Cable Force Research Articles

Strengthening Device for Improving Shear Performance of Anchor Cable in Rock Support.

Many designs of anchor cables are currently in use for rock support in civil and mining operations. Because of the exposed surface and weak shear performance of the cable bolt's free section (CBFS) in end-anchored structures, breaking failure frequently occurs. Numerical simulations and laboratory experiments were performed in this study to develop measures to improve CBFS resistance to shear failure. Analysis of shear characteristics of the CBFS showed that higher axial tension weakens the cable bolt's shear resistance, and that shear damage on the cable surface and uneven distribution of shear stress aggravate CBFS tensile-shear failure. A high-strength steel pipe is proposed to protect the shear cable bolt, and the preliminary design of a CBFS-strengthening device (CFSD) is presented. Numerical simulation revealed that the CFSD effectively improved CBFS shear resistance and provided protection from harmful shear damage. The optimal performance of a Q-type (slotted steel pipe) CFSD was confirmed. The mechanism of improvement of the cable's shear resistance to surrounding rock by employing the CFSD was analyzed. Double-shear tests were carried out on a bare cable bolt and a cable bolt with a Q-CFSD. The results revealed that the CFSD increased the peak shear force on the joint plane, cable peak axial force, and ultimate shear displacement by 31%, 18%, and 11%, respectively. The proposed device is effective in improving the shear performance of end-anchored cable bolts and enhancing surrounding rock stability.

Multi-objective optimization of cable force of arch bridge constructed by cable-stayed cantilever cast-in-situ method based on improved NSGA-II

The existing initial cable forces optimization method for arch bridges constructed by cable-stayed cantilever cast-in-situ method is computationally inefficient, and the single optimization objective cannot comprehensively consider the whole process of force state during the construction and operating periods of the arch ring. To solve the problems, the Non-dominated Sorting Genetic Algorithm II (NSGA-II) is improved in this study in terms of crowding, variation rate, elite individual preservation rate, and selection operator. A method of optimizing the initial cable force of the arch bridge constructed by cable-stayed cantilever cast-in-situ method based on the improved NSGA-II is proposed. A multi-objective optimization model of initial cable forces is constructed with the maximum tensile stress of the arch ring cross-section during the construction period and the eccentricity of the arch ring cross-section under dead load during the operating period as the optimization objectives. Combined with ANSYS and MATLAB, the optimization program based on the improved NSGA-II is implemented, and the optimization analysis of the initial cable forces is carried out with the Shuiluo River Bridge as an engineering example. The results show that the improved NSGA-II has better convergence and homogeneity than NSGA-II. The optimized initial cable forces based on the improved NSGA-II can simultaneously meet the control objectives during construction and operating periods. The optimization method proposed in this study has a very good global search capability, and can efficiently solve the optimization problem of the initial cable forces of the high-dimensional multi-objective of the arch bridge constructed by the cable-stayed cantilever cast-in-situ method.

Performance analysis of rolling multi-lug cable-strut joints with bearings under extreme loads

The tensioning process in the traditional cable strut joint leads to significant prestress loss, thereby adversely affecting the structure's performance after tension forming. This paper proposes a rolling multi-lug cable-strut joint with bearings. To investigate the rate of prestress loss in the new tension joint, we conduct testing of joint performance in a dome model experiment. The mechanical properties of the joint in the overall structure of the cable dome under ultimate load are analyzed. The investigation shows that the new joint design significantly reduces prestress loss by more than 10% compared to traditional cable support joints. Afterward, the theoretical model of the RMCS joint is proposed by analyzing the force state and deformation of the dome structure space. The test data verify the model. Based on this theoretical model, the influence of prestress loss of different levels was studied. Under severe loading conditions, the path of force transfer through the joint is efficient and can prevent large fluctuations in the cable force of the structure. The cable force on both sides of the joint still fluctuates at the same frequency even under extreme loading of the dome structure.

Modeling cable-pulley deployment systems of transformable rod structures

The aim of this article is to develop a simplified method for modeling cable-pulley deployment systems of rod structures based on the calculation of cable tensions and nodal driving forces with account for friction and other features of the system. Methods of theoretical mechanics, multibody dynamics, numerical integration of differential equations, and computer modeling were used during the research. The task of developing a simplified approach to modeling cable-pulley deployment systems for rod structures is considered. It is proposed to determine nodal driving forces by calculating cable tensions with account for friction and other features of the cable-pulley system, cables, and pulleys. To develop a model of cable-pulley deployment system, a rod system was chosen as the research object, which represents two sections of the transformable support truss of a reflector. Each section consists of diagonal and horizontal rods with tubular cross-sections. The sections are interconnected by hinge units. The structure is deployed using an upper and a lower cable, which pass through pulleys and are tensioned by an electric motor. The deploying forces are implemented by transferring the cable tension forces to the structure due to static friction and pressure between the cables and the pulleys. For further implementation of the model in an open-source software package, some simplifications were made due to the complexity of the design. A simplified method was developed for nodal driving force calculation in simulating rod structure deployment with the help of cables. The tensions, elongations, slacks, and neutral length of the cables and the forces transmitted from the cables to the pulleys were calculated as a function of time. Using them, the deployment of a rod structure was simulated for a constant cable speed. The results make it possible to control the rod system deployment time and rate depending on the characteristics and tension forces of the cables. The proposed approach is implemented using open-source software, and it provides modeling flexibility and reduces the model development and run time.

Multi-loop Nesting Algorithm and Response Analysis of Cable Forces of Long Span Cantilever Cast Arch Bridges during Construction

The existing calculation process of the cantilever cast arch-cable force has a poor fit with the actual process, leading to the lack of good parameter corrections. To improve the overall control quality of the linearity and stress of the arch ring, there is an urgent need for a solution method with higher flexibility and better practicability. Combined with the existing research results, this study proposes a multi-loop nesting algorithm. The algorithm decomposes the whole construction process into individual subsystem control modules, and sets the control indexes of stress and displacement in individual control modules. Subsequently, the analysis and calculation of other modules are completed according to the construction sequence until structure closure. Finally, we determine whether the overall construction control indexes meet the requirements. According to the findings, the results obtained by this algorithm meet the design requirements, and its applicability is verified. Compared with other algorithms, the algorithm is more effective in controlling the stress and deformation of the arch ring during the construction process. This algorithm solves the dispersion between structural systems in previous calculations and has more flexible parameter and control index settings. Additionally, the calculation control idea of this algorithm can be further extended to the construction control of the “cable-beam” cantilever structure.

A fibre Bragg grating accelerometer with temperature insensitivity for cable force monitoring of FAST

The Five-hundred-meter Aperture Spherical radio Telescope (FAST) currently holds the distinction of being the largest single-aperture telescope worldwide. To ensure its secure functioning, it is crucial to monitor the cable force on its active reflecting surface cable network structure. In this paper, a fibre Bragg grating (FBG) accelerometer is developed to acquire low-frequency vibration signals of the cables. The sensor’s cantilever beam structure enables high sensitivity measurement of low-frequency signals, while the symmetrical double fibre grating structure effectively eliminates the impact of temperature. The sensor’s specific limiting structure ensures its survival during transportation and installation. A series of laboratory tests have been performed, and they demonstrate the excellent measurement performance, temperature insensitivity and practical usefulness of the accelerometer. Ninety FBG accelerometers are successfully installed on the site of the FAST project, where they are precisely measuring and documenting the magnitude of force exerted on the edge cables.

Nonlinear Coupled Vibration Behavior of BFRP Cables on Long-Span Cable-Stayed Bridges under Parametric Excitation

Based on the cable-stayed beam model, this paper studies the nonlinear coupled vibration behavior of basalt fiber-reinforced polymer (BFRP) cables on long-span cable-stayed bridges under parametric excitation. Considering the sag, damping of BFRP cables, and the coupled interactions between stayed cables and the main girder, the nonlinear coupling vibration model of the BFRP cable–beam composite structure has been established. Taking the longest cable of Sutong Bridge as a case study, the nonlinear coupled vibration behavior of BFRP cables under parametric excitation has been numerically analyzed using the finite difference method. The analysis results indicate that (1) under parametric excitation, the large amplitude nonlinear vibration of the BFRP cable will be induced with an evident “beat” phenomenon. (2) Under the same parametric excitation, the nonlinear coupling vibration response and the beta frequency of the BFRP cable were both smaller than that of the traditional steel cable. (3) The nonlinear coupling vibration response of the BFRP cable increased with an increment in excitation amplitude and a decrement in cable force. With the increase in the excitation frequency, weight per unit length, and axial stiffness, the nonlinear vibration response of the BFRP cable increased first and then decreased. Meanwhile, the damping ratio of the BFRP cable had no significant influence on the nonlinear coupling vibration.

On the Problem of Tension Forces Distribution in Cable System of Cable-Driven Parallel Robot

The paper proposes a method for controlling tension forces in statically indeterminable cable-driven systems based on the non-negative least squares method with control of singular or near-singular solutions and a complete search of all possible cable configurations. For cable-driven parallel robots the problem of controlling the cable tension forces is critical, because in the absence of control the cable tension forces are distributed unevenly, which leads to reduced robustness of the system, increased energy consumption and increased deterioration. And in special cases of cable system configuration the tension forces become so great that they lead to cable breaks. At the same time, correction of cable tension force distribution should not lead to significant deviations from the specified position of the mobile platform or, formulating the problem in terms of forces, to violation of kinetostatic equations. Thus, the problem of controlling the tension forces in the cable parallel robot system is solved as a problem of optimizing the tension forces of the cables according to the criteria of minimizing the norm of their vector in the configuration space and minimizing the norm of incoherence of the vector of forces and moments in the operational space of the robot. The developed algorithm is based on the solution of underdetermined systems of linear algebraic equations with finding the minimum least squares norms and subsequent zeroing of negative components of the solution vector. The paper considers examples of the solution of the set problem for the lower cable group of a construction 3D printer based on a cable-driven robot and for a 12-cable system

A de-noising algorithm for bridge cable force monitoring data based on mathematical morphology

A mathematical morphological filter-based de-noising method is developed in this study for bridge cable force monitoring data. Structure elements, one of the most important parameters in the mathematical morphology, dominate de-noising effects. The de-noising effects subject to single structure element and multi-structure element filters are discussed based on the simulation signals. The results indicate that the de-noising effects by using the spherical structure element are better than using the straight line or rhombic structure element. Moreover, the multi-structure element filter outperforms the single one. Through simulation analysis, the de-noising performance of the low-pass filter, wavelet filter and morphological filter is compared. The results show that the performance of the wavelet and morphological filters is better than that of the low-pass filter. For low signal-to-noise signals, the performance of the wavelet filter is superior. With the increase of signal-to-noise ratio, the morphological filters show more advantages. Taking the cable force monitoring data of the 3rd Nanjing Yangtze River Bridge as an example, the de-noising performance of the wavelet and morphological filters is discussed. The results show that both the wavelet filters and morphological filters have satisfactory de-noising effects. The mathematical morphology method can provide an optional and effective de-nosing choice, which enriches the means of de-noising for bridge monitoring data.

Study on Active Support Parameters for Surrounding Rock with Ultra-Large Span Open-Off Cut in Thick Coal Seam

In order to effectively control the stability of surrounding rock in ultra-large span open-off cuts by employing the techniques of support strength theory calculations and analogical application methods, two sets of rational support schemes were proposed, and the optimal design of active support parameters in thick coal seams with ultra-large span open-off cuts was explored by using theoretical analysis, numerical simulation, and field experiments. The results demonstrated that the span is one of the key factors influencing the stability of the roadway roof, exhibiting an inverse quadratic relationship with the peak stress borne by the roadway roof. By utilizing the pre-stressing force of anchor cables and support strength formulas, two sets of active support schemes for controlling the surrounding rock in thick coal seams with ultra-large span open-off cuts were established, and an optimized support scheme was obtained through numerical simulation. These findings provide references and guidance for related mining engineering under actual conditions in mines.

Study on the applicability of the single cable model in cable force identification of in-service beam string structures

At present, the frequency-based cable force identification method based on single cable model assumption is still one of the most popular methods for its efficiency and convenience. However, the applicability of the single cable model assumption in the cable force identification of complex structures such as beam string structures (BSS) is worth of studying for the cables in BSS are usually short and thick, and the joints connection are complex, the cable force-frequency relationship will be possibly affected by the boundary assumption. Therefore, this paper studies the applicability of the single-cable model hinged at both ends in the cable force identification of BSS from the perspective of overall structure. Firstly, the finite element method (FEM) models for the overall BSS are established to describe the true parameters and boundary conditions of each cable within the BSS. Secondly, a “Three-criteria method” is conducted for extracting the local modes of each cable element from the global modes of the overall structure under pre-designated cable forces; and then the cable force-frequency correlation considering the influence of overall structure can be established. On this basis, the error magnitude of the single-cable model hinged at both ends for frequency-based cable force identification is analyzed corresponding to the changes of different sensitive factors. Some meaningful conclusions are obtained. Finally, the effectiveness of the method and the conclusions in this paper is verified by the testing data of an actual truss string project. The research in this paper provides a foundation for further research on improving the identification precision.

Simulation and Experimental Research on Shape Adjustment of Membrane Reflector Antenna (MRA) Combined with Electrostatic Forces and Boundary Cable Forces

Simulation and Experimental Research on Shape Adjustment of Membrane Reflector Antenna (MRA) Combined with Electrostatic Forces and Boundary Cable Forces

Parametric Updating of Steel Strand Stay Cable Force Calculation Model Based on Response Surface Method

In order to solve the problem that the calculation result of cable force deviates from the measured value because the parameters of steel strand stay cable are not exactly equal to the designed value in practical engineering, a model updating method selecting the steel strand stay cable parameters as the updating parameters and using more measured data as the objective function was proposed. This method selects the central composite design in the response surface method. In the fine-fitting model affected by the cross-term and high-order terms between parameters, the value of the parameter to be corrected is optimized according to the measured data. Using the above method, taking a cable-stayed bridge without a backstay as the engineering background, the model updating is carried out by using the cable force monitoring data during the construction monitoring process. The results show that using this method, the updated values of the parameters of the cable can be obtained according to the measured data, and the updated values of the parameters are consistent with the reality. The deviation between the calculated value of cable force and the actual cable tension obtained according to the parameter updating decreases significantly, and most of the deviation is reduced from 30% to 50% before the updating to less than 5%. The updating effect is obvious and meets the engineering requirements.

Active learning guided automated cable force monitoring based on modified S-transform

This study introduces an active learning-guided online cable force monitoring system based on a modified S-transform approach, addressing key challenges in real-time system identification: complex non-stationary excitations, computational efficiency, and robustness. The framework identifies cable tension during non-stationary wind loads, significantly improving accuracy and efficiency via an extended active learning Kriging method. It effectively detects potential outliers, identifies the cable's fundamental frequency using a data fusion technique, and calculates real-time cable force and tensile stress with empirical formulae. A comprehensive analysis, including numerical and sensitivity studies, shows an error rate of less than 4 % in all cases, proving the proposed framework's superior accuracy, efficiency, and robustness compared to traditional methods. Laboratory validations using cable test data and Jiu Zhou Bridge data demonstrate the system's stability, even under extreme conditions, such as during Super Typhoon Mangkhut, providing a reliable solution for real-world cable force online monitoring.

The modified force density method for form-finding of cable net structure

Form-finding is crucial for the design of typical cable net structures. Based on the original basic force density method, a modified force density method utilizing the concept of relation matrix is proposed in this paper. The modified method realizes the establishment of a clear correspondence between members and nodes of cable net structures. On the basis of the relation matrix, the find function is introduced, and the calculation formula of the modified branch-node matrix is derived. Meanwhile, the corresponding analysis steps and calculation process are given. The modified method is verified by the analysis of representative structural forms. The results show that for the saddle-shaped orthogonal cable net structure, the outcomes obtained from the modified force density method highly agree with the theoretical values, providing preliminary verification of the method's effectiveness. For single-layer spoke cable net structures, the relative error between the results calculated by the modified force density method and the numerical solution is approximately 5 %. The results of both methods are relatively consistent, and the relative error varies in relation to the ratio of inner ring cable force density to radial cable force density. For circular single-layer crossed cable net structure without inner ring, the results of the modified force density method are very close to the numerical solution. The maximum relative error between the two is 6.95 %, and the accuracy is higher than that of the nonlinear finite element method. The outcome of this research demonstrates the accuracy of the modified force density method and its effective application in the form-finding of actual cable net structures.

A case study of a giant reactivated landslide based on NPR anchor cable Newton force early warning

A case study of a giant reactivated landslide based on NPR anchor cable Newton force early warning

Tri-Space Operational Control of Redundant Multilink and Hybrid Cable-Driven Parallel Robots Using an Iterative-Learning-Based Reactive Approach

Cable-driven parallel robots (CDPRs) are a type of parallel mechanism in which cables are used as actuators. Due to the two levels of redundancy and numerous constraints within the CDPR actuation, joint and operational spaces (together known as the tri-space), tracking a given trajectory in the operational space while satisfying constraints in tri-space simultaneously is challenging. To the best of the authors’ knowledge, there does not exist any tri-space control framework, which is robust, effective, and directly applicable to several architectures of redundantly actuated CDPRs. This article proposes a tri-space control framework that combines reactive control (RC) and iterative-learning control (ILC) to perform repetitive tasks in the operational space. The framework allows the tracking of operational space trajectories online with feasible cable forces while avoiding undesirable situations such as cable-link interference, joint interference, and loss of manipulability. On the other hand, by finding an optimal parameter in the null space using a novel parameterization of a null-space vector, the performance can be improved through ILC when the task is repeatedly executed. Simulation and hardware results on various multilink cable-driven robots (MCDRs) and hybrid cable-driven robots (HCDRs) show that the proposed tri-space control framework can be conveniently and effectively applied to the real-time control of different CDPRs.

Feasibility study on intelligent bridge combined with smart monitoring techniques

This article proposes an innovative concept of an intelligent bridge system that integrates sensors, a processing unit, and an actuator to maintain bridge safety and performance even in the face of unexpected environmental changes and disturbances. Although technically challenging, this system is an exciting prospect for young engineers who aspire to contribute to cutting-edge technological advancements. As a practical example, this article presents an ICT-based bridge remote monitoring system called the "Intelligent Bridge," which allows real-time monitoring and control during extreme events such as earthquakes and typhoons. The Intelligent Bridge comprises a stand-alone monitoring system and a web-based internet monitoring system for bridge maintenance, which is introduced as an intelligent structure integrated into the intelligent bridge system. To verify the validity of the proposed system, it is investigated the ability to adjust cable forces on a 2-span continuous cable-stayed bridge model to control its structural performance. The development of an intelligent bridge system represents a significant advancement in bridge engineering and has the potential to improve the safety and longevity of bridges, particularly in areas prone to extreme environmental events. The system proposed in this article has practical applications that can benefit both engineers and the general public.

Study on tension control method of anchor span for three tower suspension bridge

The traditional method of adjusting cable force doesn't effectively address the coupling relationship between the splay saddle's deflection angle and the anchor span's tension. To safely and efficiently adjust the tension of the anchor span and the deflection angle of the splay saddle on suspension bridges, this study examines the effects of temperature variations and side span sag deviation on the splay saddle's deflection angle, considering the rotation stiffness of the splay saddle. On this basis, combined with the engineering practice of a three-tower suspension bridge, a simplified method of cable force adjustment considering the rotation effect of the splay saddle is proposed. Practical results indicate that temperature fluctuations are the primary cause of splay saddle deflection. A relationship has been derived between temperature changes, side span sag deviation, and the deflection angle of the splay saddle. This relationship has been validated for its accuracy and correctness in real-world engineering scenarios. The introduced simplified method for adjusting anchor span tension can notably decrease the number of required adjustments, offers precise cable tensioning, and effectively prevents cable strand slippage. This method is advantageous due to its straightforward application, time-saving nature, and enhanced safety.

True Triaxial Test and Research into Bolting Support Compensation Stresses for Coal Roadways at Different Depths

During the excavation and support construction process used in coal mine roadways, the stress path is the unloading of in situ stress and the compensation of support stress. The 150 mm × 150 mm × 150 mm coal mass samples were obtained in situ underground and prepared, the true triaxial loading–unloading–confining pressure restoring test method was used, and the mechanical response and deformation failure evolution characteristics of the coal seam during the excavation and support process of the shallow, medium depth, and deep coal roadways in the coal mine were simulated and studied. Based on the distribution law of the bolt and cable support stress field, the support compensation stress required for the stability of the surrounding rock after the excavation of the coal roadway with different burial depths was determined, and the corresponding roadways’ surrounding rock control technologies were proposed. This study’s results indicate that the compensation stress required for support in shallow coal roadways (with a burial depth of about 200 m) was much less than 0.1 MPa. A single rock bolt support can keep the surrounding rock of the roadway stable; the compensation stress required for support in the medium buried coal roadway (with a depth of about 600 m) is around 0.1 MPa, and the combined support of rock bolts and cables can meet the support requirements. Deep coal roadways under high stress (with a depth of about 1000 m) require support to provide compensation stress. Even if the compensation stress reaches 0.2 MPa, the surrounding rock of the roadway will experience varying degrees of creep. In this study, it was necessary to increase the support density and surface area of rock bolts and cables, the pre-tension forces of rock bolts and cables were improved, and in synergy with grouting modification, destressing and other technologies could control the large deformation of the surrounding rock of the roadway in 1000 m deep coal mines. This study’s results provide a theoretical basis for the selection of control technologies for use in coal roadways at different depths.