On the issue of determining the torsional stiffness of elements of load-bearing structures of bridge structures

Abstract

The torsional moment of inertia is an important geometric characteristic of the elements of spatial bridge structures. The torsional rigidity of the elements affects the nature of the structure’s operation both directly and indirectly. If this parameter is incorrectly determined, the theoretical behavior of the structure under load may show a significant difference from its actual operation. Therefore, the importance of correct calculation of the torsional stiffness of elements in the calculations of spatial structures cannot be overestimated. The main problem in determining the torsional moment of inertia is the high complexity of calculations for sections of a general type. Strict mathematical expressions only apply to circular sections. This paper discusses various methods that are most often used in the practice of engineering calculations of bridge structures. The main mathematical aspects of these methods are covered and their main advantages and disadvantages are briefly noted. For a T-section beam, typical of reinforced concrete bridge superstructures, comparative calculations were carried out using all the methods discussed in the article. It is shown that the results of calculations based on FEM, performed in the foreign program Midas Civil and the domestic program Paris, are in good agreement with each other, and show minimal deviation from the results calculated by the analytical method of membrane analogy. The sampling frequency of finite element meshes affects the uncertainty of the results. In the Midas Civil program, the selection of the optimal size of the final elements is carried out by the contractor by searching through various options. In the program Paris the selection of a finite element mesh is carried out automatically based on the conditions of minimizing calculation time and ensuring a minimum error in the results. Simplified approaches provide greater error but require minimal labor, therefore, it is advisable to use them only for sketch calculations. An increase in the frequency of dividing the section under consideration into rectangular primitives in simplified methods leads to an increase in the error of the calculation results. The most acceptable results are obtained with a minimum number of partitions.