Limit analysis of lateral buckling of slender concrete beams

An incremental analysis of concrete beams subjected to combined bending and torsion is described. The stress resultants are produced by direct loads or by the action of a perfect load acting on a geometrically imperfect beam. Both linear and non-linear moment-curvature/ specific twist characteristics are used. In the non-linear case, these characteristics are redefined at the end of a load increment on the basis of the level of moment attained in each of the other two directions; an iterative procedure is then introduced to find the solution for the subsequent increment of loading. A total of 52 rectangular beams and 72 I-beams are analysed in the linear elastic range; curves are obtained which enable values of L/b and Lh/b² that correspond to the onset of lateral instability to be deduced and compared with the values given in the existing codes of practice. Three alternative methods of defining the moment-curvature/specific twist relationships are used to analyse the beams of a previous experimental study by Sant and Bletzacker. The experimental and analytical results are discussed, and the theoretical characteristics which give the best fit are identified. The specified beams are then analysed using these characteristics. Plots of the ratio of the calculated failure load to the pure bending failure load against the L/b ratio again enable upper bounds on the values of L/b and Lh/b² to be found and compared with the values given in present codes of practice. A modification to the latter is suggested until further evidence becomes available.