Abstract
without an axial force. If the force P in each segment is specified, the analysis of either static or dynamic problems is straightforward. This is the case, for example, for beam-columns and for rotating beams. Problems in the elastic stability of columns can be handled by applying an arbitrary lateral force (or moment) and calculating the deflection with a series of successively greater axial forces. Southwell's method4 can then be applied to determine the buckling load. Incidentally, for a uniform column with any combination of end conditions, the exact expression for the elastic buckling load can be found directly from the stiffness matrix of the single beam segment. If the ends of the beam are restrained so as to prevent axial displacements, the axial force P is a nonlinear function of the lateral displacements. The customary assumption3 is that the deflection curve is a cubic. In this case, the axial force due to the stretching of the neutral axis of the beam segment shown in Fig. 3 is
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