Cable Inclination Research Articles

Calculating shear lag in steel-concrete composite beams under combined compression and bending

Long and complex composite steel-concrete structures are becoming common, requiring a deep understanding of the effects induced by the simultaneous action of axial forces and bending. In fact, the axial force generated, for instance, by cable inclination in cable-supported structures can modify the stress distribution within the elements compared to bending scenarios, thereby necessitating a revision of the effective width to be utilized. Nonetheless, current design codes, including Eurocode specifications and others, lack provisions for addressing the combined effects of axial force and bending, as they are exclusively tailored for bending. This limitation can introduce design complexities, necessitating the implementation of intricate Finite Element (FE) models, which impose substantial computational loads and design efforts. The methodology proposed in this paper overcomes these challenges allowing to assess the stress distribution and resistance of composite deck at Serviceability Limit State (SLS) and Ultimate Limit States (ULS) by leveraging results obtained from standard beam models typically used by structural designers or practitioners. A comprehensive parametric analysis using nonlinear finite element models is performed to validate the developed methodology. A comparison with the Eurocode 4 formulations highlights that the proposed method provides superior accuracy in estimating peak stress in concrete slabs under combined compression and bending. Additionally, it facilitates straightforward verification at the ULS in compliance with Eurocode requirements.

Seismic response investigation of prestressed anchor cable supporting rock slope with weak interlayer in Qinghai-Tibet Plateau, China

Earthquake-induced rock landslides in the eastern mountains of the Tibetan Plateau, especially landslides with weak interlayers pose a significant threat to major construction projects. Prestressed anchor cable is one of the main reinforcement methods of rock slopes. This paper combines shaking table model tests and numerical simulation to study the reinforcement effect and dynamic response characteristics of prestressed anchor cables applied to rock slopes with weak interlayers under strong earthquakes. The research results show that prestressed anchor cables can effectively reinforce slopes with weak interlayers. A small cable inclination, a small spacing and a high prestress are recommended in the seismic reinforcement design of prestressed anchor cable. In addition, the characteristics of slope progressive damage and prestress loss under the earthquake are found by the shaking table test. The results have been applied in hazard prevention and control of rock slopes on the Chengdu-Lanzhou Railway at the eastern Qinghai-Tibet Plateau.

Analysis of Wind Field Response Characteristics of Tethered Balloon Systems

Tethered balloon systems encounter various complex wind field environments during flight. To investigate the conditions under which the system can operate safely and smoothly, a longitudinal dynamic model for tethered balloon systems is established. The model incorporates a streamlined balloon shape with its aerodynamic center at the body’s center. Steady-state aerodynamic force coefficients are calculated through simulations and fitted to a function based on the angle of attack within a specified range. The complex cable model is simplified using the lumped mass method, considering the influence of branch cables on the main node position. Experimental results from windless oscillation tests on scaled tethered balloon systems are compared with numerical solutions obtained using the dynamic model under the same conditions, validating the feasibility of the model for simulating different wind field scenarios. Finally, the motion characteristics of tethered balloon systems in different wind fields are analyzed. The numerical simulation results show that in a horizontal step wind field, the cable tension and cable inclination angle increase with the wind speed, and the slower the wind field changes, the shorter the time required for system stabilization. Updrafts greatly increase the likelihood of balloon escape, while downdrafts greatly increase the likelihood of the system making contact with the ground. The findings of this study can provide a basis for selecting suitable wind field conditions and issuing risk warnings for tethered balloon systems.

An investigation of rain-wind induced vibrations on stay cables in a novel range of operating conditions

The large-scale rain-wind induced vibration (RWIV) dynamic test rig at the National Research Council Canada (NRC) was used in the current work to evaluate the vibration characteristics of a 0.218 m diameter smooth stay cable, for two cable inclinations and a wide range of yaw-angle conditions. The structural damping ratio was in the range of 0.05% to 0.11% and the heave frequency was approximately 1.23 Hz for a cable with a moving mass of 217 kg. The presence of RWIV was investigated at an inclination angle of 30° from the horizontal over a yaw-angle range of 25° to 45°and for an inclination angle of 55° over a yaw-angle range of −40° to ＋45°. An upper rivulet was present when vibrations were observed. For positive yaw angles, the upper rivulet was characterized by a thin line of water, approximately 5 to 10 mm wide, running along the entire length of the inclined cable on the windward side and moving along the cable span with a serpentine motion. For negative yaw angles, the upper rivulet was located near top of the cable or on the leeward sector of the cable, was wider than the rivulets observed for positive yaw angles, and was not observed to move in a serpentine motion. RWIVs were observed for each yaw angle that was investigated, including at negative yaw angles, with a maximum amplitude of motion of ±150 mm (∼0.7D). The direction of the rain impingement was an important factor affecting the formation and characteristics of the upper rivulet at the surface of the cable and, for the onset for vibrations. RWIVs were observed for wind speeds between 5 and 12 m/s. The Reynolds number corresponding to the onset of RWIV tended to increase with larger yaw angles in the positive yaw-angle range. At an inclination angle of 30°, the onset of RWIV ranged from 1.2×105 at a yaw of 25° to 1.4×105 at a yaw of 45° while at a cable inclination angle of 55°, the onset of RWIV ranged from 1.08×105 at a yaw of 25° to 1.25×105 at a yaw of 40°. The onset of vibrations for a yaw angle of 0° was at 0.77×105 for a cable inclination of 55°. RWIV was initiated at lower Reynolds numbers at an inclination angle of 55° for negative yaw angles, with vibrations observed at wind speeds as low as 5 m/s (Reynolds number of 0.7×105). The results confirmed the presence of RWIV in well-understood conditions and have effectively expanded the range of conditions over which RWIV has been observed in a wind tunnel. The expanded range over which RWIV was observed includes vibrations at an inclination angle of 55°, vibrations at a yaw angle of 0°, and vibrations at negative yaw angles from −10° to −40°.

Experimental study on aerodynamic countermeasure for galloping vibration of stay cables attached with lamps: Perforated shrouds

The aerodynamic countermeasure of the perforated shrouds is proposed to reduce the galloping vibration of stay cables installed with rectangular lamps. Ten test models with different parameters were designed and manufactured and a series of wind tunnel tests were carried out to measure the aerodynamic forces on the test models. Then, the mean aerodynamic force coefficients were obtained to further calculate the galloping force coefficients of these test models. Based on the quasi-steady theory, the effectiveness of the perforated shrouds on mitigating galloping vibration was verified by considering the effects of porosities, hole types, shroud diameter, the turbulence of approaching flow, and cable orientation (vertical and inclined). The cable inclination of 35° and a turbulence intensity of 9% was used for the force measurement wind tunnel tests, as well as shrouds with porosities of 0, 8.7%, 19.6%, 28.3%, 34.9%, 36%, 44.2%, and 49.0%. Two types of holes, including circular staggered and square array holes, were adopted, and two outer diameters of the perforated shrouds (125 mm and 88 mm) were used. The results show that the perforated shroud with a diameter of 125 mm plays an important role in mitigating the galloping vibration of both vertical and inclined stay cables with rectangular lamps. For the vertical test model, it seems that the optimal porosity of the perforated shroud is 19.6%, and the optimal porosity of the perforated shrouds for the inclined test model is within the range of 19.6%–34.9%. The minimum galloping force coefficients Cg of them is all greater than 0. The galloping critical wind velocity of the inclined cable-lamp structure without perforated shrouds is significantly lower than that of the vertical cable. However, the inclination of the stay cable induces a higher galloping critical wind velocity if the perforated shrouds are installed. The type of holes, a circular staggered and rectangular array, seems to not affect the galloping vibration. The turbulence intensity of 9% has a significant effect on the galloping critical wind velocity for the vertical and inclined cable attached with rectangular lamps without perforated shrouds but has little effect on the galloping critical wind velocity of the vertical and inclined cable-lamp system with perforated shrouds. The maximum value of combined aerodynamic mean force coefficients CC for the vertical test model with the perforated shroud is the same (1.1), the maximum wind load of the inclined test model with the perforated shroud is increased by 21∼58% due to the larger diameter.

An Experimental Study on Ice Accretion under Bridge Cable in Different Conditions

The ice accumulation on the surface of the stay cable of the bridge is a frequently identified problem that threatens the safety of bridge traffic. Therefore, it is important to investigate the ice accumulation on the stay cable under different conditions. To understand the distribution characteristics and variation rules of ice, this study analyzed the effects of ambient temperature, cable inclination angle, and diameter on the ice accumulation of the high-density polyethylene (HDPE) stay cable. The results show that the ambient temperature significantly affects ice formation in the lower part of the stay cable. Low temperature facilitates the formation and growth of icicles, while larger size and inclination angle of the stay cable inhibit the icicle growth. When the inclination angle of the cable is less than 60°, icicles easily form at the bottom of the cable. Smaller-diameter cables are more likely to accumulate icicles at the bottom.

Flame spread over cables in a utility tunnel: Effect of longitudinal wind and inclination angle

Tables in utility tunnels pose a major fire hazard. This work aims to provide a comprehensive understanding of the effects of cable inclination angle and longitudinal wind (U∞) on the flame spread behaviors of cables in a utility tunnel. Flame inclination angle (β) increases with the increase of cable inclination angle and longitudinal wind speed, while the amplification decreases as the longitudinal wind speed increases. Both flame length (xf) and pyrolysis length (xp) increase linearly with sinθ when U∞ is smaller than 0.65 m/s and they also increase with the increase of longitudinal wind speed. The increasing inclination angle and longitudinal wind speed contribute to the increasing flame spread rates. The flame spread rate accelerates significantly when the longitudinal wind speed and inclination angle are 0.65 m/s and 12° respectively. In addition, a model based on heat transfer analysis was established to predict the flame propagation rate under different cable inclination angles, and the experimental results were in good agreement with the predicted results. The results of the study contribute to cable fire risk assessment, which is beneficial for cable fire prevention and control in utility tunnels.

Nonlinear cable-deck interaction vibrations of cable-stayed bridges

In modern cable-stayed bridges, cables connect with other components such as the bridge deck and dynamic interactions occur between the cables and the rest of the structure. When the natural frequencies of a global vibrational mode and a cable mode are close, there can be significant interactions between the cable and deck. This can lead to vibration behaviour different to that of a simple cable-only dynamic system and hence vulnerability to cable fatigue or overloading. In this paper, a nonlinear cable-supported model is introduced. This model of one cable attached at the top of the deck allows for cable inclination, small sagging and multiple vibrational modes in two planes. Using scaling and averaging methods, analytical solutions in the form of non-dimensional polynomial equations have been derived for the steady state vibration amplitudes of the deck and cable of the coupled system. This analysis reveals a significant two resonance peak phenomenon which is not apparent from simpler cable-only analyses. Moreover, the feedback of the cable not only influences the cable response stability, but also the vibration amplitude of the cable and deck response. Results are presented for a typical inclined bridge cable interacting with a deck excited by the external force on the deck, highlighting the strong effect of the mass ratio between the cable and deck on the cable-deck interaction performance. The feedback of the cable vibration on the deck and cable response is non-negligible even for a relatively large mass ratio. Therefore, for practical cable-stayed bridges the interaction between cable and deck needs to be considered to obtain an accurate dynamic response in some cases.

The placement of linear transducers affects the magnitude but not the intra-session reliability of kinematic variables during the bench press exercise

BACKGROUND: While linear transducers are the most accurate velocity monitoring devices, the horizontal motion of the barbell seems to affect its measurement error. OBJECTIVE: To explore the effect of cable inclination of the GymAware and T-Force linear transducers on the intra-session reliability and magnitude of kinematic variables during the Smith machine bench press exercise. METHODS: Twenty-eight resistance-trained males performed 2 blocks of 12 repetitions (4 repetitions at 40-60-80%1RM). In half of the repetitions with each load the two measuring systems were either vertically aligned with the barbell or positioned 15-cm away from the vertical projection of the barbell. RESULTS: Displacement and mean velocity variables were recorded with a high and comparable intra-session reliability regardless of the cable position and measuring system (CV=𝑟𝑎𝑛𝑔𝑒 1.79–8.38%; ICC=𝑟𝑎𝑛𝑔𝑒 0.69–0.98). The inclined cable position provided a lower displacement and mean velocity than the vertical cable position and the differences were comparable using both the GymAware (⩽ 1.52 cm; ⩽ 0.05 m⋅s-1) and T-Force (⩽ 1.53 cm; ⩽ 0.04 m⋅s-1). CONCLUSIONS: These results indicate that repeatable findings of kinematic variables can be obtained regardless of the cable position, but for comparative purposes, the cable position should remain constant from the start to the end of the lifts.

Experimental Investigation of the Influence of the Anchor Cable Inclination Angle on the Seismic Response Characteristics of Anchored Piles

Studies show that prestressed anchor cable antislide piles have good antiseismic characteristics. As an important parameter in the design of anchor-cable piles, the effect of anchor-cable inclination on the seismic response of the anchor-cable pile system has been rarely studied so far. In the present study, the seismic response characteristics of the anchor-pulled pile under different cable inclinations are studied using a large-scale seismic model test platform and numerical methods. The obtained results show that the inclined angle of the anchor cable has a great influence on the seismic response of the pile-anchor system. It is found that under the same seismic conditions, the axial force of the anchor cable becomes smaller as the anchor dip angle increases, while the pile top displacement becomes larger. The dynamic earth pressure behind the pile changes from the sliding surface to the pile top, indicating that the earth pressure near the sliding surface and the pile top is of active and passive earth pressure types, respectively. This pressure decreases with the increase of the anchor dip angle, thereby affecting the performance of the antisliding pile.

Autonomous Control and Transportation of Underslung Load With Single and Dual Lift Helicopter Systems

Abstract This paper discusses the development of a single-lift and dual-lift helicopter underslung load transportation system for practical applications. A control law is developed to damp the load swing and stabilize the oscillation while performing the transportation task. For the dual-lift system, the load transportation is achieved by using a load distribution controller, developed for this purpose, to maintain equal load distribution among the vehicles. The load damping and load distribution controllers require accurate measurement of load states, which is achieved through the design and development of innovative, simple, and lightweight sensors units, namely, load tension measurement unit (LTMU) and load swing measurement unit (LSMU). LTMU sensor consists of a unique design that utilizes a flexi-force sensor, capable of measuring compressive load, for measurement of cable tension. The cable inclination in the longitudinal and lateral directions is measured by the LSMU sensor. These units are integrated with the helicopter autopilot for autonomous flight. The performance of the developed system is experimentally validated in the outdoor environment with single and dual-lift systems.

Influence of cable inclination angle and longitudinal ventilation on temperature distribution during cable fire in utility tunnel

Cable fire in utility tunnel commonly cause severe economic lost. This work experimentally investigates influence of cable inclination angle and longitudinal ventilation on temperature distribution during cable fire in utility tunnel. The position of the maximum ceiling temperature is located near the fire source. The position of the maximum ceiling temperature shifts with the increase of the wind speed. When the wind speed is less than 0.45 m/s, the maximum ceiling temperature increases with the increase of wind speed. When the wind speed is greater than 0.45 m/s, the conclusion is opposite. The dimensionless temperature rise and the longitudinal distance accord well with the attenuation law of power-exponential function. In the area between the cable bearer and the fan, larger wind speed corresponds to faster decay of the dimensionless temperature rise. In the area between the cable bearer and the outlet, the conclusion is opposite. The position of the maximum ceiling temperature is independent of the cable inclination angle. When the cable inclination angle is less than 15°, the maximum ceiling temperature increases with the increase of the cable inclination angle. When the cable inclination angle is greater than 15°, the conclusion is opposite.

Numerical simulation and experimental study of submerged floating tunnel subjected to moving vehicle load

To investigate the dynamic behavior of the submerged floating tunnel (SFT) under moving vehicle load, a SFT experimental model is designed and analyzed. Through typical experiment cases, the effects of cable and vehicle with different parameters on the SFTs are discussed. Besides, the numerical simulation method is proposed in ABAQUS/EXPLICIT module for contrastive analysis. The *VUMAP and the *VDLOAD subroutines are used for implementing the tube fluid force and the moving vehicle load in the numerical model. The results show that the vertical vibration of the SFT is relatively independent to other directions, and the connection between the tubes will partially weaken the overall stiffness of the SFT. In addition, the deviation amplification effect exists in the SFT subjected to moving vehicle load. Increasing the cable inclination angle and the cable diameter can reduce the amplification effect. For the SFT with different cable spacing, the deviation amplification effect of dense cable arrangement is smaller than that of the sparse cable arrangement. But their sensitivities to vehicle velocity are not very different. In the practical project, the cables should provide sufficient strength to the SFT for safety.

Dynamic analysis of anti-dip bedding rock slopes reinforced by pre-stressed cables using discrete element method

Pre-stressed cables were found to be a viable approach of reinforcing anti-dip bedding rock slopes (ABRSs) in the Wenchuan earthquake. However, the dynamic response law and failure mechanism of reinforced ABRSs are still unclear, which was studied using the Universal Distinct Element Code (UDEC) method in this work. A numerical model of a typical ABRS was first built up using UDEC. Then, a comparison of the dynamic response of reinforced and unreinforced ABRSs was carried out. Moreover, a systematic parameter study was performed to investigate the effect of cable inclination, cable spacing, and pre-stressed force on the reinforcement effect. The results show that pre-stressed cables can be very effective in controlling the deformation and improving the dynamic stability of ABRSs subjected to dynamic loading. For both unreinforced and reinforced ABRSs, a remarkable acceleration amplification occurs on the surface of the slope from half of the slope height upwards. A small cable inclination and a high pre-stressed force are recommended in the seismic reinforcement design of ABRSs. The results of this work could guide the design of reinforcement of ABRS in earthquake-prone areas.

Design and Implementation of a Cable Inspection Robot for Cable-Stayed Bridges

SUMMARY Cable is the most important bearing structure of the cable-stayed bridges. Its safety has been of crucial public concern. Traditional manual cable inspection method has many defects such as low inspection efficiency, poor reliability and hazardous working environment. In this paper, a new wirelessly controlled cable-climbing robot enabling safe and convenient inspection of stay cables is proposed. The designed robot is composed of two modules, joined by four turnbuckles to form a closed structure that clasps the cable. The robot is controlled wirelessly by a ground-based station, and a DC power is supplied via an onboard lithium battery. The climbing principle and mechanical structure of this robot are introduced. The static model of the robot during obstacle negotiation is established. The relationships of the driving force and resistance with obstacle height to determine the obstacle-negotiation capability of the robot are obtained. The effects of cable diameter, cable inclination and preload force on obstacle climbing ability of the robot are also analyzed. The experiments verify that the robot could climb random inclined cables and overcome an obstacle of 2.42 mm in height with a mass of 5 kg payload.

Study on temperature distribution and CO diffusion induced by cable fire in L-shaped utility tunnel

Numerical simulation study was conducted to investigate temperature distribution and CO diffusion induced by cable fire in a L-shaped utility tunnel. The maximum ceiling temperature in region I of tunnel decreases as horizontal distance from the fire source rises, while temperature in region II first increases and then decreases. Larger cable inclination angle (θ) leads to lower temperature in region I, while the conclusion is reverse in region II. An equation is proposed to predict maximum temperature rise along the tunnel ceiling. As vertical height rises, the maximum temperature above the fire source first drops and then rises for larger inclination angle. The vertical maximum temperature increases as fire source power or ventilation velocity rises under most conditions. For stable fire, the CO concentration shows "V-shaped" variation with a change in horizontal distance from the fire source under most conditions. The CO concentration is higher when the ventilation is conducted compared with no ventilation condition. The influences of fire source power on the CO concentration is not obvious. The low CO concentration area significantly increases to half of region I as inclination angle rises to 4°. Research results will contribute to fire hazard evaluation and safety design of utility tunnels.

Mitigation mechanism of longitudinal ribs on rain-wind induced vibrations of stay cables

For cable stayed bridges rain-wind induced vibrations of stay cables are probably one of the most widespread phenomenon. Aerodynamic countermeasures have been implemented to tackle such vibrations, but there is still not sufficient insight on the inherent mitigation mechanisms. To this goal, a numerical model, based on lubrication theory, was employed in order to study the coupled cable vibration response, aerodynamic forces, and formation and oscillation of rivulets for stay cables equipped with longitudinal ribs. Coupled equations governing the synchronous cable motion and water film evolution were established in order to understand the effects of several key parameters associated with the vibration mitigation performance of the ribs. Such parameters include the cable inclination angle, the wind yaw angle, the number and the height of the ribs. Computed results were successfully validated against experimental data. For the various studied cases, it was apparent that the ribs did not stop the formation of rivulets, but they could affect both their position and oscillation ranges. Through such a control action they could further affect the oscillation range and frequency content of aerodynamic forces, mitigating or not cable vibrations.

Prediction of ice accumulation on bridge cables during freezing rain: A theoretical modeling and experimental study

Accreted ice falling from bridge cables is a hazard to vehicles crossing the bridge. The falling ice can startle drivers, cause accidents, and break windshields. Therefore, predicting ice accretion on bridge cables is vital in determining the severity of the event and making decisions concerning bridge or lane closure. In this study, a simple ice accumulation model for freezing rain on bridge cables was developed that accounts for the cable inclination and determines the accretion orientation and shape. Indoor experiments in an icing wind tunnel were conducted on stainless steel cylindrical specimen with various inclinations. It was found that the inclination of the cables affected the ice thickness and prevalence of icicles. The model was evaluated by two icing events on the Veterans' Glass City Skyway Bridge in Toledo, Ohio. The modeled ice results were consistent with the observations. The model can be a valuable tool for ice accumulation prediction on bridge cables using forecasted weather data.

Effect of cut-off order of nonlinear stiffness on the dynamics of a sectional suspension bridge model

The nonlinear dynamics of a suspended bridge deck with inclined main cables and its sensitivity to the nonlinear stiffness are investigated via a 6-DoFs sectional model in this study. Four configurations with different main cable inclination angles are investigated. Two higher order numerical models are analyzed to examine the effects of higher order nonlinear stiffnesses on the dynamic properties, with one considering the linear and quadratic stiffness terms and the other includes additionally the cubic stiffness term. Incremental harmonic balance method is adopted for the nonlinear dynamic analysis, and primary resonances at the first and second modes are studied in details. Results show that the nonlinearity introduced by the inclined main cables has only very minor effects on the first primary resonance modal response. However, the cubic stiffness term shows quite strong effect on the dynamic response of the second mode. If only the linear and quadratic stiffnesses are included in the model, the frequency-response curve from the first harmonic term shows weak softening features. The system, however, performs like a hard spring when the cubic stiffness is included which is totally different from existing published results. The observations on the super-harmonic resonance at the first two modes of the system also show great differences in the behavior of the two numerical models. Results from this study suggest that the cubic nonlinear stiffness should be included for better modeling of a sectional suspension bridge model.

Design formulas for vibration control of sagged cables using passive MR dampers

In this paper, a method for analyzing the damping performance of stay cables incorporating magnetorheological (MR) dampers in the passive control mode is developed taking into account the cable sag and inclination, the damper coefficient, stiffness and mass, and the stiffness of damper support. Both numerical and asymptotic solutions are obtained from complex modal analysis. With the asymptotic solution, analytical formulas that evaluate the equivalent damping ratio of the sagged cable-damper system in consideration of all the above parameters are derived. The main thrust of the present study is to develop an general design formula and a universal curve for the optimal design of MR dampers for adjustable passive control of sagged cables. Two sag-affecting coefficients are derived to reflect the effects of cable sag on the maximum attainable damping ratio and the optimal damper coefficient. For the cable configurations commonly used in cable-stayed bridges, the sag-affecting coefficients are directly expressed in terms of the sag-extensibility parameter to facilitate the control design. A case study on adjustable passive vibration control of the longest cable (536 m) on Stonecutters Bridge is carried out to demonstrate the influence of the sag for the damper design, and to figure out the necessity of adjustability of damper coefficients for achieving maximum damping ratio for different vibration modes.