Main Cables Research Articles

Estimating design positions of suspension bridge tower saddles in the completed bridge state: An analytical approach

Saddle position is an essential parameter in the form-finding of main cables and for the construction control of suspension bridges. In actual suspension bridges, the center of the arc-shaped tower saddle in the completed bridge state may sometimes deviate toward the river and the river bank. However, the influencing factors and the judgment method for the deviation have yet to be thoroughly studied. This study proposes an analytical approach for estimating saddles positions in the completed bridge state of suspension bridges under two definitions of the intersection point (IP) of the main cable in the tower top: (i) IP between the two extended catenary segments of the main cable and (ii) IP between the two extended straight lines of the main cable. For catenary-based IP, the calculation of the saddle position is separable from the form-finding of the main cable. Once the shape of the main cable is derived, equations can be established based on the geometric compatibility conditions for the saddle and main cable, their solving required for deriving saddles positions. For straight line-based IP, the calculation of the saddle position is inseparable from the form-finding of the main cable, and the two processes are conducted simultaneously. Equations can be established based on mechanical equilibrium and the geometric compatibility conditions for the saddle and the main cable and then solved. The relationship between the position of the center of the arc-shaped tower saddle and the centerline of the tower is analyzed, proving that the saddle deviates toward the side with a smaller catenary parameter. The eccentric compression of the tower is analyzed, implying that the eccentric moment acting on the tower in the completed bridge state is primarily produced by the self-weight of the saddle and the main cable segment in the saddle. Finally, the feasibility of the proposed method and the correctness of the above findings are verified through a suspension bridge with a main span of 730 m.

Twinning of the Egongyan Bridge

The First Egongyan Bridge in Chongqing, China was opened to traffic on December 27, 2000. It carries six-lanes of city traffic and two pedestrian paths, one on each side. It is a 600 m span suspension bridge. It was planned that the two pedestrian paths might eventually be converted to transit tracks in the future. However, with the rapid increase in urban traffic, the deck was transformed into an 8-lane bridge instead. Therefore, a new bridge parallel and adjacent to the old bridge was built for the rail transit. For aesthetic reasons, the city decided that the new bridge should also be a suspension bridge, with the same span length and tower height as the first bridge. The First Egongyan Bridge was a true suspension bridge with main cables anchored to ground anchors. However, the new bridge bridge’s proximity to the first bridge necessitated the construction of a self-anchored suspension bridge that did away with a second set of ground anchors. This 600 m span happened to be the world’s longest span for a self-anchored suspension bridge.

Experimental study of the temperature characteristics of the main cables and slings in suspension bridge fires

Fire raises key issues in the safety assessment and thermal protection of a suspension bridge, where the temperature profile of the main cables and slings (cable) is an important parameter that has not been quantified in previous studies. The present research investigated its evolution in fire scenarios on the emergency lane and inside lane. A suspension bridge fire experiment platform was built, and 30 sets of pool fire tests simulating vehicle fire were conducted considering the wind velocity, pool size, and pool location. The focus was on the mass burning rate of gasoline and the temperature profile of cables during fires in different lanes. The results showed that the mass burning rate increased with pool size and cross-wind. A new characterization of the gasoline burning rate was introduced. A vehicle fire in the emergency lane posed a greater thermal threat to cables than an inside-lane fire. An exponential model representing the temperature profile of cables was derived. A uniform prediction model for the maximum temperature of cables exposed to different lane fires on a suspension bridge was proposed for the first time. The predicted values of proposed model were compared with measured maximum temperature, and reliable results were obtained.

IOT-Based Erection Techniques for Main Cables of Nizhou Waterway Bridge of Nansha Bridge

IOT-Based Erection Techniques for Main Cables of Nizhou Waterway Bridge of Nansha Bridge

Investigation of torsion angle measurement method in spatial cables of suspension bridges

Spatial cables in suspension bridges may twist between two adjacent suspension points due to transverse tension. To determine the spatial torsion angle of the cables, a scale-reduced suspender bridge model was fabricated and tested in this study. The cable torsion angles of the bridge model under different loading cases were obtained and presented. Theoretical methods (e.g., the coordinate method and the angle method) to calculate the spatial cable torsion angle in the suspender bridge were developed by analyzing the deforming characteristics of the suspender cables. The feasibility and predictive accuracy of the proposed methods were assessed using the experimental results. Results show that the proposed coordinate and angle methods produced similar torsion angles for the main cables, showing a maximum relative error of 10.4 %. Compared to the coordinate method's complex data transformation and measurement procedures, the angle method is more convenient, efficient, and easier to calculate the torsion angle of the main cable. Despite the capability of calculating the spatial cable torsion angles, the coordinate method also exhibits advanced capability in determining the geometric curves of the main cable under different spatial angles.

Spanning capacity analysis of self-anchored suspension bridges based on the stability and compression strength of stiffening girder

ABSTRACT Considerable axial compression stress exists in the stiffening girder of self-anchored suspension bridges. Therefore, failures of self-anchored suspension bridges will be either due to material failure or instability of the stiffening girder, which will be the major concerns. In this study, the spanning capacity of self-anchored suspension bridges is studied based both on the stability and compression strength of the stiffening girder. Theoretical analysis reveals that, due to the elastic supports provided by the main cables and suspenders, in-plane elastic buckling of the stiffening girder is prevented. However, the stiffening girder may still buckle in the transverse direction. The extreme span length of self-anchored suspension bridges increases as the rise-to-span ratio increases. For general bridge designs, when the rise-to-span ratio is smaller than that of a bridge-specific turn point value, the spanning capacity of self-anchored suspension bridges is directly proportional to the rise-to-span ratio; however, when the rise-to-span ratio is larger than that of the turn point value, the spanning capacity of self-anchored suspension bridges is proportional to the 1/3rd power of the rise-to-span ratio. Besides, the spanning capacity of self-anchored suspension bridges will increase as the width or yielding strength of the stiffening girder increases.

A passive fire protection method for main cables and slings of suspension bridges utilizing fiber felt/aerogel composites

The paper proposes a fire protection method for the main cables and slings (cables for short) of suspension bridges based on fiber felt/aerogel composites. Glass fiber felt/aerogel composite (GFAC), basalt fiber felt/aerogel composite (BFAC), and high silica fiber felt/aerogel composite (HSFAC) were prepared using silica aerogel as filler. Heat-shielding tests and thermal stability analysis were conducted on these three thermal insulation composites. A fire test platform was established to study temperature distribution and fire protection range of suspension bridge cables. The following results were obtained: (1) Within 6000 s, the 5 mm-thick HSFAC can resist 700 °C butane fire, while 7 mm-thick HSFAC blocks 1000 °C flame. The 10 mm-thick HSFAC provides better thermal insulation. (2) Two fire protection zones are identified according to temperature ranges of 1000 °C to 700 °C and 700 °C to 300 °C, respectively, with minimum heights of 12.8 m and 20.8 m. (3) For a 90-minute fire protection, the main cables in the former zone are wrapped with 10 mm-thick HSFAC, while the slings are chosen to be 7 mm-thick HSFAC. In the latter zone, main cables and slings are covered with 5 mm-thick HSFAC. The fire protection method has been implemented on a suspension bridge in Guangzhou, China.

HYDRODYNAMIC BEHAVIOR OF SUBMERGED FLOATING BRDIGE WITH SUSPENSION SUPPRORT AFTER CABLE FAILURE

Submerged floating tunnels with suspension supports (SFTSS) resemble to suspension bridges on lands, which are installed a number of hangers on the main tower and main cables to support the girder. On the other hand, as the SFTSS installed underwater has to resist the buoyancy and the forces in an offshore environment, the main cable was installed at the bottom of the tunnel body and connected with a hanger. The concept of the SFTSS was first proposed by Won et al (2019, 2022). It was found that the SFTSS was generated itself a tuned mass damper (TMD) effect due to the interaction between the body and the main cable. This can induce the vibration of the body to be attenuated according to the offshore environment conditions such as waves and currents, and had a feature that the length between the main towers can be longer than 3 km (Won et al., 2022). The body of the SFTSS was supported by main cables and hangers as aforementioned. In case of the hanger was down by failures, the behavior characteristics of the SFTSS would be changed and be greatly reduced the structure safety. In this study, the behavioral characteristics of the SFTSS were analyzed according to five scenarios on the cable failure.

The Effect of Conducted Emissions of Grid-Tied Three-Phase Adjustable Drives

Electromagnetic Interference (EMI) is generated and mitigated in power converters. EMI problems are related to high-speed power converters. This article focuses on conducted electromagnetic interference in adjustable-speed drive (ASD) systems. The electromagnetic compatibility of three-phase/level grid-connected drive inverters is investigated. The test setup is built per the CISPR16-1–2 standard, and the interferences produced from the inverter to the grid are measured. The main dependencies of conducted emissions of a power inverter, changes in the length/shape of main cables, and motor speed have been investigated under load and no load conditions. Factors affecting EMI performance and filter design issues will be addressed. A statistical approach to quantifying the frequency domain impact of conducted emission noise created on the three-phase system by operating various emission sources. Fast Fourier Transform (FFT) was applied for time–frequency domain conversion, and to evaluate with a statistical approach Minitab software was used. Then, a filter design is created to prevent these interferences from being conducted to the grid. Also, the noise attenuation of the EMI filter has been validated in the simulation. Briefly, this study fills in the blanks of uncertainties involved in measuring three-phase emissions, which helps the engineers at the design stage of three-phase converters.

A Novel Methodology for Inspection and Strength Evaluation of Suspension Bridge Main Cables

A novel methodology is proposed to evaluate the ultimate strength of the main cables of suspension bridges using information obtained from site inspections and from tensile strength tests on selected wire samples extracted from the bridge’s main cables. A new model is proposed accounting for the spatial variation of individual wires’ strength along their length, an important physical attribute of corroded wires considered here for the first time. This model includes (1) mapping the corrosion stage variation along one-panel-long wires that are visible during an inspection; (2) establishing probability distribution functions for the ultimate tensile strength of 0.46 m (18 in.)–long wire segments in each corrosion stage group; (3) generating random realizations of the ultimate strength of all the wires in the cable’s cross section, accounting for their strength variation along the entire panel length; and (4) accounting for the effect of broken wires in the evaluation panel as well as in adjacent panels. A Monte Carlo simulation approach is finally proposed to generate random realizations of the ultimate overall strength of the cable, using an incremental loading procedure. The final outcome is the probability distribution of the ultimate strength of the entire cable. The methodology is demonstrated through the cable strength evaluation of the Franklin Delano Roosevelt Mid-Hudson Bridge using results of a 2009 inspection, and compared with corresponding results obtained using current guidelines. The proposed methodology provides estimates of higher accuracy and reliability for the cable’s ultimate strength, without essentially increasing the cost of inspections.

High-mode vortex-induced vibration and its mitigation of no-hanger main cable of the side span in a cable-stayed suspension bridge

In recent years, harmful vortex-induced vibrations of high-order modes of super long stay cables have been observed on several cable-stayed bridges with the main span near 1000 m. The possibility of high-mode vortex-induced vibrations of the no-hanger main cable of the side span of a cable-stayed suspension bridge was carefully investigated based on wind tunnel tests by using a three-dimensional elastic test model. First, the cable’s three-dimensional elastic test model was designed and manufactured. Second, a series of wind tunnel tests were carried out to measure the no-hanger main cable’s wind-induced responses. The results show that large-amplitude oscillation of the test model was observed under the wind angles of 0°, ±50° and +60°, and the highest mode observed in the test is 16th order. The Strouhal number for α = 0° is about 0.195, while the values for α= ±50° are about 0.12. Third, the effects of structural damping and helical wire on the high-mode vortex-induced vibration of this main cable were studied in detail. The results show that the high-order vortex-induced vibration of the cable can be successfully mitigated by increasing the damping ratios up to 0.25% or by the helical wire with a pitch of 12D.

Numerical Simulation of Airflow in the Main Cable of Suspension Bridge with FPM Model

The main cable of suspension bridges is subject to corrosion and requires advanced anti-corrosion technology. Consequently, the internal airflow of the main cable has become a significant research focus. This study employs image processing and machine learning to analyze the cross-sectional images of the main cable and reveals the distribution characteristics of pores and fractures within the main cable cross-section. The numerical simulation model of the main cable is divided into inner and outer parts based on porosity, with porosity levels of 18.16% and 32.11%, respectively. Fractures randomly occurred in the inner part, with a probability of 31.37%. A simulation model based on fractured porous media (FPM) is developed, which innovatively incorporates the fracture flow model into the numerical simulation of the internal airflow of the main cable. The numerical simulation clearly explores the intricate details of the internal flow field of the main cable, revealing that the existence of fractures has a great impact on the internal flow field of the main cable. Additionally, the relative deviation of specific frictional head loss between the field experiment and numerical simulation is about 6.83%, indicating that the numerical simulation results are relatively reliable.

Parameter Selection for the Dehumidification System of the Main Cable of Suspension Bridge Based on Ventilation Experiments

Moisture in the main cable is the main cause of steel wire corrosion. Modern suspension bridges utilize main cable dehumidification systems to prevent corrosion. The main cable ventilation experiment can help the selection of the system parameters. This research is based on the ventilation experiment of the main cable of Xihoumen Bridge to obtain the design parameters of the dehumidification system. According to the experiment, the suitable dehumidification distance is 150–180 m; the pressure loss of the main cable with a length of 150 m is 200–300 Pa, so the inlet pressure should be higher than 300 Pa; increasing the outlet clamp can increase the dehumidification efficiency; Under single inlet and double outlet situation, every 100% increase in air volume increases the dehumidification capacity is about 35%. The water content of the main cable of Xihoumen Bridge is 5.74 kg/m3, and 1 m3 of dry air can remove 5.5 g of water under experimental conditions, and the minimum air volume is 30 m3/h. The main factors affecting the dehumidification time are air volume and leakage rate. Input these parameters into the dehumidification system for the dehumidification experiment, and the water content of the outlet clamp will drop by about 37.5% within ten days.

Evaluasi Struktur Jembatan Gantung Pejalan Kaki Dumpoh, Magelang Jawa Tengah

The bridge analyzed is a suspension type with a function as a pedestrian bridge. The bridge has a total span of 53.75 m and a width of 1.8 m, steel construction with wooden deck. The service life factor, damage to the bridge frame, and overload are certainly a problem for this bridge structure. Evaluation of the structure using survey data from existing measurements at the bridge location, then analyzed using the SAP2000 program. The result is that all tower frames, girders, main cables, hangers, and bridge decks, the nominal capacity is still able to withstand the ultimate load. However, the deflection in the middle of the bridge span is 0.72 m and has exceeded the allowable deflection (L/200). So based on the results of the evaluation of the Dumpoh suspension bridge structure, the cross-sectional strength of the frame is still safe, but the stiffness of the deflection value does not meet.

Analytical algorithm for the full-bridge response of hybrid cable-stayed suspension bridges under a horizontal transverse live load

Hybrid cable-stayed suspension bridges (HCSSB) enjoy broad application prospects due to their excellent stability and economic benefits. The full-bridge response of this novel bridge type under a live load is a shared concern during the design and use stages. This paper proposes an analytical algorithm for solving the full-bridge response under the horizontal transverse live load. First, the entire bridge is subdivided into several components, and the mechanical model and response calculation theories are built for each component. However, some critical parameters for solving these models are still unknown, and these unknown parameters are treated as basic unknown quantities. The system of governing equations is built, considering the conservation of the unstrained lengths of cables, closure of span lengths, and elevation difference across the spans. Finally, the system of governing equations is solved to obtain the full-bridge response. The results include the deformation and internal force of the main cables, main beam, towers, stay cables, and hangers. Finally, the feasibility and effectiveness of the analytical method are verified in an HCSSB with a main span of 1400 m by comparing the full-bridge response results against those from the finite element model.

Design and Static Analysis of Long-span Steel Truss Suspension Bridge

In order to effectively improve the structural safety status of suspension bridges, this paper proposes a design and static analysis method of long span steel truss suspension bridge based on Midas civil finite element calculation software. Taking the Guojiatuo Yangtze River Bridge as a case, the paper studies the mechanical characteristics of the key parts of the bridge in the completion state and operation stage, and determines the structural safety state. The results show that the minimum safety factor of main cable is 2.64, and the minimum safety factor of the suspender is 3.90, and the maximum downward deflection of the main beam is 1.231m < L/400. The structural strength and stiffness can meet the design requirements.

Study on Finite Element Simulation Method and Broken Sling Effect of Single Side Suspension Bridge with Curved Decks

As a new type of bridge structure system, the single side suspension bridge with curved decks has the characteristics of typical special-shaped bridge structure, and its forces are relatively complex. The slings are usually fragile components, and the breakage of the slings will affect the safety of the whole bridge structure. Based on a single side curved suspension bridge, the static and dynamic nonlinear models of the bridge were established by using ANSYS general finite element software. Based on the analysis of the parameters, the reasonable values of failure time of sling, the damping ratio of the bridge structure, the effect of the broken sling on the residual internal force, the tensile force of the main cable, the bending moment of the main beam and the vertical displacement are discussed. The results show that the effect of sling breakage increases with the decrease of sling failure time and structural damping ratio, and the effect of sling breakage on the internal force of the main cable is small, but it will cause a rapid increase of the internal force of the adjacent slings on the same side and the main beam.

Study on Fatigue Performance of 2200 MPa High-Strength Wire of Main Cables Based on FE-SAFE

In order to estimate the fatigue life of 2200 MPa high-strength steel wire for main cables at the outlet of the cable saddle, a fatigue loading test of a single steel wire was designed, and the value of the friction coefficient in finite element simulation and the scale factor in fatigue life analysis were determined. The fatigue life of the steel wire was analyzed by two-stage modelling. The results showed that the fatigue life of steel wire can be simulated effectively when the friction coefficient is 0.21 and the scale factor is 1.15. The fatigue life of 2200 MPa main cable wire at the saddle outlet is 4.78 million loading cycles. The research results laid a foundation for practical engineering application of high-strength steel wire for 2200 MPa main cables.

Analytical solutions for thermal effects of suspension bridges based on a surrogate model with longitudinal restraint stiffness

Ambient temperature variation has a significant influence on the deformation of main cables and the internal force of towers of long-span suspension bridges. Currently, the finite element method (FEM) is mainly used for these calculations. This paper intends to present an analytical solution of the thermal effects on suspension bridges. First, three typical temperature patterns are defined. Then, a surrogate model is established by replacing the longitudinal restraint stiffness of the main cable and the tower lateral stiffness with a set of equivalent horizontal springs. The stiffnesses of the suspended cables are formulated according to the energy conservation principle, while the tower lateral stiffnesses are obtained by incorporating the pure bending and Euler buckling solutions, namely considering the effect of the axial force placed on the tower top. Following the force equilibrium conditions, two governing equations are built, which can calculate the variations in the longitudinal displacement of the tower top caused by the temperature variation. After that, some other significant thermal effects, such as the horizontal force of the main cable, the sag of the main cable and the bending moment of the tower bottom, are obtained. Finally, the analytical solution is verified through the field test data of the Tsing Ma Bridge in Hong Kong and the FEM results of four typical examples. The proposed surrogate model offers a quick and easy approach for thermal effect analysis with acceptable accuracy. It is helpful to clarify the mechanical nature of temperature effects to facilitate the preliminary bridge design.

A Parallel Scheme of Friction Dampers and Viscous Dampers for Girder-End Longitudinal Displacement Control of a Long-Span Suspension Bridge under Operational and Seismic Conditions

Benefitting from economic development and technological progress, long-span suspension bridges, with their superior span capacity and good economy, have been built in large numbers in recent decades. However, the excessive cumulative longitudinal displacement at the girder ends in the process of bridge operation leads to the degradation of, and fatigue damage to, the connecting components. This study aims to solve the problem with an effective parallel damping scheme of friction dampers and viscous dampers. Firstly, the phenomenon that quasi-static longitudinal displacement accounts for the majority of cumulative displacement is confirmed by the decomposition of measured displacement data at the girder end, which is caused by the asymmetric geometric deformation of the main cable induced by the moving vertical loads of a long-span suspension bridge. An efficient control performance analysis method is proposed based on the formation mechanism of the quasi-static longitudinal displacement. Secondly, the friction damper with a continuous damping model is employed to achieve an effective control performance with respect to the quasi-static longitudinal displacement. Thirdly, in order to realize the target of operational and seismic dual control, a parallel scheme of friction dampers and viscous dampers is proposed, aiming to reduce the cumulative value in the operational state, and maximum value in the seismic state, for longitudinal displacement at the girder ends of a long-span suspension bridge.