Optimization of bridge trusses height and bars cross-sections

The problems of optimal design of truss-type structures, aimed at determining the minimal volume (weight) of the structure, while optimizing the bar cross-sections and the truss height, are considered. The considered problem is treated as a nonlinear problem of discrete optimization. In addition to the internal forces of tension or compression, the elements of the truss can have the bending moments. The cross-sections of the bars are designed of the rolled steel profiles. The mathematical models of the problem are developed, taking into account stiffness and stability requirements to structures. Nonlinear discrete optimization problems, formulated in this paper, are solved by the iterative method using the mathematical programming environment MATLAB. The buckling ratios of the bars under compression are adjusted in each iteration. The requirements of cross-section assortment (discretion) are secured using the method of branch and bound.