Dynamic reduction in the calculation of bridge structures

Aleksander Makarov,Sergey Kalinovsky,Natalia Ermilova,P Akimov,N Vatin,A Tusnin,A Doroshenko

doi:10.1051/e3sconf/202126303002

Aleksander Makarov, Sergey Kalinovsky + Show 5 more

Open Access

https://doi.org/10.1051/e3sconf/202126303002

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Abstract

In modern bridge construction, on the one hand, there are increasing trends towards increasing bridge spans, which requires reducing the weight of structures. On the other hand, the use of structural elements made of various composite materials is expanding, which allows to significantly reduce the weight of the bridge structures as a whole. However, the creation of new forms of span structures of bridges requires more detailed calculations in order to optimize such forms, in particular the role of calculating the dynamic impact, because with increasing spans and weight loss, increases design flexibility and sensitivity to dynamic loads. In the present paper, the problems of solving an incomplete algebraic problem of eigenvalues and eigenvectors are considered. To increase the accuracy of the calculation and exclude the use of high-order matrices, a method of sequential reduction of the stiffness and equivalent mass matrices is proposed. The method is based on the construction of partial systems using a static transformation, followed by the solution of its own problem for the partial system. In the process of solving this problem through the eigenvectors of the system, the minor unknowns are reduced to the main ones. Dynamic reduction showed high calculation accuracy..

Highlights

A large number of bridges are built according to individual projects
Modern technologies allow us to use an extensive list of materials in bridge construction: aluminum, steels of various strengths-bimetallic [3], carbon fiber and other composites [4,5,6]
The problem is most often solved by increasing the thickness of the coating, which increases the weight of the structure and the stress in the longitudinal edge of the orthotropic plate adjacent to the main beam of the superstructure

Summary

Introduction

A large number of bridges are built according to individual projects. both unique structures and quite ordinary ones are created [1,2]. The problem is most often solved by increasing the thickness of the coating, which increases the weight of the structure and the stress in the longitudinal edge of the orthotropic plate adjacent to the main beam of the superstructure. Such a design solution is not effective and requires a detailed comprehensive study to find other solutions. The pronounced tendency to increase the length of bridge spans requires a reduction in the weight of the spans, which leads to an increase in the flexibility of the structure This means that the superstructure becomes more sensitive to dynamic loads. To avoid the appearance of resonant oscillations or a significant decrease in their amplitudes, calculations for dynamic effects are necessary, which are carried out by software complexes based on the finite element method

Justification of the dynamic reduction technique

The main stages of solving the problem and their analysis

Findings

Conclusions