Response Of Long-span Suspension Bridges Research Articles

A simplified analysis method for long-span suspension bridges within the deck overlay retrofitting process from asphalt to UHPC

The steel-ultrahigh performance concrete (UHPC) lightweight composite deck (LWCD) is increasingly adopted by in-service steel bridges to address the fatigue cracking issue for orthotropic steel decks (OSDs) and the premature damage issue for asphalt overlays. While for in-service long-span suspension bridges that need to be retrofitted by LWCDs, the response of the UHPC layer in casting is complex. Within the UHPC casting process, the moment of the stiffening girder changes continuously as the self-weight of the stiffening girder changes in casting, and the change of moment will produce strains in the UHPC portion set earlier; in other words, the UHPC portion cast latter will produce strains in the UHPC portion cast earlier. If the resultant tensile strains are too high, the UHPC layer may crack within the casting process, which should be avoided. In this paper, a simplified analysis method, based on the linearized deflection theory, was proposed to rapidly obtain the response of long-span suspension bridges in retrofitting without significantly compromising the accuracy of the analysis results. A new solving method based on exponential functions was proposed, which is simpler than the commonly used hyperbolic function-based method. The proposed method was implemented as computer codes in Matlab and verified through two examples: a single-span suspension bridge and a three-span suspension bridge. The simplified analysis method was used to perform a detailed analysis for the Yichang Yangtze River Expressway Bridge (YYREB), a 960-m-long single-span suspension bridge in China, for which the existing asphalt overlay was replaced by an LWCD in 2021. In the analysis, three cast sequences were considered for the UHPC layer, i.e., from end to end, from mid-span to ends, and from ends to mid-span. It is revealed that the mid span-to-ends cast sequence produces the minimum tensile strain in UHPC, so the cracking risk of UHPC could be well controlled by using this casting method. Thus, the mid span-to-ends cast sequence was adopted by the YYREB within the deck overlay retrofitting process from asphalt to UHPC.

Buffeting response of a suspension bridge based on the 2D rational function approximation model for self-excited forces

In the last thirty years, the aerodynamic nonlinearities related to the slow variation of the angle of attack produced by large-scale atmospheric turbulence and their impact on the buffeting response of long-span suspension bridges have been a hot topic in wind engineering research. Self-excited forces accounting for such an effect of turbulence have been crucial in predicting the dynamic response of bridge sectional models subjected to multi-harmonic gusts. In contrast, only few studies on full suspension bridges in realistic turbulent flows are available. To fill this gap, the 2D RFA model for self-excited forces, recently developed and experimentally validated by the authors, in this paper is incorporated into a stochastic time-variant state-space framework to assess the nonlinear buffeting response of a suspension bridge. The most important feature of this model is the modulation of the self-excited forces due to the spatio-temporal fluctuation of the angle of attack produced by low-frequency turbulence. Moreover, the nonlinear external buffeting forces are formulated to achieve a reasonable compromise between the conflicting needs of modelling both nonlinear and unsteady effects of wind velocity fluctuations. The model is applied to the Hardanger Bridge in Norway, considering different wind conditions. Indeed, the aerodynamic derivatives of this bridge deck cross-section present a strong dependence on the mean angle of attack. The results emphasise the significant impact on the buffeting response and flutter stability of considering time-variant self-excited forces, though in specific cases the classical time-invariant approach is found to provide accurate predictions of the bridge vibrations. Finally, the paper investigates the sensitivity of the response statistics to the model cut-offs used to separate the low-frequency and the high-frequency turbulence bands.

Time-variant self-excited force model based on 2D rational function approximation

Large-scale atmospheric turbulence produces large-amplitude low-frequency fluctuations of the angle of attack, which can significantly change the self-excited forces acting on a bridge deck. Such a nonlinear effect must be carefully modelled for an accurate prediction of the dynamic response of long-span suspension bridges to the turbulent wind. By assuming that the angle of attack varies slowly, a time-variant linear model relying on Roger’s rational function approximation (RFA) of the force transfer function is proposed, and a formulation of the problem in the state space is outlined. In particular, an existing model is improved by a flexible fitting of the RFA directly in the multivariate space of reduced velocity and angle of attack. Another contribution of the present work is the setup of an experimental procedure based on bi- or multi-harmonic forced-vibration tests to underscore the variation of magnitude and phase of self-excited forces under a time-variant angle of attack. These wind tunnel tests also allowed a sound experimental validation of the proposed model, considering two quite different bridge deck cross-sections as case studies. Aerodynamic derivatives for various angles of attack were measured to determine the parameters of the model. Despite its simplicity, the model yields accurate results up to relatively fast variations of the angle of attack, and it can reproduce the complicated behaviour of the self-excited forces revealed by the experiments. The performance of the model strongly depends on the goodness of the RFA-based fitting of aerodynamic derivatives, and the excellent results obtained were possible thanks to the high flexibility of the proposed method.

Study on Energy Dissipation of Viscous Damper for Long-Span Suspension Bridges

Viscous dampers are important devices to dissipate the vibration energy of long-span bridges. In the paper, nonlinear time history analysis was used to study the effects of this type of dam-per on suspension bridges. The influence of nonlinear viscous dampers on the seismic response of long-span suspension bridges was analyzed, which was based on a real project. The quantitative relationship between the displacement of the bridge girder and the tower with the damping coefficient and velocity index was investigated. The results showed that the displacement of the bridge girder under earthquakes can be effectively reduced by selecting the appropriate damping coefficient and velocity index of the nonlinear viscous dampers, and the best energy dissipation and seismic reduction effect for long-span suspension bridges can be obtained.

Seismic Performance of the Buckling-Restrained Brace Central Buckle for Long-Span Suspension Bridges

In this paper, a novel central buckle composed of buckling-restrained braces (BRBs) is developed for long-span suspension bridges, and its preliminary design procedure is presented. Seismic performance of suspension bridges equipped with BRB central buckles is investigated and compared with those with conventional central buckles (e.g. rigid or flexible central buckles). Furthermore, the effect of BRB yield force, as well as the effectiveness of BRB central buckles combined with viscous dampers, is evaluated using parametric analyses. The results indicate that the BRB central buckle is more effective than other central buckles in reducing both the longitudinal girder displacements and force demands on towers during an earthquake. Furthermore, the combination of BRB central buckles and viscous dampers is a superior option for mitigating the seismic response of long-span suspension bridges.

Vehicle-Induced Response of Long-Span Suspension Bridges with Steel and Carbon Fiber-Reinforced Polymer (CFRP) Cables and Suspenders

Vehicle-Induced Response of Long-Span Suspension Bridges with Steel and Carbon Fiber-Reinforced Polymer (CFRP) Cables and Suspenders

Study on Dynamic Characteristic and Seismic Response of Long-Span Suspension Bridge with 1960 MPa Cable Wire

In order to break through the limitation of the width of river, depth of water, channel and etc., it is an optimal choice to construct a long-span suspension bridge. In a suspension bridge, the main cable is the major bearing member; and the use of super high strength cable wire can lighten the dead weight and obtain an economical design. 1960 Mpa cable wire is adopted by an under-construction suspension bridge, namely Ni-Zhou Channel Bridge, for the first time in China. In this paper, taking the Ni-Zhou Channel Bridge as a case-study, comparative analyses on dynamic characteristic and seismic response of long-span suspension bridge with 1960 Mpa cable wire are performed. Firstly, dynamic calculating model for Ni-Zhou Channel Bridge is built and its dynamic characteristics are studied; then by using response spectrum and time history analysis method, seismic response of Ni-Zhou Channel Bridge is investigated on the basis of design response spectrum and artificial seismic ground motions; finally, the energy dissipation performances of a seismic protection devices (viscous damper) are also discussed. The results show that long-span suspension bridge with 1960 Mpa cable wire has a longer natural vibration period; the use of viscous damper can effectively reduce the peak value of bending moment in stiffening girder. This paper can provide references for the project’s construction.

Effect of Pounding at Expansion Joints on Seismic Response of Long-Span Suspension Bridge under Strong Earthquakes

For a long-span suspension bridge, owing to a flexible structure system, the seismic displacement at the end of the deck may severely exceed the allowance under earthquake which due to the occurrence of the pound between the main span and the approach span usually which can causes the collision of falling-beams and structures. In this paper, based on the pounding phenomenon at expansion joints of long-span suspension bridge under strong earthquake and employing a typical long-span suspension bridges. With the time history analysis method of determining the nonlinear seismic responses, the pounding effects of adjacent girders at expansion joints on seismic responses of long-span cable-stayed bridge were studied. The results indicate that pounding can amplify the seismic demand of piers of the approach span and can also amplify the displacement of beam of the approach span, the relative displacement between main span and approach span and the hinge seat width of beam of approach span obviously and it causes easily the collision of falling-beams and structures under earthquakes.

Suppression of aerodynamic response of suspension bridges during erection and after completion by using tuned mass dampers

The suppression of aerodynamic response of long-span suspension bridges during erection and after completion by using single TMD and multi TMD is presented in this paper. An advanced finite-element-based aerodynamic model that can be used to analyze both flutter instability and buffeting response in the time domain is also proposed. The frequency-dependent flutter derivatives are transferred into a time-dependent rational function, through which the coupling effects of three-dimensional aerodynamic motions under gusty winds can be accurately considered. The modal damping of a structure-TMD system is analyzed by the state-space approach. The numerical examples are performed on the Akashi Kaikyo Bridge with a main span of 1990 m. The bridge is idealized by a three-dimensional finite-element model consisting of 681 nodes. The results show that when the wind velocity is low, about 20 m/s, the multi TMD type 1 (the vertical and horizontal TMD with 1% mass ratio in each direction together with the torsional TMD with ratio of 1% mass moment of inertia) can significantly reduce the buffeting response in vertical, horizontal and torsional directions by 8.6-13%. When the wind velocity increases to 40 m/s, the control efficiency of a multi TMD in reducing the torsional buffeting response increases greatly to 28%. However, its control efficiency in the vertical and horizontal directions reduces. The results also indicate that the critical wind velocity for flutter instability during erection is significantly lower than that of the completed bridge. By pylon-to-midspan configuration, the minimum critical wind velocity of 57.70 m/s occurs at stage of 85% deck completion.

Motion Stability of Long‐Span Bridges under Gusty Winds

The effects of spanwise wind-velocity correlation and turbulence intensity on the coupled vertical-torsional response of long-span suspension bridges are studied. Turbulence is accounted for in the self-excited loads that are expressed in terms of the indicial aerodynamic functions. Buffeting forces enter the stability calculations because they are related to the self-excited loads through the common turbulence field. Assuming the wind-turulence terms to be Gaussian white-noise processes, the coupled parametric-type equations of motion are transformed into an Ito stochastic differential equation. Stationary response moments are obtained for both vertical and torsional displacemnts for different degrees of spanwise correlation and turbulence intensity. Motion instability is determined when responses become asymptotically unbounded. Higher turbulence leads to lower critical wind velocity for constant correlation, but less correlation results in higher critical velocity for constant turbulence. Higher turbulence leads to a more gradual transition from a stable to an unstable state.