Lateral Stability of Beams with Initial Imperfections

The design of large flat‐roof systems necessitates a means of analyzing the required strength of bracing members. If the braced beam is initially perfectly straight, it will remain straight until it buckles; the prebuckling stresses in the braces are theoretically zero. If the braced beam has initial imperfections, they will grow under load and so will the stresses in the braces. Thus, there is need to analyze the buckling of beams with initial imperfections. This was done in the context of linear small‐deflection theory; the results are simple and suitable for use in design where loads are well below buckling and initial deformations are small. This paper presents a variational derivation of a set of linear differential equations and boundary conditions and applies them to the calculation of forces in midspan diagonal bracing members on a simply supported beam under constant bending. A sample calculation for a typical wood roof application shows the forces in the bracing to be quite small. Only rectangular beams are treated in detail, but the extension to singly symmetric I‐beams is sketched.