Post Lateral Buckling Behavior of Beams

The large deflections which occur when a uniform rectangular cantilever beam has an end load greater than the lateral buckling load are found by solving a set of three simultaneous, first-order, nonlinear, differential equations. These equations, derived through considerations of moment equilibrium, are numerically integrated using the improved Euler method from the fixed end where boundary values are known, to the free end where boundary values must initially be guessed. The integration process is repeated until the computed boundary values at the free end are sufficiently close to the guessed values. Convergence problems arise for beam cross sections which are almost square. Deflections in three directions are presented graphically as a function of the length, width, height, and lateral buckling load of the beam.