Chaos theory analysis of a cable-stayed bridge: Part I. Finite element model development

Cable-stayed bridges can exhibit large amplitude irregular stay cable oscillations under certain conditions of combined traffic flow and rain-wind loads that can pose severe risks to structural integrity. To investigate the mechanisms causing this behavior, a high fidelity nonlinear finite element model of a typical cable-stayed bridge has been developed using LS-DYNA based on the design of the Bill Emerson Memorial Bridge at Cape Girardeau, MO. The model uses over 540,000 finite elements representing 1254 bridge components to fully describe the detailed real geometry of the bridge tower, deck, stay cables, edge girders and floor-beam support girders. Traffic loads on the bridge deck are simulated by a Poisson Distributed Pulse (PDP) stochastic process model involving multi-lane traffic flows of more than 300 vehicles of various axle loads with varying arrival rates. The response data sets generated by the LS-DYNA simulations were then analyzed for chaotic behavior with the software CTBR. This extracts the nonlinear system invariants, the Lyapunov exponents, to identify the chaotic behavior from the dynamics of the structural system. The simulations showed positive Lyapunov exponents at various locations of the bridge deck and the bridge stay cable network. The analysis of these results revealed that even in the absence of strong rain-wind excitations the bridge deck vibration exhibits significant chaotic behavior that could excite the stay cables into a stronger chaotic regime, especially at the upper portion of the networked stay cables. This illustrates a phenomenon often ignored or unable to be captured by conventional linear dynamics analysis. Analysis of actual data sets collected from a monitoring network on the bridge also confirmed this chaotic behavior.