Dynamic instability criteria of large-span ground-supported truss arches

This research focuses on ground-supported steel truss arches for a gymnasium in Guangzhou, China, addressing potential elastoplastic dynamic instability issues caused by typhoons. An energy conversion criterion was initially proposed based on a discrete Lyapunov functional. The vibration responses, energy conversion patterns, and plastic deformation characteristics of the truss arches under 1.0, 1.2, and 1.3 times the reference wind pressure (RWP) were examined using the dynamic relaxation method in conjunction with finite element analysis (FEA). The results indicated that, under a load release of 1.0 to 1.2 times the RWP, the system exhibited stable periodic energy conversion, with an absolute Lyapunov exponent value of less than 1, demonstrating the dynamic stability of the structure. However, as the load release increased to 1.3 RWP, the energy conversion process displayed abrupt changes, leading to the formation of plastic hinges at the abutments, which resulted in asymmetric degradation of structural stiffness. The Lyapunov exponent diverged, causing the system to enter a state of nonlinear dynamic instability. The release of wind load resulted in an asymmetric distribution of plastic hinges along both sides of the truss arches, complete interruption of energy conversion, and significant vibration amplitudes in the Poincaré section, ultimately leading to a loss of load-bearing capacity. This research highlights the effectiveness of the discrete Lyapunov function in exploring dynamic stability, providing a theoretical basis for safety control in wind resistance engineering.