Determination of Elastic Critical Loads

For the determination of elastic critical loads in frameworks, slope deflection equations are given in which the effects of initial imperfections are included. A Southwell plot is then used to avoid the nonlinear extrapolation inherent in the use of the usual determinant solution. Two distinct practicable methods are shown to exist for improving the estimate of the critical load obtained from a Southwell plot. The first involves iteration with recomputation of deformation at different loads, whereas the second method concentrates on improving the agreement between the assumed initial imperfections and the primary buckling mode. In the first method, no more than two trial loads are normally required to give a good estimate of the critical load. In the second method, one trial load may be sufficient. Three examples are outlined to show the variation in estimated critical load with trial load in each case.