# Optimisation of Box Girder Design of Overhead Cranes
## 3 Application of the Developed Methodology and Parameterisation of the Bridge Crane Cross-Section  
Based on the given input parameters (boundary conditions), the objective of this chapter will be to use the developed optimisation methodology to design and parameterise the box section of the overhead crane. The optimisation is solved for a closed box girder cross-section with longitudinal and transverse stiffeners. In any structural design, some structural parameters are given, and some can be changed at will by the designer. In the case of gantry crane structures, the capacity of the structure is specified, as well as the speed of travel and stroke, height of travel, and span of the bridge. The choice of the type of structure, the choice of materials, and the dimensions of the load-bearing parts remain the task of the designer, and the design is usually based on an already implemented solution. Normally, the choice of the cross-section of the girder (bridge) depends on the dimensional parameters and on the type of crane service load expected. The height of the bridge girders is determined by the optimum between structural, functional, deformation, and strength requirements. The crane bridge itself must be sufficiently rigid so that it does not deform under loading. However, an unnecessarily large weight of the crane bridge increases not only the production cost of the crane but also the operating costs and, at the same time, the stresses on the crane runway. Thus, great emphasis is also placed on the weight of the girder itself, and the height of the main girder is always influenced by the bending moment in the strength check with regard to the ultimate limit state. Emphasis is also placed on the serviceability limit state, which is defined as the quadratic moment of the cross-section in the deflection check. In terms of structural stresses, the crane bridge is bent as a closed frame, bent in the horizontal and vertical planes and, in addition, twisted. Therefore, the main girder often takes the form of a box structure with a rectangular cross-section (Figures 6 and 7). In such cases, the flanges are of greater thickness and the uprights are thin-walled; local stability of the wall is achieved by reinforcement at regular intervals (transverse reinforcement). In order to make the cross-section better able to withstand torsional stresses, the walls are reinforced internally with transverse baffles (diaphrags) [24]. Figure 5: Procedure for finding the optimal solution. As the stability failure of uprights usually occurs in the upper fifth to quarter of the beam height, the risk of buckling can be reduced by welding in longitudinal reinforcing angles. The transverse stiffeners are spaced 100 to 125% of the height of the main beam. Normally, the width of the projecting part of the bracing should not be less than \(1/15\) of the width of the projecting part of the structure. The height of the box girder shall be selected in the range of \(1/15\) to \(1/20\) of the span. The ratio of the height to the width of the rectangular cross-section should not be greater than 3.5 times. The thickness of the rack shall be at least 5 mm and shall be increased with regard to the stability of the wall. All bent beams shall have part of the cross-section loaded in compression. For this reason, there is an increased risk of loss of shape stability in these beams and therefore the loss of stability must be taken into account in the form of constraining conditions when optimising the design. Using the example of a steel structure of an existing 50 t capacity crane with box girder beams as shown in Figure 8, we will show the dimensional optimisation procedure and its results, where the main optimisation criterion was the weight of the beams. Figure 6: Single crane box girder cross-sections. Figure 7: Cross-sections of box girders with reinforcements of a 250 t capacity casting crane.