Behavior analysis of span structures with cracks during vibrations

Abstract

Introduction: An important engineering task is to assess the state of span structures during their operation in various conditions and develop a methodology not only for determining the current state of the structure and its individual elements but also for predicting life cycle stages. This work is dedicated to the study of the influence of the location and crack size located in the tension region of the beam cross-section on the value of the natural oscillations frequency of the main beam of the superstructure. The article proposes a method for determining the location and parameters of crack opening in the tension region of a pin-ended beam, which is the span structure base, by analyzing several vibration frequencies. Methods: The bridge crossing beam is modeled using the Euler-Bernoulli-type flexural theory. Crack modeling was carried out using the flexibility function, with the account of the location and length of the crack. A mathematical expression is formulated to determine the location and length of an open crack in the tension region of a pin-ended beam. The MATLAB program was used for numerical studies and simulation modeling of the problem of determining the crack parameters. Results: Values of the bridge girder’s natural resonance frequency with a crack in different places along the span and different lengths of the crack in the tension region of the cross-section were obtained. The relationship between the relative crack length and the relative fundamental beam frequency with a crack for different coordinates of its location and also the relationship between the relative location and the relative fundamental beam frequency with a crack for different crack length values are constructed. These given values are proposed to be used as criterion parameters for assessing the state and possible scenarios for the further operation of the beam span. Discussion: The results obtained show that with an increase in the relative length and relative coordinate of the crack initiation site, the natural frequency decreases. Based on the study results, the conclusion was formulated that cracks in the hinged beam tension region with a relative crack length and a relative location of less than 0.1 deserve the least attention. On the other hand, it is necessary to conduct a study to assess the state of a damaged bridge beam with a relative crack location of more than 0.1 and a relative crack length of less than 0.3, and after the analysis, a decision should be made on the possible modes of further operation of the engineering structures. For span structures whose beams have cracks with a relative crack location of more than 0.1 and a relative crack length of more than 0.3, a detailed study and examination of a structure are required, with the development of recommendations for the required repair work.