Research on dynamic characteristics model test scheme for middle pylon of multi-pylon multi-span suspension bridges

Multi-pylon multi-span suspension bridge is a new type super flexible structure system, and the rigidity design of middle pylon is one of the main difficult technical issues. Due to the requirements of longitudinal rigidity, the structural form and the corresponding foundation type of middle pylon are different from those of the ordinary steel pylon, and the complicated dynamic characteristics make the calculation quite difficult. In this article, exploration has been made in selection of similarity ratio and model materials, section simulation, restriction conditions simulation, fixing of mass blocks, fabrication scheme and testing method by taking into account different construction and working conditions such as restriction conditions and working environment of a three-pylon suspension bridge, to conduct the test experimental design of the dynamic behavior of the middle pylon, with the purpose to reveal its dynamic characteristics and make comparison and analysis with theoretical assumptions, to provide basis for anti-wind and anti-seismic design and reference for the design and research of three-pylon two-span suspension bridges in the future.

Defect Inspection Technology for Steel Truss Suspension Bridges

Steel truss suspension bridges are prone to developing defects after prolonged use.These defects may include corrosion of the main cable or the steel truss.To ensure the normal and safe functioning of the suspension bridge,it is necessary to inspect for defects promptly,understand the cause of the defect,and locate it through the use of inspection technology.By promptly addressing defects,the suspension bridge’s safety can be ensured.The author has analyzed the common defects and causes of steel truss suspension bridges and proposed specific inspection technologies.This research is intended to aid in the timely discovery of steel truss suspension bridge defects.

A method for calculating strand tension in the anchor span of a suspension bridge considering the rotation of a splay saddle

This paper reports a method for strand tension in anchor spans considering rotation.A kind of co-moved coordinate system,a saddle local coordinate system,was set up.This system implemented the rotation of the splay saddle through the rotation of the coordinate system,and all calculations proceeded in this coordinate system.Considering the rotation of the anchoring surface by the rotation of the local coordinate system of the anchoring surface,the anchorage point coordinates of strands were transformed to the local sadle coordinate system.There was a two-layer iteration adopted in the calculation.In the inner iteration,the cable force at the end of the vertical bend was taken as the variable,and the ordinate of the anchorage point was taken as the target value.In the outer iteration,the vertical tangential angle at the end of the vertical bend was taken as the variable,and the ordinate of the anchorage point was taken as the target value.The method carried out the rotation of the splay saddle and anchor surface and was simple,convenient and without approximation.The effect of rotation was considered precisely;it showed stability during the process of two-layer iteration,powerful adaptation and higher efficiency and had been successfully applied in the construction control of the Wufengshan Yangtze River Bridge,the world's first kilometer-level combined highway and railway suspension bridge.

Mechanical deformation properties of Continuous Welded Rail on kilometer-span suspension bridge for high-speed railway

The complex bridge-track interaction between kilometer-span bridges and continuous Welded Rail(CWR)brings great challenges to CWR designing.Taking a suspension bridge with laying CWR as a case,the mechanical properties of CWR on the bridge are analyzed to reveal the sensitive areas of the track,and the design method of CWR and track structures on the beam ends are proposed.The results show that the unidirectional Rail Expansion Joints(REJ)need to be installed on the beam end of the kilometer-span bridge to reduce rail longitudinal force.Due to the bridge characteristics,there is no CWR fixed area on the kilometer-span bridge,and rail longitudinal force on the main span caused by bending loads needs to be concerned.The deformation of track on the beam end is complex,which is the weak area on the kilometer bridge,the large relative displacement between the stock rail of REJ and the main beam can cause poor stability of ballast bed on beam end,small resistance fasteners need to be laid on the sides of stock rail on the main beam to increase the stability of ballast and fasteners on the beam end.To improve the driving safety and comfort of beam end,the Sleeper-Supporting Apparatus(SSA)should be specially designed to ensure the uniform transition of track on beam ends.Temperature and wind loads have a significant impact on track regularity on the kilometer span bridge,the dynamic response of trains and bridges under those loads needs to be attended to.

Long-Time Behavior of Solution for Autonomous Suspension Bridge Equations with State-Dependent Delay

This work is devoted to the following suspension bridge with state-dependent delay: . The main goal of this paper is to investigate the long-time behavior of the system. Under suitable hypothesis, the quasi-stability estimates of the system are established, based on which the existence of global attractor with finite fractal dimension is obtained. Furthermore, the existence of exponential attractor is proved.

Comparable study on typhoon and strong northern wind characteristics of the Runyang Suspension Bridge based on field tests

The strong wind characteristics of the Runyang Suspension Bridge（ RSB） including the wind speed and direction, the turbulence intensity, the turbulence integral length and power spectrum are analyzed based on measurement data from the wind environment monitoring subsystem of the structural health monitoring system （SHMS）of the RSB and field tests during strong winds. The differences between the typhoon and the strong northern wind are especially studied. It is found that the mean wind speed of the strong northern wind is a little smaller and the mean wind direction is more stable than that of the typhoon. The turbulence intensity of both the typhoon and the strong northern wind is greater than the values suggested in Chinese code, and the turbulence integral length difference between the typhoon and a strong northern wind is not clear. As for the along-wind turbulence power spectrum, the spectrum of the strong northern wind can fit the Kaimal spectrum better than that of the typhoon. The obtained results can provide measurement data for founding a strong wind characteristic database and determining the strong wind characteristic parameter values of the RSB.

Measurement of wind field characteristics at a long-span suspension bridge

In order to provide a reliable basis for wind resistant evaluation of a long-span suspension bridge, a structural health monitoring system is installed on a bridge in the East China Sea and the simultaneous wind data at the bridge deck and at the top of the bridge tower are recorded. The average wind speeds and directions, variations of wind speeds with height, turbulent characteristics, spatial correlation and characteristics of wind flow around the bridge deck are analyzed by using statistical methods and spectral analysis. It is found that the average wind speeds along the bridge girder are almost identical; however, the mean wind directions vary greatly at different locations. The dimensionless exponent decreases as the average wind speed increases. The measured turbulence intensities are greater than the recommended values, and the turbulence power spectrum can well fit the standard spectrum. However, the measured spectral values are considerably smaller in low frequency ranges. The mean wind speed of the wake flow decreases and the turbulence intensity increases significantly, and the spectral characteristics of the wake flow change obviously while the feature frequency of vortex shedding has not yet been observed.

Operational modal identification of suspension bridge based on structural health monitoring system

An output-only modal identification method by a combination use of the peak-picking method and the cross spectrum methods are presented. Meanwhile, a novel mode shape optimum method of the deck is proposed. The methods are applied to the operational modal identification system of the Runyang Suspension Bridge, which can be used to obtain the modal parameters of the bridge from out-only data sets collected by its structural health monitoring system （SHMS）. As an example, the vibration response data of the deck, cable and tower recorded during typhoon Matsa excitation are used to illustrate the program application. Some of the modal frequencies observed from deck vibration responses are also found in the vibration responses of the cable and the tower. The results show that some modal shapes of the deck are strongly coupled with the cable and the tower. By comparing the identification results from the operational modal system with those from field measurements, a good agreement between them is achieved, but some modal frequencies identified from the operational modal identification system （OMIS）, such as L1 and L2, obviously decrease compared with those from the field measurements.

Finite element model updating and validating of Runyang Suspension Bridge based on SHMS

Based on the finite element （FE） program ANSYS, a three-dimensional model for the Runyang Suspension Bridge （RSB） is established. The structural natural frequency, vibration mode, stress and displacement response under various load cases are given. A new method of FE model updating is presented based on the physical meaning of sensitivity and the penalty function concept. In this method, the structural model is updated by modifying the parameters of design, and validated by structural natural vibration characteristics, stress response as well as displacement response. The design parameters used for updating are bounded according to measured static response and engineering judgment. The FE model of RSB is updated and validated by the measurements coming from the structural health monitoring system （SHMS）, and the FE baseline model reflecting the current state of RSB is achieved. Both the dynamic and static results show that the method is effective in updating the FE model of long span suspension bridges. The results obtained provide an important research basis for damage alarming and health monitoring of the RSB.

Damage warning of suspension bridges based on neural networks under changing temperature conditions

This paper aims at successive structural damage detection of long-span bridges under changing temperature conditions.First,the frequency-temperature correlation models of bridges are formulated by means of artificial neural network techniques to eliminate the temperature effects on the measured modal frequencies.Then,the measured modal frequencies under various temperatures are normalized to a reference temperature,based on which the auto-associative network is trained to monitor signal damage occurrences by means of neural-network-based novelty detection techniques.The effectiveness of the proposed approach is examined in the Runyang Suspension Bridge using 236-day health monitoring data.The results reveal that the seasonal change of environmental temperature accounts for variations in the measured modal frequencies with averaged variances of 2.0%.And the approach exhibits good capability for detecting the damage-induced 0.1% variance of modal frequencies and it is suitable for online condition monitoring of suspension bridges.

Synthetical condition assessment of long span suspension bridge based on closeness degree and FAHP

Based on the theory of pattern recognition, the concept of closeness degree between fuzzy sets is brought into the condition assessment of long span bridges. Using the fuzzy analytic hierarchy process （FAHP）, a mathematical model of a multi-objective assessment of a long span suspension bridge is set up. An example is given to show the procedure in the synthetical condition assessment of the Runyang Suspension Bridge, which includes the hierarchical division, the definition of factor weights and fuzzy membership functions, and the calculation of closeness degrees, etc. The assessment combines both the data from the health monitoring system and the manual tests. The classification of evaluation items as well as the calculation of deterministic and nondeterministic items is presented. Compared with the traditional method of point rating, this method can better describe the discreteness of monitoring data and the fuzziness in the condition assessment.

Spatial structural analysis of main saddle for single tower spatial cable self-anchored suspension bridge

Based on the engineering background of the Jiangxinzhou Bridge in Nanjing, issues related to the spatial main saddle of the self-anchored suspension bridge are studied. The refinement finite element model is established by the secondary development technology based on the platform of the general finite element program, and a reasonable load pattern is used in its spatial structural analysis, by which its path of force transference and stress distribution are obtained. Matched with the spatial main cable, the tangency point correction method is also discussed. The results show that the lateral wall stress of the saddle groove is higher than the stress within the wall due to the role of lateral forces in the finished bridge state; the horizontal volume force of the main cable can generate a gradient distributed vertical extrusion pressure on the saddle clamping device and the main saddle body; the geometric nonlinear effect of the self- anchored suspension bridge cable system in the construction process is significant, which can be reflected in the spatial tangent point position of the main cable with the main saddle changes a lot from free cable to finished cable.

Structural condition assessment of long-span suspension bridges using long-term monitoring data

This paper focuses on developing an online structural condition assessment technique using long-term monitoring data measured by a structural health monitoring system. The seasonal correlations of frequency-temperature and beam-end displacement-temperature for the Runyang Suspension Bridge are performed, first. Then, a statistical modeling technique using a six-order polynomial is further applied to formulate the correlations of frequency-temperature and displacement-temperature, from which abnormal changes of measured frequencies and displacements are detected using the mean value control chart. Analysis results show that modal frequencies of higher vibration modes and displacements have remarkable seasonal correlations with the environmental temperature and the proposed method exhibits a good capability for detecting the micro damage-induced changes of modal frequencies and displacements. The results demonstrate that the proposed method can effectively eliminate temperature complications from frequency and displacement time series and is well suited for online condition monitoring of long-span suspension bridges.

Non-linear buffeting response analysis of long-span suspension bridges with central buckle

The rigid central buckle employed in the Runyang Suspension Bridge (RSB) was the first time it was used in a suspension bridge in China. By using a spectral representation method and FFT technique combined with measured data,a 3D fluctuating wind field considering the tower wind effect is simulated. A novel FE model for buffeting analysis is then presented,in which a specific user-defined Matrix27 element in ANSYS is employed to simulate the aeroelastic forces and its stiffness or damping matrices are parameterized by wind velocity and vibration frequency. A nonlinear time history analysis is carried out to study the influence of the rigid central buckle on the wind-induced buffeting response of a long-span suspension bridge. The results can be used as a reference for wind resistance design of long-span suspension bridges with a rigid central buckle in the future.

Structural health monitoring of long-span suspension bridges using wavelet packet analysis

During the service life of civil engineering structures such as long-span bridges, local damage at key positions may continually accumulate, and may finally result in their sudden failure. One core issue of global vibration-based health monitoring methods is to seek some damage indices that are sensitive to structural damage, This paper proposes an online structural health monitoring method for long-span suspension bridges using wavelet packet transform （WPT）. The WPT- based method is based on the energy variations of structural ambient vibration responses decomposed using wavelet packet analysis. The main feature of this method is that the proposed wavelet packet energy spectrum （WPES） has the ability to detect structural damage from ambient vibration tests of a long-span suspension bridge. As an example application, the WPES-based health monitoring system is used on the Runyang Suspension Bridge under daily environmental conditions. The analysis reveals that changes in environmental temperature have a long-term influence on the WPES, while the effect of traffic loadings on the measured WPES of the bridge presents instantaneous changes because of the nonstationary properties of the loadings. The condition indication indices VD reflect the influences of environmental temperature on the dynamic properties of the Runyang Suspension Bridge. The field tests demonstrate that the proposed WPES-based condition indication index VD is a good candidate index for health monitoring of long-span suspension bridges under ambient excitations.

Determination of reasonable finished state of self-anchored suspension bridges

A systematic and generic procedure for the determination of the reasonable finished state of self-anchored suspension bridges is proposed, the realization of which is mainly through adjustment of the hanger tensions. The initial hanger tensions are first obtained through an iterative analysis by combining the girder-tower-only finite element(FE) model with the analytical program for shape finding of the spatial cable system. These initial hanger tensions, together with the corresponding cable coordinates and internal forces, are then included into the FE model of the total bridge system, the nonlinear analysis of which involves the optimization technique. Calculations are repeated until the optimization algorithm converges to the most optimal hanger tensions(i.e. the desired reasonable finished bridge state). The "temperature rigid arm" is introduced to offset the unavoidable initial deformations of the girder and tower, which are due to the huge axial forces originated from the main cable. Moreover, by changing the stiffness coefficient K in the girder-tower-only FE model, the stiffness proportion of the main girder, the tower or the cable subsystem in the whole structural system could be adjusted according to the design intentions. The effectiveness of the proposed method is examined and demonstrated by one simple tutorial example and one self-anchored suspension bridge.

Test and numerical investigations on static and dynamic characteristics of extra-wide concrete self-anchored suspension bridge under vehicle loads

The present work is aimed at studying the mechanic properties of the extra-wide concrete self-anchored suspension bridge under static and dynamic vehicle loads. Based on the field test using 12 heavy trucks and finite element simulations, the static deformations of different components, stress increments and distributions of the girder, as well as the vibration characteristics and damping ratio of the Hunan Road Bridge were analyzed, which is the widest self-anchored suspension bridge in China at present. The dynamic responses were calculated using the Newmark-β integration method assisted by the simulation models of bridge and vehicles, the influences on the dynamic impact coefficient(DIC) brought by the vehicle parameters, girder width, eccentricity travel and deck flatness were also researched. The spatial effect of the girder is obvious due to the extra width, which performs as the stress increments distribute unevenly along the transverse direction, and the girder deflections and stress increments of the upper plate change as a "V" and "M" shape respectively under the symmetrical vehicle loads affected by the shear lag effect, cross slope and local effect of the wheels, the maximum of stress increments are located in the junctions with the inner webs. The obvious girder torsional deformation and the apparent unevenness of the hanger forces between the two cable planes under the eccentric vehicle loads, together with the mode shapes such as the girder transverse bending and torsion which appear relatively earlier, all reflect the weakened torsional rigidity of the extra-wide girder. The transverse displacements of towers are more obvious than the longitudinal ones. As for the influences on the DIC, the static effect of the heavier vehicles plays a major role when pass through with a higher speed and the changes of vehicle suspension stiffness generate greater impacts than the suspension damp. The values of DIC in the vehicle-running side during the eccentric travel, affected by the restricts from the static effects of the eccentric moving trucks, are significantly smaller than the vehicle-free side, the increase in the road roughness is the most sensitive one among the above influential factors. The results could provide references for the design, static and dynamic response analysis of the similar extra-wide suspension bridges.

Numerical investigation of temperature gradient-induced thermal stress for steel–concrete composite bridge deck in suspension bridges

A3D finite element model(FEM)with realistic field measurements of temperature distributions is proposed to investigate the thermal stress variation in the steel–concrete composite bridge deck system.First,a brief literaturereview indicates that traditional thermal stress calculation in suspension bridges is based on the2D plane structure with simplified temperature profiles on bridges.Thus,a3D FEM is proposed for accurate stress analysis.The focus is on the incorporation of full field arbitrary temperature profile for the stress analysis.Following this,the effect of realistic temperature distribution on the structure is investigated in detail and an example using field measurements of Aizhai Bridge is integrated with the proposed3D FEM model.Parametric studies are used to illustrate the effect of different parameters on the thermal stress distribution in the bridge structure.Next,the discussion and comparison of the proposed methodology and simplified calculation method in the standard is given.The calculation difference and their potential impact on the structure are shown in detail.Finally,some conclusions and recommendations for future bridge analysis and design are given based on the proposed study.

Parametric analysis on buffeting performance of a long-span high-speed railway suspension bridge

The buffeting performance of kilometer-level high-speed railway suspension bridges has a great impact on the smooth operation of high-speed trains.To investigate the buffeting performance of the structure significantly different from traditional suspension bridges,the first long-span high-speed railway suspension bridge,Wufengshan Yangtze River Bridge(WYRB),is taken as a numerical example to demonstrate the effects of structural parameters and wind field parameters on the buffeting responses.Based on the design information,the spatial finite element model(FEM)of WYRB is established before testing its accuracy.The fluctuating wind fields are simulated via both classical and stochastic wave based spectral representation method(SRM).Finite element method is further taken to analyze the parametric sensitivity on wind induced buffeting responses in time domain.The results show that the vertical displacement is more sensitive to the changing dead load than the lateral and torsional ones.The larger stiffness of the main girder and the lower sag-to-span ratio are both helpful to reduce the buffeting responses.Wind spectrum and coherence function are key influencing factors to the responses so setting proper wind field parameters are essential in the wind-resistant design stage.The analytical results can provide references for wind resistance analysis and selection of structural and fluctuating wind field parameters for similar long-span high-speed railway suspension bridges.

Influence of central buckle on suspension bridge dynamic characteristics and driving comfort

The central buckle, which is often used in a suspension bridge, can improve bridges' performance in the actual operation condition. The influence of the central buckle on natural vibration characteristics and bridge-deck driving comfort of a long-span suspension bridge is studied by using a case study of Siduhe Suspension Bridge in China. Based on the finite element software ANSYS and independently complied program, the influence of the central buckle on the structure force-applied characteristics of a long-span suspension bridge has been explored. The results show that the huge increases of natural frequencies can result in the presence of central buckles because of the increases of bending and torsional rigidities. The central buckle basically makes the stiffening girders and cables within the triangular area covered as a relatively approximate rigid area. Hence, the central buckle can reduce the torsional displacement of the main girder. However, the increases of bending and torsional rigidities have little influence on the impact factor, which is obtained by using vehicle-bridge coupled vibration analysis. This means that the central buckle has little effect on the comfort indices. In addition, it is found that the central buckle can enhance the bridge deck's driving stability due to the decrease of the torsional displacements of the main girder.