OPTIMIZATION OF THE BOX SECTION OF THE MAIN GIRDERS OF THE BRIDGE CRANE FOR THE CASE OF PLACING THE RAIL IN THE MIDDLE OF THE TOP FLANGE

Abstract and figures

This paper considers the problem of optimization of the box section of the main girder of the bridge crane for the case of placing the rail in the middle of the top flange. Reduction of the girder mass is set as the objective function. The method of Lagrange multiplier was used as the methodology for approximate determination of optimum dependences of geometrical parameters of the box section. The criterion of strength were applied as the constraint function. The analysis of the optimization results and the solutions was the basis for recommendations which are significant for designers during construction of cranes. The main task in the process of designing the carrying structure of the bridge crane is determination of optimum dimensions of the main girder box section. The mass of the main girder has the largest share in the total mass of the bridge crane, so it is very important to perform its optimization in order to reduce the total costs of manufacturing the whole carrying structure. That is the reason why the selection of the optimum shape and geometrical parameters which influence the reduction of mass and costs of manufacturing is the subject of research of a lot of authors ([2], [3], [5], [7], [8], [9], [10], [11], [12], [14], [15], [16], [17] and [18]). Most authors set permissible stress or two constraint functions: permissible stress and permissible deflection as the constraint function. The analysis of cost structure for manufacturing metal structures made in [2], showed that the participation of material costs in the total costs is the largest (30-73) %, and that the other costs are lower. Having in mind all the above mentioned results and conclusions, the aim of this paper is to define optimum values of geometrical parameters of the box girder cross-section that will lead to the reduction of its mass. 2. MATEMATHICAL FORMULATION OF THE OPTIMIZATION PROBLEM