Analysis of Beam-Columns on Elastic Supports

The analysis of beam-columns on continuous elastic foundations is required for applications in systems as diverse as a nail embedded in wood, laterally braced beam-columns, bearing piles, or beams on soil foundations. In addition, related problems such as a network of beams on soil foundations. In addition, related problems such as a network of beams, stiffened thin-walled tubes, ribbed plates, or ribbed shells all have a mathematical form identical to that of the beam-column on elastic supports. For these cases it is sometimes necessary to obtain not only a deflection and stress analysis but a stability analysis as well. The purpose of this paper is to present Fourier series analysis techniques for performing the elastic stability analysis of beam-columns supported by continuous Winkler supports including arbitrary rotational and translational restraints at the boundaries. As a byproduct of the stability analysis, the deflection analysis for general loadings will also be generated.