Buckling of Multi-Span Frames with Newmark Method

The Newmark’s numerical method of computing deflections, moments and buckling loads of isolated columns is extended for the analysis of elastic buckling loads and buckling modes of prismatic and non-prismatic single story, multi-span frames with combinations of hinged and fixed columns. Step-by-step description of the developed procedure is presented, using statics equilibrium, slope deflection equations and boundary conditions. The elastic line of the buckling mode is determined as a major part of the solution, and the numerical procedure is used to calculate the buckling loads and the columns’ effective length factor for multi-span frames. The most favorable variation of cross-section of tapered frame columns is calculated, giving the maximum possible elastic critical load of the frame for constant columns’ volume.