The Buckling Load of a Truss Determined by the Convergence Criterion of the Moment Distribution Method

Abstract

The buckling load analysis of a truss and bars has been and continues to the subject of numerous researches, since it embraces a wide class of problem with immense importance in engineering science. When the buckling load of these trusses exceeds the permissible limit failure of the structure occurs. The ends of the bars in actual not ideal, frameworks are welded or riveted together rather than connected by pin joints. When a compression member of a framework buckles its ends are consequently not free to rotate but are restrained by the other members. Naturally this restrained is not absolutely rigid. There is some given in the system and the joints to which the compression member is attached rotate slightly and elastically because of moments exerted on them by the member that buckles. Basically it depends on stiffness of the member and carryover factor and moment of the members. Depending on the assumptions adopted, the type of analysis used, the kind of loading or excitation and the overall truss characteristics a variety of approaches have been reported in the literature and a great a number of both theoretical and experimental findings are related to load analysis. This paper describes a numerical method which is used to determine the most unstable post buckling mode capable of developing at the ultimate critical state of complex pin-jointed structures. In this method, the set of independent variables are the flexural shortenings of those members that are a subset of the critically loaded members in the lattice structure. This choice of independent variables greatly simplifies the analysis and promotes the evaluation of the most degrading mode under both equilibrium and collapse conditions. In this Technical Note, this method is used to evaluate these two modes for some rather simple structures. The deformed modes are plotted in each case and differences between the most degrading mode under equilibrium and collapse conditions are noted.