Second-Order Analysis of Multistory Building Frames by Marching Technique

A computer algorithm, expressed in the BASIC language, is described to make the second order analysis of multistory building frames by marching technique. Material property has to be linear elastic, and deformation due to axial force is ignored. Two second-order effects are considered; they are the reduction of column stiffness due to the presence of axial force, and the inclusion of the overturning moment arising from the product of the column load and the sidesway.
To minimize computer storage and running time, the marching technique is used wherein the global stiffness matrix is established one story at a time upon calling input data progressively downward beginning with the top story. Joint displacements of each story are expressed in terms of those of the story immediately below so that their values of the lowest story are obtained first. In this way, the largest inversion is of the size of the degree of freedom at any one story level. One file is used to store the intermediate information so that the joint displacements of each story, along with the moments at ends of all beams and columns in that story, may be computed progressively upward beginning with the lowest story.