Aerostatic stability analysis of a suspension bridge based on the stiffness matrix singularity criterion

Abstract

The risk of aerostatic instability of long-span bridges grows with their span length increase. The judgment criteria for the critical state of aerostatic stability vary across the studies, implying large errors and difficulty in revealing the instability mechanism. Addressing the above issue, this study proposes a new judgment criterion, implying that the structure's stiffness matrix should be singular, while the product of the eigenvector of zero eigenvalues and the load vector should not be zero. The proposed criterion is expected to locate the limit points of structural instability and shed more light on its essence, including the critical wind velocity and aerostatic stability mechanism. To this end, the detailed calculation process of the proposed method is presented. Its effectiveness and accuracy are verified by a case study of the Ma'anshan Yangtze River Bridge in China, featuring a suspension bridge with three towers. For the initial wind angles of attack at 0° and +3°, the overall stiffness matrix of the bridge was singular at the last loading step. The limit points of instability of the bridge were inferred based on the above criterion. The critical wind velocities for aerostatic stability were 122.7 and 120 m/s, respectively. However, the stiffness matrix was not singular at the −3°initial angle of attack.