Lateral Buckling of Intersecting Connected Beams

Under transverse loadings, components of gridworks composed of deep slender beams may become unstable with the response characterized by twist and lateral deflections of the beams. A beam-cross having symmetrical geometric properties, cross sections, support conditions, elastic end restraints, and loadings is isolated and analyzed. Basic equilibrium equations, boundary conditions, and joint compatibility requirements are developed by variational calculus. For beam-crosses with rectangular cross sections under a single concentrated load applied at the intersection (joint) of the two beams, closed-form solutions result in the determination of the eigenvalues and corresponding mode shapes. Design curves identify the effects of changes in geometric ratios upon the buckling loads for practical ranges of such parameter variations.