Cable Force Research Articles

Finite element analysis method for the sliding cable analysis: The sliding variable method

A sliding cable structure is typically characterized by uncertainty of sliding and complexity of friction at the cable-strut joints, which makes accurate and efficient analysis difficult. In this study, we have proposed the sliding variable method, to simulate the cable sliding process considering friction equivalently and analyze the internal force and deformation response at the equilibrium state quickly and accurately. The sliding variable method takes the sliding vector of the cable at cable-strut joints as the basic variable, extracts the slippage stiffness matrix and establishes the cable force balance equation to solve the sliding vector, and simulates the change of cable original length and cable force by applying equivalent temperature load. In this paper, first, the basic principles and calculation procedures of the sliding variable method without considering friction, are discussed in detail to simulate frictionless slip of continuous cable, using with roller-type cable-stayed joints. as an example. On this basis, a calculation model incorporating the effects of friction is analyzed, a method to judge the sliding situation and balance relation of cable-forces is revealed, and the calculation principle and steps of the method are further deduced. Meanwhile, choosing a multi-joint cable–pulleys model as an example, the accuracy and rationality of the sliding variable method with and without considering friction are verified respectively. This method requires a conventional finite element calculation and second calculation alternately. Finally, to improve the practicability and computational efficiency of the sliding variable method, a macro document was compiled using the secondary development function of ANSYS parametric programming language (APDL) according to the basic framework of the sliding variable method. The frictional sliding behaviors in two typical engineering cases, a cable girder and a prestressed fish-belly girder on a foundation pit, are analyzed by using the compiled macro document in finite element program. The results show that the compiled macro document can be both accurate and efficient in calculating and analyzing cable sliding problems and can be easily popularized and applied in engineering practices.

Design theory of self-centering column foot joint with dog bone weakened flange cover plate

Basing on the concept of post-earthquake repairability, plastic damage control, and self-centering, this study introduces a novel self-centering column foot joint with dog bone weakened flange cover plate (FCP) for prefabricated steel structure. The method and design theory for the target yield load and initial stiffness of the new joint were established. Parametric research was conducted using finite element simulation to assess the influence of the dog bone weakened FCP thickness, initial cable force, and axial compression ratio on the bearing performance of the new joint, thereby verifying the above method and theory. The results reveal the accuracy of the proposed method for determining the target yield load and initial stiffness, and provide practical design guidance for the new joint. The design theory values of the new joint and the simulation values demonstrate an error within 10%, which satisfies the engineering accuracy requirements. The corresponding procedures and suggestions for the design theory of this new joint were finally provided. Based on design theory, the overall plastic damage concentrates on the dog bone weakened FCP, successfully controlled by the new joint design, ensuring minimal damage to the main structure and demonstrating good bearing capacity and self-centering performance.

Time-varying cable force identification in cable-stayed bridges by a high-resolution time-frequency method

Accurate monitoring of time-varying cable force plays a vital role in the condition assessment of cables. However, most current methods for identifying the cable force can only provide an average cable force over a period. The vibration method correlates the cable force with cable frequency via a formula, transforming the time-varying cable force identification into the instantaneous frequency (IF) identification of the cable. Synchroextracting transform (SET) is a powerful time-frequency method with the ability to identify the cable’s IF from the measured response. However, the performance of SET in identifying the IF is heavily influenced by the choice of window length, limiting its practical application. In this study, an improved SET (ISET) is proposed to overcome this limitation and is utilized to identify the time-varying force in bridge cables. In ISET, the variational mode decomposition is first employed to decompose the measured response into several mono-component modes. A hyperparameter optimization algorithm, adopting Rényi entropy as the evaluation index, is then introduced to determine the optimal window length for each mono-component mode. Furthermore, the proposed ISET with the optimal window length is used to identify the cable’s IF, thereby calculating the time-varying cable force using the vibration method formula. Cases involving finite element model of the cable, along with laboratory experiments on a scaled cable, show that the proposed method successfully addresses the limitations of SET and accurately identifies time-varying cable force. Finally, to validate the practicality of the proposed method, the field test data from an unsymmetric cable-stayed bridge is adopted. The results demonstrate that the proposed method is straightforward and efficient, capable of accurately monitoring the time-varying cable force in both new and existing cables of cable-stayed bridges.

Research on high‐pressure abrasive water jet slotting and pressure relief technology for hard rock roof

AbstractTo solve the problem of severe rock pressure near coal mining face tunnels, a high‐pressure abrasive water jet slotting and roof breaking pressure relief technology is proposed. First, the laneway deformation mechanism and the process of hard rock slotting using high‐pressure abrasive water jets under long‐distance cantilever conditions are analyzed, and the crack initiation conditions of roof strata are obtained. Second, slotting tests under different slotting pressures, nozzle diameters, abrasive particle sizes and slotting times were carried out, and the slotting parameters of a high‐pressure abrasive water jet on a typical roof rock were obtained. Finally, industrial application was carried out in the 81,403 working face of Huayang No.1 Mine. After the hydraulic roof slotting measures were implemented in the test area, the maximum axial force of the anchor cable was reduced to 67 kN, which was 35.5% lower than that of the comparison. The average stress of the coal seam was 15 MPa, which was approximately 25% lower than that of the comparison. The deformation of the tunnel in the experimental area was significantly controlled, with an average movement of 30.0% toward the roof and floor of the tunnel and an average movement of 23.2% toward the two sides of the tunnel. Compared with the movement in the comparison section, the movement toward the roof and floor of the laneway was 42.3% lower, and the movement toward the two sides was 38.2% lower. The industrial application results show that high‐pressure abrasive water jet roof slotting and pressure relief technology can cut off the stress transmission path between the roof rock on both sides, effectively improve the stress state of the surrounding rock of the laneway, reduce the deformation of the roof, floor and two sides of the working face in the later stage of the mining laneway.

Development of fiber Bragg grating vibration sensor for bidirectional monitoring of thin rod cantilever beam

Monitoring of vibration frequencies and forces in cables and suspension rods of bridges is crucial. In order to achieve high-precision and bidirectional low-frequency monitoring of cable force and suspension rod, in this work, a thin rod cantilever beam type FBG vibration sensor was developed for bidirectional monitoring based on theory, experiment, and finite element simulation. Firstly, elastic structure of the thin rod was analyzed, and the structural parameters of the sensor were optimized based on theoretical analysis and finite element simulation. Then, the frequency and sensitivity of the sensor were tested. The obtained test results showed that the resonant frequency of the sensor in the x/y direction was 48 Hz, sensitivity was 90.5/102.3 pm/g, and error in frequency was less than 2 %. Furthermore, the force in the cable measured by the sensor was verified through indoor tension tests. The test results showed that the maximum error in the force measured in the cable was 0.86 % relative to the actual tension in the cable, indicating high measuring accuracy of the developed sensor. Finally, the sensor was applied to monitor forces in actual engineering cables, where an error of 4.21 % was noticed, which further validated the accuracy and applicability of the sensor. The research results of the present would provide guidance for improving the ability of the bidirectional low-frequency FBG vibration sensors to measure low-frequency random vibrations.

IMST-based identification of time-varying cable forces in cable-supported bridges: Numerical, experimental, and field test validation

Accurately assessing the structural integrity of cable-supported bridges hinges upon the precise determination of time-varying cable forces. In this study, a novel method is proposed for identifying these forces, even with the challenge of having only a single accelerometer available. Leveraging an improved Multisynchrosqueezing Transform (IMST) with an efficient ridge extraction algorithm, this method offers a robust solution. The IMST is employed to construct a clearer time-frequency spectrum based on the monitored acceleration response of a cable. Subsequently, the time-frequency ridge extraction algorithm enables the derivation of the cable's instantaneous frequency. Ultimately, the time-varying cable forces are computed by using the axially loaded beam theory and considering the influence of bending stiffness. Validations through a numerical benchmark model and a scaled cable testing confirm the efficacy of this approach. Result indicates that the average error in identifying cable forces is less than 2.50% in the numerical simulation. Moreover, the method is successfully applied to a real-world bridge scenario, demonstrating its ability to accurately evaluate cable forces despite having access to only a single-point noisy acceleration response.

Load-bearing behaviors of the composite gravity-type anchorage: Insights from physical model and numerical tests

Gravity-type anchorages (GTAs) have been extensively applied in large-span suspension bridges across the globe, but the load-bearing performance of composite GTA is not yet fully investigated. Here, the comprehensive load-bearing performance of GTA is investigated using a combination of physical modelling and numerical modelling methods, considering the impact of anchorage’s burial depth, notched sill, and pile. Six model tests are first conducted using a self-reversing force loading equipment, including flat bottom anchorage, notched sill anchorage, and notched sill anchorage with pile. Each type of anchorage is tested under two different burial depth conditions. The failure process, anchorage displacement, cable tension force, and the internal strain field of the foundation, were examined during the model tests. Additionally, through the numerical simulations, the evolution characteristics of contact stresses and load sharing ratio associated with various forms of anchorage are discussed. The results indicate that the anchorage’s burial depth and pile significantly impact on anchorage’s bearing capacity. The presence of the notched sill can change the distribution of contact stress between the anchorage and foundation, which can still resist the horizontal force until the foundation before the notched sill occurs shear failure. The failure process of the anchorage-foundation system was divided into four stages: stable bearing, sliding, sliding and overturning, and failure stage. The anchorage starts overturning with the applied load reaching to 3*Tm, except for the flat bottom anchorage of shallow burial depth condition. Under the same conditions, the greater the anchorage’s burial depth, the smaller the load shared by the friction between the anchorage bottom and foundation, the greater the load shared by the notched sill and foundation before the anchorage. In addition, the load shared by pile continuously increasing as the anchorage starts overturning. The findings from this study can provide a theoretical basis and valuable insights for the optimization design of GTA.

Dynamics Modeling and Motion Evaluation of a Near-Ground Tethered Balloon Cable System under Severe Wind Environments

Weather survival poses a significant challenge for the utilization of tethered balloons. The dynamic modeling of tethered balloon systems presents challenges due to the flexible nature of the cables and the intricate nature of gust forces. The present study introduces a new approach for modeling near-ground tethered balloon systems, which enables the analysis of their dynamic responses and performance evaluation under complex boundary conditions. First, finite cylindrical rigid bodies that are joined together by bushing forces to describe the dynamics of the tethered cable. The properties of the flexible cables under severe bending and translation can be illustrated by the dynamics model. Second, a three-dimensional dynamics model based on the multibody dynamics theory is created to deal with the interaction of the tethered balloon system and flexible cables. The dynamic responses of the tethered balloon system under challenging operating conditions are investigated, focusing on the number of cable segments and the place and direction of gust wind impacts. This model allows for precise assessment and optimization of the system’s overall performance to improve weather resistance. The results show that compared to computational fluid dynamics (CFDs) methods, the multibody system dynamics-based balloon model improved the solution time by 80%, with a pitch angle deviation of only 0.0016°. Moreover, the bushing model effectively reduced cable force and enabled accurate reflection of the system’s motion characteristics.

Finite element study on the mechanism of the influence of pretension force and block strength on the shear resistance of the anchor cable with C-shaped tube

To prevent the early breakage of anchor cables under shear loads in support engineering, a combined structure of Anchor Cable with C-shaped Tube (ACC) has been proposed. The shear resistance enhancement mechanism of this structure and the mechanisms of various influencing factors have yet to be fully revealed. A refined nonlinear finite element model of ACC was original established using ABAQUS software, taking into account the actual structure of the steel strands and the interactions, such as contact and failure between the various components. Various anchor cable pretension forces and block strengths were set to investigate their effects on the shear mechanical response of ACC. The results successfully demonstrated a high correlation between peak shear load and pretension force. The results demonstrate that an increase in pretension force reduces the ACC’s peak shear load and break displacement. Additionally, the structure exhibited higher flexural stiffness, the block strength was mobilized earlier, and the block failed locally more quickly. Under high pretension forces, the system exhibited higher shear stiffness in the early stages of shearing due to the influence of the axial force component. With low pretension forces, the ACC exhibited a larger break displacement due to the minor tensile deformation at the shear plane position for the same shear displacement. At low pretension forces, the structure’s bending angle increased more rapidly during the middle and later stages of shearing, accompanied by a larger break displacement. Both of these factors led to a greater bending angle at the shear plane position at the point of failure. The results reveal the characteristic of the peak shear load initially increasing and then decreasing with the increase in test block strength, along with its underlying mechanism. As the block strength increased, the bending angle of the structure at the shear plane position increased more rapidly, resulting in higher shear stiffness. With high block strength, the combination of smaller break displacement and greater shear stiffness led to an initial increase followed by a decrease in peak shear load. A comprehensive RSSB (Relative Stiffness between Structure and Test Block) that considers both structural and test block stiffness was proposed. The deformation pattern of the structure was controlled by the RSSB. The higher the RSSB, the wider the plastic hinge extension range for the same shear displacement, the smaller the bending angle at the shear plane position, and the smaller the maximum curvature of the structure. The contact force of the C-shaped tube generally exhibited a “single peak” distribution. As the shear displacement increased, the peak position of the contact force moved away from the shear plane, and the maximum contact force increased rapidly and remained relatively stable. At the end of the shearing process, the contact force of the C-shaped tube exhibited a “double peak” distribution.

Analysis of the response of wind-induced vibrations on flexible photovoltaic mounts

Abstract This article investigates a flexible photovoltaic bracket’s response to wind vibration. A finite element model is established using SAP2000 software for time course analysis. Representative units and nodes were selected to analyze internal force response, displacement response, and acceleration response. The prestress and span change rule of the flexible photovoltaic bracket are also explored, and quantitative research is conducted on the size of prestress and span size. The magnitude of the prestress affects a structure’s responsiveness to wind vibration. As prestress grows, so do deflection and acceleration, and the rate at which axial force is increasing also increases. Conversely, when prestress increases, the rate of deflection reduction falls. Consequently, considering the prestress size, it is advised that 50-kN prestressing be used for the support and wind cables. As the span rises, so do the mid-span span and the axial force of the wind cables, while acceleration also increases. The rate of mid-span deflection increases gradually with the flexible PV mount span, but the rate of axial force increase decreases. It is recommended to limit the span to below 50 m.

Machine learning-based multi-objective prestress optimization framework of suspend dome structure and case study

Intelligent optimization algorithms are widely employed for the prestress optimization of suspend domes to determine the optimal cable forces. This process involves numerous complex iterative calculations, with each iteration including a corresponding finite element analysis. Such a process is both cumbersome and time-consuming. In this study, a machine learning-based surrogate model integrated with an intelligent optimization algorithm was developed to address the prestress optimization problem in suspend domes. This optimization problem incorporates multiple objective constraints, including maximum vertical displacement, maximum lateral displacement of the support, uniformity of the cable force, and maximum cable force value. The efficiency and effectiveness of the proposed method were demonstrated through two case studies. Results show that the proposed method reduced computational time by 95 % and ensured convergence by effectively integrating the surrogate model with a multi-objective optimization strategy.

Instrumented bio-inspired cable-driven compliant continuum robot: static modeling and experimental evaluation

Abstract Energy efficiency is inherent for autonomous robotic device. Snakes are well known for their ability to low energy consumption when swimming. However, the swimming know-how is poorly understood. Designing a snake robot inspired by snakes as a tool to find out the swimming energy efficiency crucial point will lead to the development of hyper efficient undulating locomotors. In this article, we introduce a four tendons driven continuum robot made of bio-inspired compliant vertebrae to assess the energy consumption of a planar and a spatial snake motion. The tendon-driven continuum robot constitutes the head–neck part of a locomotor snake robot. A static modeling coupled with an optimization method was implemented to generate bio-inspired motions recorded on snake swimming head. A friction model describing the friction between cables and the disks is investigated and compared to a frictionless model. The proposed prototype is equipped with exteroceptive sensors to record motion and proprioceptive sensors to measure cable forces applied at the tip of the robot. Hence, the work of the forces, thus the energy required to execute a trajectory are computed and analyzed. The energy is introduced as a key criterion to assess the swimming motion of a locomotor snake robot.

Crossing cable design optimization of multi-tower cable-stayed bridge based on joint analytical method and genetic algorithm

As the length of the main span increases, the stiffness of multi tower cable-stayed bridges continues to decrease. The performance of the structure can be improved by setting crossing cables at the main span. The setting of crossing cables is a key issue in the overall design of bridges. This study presents a new optimization strategy to achieve the optimal setting of crossing cables. The developed technique combines analytical algorithm, optimization algorithm and finite element method. The anchor position, number, cross-sectional area and cable force of crossing cable are taken as variables. Firstly, an analytical algorithm is used to determine the feasible interval of the number and area of crossing cables, and then the genetic algorithm is used to search for the optimal solution within the feasible interval to obtain the crossing cable layout with minimum steel. Based on the analytical method, the feasible interval is determined, so that the population is close to the convergence point from the initial state, and the optimization efficiency is improved. The effectiveness of the proposed method is verified by four optimization problems, and the influence of the deck stiffness on the anchor position of crossing cable is discussed, which provides a reference for the setting of the crossing cables in the preliminary design stage.

Simplification and improvement of cable tension identification based on effective vibration length estimated from multiple sensors located near one support

Effective vibration length (EVL) has been proposed and found able to accurately identify tension force in short cables with unknown boundaries. However, EVL estimation accuracy is degraded when measurements are distributed only near the cable-deck end. This study investigates the EVL and modal characteristics of cables under different factors using a finite element model. The corresponding conclusions are then utilized to simplify and improve the original method. Method 1 is proposed by simplifying the original method using a fixed EVL for different modes. Method 2 is developed by enhancing Method 1 with additional tests where masses are attached on the cable near the sensors. In numerical experiments with 1 % random noise, the proposed methods achieve 70 %–80 % of results with errors less than 5 % while 1 % of results from the original method achieve this level of accuracy. Full-scale cable experiments have further validated the effectiveness of the proposed methods.

Seismic performance of friction damped posttensioned steel frame equipped with SMA strands

The post-tensioned friction dissipating (PTFD) connection for steel frames has drawn significant attention from researchers due to its excellent seismic performance. A simplified numerical algorithm suitable for modeling the SMA strands is proposed. The simplified numerical model of the SMA-PTFD is established. Parametric analysis is performed based on hysteresis analysis and transient dynamic analysis to reveal the influence of SMA strands on the seismic performance of SMA-PTFD frames. The changing rule of seismic response of SMA-PTFD frames, along with the fmax for SMA strands and the Fmax for the friction device, is systematically investigated. The value of the objective function can be reduced by about 50 % when the fmax is increased from 1 kN to 13 kN. The fundamental frequency is 1.25 Hz for three analyzed conditions. The value of the second frequency is significantly affected by Fmax. The values of the second frequency are 1.5 Hz, 1.58 Hz, and 1.42 Hz. The characteristics of seismic response, including displacement and cable force, are deeply studied. The seismic response is also investigated in the frequency domain. The results presented in this work reveal the collaborative energy dissipation mechanism of the friction device and SMA strands.

MRI-compatible and sensorless haptic feedback for cable-driven medical robotics to perform teleoperated needle-based interventions.

Surgical robotics have demonstrated their significance in assisting physicians during minimally invasive surgery. Especially, the integration of haptic and tactile feedback technologies can enhance the surgeon's performance and overall patient outcomes. However, the current state-of-the-art lacks such interaction feedback opportunities, especially in robotic-assisted interventional magnetic resonance imaging (iMRI), which is gaining importance in clinical practice, specifically for percutaneous needle punctures. The cable-driven 'Micropositioning Robotics for Image-Guided Surgery' (µRIGS) system utilized the back-electromotive force effect of the stepper motor load to measure cable tensile forces without external sensors, employing the TMC5160 motor driver. The aim was to generate a sensorless haptic feedback (SHF) for remote needle advancement, incorporating collision detection and homing capabilities for internal automation processes. Three different phantoms capable of mimicking soft tissue were used to evaluate the difference in force feedback between manual needle puncture and the SHF, both technically and in terms of user experience. The SHF achieved a sampling rate of 800Hz and a mean force resolution of 0.26 ± 0.22N, primarily dependent on motor current and rotation speed, with a mean maximum force of 15N. In most cases, the SHF data aligned with the intended phantom-related force progression. The evaluation of the user study demonstrated no significant differences between the SHF technology and manual puncturing. The presented SHF of the µRIGS system introduced a novel MR-compatible technique to bridge the gap between medical robotics and interaction during real-time needle-based interventions.

Calculation method of temporary cable force in incremental launching construction of large span steel box girder without auxiliary pier

The Fenshui River Bridge is a steel–concrete composite girder bridge with a main span of 90 m. Due to the topographical constraints, the steel box girder was constructed without the use of auxiliary piers, employing incremental launching techniques. This article focuses on the construction technology used for the steel box girder of the Fenshui River Bridge. Firstly, using the influence matrix method, the cable force is determined based on the maximum cantilever state of the structure, with the vertical deformation of the front end of the guide beam and the horizontal deformation of the top of the tower as the control objectives. The unstressed cable length is then calculated based on the mechanical relationship between cable deformation and cable force. A calculation method for adaptive cable force is proposed, which is based on the variation of the stress-free cable length within the adaptive structural system. Next, the finite element analysis method was employed to determine the optimal layout position for the tower. The results indicate that during the incremental launching construction of the steel box girder, the calculated cable forces using the method proposed in this paper are in close agreement with the measured cable forces. At the maximum cantilever state of the structure, the calculated and measured values of the cable force resulted in a percentage difference of 3.96%. The calculated values of deformation and stress in key sections showed a percentage difference of 6.4% for deformation and 6.6% for stress. To maximize the effectiveness of the tower and cable, the tower should be positioned above the bridge pier when the guide beam crosses the maximum span. The findings of this paper can serve as a reference for the construction of similar types of bridges.

White City pedestrian Bridge –structural design of the cable‐stayed future landmark, Baku (AZ)

AbstractOnce constructed, the Baku White City pedestrian bridge will be a landmark for the newly developed White City district in the east of the Capital. Designed by UNStudio, the bridge crosses the highway of 8th November Avenue and connects the newly build city to the seaside, forming a wide promenade.Due to the pending construction of the mall as future bridge support, the bridge had to be redesigned. A cantilevering viewing platform will highlight the bridge's ending.This paper covers the structural design of the architecturally shaped cable stayed bridge, supported through a 46 m high A‐shaped, slightly curved pylon. Based on 3‐D modelling in Rhino® and Grasshopper®, the FE‐software SOFISTIK® is used both for cable force finding and bridge design.The structural system, steel structure's specific detail for cable connection and its design approach have been documented.

Development and engineering application of fiber bragg grating intelligent cable in large-span hyperbolic parabolic spatial cable network

In order to accurately control the prestress force of cables in long-span cable net structures, a new type of fiber Bragg grating (FBG) intelligent cable was developed. The FBG sensor was directly encapsulated inside the cable, and the sensing performance of the intelligent cable was verified by the cyclic tensile tests. The results show that the sensitivity coefficients of FBG monitoring are basically consistent, and the linearity deviation of the fiber Bragg grating is less than 4.67 %. Based on a real project Shunde Desheng Sports Center, a 114 m long-span saddle-shaped cable net structure model was established using finite element analysis, and the distribution and correlation of internal forces of cables in different tension stages were calculated and compared with the actual monitoring results of intelligent cables. The analysis results indicate that the force changes of intelligent cables is basically consistent with the value of finite element simulation. According to the data of long-term intelligent cable monitoring, the change of cable force caused by the temperature deformation of the steel ring beam is much greater than the influence of the temperature rise and fall of the cable itself on the cable force. Intelligent cables can provide a reference for cable force monitoring of long-span cable net structures.

Study on static performance and dynamic characteristics of a spoke cable-truss suspen-dome system

The proposed spoke cable-truss suspen-dome structure is a new structure system based on the traditional chord-supported dome structure. In this structure, the upper lattice shell is modified to a radial cable-truss structure. The lower part of the structure is a cable network structure composed of radial cables, ring cables and radial cables. There are few research results on the mechanical properties of the new structure, so a 1:10 scale model is established, multi-condition static loading test, local cable force failure test and natural vibration characteristic test are carried out, and the measured results are compared with the finite element results. The changes of axial force and joint displacement under different loads, the changes of static properties under cable damage and the dynamic characteristics of the structure are obtained. The results show that the loading method adopted meets the test accuracy requirements. Under the action of uniform load, the upper chord, the lower chord end and the inner ring truss of the main truss are in a pure compression state. The middle bar of the lower chord span and the outer ring truss change from the compression state to the tension state with the increase of load. The structure is still in the elastic stage when part of the cable fails, and the coordinated deformation ability is strong. The base frequency of the measured structure is 7.97 Hz, and the stiffness distribution is uniform.