Main Span Research Articles

Seismic behavior analysis of long-span cable-stayed bridge under bi-directional near-fault ground motions

In this paper, the seismic behaviors of a long-span cable-stayed bridge subjected to bi-directional near-fault ground motions are analyzed. The cable-stayed bridge with a main span of 432 m is selected as the research object and appropriately modeled using the OpenSees software. Ten sets of historical near-fault and far-field ground motions associated with the same earthquake event and site class are utilized as input excitations. Nonlinear time-history analyses are conducted to explore three key aspects: the influence of ground motion directionality, the effectiveness of the percentage rule and simplified Square-Root-of-Sum-of-Squares (SRSS) rule, and the main influential factors. The findings reveal that near-fault ground motions induce larger seismic responses compared to far-field ground motions. Moreover, the effects of ground motion directionality are more pronounced in near-fault scenarios than in far-field events. The percentage rule and simplified SRSS rule demonstrate minor significance in predicting the critical seismic responses. The bi-directional peak ground velocity (PGV) of seismic motions in the principal directions of the cable-stayed bridge may emerge as the primary factor influencing the seismic responses, making it a suitable intensity measure for bi-directional seismic fragility assessment.

Experimental and theoretical investigation of shear lag effect in twin box‐shaped composite girders of long‐span cable‐stayed bridges

AbstractSteel‐concrete composite box girders offer notable advantages such as high stiffness, excellent torsional performance, and light self‐weight, making them prevalent in large‐span bridges, particularly in cable‐stayed configurations. However, a persistent challenge arises from the shear lag effect in the concrete slab within the flanges induced by shearing interactions between the webs and flanges. Limited attention has been devoted to investigating the experimental and theoretical aspects of shear lag in long‐span cable‐stayed bridges with twin box‐shaped composite girders. This research addresses this gap by designing a segmental scale twin box‐shaped composite model specimen to simulate the cable spacing of the main girder in a cable‐stayed bridge, specifically targeting the shear‐lag effect. The study successfully captures the non‐uniform distribution of cross‐sectional strain in the top concrete slab. Subsequently, analytical strain solutions for the composite girder under mid‐span concentrated load and axial load are derived using the energy variation method. The theoretical model's applicability is then calibrated against experimental results. The investigation extends to the in‐situ testing of the Chibi Yangtze River Bridge, the world's largest steel‐concrete composite girder cable‐stayed bridge, boasting a main span of up to 720 m. An established finite element (FE) analysis model for the Chibi Yangtze River Bridge simulates the transverse stress distribution under typical construction conditions of CC6. Comparative analyses between the simulated results, calculated values from elementary beam theory, and the theoretical model against field‐measured values reveal that the FE model provides a more accurate estimation of the shear lag effect in the concrete slab. Notably, the FE model effectively reflects the bridge's characteristics and serves as a baseline for subsequent studies. This comprehensive investigation contributes significantly to the understanding and analysis of shear lag phenomena in twin box composite girders of cable‐stayed bridges. The integration of experimental, analytical, and construction site validations establishes robust tools for engineering design and the construction of safe and serviceable cable‐stayed bridges. The research augments knowledge regarding shear lag behavior and underscores the necessity to appropriately consider its effects in bridge analysis and design.

The influence of shear surface quality on the mechanical properties of long-span prestressed continuous rigid-frame bridge

PurposeThe long-span continuous rigid-frame bridges are commonly constructed by the section-by-section symmetrical balance suspension casting method. The deflection of these bridges is increasing over time. Wet joints are a typical construction feature of continuous rigid-frame bridges and will affect their integrity. To investigate the sensitivity of shear surface quality on the mechanical properties of long-span prestressed continuous rigid-frame bridges, a large serviced bridge is selected for analysis.Design/methodology/approachIts shear surface is examined and classified using the damage measuring method, and four levels are determined statistically based on the core sample integrity, cracking length and cracking depth. Based on the shear-friction theory of the shear surface, a 3D solid element-based finite element model of the selected bridge is established, taking into account factors such as damage location, damage number and damage of the shear surface. The simulated results on the stress distribution of the local segment, the shear surface opening and the beam deflection are extracted and analyzed.FindingsThe findings indicate that the main factors affecting the ultimate shear stress and shear strength of the shear surface are size, shear reinforcements, normal stress and friction performance of the shear surface. The connection strength of a single or a few shear surfaces decreases but with little effect on the local stress. Cracking and opening mainly occur at the 1/4 span. Compared with the rigid “Tie” connection, the mid-span deflection of the main span increases by 25.03% and the relative deflection of the section near the shear surface increases by 99.89%. However, when there are penetrating cracks and openings in the shear surface at the 1/2 span, compared with the 1/4 span position, the mid-span deflection of the main span and the relative deflection of the cross-section increase by 4.50%. The deflection of the main span increases with the failure of the shear surface.Originality/valueThese conclusions can guide the analysis of deflection development in long-span prestressed continuous rigid-frame bridges.

Full-field displacement measurement of long-span bridges using one camera and robust self-adaptive complex pyramid

Full-field motion with a high spatial resolution can reflect the health state of long-span bridges. Traditional structural health monitoring (SHM) systems measure the structural displacement at sparse points only. Despite the development of various methods for obtaining high-resolution responses, they fail to estimate the multi-scale motions of real long-span bridges. A novel full-field motion estimation method is proposed to directly measure the entire structural responses using one digital camera. In this approach, multi-scale motions of different components under unknown excitations are encoded in a complex pyramid. The parameters of the complex pyramid are determined by the localization index to record robust local phases at each measurement point. Two indices, namely, the spatial Laplacian of the phase and the amplitude value degradation index, are designed to adaptively estimate multi-scale displacements contained in the complex pyramid. The proposed method estimates the full-field displacements of a steel frame accurately in an experimental test. Moreover, the full-field displacement of the 1377-m long main span Tsing Ma Bridge is estimated using only one shot. Results suggest that the displacement estimated by the proposed method matches well with the GPS data and further visualizes the bridge mode shapes with a high resolution.

Effects of key parameters of hybrid cable-stayed suspension bridge on the fatigue resistance of side hangers in bonding zones

Hybrid cable-stayed suspension bridges (HCSBs) have excellent mechanical and spanning capacities. However, their hangers in the bonding zones experience high cyclic stresses, and their fatigue failure jeopardize HCSB safety. This study adopted a HCSB finite element model and applied the influence line method to assess the effects of the following six factors on the stress amplitudes of side hangers: ratio of hanger force to vertical force in the stay cable in the bonding zone, relative stiffness of the main beam in the bonding zone, number of hangers in the bonding zone, arrangement pattern of stay cables and hangers, suspension-to-span ratio, and number of auxiliary piers. The exemplary HCSB had asymmetric span arrangement and a main span of 1400 m. Nodal loads were imposed on the main beam in the entire bridge to obtain the influence lines of each hanger and identify the most unfavorable hanger. The values of the above six parameters of the model varied to obtain the new influence lines of each hanger and identify the most unfavorable hanger in the new reasonably completed state. The stress amplitudes of the hangers thus obtained ware compared with those in the original model, reflecting the effects of these six factors on the stress amplitudes in the most unfavorable hanger. Based on the above, the cyclic stress amplitudes of the side hangers were reduced by installing additional stay cables with optimization of their arrangement pattern and relative cross-sectional areas. The results are considered instrumental in improving the fatigue resistance of HCSBs hangers under realistic bridge engineering scenarios.

Basic Characteristics and Vibration-Serviceability-Related Properties of Recent Footbridges in China

Abstract Purpose This study identifies basic characteristics and vibration-serviceability-related properties of recent footbridges in China. Also, it characterizes relations between vibration-serviceability-related properties and basic characteristics. Methods A database is constructed for recent footbridges in China based on systematic literature survey. For each footbridge, it collects basic information (name, function, province, location, service year), structural information (girder cross-section type, main span length, width, bridge type, girder material, deck material, first lateral and vertical natural frequencies, first lateral and vertical damping ratios), response information (crowd density, acceleration responses, mitigation measures), etc. Results Data analysis shows natural frequencies decrease with increasing bridge span. Estimation relations are proposed to quantitatively express fundamental natural frequencies and main spans in vertical and lateral directions. Damping ratios vary from 0.0015 to 0.0325, indicating the low damping capacity of the footbridges. Footbridges with non-solid cross-section are more vulnerable to human-induced excitations. Most footbridges apply mitigation measures, with mitigation efficiency from 18% to 70%. Conclusion This study provides designers with first judgements on feasibility of footbridges’ design scheme, for instance, a first estimation of natural frequency. Also, the reported information may guide them towards right directions of better design scheme, for example, by adjusting structural information.

Novel long-span cable-stayed deck arch bridge: Concept and structural characteristics

To explore a cost-efficient bridge structure system and expand the options for long-span bridges in mountainous regions, we propose an innovative cable-stayed deck arch (CSDA) bridge with significant potential benefits. This paper discusses the conceptualization, structural design considerations, and implementable construction methods of this bridge-type. We trial designed two CSDA bridges with span arrangements of 268 + 350 + 268 m and 280 + 3 × 380 + 280 m to demonstrate the versatility of our proposal in different topographic situations and its ability to accommodate both single and multiple main spans. The finite element analysis confirms the mechanical properties and structural feasibility of the conceptual designs. A comprehensive comparison with other types of bridges under identical conditions reveals that this new hybrid bridge is not only lightweight in structure, excellent in performance, and elegant in form, but also cost savings and with minor environmental impact. The preliminary study indicates that the CSDA bridges are suitable for the construction demand of high-rise pier and long-span bridges in mountainous terrain, and also an economical option for the main span between 350 to 400 m.

Shake table test on support uplift force of long-span cable-stayed bridge under longitudinal ground motions

Since the excessive seismic support uplift force may cause the support failure of long-span cable-stayed bridges, this study focused on the support uplift force at the auxiliary pier for a double-tower cable-stayed bridge with a main span of 1088 m. A shake table test was designed and performed based on the 1/35-scale test model scaled from the prototype bridge. Details of the test model, including the scale factor, structural member configurations, boundary conditions, and the numerical validation were briefly presented. The test results show that although only the longitudinal ground motion was applied, significant seismic support uplift and compression forces would be generated in the bearings at the auxiliary pier, resulting in the bearing uplift. The vertical vibration of the deck contributed by the first vibration mode of the test model was one of the main causes of the bearing uplift, but no rigid-like pounding effect occurred due to the vertical nonlinear mechanical behaviour of the bearing. Furthermore, the effect of the bearing uplift on the main seismic responses of the test model was negligible.

A recurrence algorithm of time-dependent analysis for concrete bridges

This paper proposes an algorithm for time-dependent effects in the finite element analysis of concrete bridges. Based on the primary influence of concrete shrinkage and creep on bridge structures, the calculation formulas for the equivalent nodal load increments of beam elements caused by the shrinkage and creep effects were deduced according to the initial strain method. To simplify the calculation process and improve calculation speed, the formulas for shrinkage and creep in the bridge design code were fitted with an exponential function, and the recurrence equations for shrinkage and creep calculation were obtained. Thus, a finite element method formulation for concrete shrinkage and creep calculated according to the divided time steps was established. The algorithm was programmed into a self-developed program, and the correctness of the program's calculation was verified through 20 years of on-site monitoring results of a concrete girder cable-stayed bridge with a main span of 500 m. The method proposed in this paper can substantially improve the speed of the program to calculate the time-dependent effects during the construction and operation of large-span concrete bridges, while ensuring the reliability of the calculation results, and is easy to be applied in various types of finite element method programs.

Thermal boundary conditions for heat transfer analysis of bridges considering non-uniform distribution of internal air temperature by computational fluid dynamics

Heat transfer analysis has been used to calculate the temperature distribution in bridges. Thermal boundary conditions play a critical role in this analysis. However, existing studies on thermal boundary conditions simplify the air temperature inside the bridge deck as uniform, which is not realistic and thus causes inaccurate simulation results. This study proposes a new approach to thermal boundary conditions in the heat transfer analysis of bridges. For the first time, computational fluid dynamics is used to calculate non-uniform air temperatures inside the bridge deck. In addition, non-approximate heat exchange equations for long-wave radiation are also incorporated into the approach. The techniques are applied to the 1377-m main span Tsing Ma Suspension Bridge to calculate the internal air temperatures of a deck segment. Transient heat transfer analysis is then conducted to calculate the time-dependent temperature distribution of the segment. As compared with the field monitoring results, the proposed approach can simulate the temperature distribution of the bridge with an average discrepancy of 0.88 °C and is more accurately than other existing approaches.

Study via the finite element method of the behavior of deck joints in a bridge composed of precast concrete segments

AbstractThere is a demand for research to better understand the structural performance of segmental bridge joints. In this context, the main objective of this work is to present a 3D numerical modeling using the Finite Element Method (FEM) to physically simulate the behavior of concrete joints in a segmental concrete bridge. The analysis was conducted using the design of a real bridge, and the structure studied was the main span of the New Guaíba Bridge, located in Porto Alegre, RS, Brazil. The modeling was implemented using ANSYS software, version 21.2. The simulation considers a complete model of the span to provide a more realistic determination of the joint openings and the stress distributions in the elements. It is crucial to emphasize that the results obtained from the model do not reproduce the observed behavior of the studied bridge. The analysis considered only one span with simplified boundary conditions and higher loads than those typically adopted in usual design procedures.

Rapid design for large-scale parallel CFRP cable with multi-source experimental data

With advancements in material properties and reduced costs, carbon fibre reinforced polymer (CFRP) cables are gaining popularity in engineering applications due to their superior strength-to-mass ratio and durability. However, the tensile strength of large-scale parallel CFRP cables remains a critical issue, warranting further research and engineering expertise. To address this issue, this paper proposes a method to rapidly predict and adaptively correct the tensile strength of large-scale parallel CFRP cables using multi-source experimental data and an integrated approach that incorporates Monte Carlo simulations, Neural Network algorithms, and Genetic algorithms. This comprehensive method takes into account the influence of various factors including small-scale material strength and its coefficient of variation, cable length, the number of parallel wires, installation errors, and anchorage errors. Validated by reported experimental data, the method demonstrates its effectiveness in accurately predicting the tensile strength of parallel CFRP cables. Moreover, a design method for large-scale parallel CFRP cables is proposed based on the reliability theory. Lastly, the efficiency and effectiveness of the proposed method are validated through the design and optimization of a cable-stayed bridge featuring a main span of 1984 m, utilising both parallel steel and CFRP cables.

SINGULARITIES OBSERVED IN THE CALCULATION OF THE MODAL DAMPING RATIO OF A LONG‐SPAN METAL ARCH BRIDGE

AbstractWithin the recent studies that are being carried out in the structural health monitoring of bridges, it has been observed that the results of the modal damping ratio can be influenced by some ambient variables and significantly depend on the calculation method that is adopted. In this paper, the main conclusions obtained in the study of the dynamic behaviour of a real structure, the viaduct “Arcos de Alconétar”, in Spain, whose main span is a long metal arch, is reviewed. With this aim, the results obtained from the instrumentation installed during the initial months after its traffic opening are analysed.

Numerical study on the dynamic amplification factors of highway continuous beam bridges under the action of vehicle fleets

The mechanism and reasonable values of the dynamic amplification effect of highway continuous beam bridges under the action of vehicle fleets are quite complex and very unclear at present. This study, using 23 highway continuous beam bridges with the main span lengths from 32 m to 165 m as research objects, investigates the mechanism and influencing factors of the dynamic amplification factors (DAFs) of highway continuous beam bridges under the action of vehicle fleets based on the vehicle-bridge coupled vibration analyses. The results show that the travelling speeds and vehicle intervals (VIs) exert an important influence on the DAFs of continuous beam bridges. The maximum dynamic response at different travelling speeds and VIs is searched in this study, the maximum static response at different VIs is also searched, and their ratio is regarded as the effective DAFs. Based on the calculation results, it is concluded that when the roughness surface condition (RSC) is ‘good’ (or ‘average’), the effective DAFs for the vertical displacement and vertical bending moment at the mid-spans can safely take a value of 1.15 (or 1.30); those for the vertical bending moment at the inner supports and shear force can safely take a value of 1.10 (or 1.20); and when the bridge fundamental frequency is less than 1.0 Hz, all DAF values can take a value of 1.05 (or 1.10). Meanwhile, the relevant provisions in AASHTO LRFD (2017) and CEN (2003) are considered on the safe side when RSC is ‘good’ or ‘average’.

Buffeting Characteristics of a Long-Span Cable-Stayed Bridge Crossing a Deep Canyon during Erection: Response Evaluation and Vibration Control

The stiffness of a long-span cable-stayed bridge under construction may be much lower than that observed in service, making it more susceptible to wind effects, especially for a bridge designed using high piers crossing a deep canyon. To study the buffeting characteristics of such cable-stayed bridges under construction, a long-span cable-stayed bridge (the main span is 575 m) is taken as the engineering background. In this study, the buffeting responses and vibration countermeasures at three different construction states were systematically studied using time-domain analysis. It was found that the buffeting response enlarges with an increase in the wind attack angle. The RMS values of the vertical buffeting of the bridge deck end are relatively greater at the maximum double cantilever construction state and maximum single cantilever state. At maximum double cantilever construction state, the traditional wind-resistant cable connecting the bridge deck end to the bridge pile cap significantly reduces the vertical buffeting response, while the suppression effect on lateral and torsional buffeting is limited. When the bridge deck nears completion, wind-resistant cables installed at both cantilever ending in the ‘soft connection’ method would effectively suppress the vertical, lateral, and torsional buffeting. The suppression effect of cross-arranged wind-resistant cables is superior to that of the parallel arrangement. It is recommended that a reasonable wind-resistant cable layout scheme according to different construction conditions is selected.

Influence Law of Axis Deflection on the Mechanical Properties of Steel Stranded Short Slings in Arch Bridges

Most cable arch bridge damage accidents are caused by bridge collapse due to fracture of the short sling of the arch bridge. The service life of the short sling is much lower than the design life, mainly resulting from the action of vehicles and temperature, and the arch rib and the bridge floor will have relative displacement along the bridge direction, which leads to the emergence of bending stress due to the different axes at both ends of the short sling, forming local stress concentration. The stress concentration is coupled with corrosion to accelerate the damage to the sling. To study the influence of shaft deflection on the mechanical properties of short slings of steel strands in arch bridges, this study analyzes the distribution law of the shaft deflection angle of arch bridge slings under the action of vehicle and temperature loads for a medium-bearing arch bridge with a main span of 560 m. The results show that under different vehicle and temperature loads, the axial deflection angle of the short sling is the largest, and the closer it is to the center of the span, the smaller the axial deflection angle. The static and fatigue properties of 1, 3, 7, 9, 12, 19, and 27 strands of whole bunch extruded strand slings were simulated and analyzed under a 0.45σb force when the axial deflection angle of the strand slings was 0 mrad, 10 mrad, 20 mrad, and 30 mrad. The results show that the ultimate tensile properties, breaking strength, and fatigue life of the strand slings decreased to a certain extent with increasing shaft deflection angle. The accuracy of the finite element models is verified by the ultimate tensile test and the fatigue test. This study explores the bending deflection results of the short slings of arch bridges due to the different axes of the upper and lower anchorages and provides the necessary theoretical support for the design and fatigue life estimation of the short slings of arch bridges.

Super-long-span bridges: wind-resistant design developments and open issues

Suspension bridges with spans exceeding 1500 m were only achieved in 1998 with completion of the Akashi Kaikyo Bridge in Japan and the Great Belt Bridge in Denmark. The most recent record is the 1915 Çanakkale Bridge in Turkey, with a main span of 2023 m. A slightly longer bridge is currently under construction in China and significantly greater spans are in planning, such as the Messina Strait Bridge, aiming for an impressive 3300 m span connecting Sicily with mainland Italy. Three critical challenges associated with such ambitious designs are addressed in this article. The first challenge centres on the significance of vortex-induced vibrations, particularly in multi-box girders. The prediction of these vibrations before construction relies on wind tunnel tests with scaled-down models characterised by inherent uncertainties. The second issue involves non-synoptic winds, such as downbursts. Although these events are relatively small and short-lived, they have a non-negligible probability of occurrence on large structures and may induce damage and loss of serviceability due to their intensity and the presence of vertical velocity components. Finally, the importance of robust design practices is underlined, emphasising the potential risks of relying solely on aerodynamic cross-section optimisation without providing additional structural stiffness and damping resources in these critical structures.

Study on the application of TLS for bridge deflection inspection in Vietnam

Inspecting defects, geometric size discrepancies compared to the design profile, and displacement under theload of the bridge structure aims to gather information and current data before putting the bridge into operation. However, the quality of inspection on the structure size performed by traditional methods usually takes time consuming and potentially unsafe due to difficulties in accessing because the bridge dimension is high and the rugged terrain is challenging, especially with bridges crossing rivers, deep valleys, etc. Therefore, applying modern, effective, and reliable inspection methods is essentially required. The Terrestrial Laser Scanner (TLS) is a technique to quickly and accurately gather topographic data points of objects’ surfaces. TLS is applied in many survey fields, including surveying the structure of bridge engineering. To evaluate the effectiveness of applying TLS, the research conducted a determination of the main span P61-62’s deflection of the balance casting bridge crossing the Vong intersection of the urban traffic bridge project Ring Road 2, Hanoi city during static load testing. Three methods to determine the deflection of the bridge span structure were implemented (1) Using dial indicators; (2) Using a total station to measure points reflecting attached to the structure of the bridge girder; (3) Applying TLS to inspect the structure at the time of no load and load. The results led to the conclusion that TLS methodology facilitates the determination of the bridge deflection with acceptable accuracy.

Half-precast “crossbar-slab-column” frame joint

Introduction. Half-precast frames embodied the positive properties of both precast and cast-in-situ structures. These structural systems are difficult to introduce due to their low level of knowledge, lack of experimental data, and an almost complete absence of a regulatory and technical framework for a design. This stimulates a need to improve and develop new joints with high operational reliability and manufacturability.Aim. To identify the causes of the frame joint destruction.Materials and methods. The frame joint is provided by the hidden cast-in-situ column cantilever in the grooves of crossbars and half-precast floor slab with the installation of additional longitudinal and transverse reinforcement. Precast and cast-in-situ elements interact mainly by reinforcement starter bars. The destruction of frame joints was considered using the example of a half-precast frame with the main spans of 9 and 12 m in a two-storey building according to the results of a full-scale survey during the construction period.Results. At the joints of most crossbars with columns, inclined cracks were detected in the support zones along the lateral surfaces with an opening width of 0.1–5 mm. In addition, cracks were observed along the contact area of the support crossbar groove with the column grouting concrete. An opening revealed them spreading into the body of the groove grouting concrete along the column edge. No adhesion between the walls of a crossbar groove with the joint grouting concrete is observed. The crack formation pattern indicates the determined contour of the floor slab punching above the column.Conclusion. The cause for the destruction of half-precast frame joints involves the insufficient bearing capacity of the section for the action of transverse forces due to the ductility of precast and cast-in-situ elements.

Research on the Influence of Geotextile and Elastic Cushion on the Static Performance of Ballastless Track on Long-Span Cable-Stayed Bridges

The elastic cushion is mostly used between the layers of ballastless tracks laid on a large-span cable-stayed bridge with a main span of more than 300 m. The rubber material is easy to harden and age, the geotextile has good acid-alkali resistance and antiwear performance, and the feasibility of geotextile application on the large-span cable-stayed bridge can be explored. The coupling model of a long-span cable-stayed bridge and the ballastless track was established to analyze the longitudinal mechanical characteristics of the seamless line, the deformation of the track structure, and the separation of the track plate and base plate under different loads. The results show that the application of geotextile or elastic cushion has little effect on the longitudinal mechanical properties of seamless lines. Compared to the elastic cushion, laying the geotextile increases the longitudinal stress of the slab by 0.13 Mpa, 0.025 Mpa, and 0.06 Mpa under different types of loads. The strength calculation of the seamless track is within the safety range. Laying elastic cushion can restrain the generation of separation under vertical loads, but there is no effect laying elastic cushion under temperature loads and braking loads, and the height of separation was less than 0.4 mm. The stress and deformation of the ballastless track do not exceed the standard when applying geotextile; it is feasible to apply geotextile on ballastless tracks on a large-span cable-stayed bridge. The next step is to study the vehicle–bridge–track dynamic response when elastic cushion and geotextile are laid.