A Stochastic Finite Element Approach to Determine the Safety of Suspension Bridge Cables

Abstract

A new methodology to determine the safety of suspension bridge main cables is proposed and illustrated on a corrosion-deteriorated cable composed of 9061 wires. The approach is the first one incorporating a finite element (FE) model to predict the cable’s failure load, accounting for load recovery due to friction in broken wires and simulating the reduced cable's strength as a three dimensional random field. In order to obtain the breaking load of a cable, the load is increased gradually (quasi-static loading) in a cable’s FE model, having wires break a few at a time according to their residual strength. Because of the load transfer to surrounding wires, the breakage of an individual wire affects the stress state inside the surrounding wires. This local damage eventually causes a global reduction in the load carrying capacity of the cable, up to a complete failure. The safety of the cable is determined through a Monte Carlo simulation, in which the reduced strength of the cable is generated for every realization through the Spectral Representation Method (SRM) and is input as a material parameter in the FE model. The statistics of the load that will drive a suspension bridge cable to failure under a hypothetical deterioration state are obtained at the end of the simulation. INTRODUCTION The structural function of the main cables in suspension bridges is to transfer the tension load, derived by supporting the roadway, to the towers. The main cables are composed of thousands of high strength parallel steel wires with a diameter of approximately 5 mm bundled together in strands either built in situ or prefabricated. These strands are then compacted and tightened together and eventually the cross section of the cable becomes semi-circular. The wires in pristine conditions have a strength ranging from 1570 MPa to 1800 MPa. However with aging, fatigue loading, and harsh environmental conditions, the wires strength reduces significantly (Shi et al., 2007). Field observations of aging suspension bridges indicate serious distress of