MATHEMATICAL MODEL OF HEAD BEAMS OF BRIDGE CRANES WITH PRESTRESS

This paper examines issues related to the stress-strain state of a prestressed crane bridge. The purpose of the work is to develop a new mathematical model of the main girder of bridgetype cranes, which allows for investigating its stress-strain behavior under the simultaneous action of a vertical moving load, a static load from the weight of the girder itself, and an axial eccentric load. The main challenge lies in accurately accounting for these different forces, which act on the structure in complex ways, especially when considering the variable nature of the loads involved in crane operations. The presented new mathematical model is based on the general theory of stability of elastic systems, during the development of which the real conditions of the crane bridge construction were taken into account. In particular, the model reflects the effects of prestressing, which significantly influences the behavior of the bridge under load, as well as the geometric and material properties of the girder. The model also accounts for various factors, including the distribution of forces along the length of the girder, the effects of eccentric loading, and the impact of moving loads, which can cause dynamic responses that complicate the analysis. The obtained equations of the deflection curve of this beam made it possible to conduct research and analyze one of the main performance criteria of lifting machines – static stiffness and static strength, depending on the ratio of longitudinal and transverse forces acting on the beam. By studying these parameters, it is possible to determine how the crane's structure will respond to different loading scenarios, ensuring that the crane can perform its intended functions safely and efficiently. The results obtained in this work can be used in the future in the design and modernization of cranes to increase their load capacity, extend their service life without dismantling, and improve the existing engineering calculation methods at both the design stage and in real operation conditions. This research also opens the door to developing more advanced models for even greater accuracy in crane design.