Structural behaviour of cable-stayed bridges taking into account time-dependent behaviour

Abstract

The creep and shrinkage of concrete and the relaxation of cables cause long-term redistribution of internal forces and time-dependent deformations in concrete structures, steel-concrete composite structures and concrete cable-stayed bridges. They should be properly modelled for accurate prediction of their long-term behaviour and its effect on instantaneous structural responses at service.

An equivalent stress relaxation model is proposed for prestressing tendons based on the intrinsic stress relaxation, from which the equivalent creep coefficients can be obtained through a recursive algorithm. Based on the equivalent stress relaxation model, an accurate finite element analysis of time-dependent behaviour by time integration has been devised considering concrete creep, concrete shrinkage and cable relaxation. Concrete members are modelled by beam-column elements while tendons are modelled by truss elements with nodes connected to the beam axis by perpendicular rigid arms. It is found that the proposed relaxation model with time integration can provide a reliable method as well as benchmark solutions for time-dependent analysis. The numerical results obtained indicate that the interactions among these factors should be properly considered in analysing the long-term performance of concrete bridges.

Although time integration provides a reliable method for time-dependent analysis, both the computing time and memory requirement increase drastically with the number of time steps as the time-dependent strains of concrete and tendons within a time interval depend on the loading history up to that time. It is therefore necessary to develop a more efficient method to conduct time-dependent analysis.

The relaxation-adjusted elasticity modulus is introduced on the basis of equivalent creep coefficients of tendons. Then, an efficient tendon sub-element is put forward to cope with cables with arbitrary profiles. Finally, a more general single-step method is devised using the classical age-adjusted elasticity modulus to account for external loading and creep effect, the shrinkage-adjusted elasticity modulus to consider shrinkage effect and its interaction with concrete creep, and the relaxation-adjusted elasticity modulus to consider the effect of cable relaxation based on the finite element method. The numerical results obtained indicate not only the accuracy of the single-step method but also the significance of interaction among various time-varying factors.

Based on the time integration or single-step method, a systematic method is developed to monitor the long-term variations of dynamic properties of cable-stayed bridges taking into account various time-varying factors and geometric nonlinearities. Numerical studies show that, although geometric nonlinearities tend to reduce the natural frequencies, the time-dependent behaviour of concrete more than offsets it and tends to increase the natural frequencies in the long run.

A generic method is further presented to investigate the long-term dynamic response of vehicle-bridge interaction systems taking account of time-dependent behaviour. The vehicles are represented by a combination of mass-spring-damper systems while the bridge is modelled by finite elements. The surface roughness of bridge deck is simulated by spectral representation method and introduced to the coupled system properly. Based on the method, the individual and combined effects of various time-varying factors are studied in detail using various numerical examples.