem is reduced to a system of six linear first-order difference equations which are solved in terms of discrete complex exponentials. Because the coefficients of the determinant to varnish depend on axial loads nonlinearly, by means of explicitly inexpressible complex roots and eigenvectors of another 6 times 6 matrix and the well-known nonlinear stability functions, the critical load is determined numerically by a procedure analogous to the method regula falsi. The ratio of column critical force to column Euler load depends eessentially on the ratio of column and beam bending stiffnesses, the ratio of building slenderness to column slenderness, and weakly on column slenderness ratio.