Fiber Reinforced Polymer Cables Research Articles

Statistical modeling and reliability analysis of large-scale multi-tendon fiber-reinforced polymer cables

In this study, the classic fiber bundle model is exploited in the statistical modeling of fiber-reinforced polymer (FRP) cables. Important features of large-scale multi-tendon FRP cable are considered including initial random slack, uneven tensile deformation among tendons, and other statistical mechanical properties of tendon. Aiming at the prediction of load-displacement relation and design of thousand-meter-scale FRP cables, a parametric study and reliability analysis are conducted, in which the relation of reliability index β of cable and safety factor γ of FRP material is emphasized. In four different types of FRP cables from previous studies, the simulated load-displacement curves are in good agreement with experimental ones. The random slack and non-uniform deformation of tendons are found to have significant impacts on cable capacity. For a 10,000 m-long cable, compared to the original strength of the tendon, the retention rate of strength in real FRP cable can vary from 0.26 to 0.82, depending on the scattering of tendon strength. The recommended γ is 3.0, 3.2, and 3.4 for target reliability index βT = 3.7, 4.2, and 4.7, respectively. Then, the limits of design parameters for large-scale FRP cables are calculated under a given reliability index.

Enhancement of Bond Performance of Advanced Composite Materials Used in Cable Bridge Structures Based on Tensile Tests.

Structural steel and concrete are essential materials for the construction of social infrastructures. However, these materials undergo degradation over time, thereby causing steel corrosion. To address this problem, a fiber-reinforced polymer (FRP) is used for reinforcement. In this study, tensile tests were performed to evaluate the material properties for the application of the FRP to cable bridge structures. These tests aimed to investigate various parameters to improve bond performance. Based on experiments with different parameters, sufficient bond performance could be achieved if the following conditions are met: mortar water ≤16%, regardless of the manufacturer; a depth of splitting and steel pipe length ratio ≥75%; upward/downward directions for the mortar injection; and the use of fiber-sheet reinforcement. In addition, the steel pipe used in the test (length of 410 mm and outer diameter of 42.7 mm) performed the best in terms of workability and cost effectiveness. By conducting more accurate tests to study the basic properties of materials, more accurate conditions to accomplish sufficient bond performance can likely be achieved. This will contribute to improved cost effectiveness and safety in the use of carbon FRP cables in cable bridge constructions.

Mechanistic model for prediction of the residual tensile strength of FRP wires

In-service cables made of fiber-reinforced polymer (FRP) wires experience repeated loading during their service life, which gradually degrades their load-carrying capacity. This paper proposes a mechanistic model to predict the residual tensile strength of the FRP wire, based on the state of damage inside the FRP wire as a function of the loading cycle. The mechanistic residual strength model developed here is an extension of the progressive fatigue damage model (PFDM) proposed recently by the authors. The main failure mode in the FRP wire in the PFDM is fiber breaks, allowing for the state of damage in the FRP wire to be determined for a specified maximum fatigue stress level and number of cycles. These results are then used as the input to calculate the residual strength of the FRP wire. Results indicate that the model can predict the residual strength of FRP wires well compared with the experimental data that has appeared in the literature. The proposed model is shown to provide a better understanding of the influence of the fatigue loading conditions on the residual tensile behavior of FRP wires, specifically, the effect on the residual stress-strain response, the kinetics of fiber element breaks, and the critical damage cluster. Moreover, the proposed model allows validation of the adequacy of safety factors typically adopted by designers to consider the degradation in strength of FRP cables, which is critical for the successful design and realizing the full potential of FRP cables.

Evaluation of a large-tonnage FRP cable anchor system: Anchorage design and full-scale experiment

Due to anisotropy of fiber-reinforced polymer (FRP) material, the anchoring of large-tonnage multiple-tendon FRP cable is a challenge. To solve this problem, a large-tonnage FRP cable anchor system (CAS) was designed numerically by optimizing five key anchorage parameters affecting the anchor efficiency and implemented in three full-scale basalt FRP (BFRP) cables with 37 Φ7 tendons. The numerical results showed that the cable radial displacement increases with the spacing of tendons increasing. The cable radial compressive stress and displacement decrease with the thickness of the load transfer component (LTC) increasing. Increasing anchor length and conical angle have significant reducing effect on the cable axial displacement but a negligible effect on the cable radial displacement. Experimental verification showed that the mean anchor efficiency and ultimate load of the BFRP cables were 95% and 1919 kN, respectively. The maximum axial strain difference of the BFRP cable at the loading and free ends increased with the load. The shear stress of the center BFRP tendon first increased rapidly, then decreased slowly, then increased gradually again, and finally decreased quickly. The axial strains and shear stress of the BFRP cable in the anchor zone were consistent with the FE results, and were proved to follow linear and cubic functions, respectively.

Failure mechanism and optimization of fiber-reinforced polymer cable-anchor system based on 3D finite element model

In this study, a three-dimensional (3D) finite element (FE) model of multiple-tendon fiber-reinforced polymer (FRP) cable-anchor system (CAS) was established to reveal the stress and deformation of an FRP cable. The model was firstly validated by the previous experimental results. The failure mechanism of FRP cable was clarified through FE analysis. Three types of optimizations, including changing the spacing of the FRP tendons, conducting the radial variable stiffness of the load transfer component (LTC) and changing the inner cone form of the anchorage, were conducted to improve anchor behavior. For FRP tendons, the radial compressive stress, as well as the relative radial displacements, were found to be nearly identical at different positions. An evident uneven axial tensile stress was observed for both the intra- and inter-tendon scenarios, in which the maximum axial tensile stress occurred in the outermost layer tendon. The failure of the FRP cable was dominated by the excessive tension-bending stress and radial compressive stress at the loading end. Applying radial variable-stiffness LTC was found to be the most effective method, and was validated in different tendon diameters and number of tendons.

FRP Cables to Prestress RC Beams: State of the Art vs. a Split Wedge Anchorage System

Versatility and high performance in terms of specific stiffness and strength, as well as non-corrosive sensitivity, make FRP (Fiber-Reinforced Polymer) cables a viable alternative to steel ones in the development of prestressing systems. On the other hand, the orthotropic and brittle nature of FRPs could trigger a premature failure of the cable in the anchorage system, for which several solutions have been proposed so far in civil structural applications. In this context, after a preliminary state of the art, the work introduces a split wedge anchorage for FRP (ϕ = 12 mm) cables proposing two different solutions for steel wedges having the external surface: either (1) a constant (3 degrees) slope or (2) a double slope obtained by shaping it with an angle of 3.0 degrees before and then of 3.1 degrees along the most tapered part. The goal was to exploit the nominal cable capacity (257 kN), avoiding stress peaks that cause its premature failure. The proposed solutions have been experimentally tested and, as far as the double angle solution is concerned, the failure loads were equal to 222 and 257 kN, denoting that the proposed solution can reach the cable capacity. Clearly, further investigations are needed to check the variability of the results and eventually improve the system.

Multiscale strength prediction of fiber-reinforced polymer cables based on random strength distribution

The strength prediction of fiber-reinforced polymer (FRP) cables provides a non-destructive technique for evaluating the cable properties. In this study, a shear-lag model that assumes impregnated fiber bundle (IFB) and resin matrix as the basic elements is proposed and complemented in finite element (FE) models. By importing the strength distribution of IFB fitted from experiments, the effectiveness of the proposed model was validated for four types of basalt FRP single tendons. The simulated strength demonstrated high accuracy with an error of less than 6%, which was more reliable than conventional methods. The full-scale failure mechanism and damage process of FRP cable can be explained from the aspect of IFB element, which is different from filament-based models. The effect of fiber strength randomness and the contribution of sheared resin matrix could be quantified. Then, a multiscale evaluation of basalt FRP cable was carried out, and the different failure patterns of the tendon and cable were identified. Based on the other external data of carbon FRP cable, the simulated cable force was found to be in better agreement with experimental one, compared to directly taking a strength reduction on the total tendon force.

Life cycle cost analysis of FRP cables for long-span cable supported bridges

Based on life cycle cost (LCC) analysis, the study evaluates the economic performance of fiber reinforced polymer (FRP) cables for super long-span cable supported bridges, and this includes cable-stayed bridges and suspension bridges. Based on the principle of life cycle cost, the main factors that affect the life cycle cost of different material cables are examined; these include the initial construction cost, maintenance time, maintenance cost and interest rates. Subsequently, the life cycle costs of different material cables are analyzed based on the principle of life cycle cost, and this includes four typical bridges, namely, two long-span suspension bridges and two cable-stayed bridges. The analysis results indicate that (1) When the time value of capital is considered, the life cycle cost of different material cable increases with the interest rate, although the steel cable is more sensitive to the interest rate when compared with that of the FRP cables due to poor durability. (2) The life cycle costs of a long-span suspension bridge with FRP cables are superior to those of traditional steel cable due to their significantly higher corrosion resistance and anti-fatigue performance. (3) The application of different FRP cables at a reasonable span enables cable system with a hybrid arrangement of FRP cables to effectively optimize the economic performance of long-span cable-stayed bridges.

Long-span cable-stayed bridge with hybrid arrangement of FRP cables

This paper proposes a new design for long-span cable-stayed bridge with a hybrid arrangement of fiber reinforced polymer (FRP) cables. Based on the considerations of the mechanical properties and economic performance, the reasonable spans of various FRP cables are analyzed according to the key parametric studies by means of analytical solutions. Through applying different FRP cables at their reasonable spans, a new design for a cable-stayed bridge with a hybrid arrangement of FRP cables is proposed. The related mechanicals properties and economic performances are analyzed by a case study of a crossing sea bridge with a span of 2038 m. The analysis results indicate that the proposed bridge design of a hybrid arrangement of FRP cables can meet the static requirement of long-span cable-stayed bridges including the deflection limitation of the middle span. The seismic behavior and the wind resistance stability of the long-span cable-stayed bridge are improved by applying a cable system with a hybrid arrangement of FRP cables. In addition, according to the life cycle cost analysis, the economic performance of the cable system with a hybrid arrangement of FRP cables is better than that of the pure FRP and hybrid FRP cable systems. The cable system with a hybrid arrangement of FRP cables offers an optimum design for the long-span cable-stayed bridge with a main span of more than 2000 m.

Static Behavior of Circumferential Stress-Releasing Anchor for Large-Capacity FRP Cable

AbstractIn this study, an optimized anchor system to enhance the anchor performance of multiple-tendon fiber-reinforced polymer (FRP) cables was proposed and evaluated. The manufacture of the cable...

Effect of linear transformation on nonlinear behavior of continuous prestressed beams with external FRP cables

Abstract In continuous prestressed members, linear transformation of the cable line is an interesting topic that has not yet been adequately addressed. This paper presents a numerical study on the flexural response of two-span continuous externally fiber reinforced polymer (FRP) prestressed concrete beams having various linearly transformed cable profiles, with emphasis on the redistribution of moments. The study is conducted by using a robust computational method that has been validated against experimental tests. The results confirm that the cable shift by linear transformation does not affect the basic performance at all stages of loading up to failure. The secondary moments are shown to vary linearly with the cable shift. The development of moment redistribution over the center support is significantly affected by linear transformation. An upward cable shift leads to a decrease in moment redistribution at ultimate. The results indicate that the effect of linear transformation on moment redistribution is neglected or incorrectly included in various design codes.

Damping Behavior of Hybrid Fiber-Reinforced Polymer Cable with Self-Damping for Long-Span Bridges

This paper studies the vibration characteristics and damping properties of a newly developed fiber-reinforced polymer (FRP) cable with a self-damping function using a model vibration experiment. To verify the self-damping effect of the designed FRP cable, the scaled model vibration test of the FRP cable was designed according to the real cables of the Su-tong Bridge. The damping properties of the FRP cable with self-damping were studied by excitation with small amplitude, middle amplitude, and high amplitude, respectively. The experimental results show that the model vibration test, designed based on similarity criteria, could effectively simulate the vibration characteristics of the real cable according to the experimental results of the natural frequencies. The properties of the energy dissipation of the self-damping FRP cable were superior to those of the FRP cable without self-damping based on the comparison of the modal damping ratios. Furthermore, the modal damping ratios of the FRP cable with self-damping increase with the vibration amplitude of the cable, indicating that the designed FRP cable can efficiently dissipate vibration energy with respect to the vibration amplitude.

Experimental study of vibration characteristics of FRP cables based on Long-Gauge strain

Steel cables as the most important components are widely used in the certain types of structures such as cablesupported bridges, but the long-span structures may result in an increase in fatigue under high stress and corrosion of steel cables. The traditional steel cable is becoming a more evident hindrance. Fiber Reinforced Polymer (FRP) cables with lightweight, high-strength are widely used in civil engineering, but there is little research in vibrational characteristics of FRP cables, especially on the damping characteristic. This article studied the two methods to evaluate dynamical damping characteristic of basalt FRP(BFRP) and glass FRP(GFRP) cables. First, the vibration tests of the B/G FRP cables with different diameter and different cable force were executed. Second, the cables forces were calculated using dynamic strain, static strain and dynamic acceleration respectively, which were further compared with the measured force. Third, experimental modal damping of each cables was calculated by the half power point method, and was compared with the calculation by Rayleigh damping theory and energy dissipation damping theory. The results indicate that (1) The experimental damping of FRP cables decreases with the increase of cable force, and the trend of experimental damping changes is roughly similar with the theoretical damping. (2) The distribution of modal damping calculated by Rayleigh damping theory is closer to the experimental results, and the damping performance of GFRP cables is better than BFRP cables.

Evaluation of the Static and Dynamic Behaviors of Long-Span Suspension Bridges with FRP Cables

AbstractTo overcome the limitations of traditional long-span suspension bridges with steel cables, the mechanical behavior of suspension bridges with various fiber-reinforced polymer (FRP) and hybrid FRP cables have been investigated comprehensively. The authors adopted a prototype of the proposed Messina Strait Bridge with a main span of 3,300 m to use as a suspension bridge model for analysis. The static and dynamic behaviors of the entire suspension bridge with steel and different FRP cables were analyzed by using the finite-element method. The results indicate that the application of FRP cables in a long-span suspension bridge benefits the spanning ability, improves the load-carrying efficiency, and reduces the axial force of the cable. The modal analysis results show that the long-span suspension bridge with cables of different materials have similar mode shapes, although the natural frequencies of the bridges with FRP cables are larger than that of the bridge with steel cable because of lower self-w...

A Novel Anchor Method for Multitendon FRP Cable: Manufacturing and Experimental Study

AbstractThis paper investigates the manufacturing technology and anchoring effectiveness of a proposed novel wedge anchor for multitendon fiber-reinforced polymer (FRP) cables. Manufacturing of the FRP cable used 19 FRP tendons with a diameter of 4 mm, and its anchor system was first studied by addressing the reliable bonding between each tendon and the realization of the variable elastic modulus of the load-transfer component (LTC) in the anchor zone. The experimental demonstration included evaluating the tensile properties of the FRP cable, the strain distribution in the anchor zone, and the stress-strain relationship of the cable. The anchor effect was evaluated through a comparison of strain distributions among the finite-element simulation and experimental results. Furthermore, the anchor efficiency of the tested cables was evaluated. The results indicate that the winding of fiber roving around each tendon at the anchor zone benefits the integration of the tendons, and the variable elastic modulus of...

A novel anchor method for multi-tendon FRP cable: Concept and FE study

This paper proposes a novel anchor toward large-sized fiber-reinforced polymer (FRP) cable with multi tendons and optimizes the key factors that affect anchor efficiency using finite element method (FEM). The limitations of conventional anchors for FRP tendons/cables were first analyzed. A new type of conical anchor with novel continuous-fiber-reinforced load transfer component (LTC) was proposed to overcome shortcomings of conventional anchors. The four key factors affecting anchor efficiency including modulus variation, conical degree, anchor length and the thickness of LTC were analyzed respectively. The results show that the proposed anchor not only owns an essential advantage in bonding by integrating LTC and FRP cable but also realizes the variable modulus of LTC by changing the winding angle of fiber roving. The optimization of key factors reveals that the avoidance of shear and compressive stress concentration can be realized by LTC modulus variation, while the conical degree of LTC significantly affects compressive stress distribution and cable axial displacements. The anchor length controls both compressive stress distribution and peak shear stresses, whereas the LTC thickness at the loading end only affects the peak compressive stresses and axial displacement. The optimization of above four factors determines the design of the proposal anchor.

VIBRATION CONTROL OF DIFFERENT FRP CABLES IN LONG-SPAN CABLE-STAYED BRIDGE UNDER INDIRECT EXCITATIONS

To identify the vibration characteristics and potential vibration control of different fiber reinforced polymer (FRP) cables for long-span cable-stayed bridges, the critical resonant responses of these cables under indirect excitations including external and parametric excitations are studied in this paper. Based on theoretical equations, the primary resonant responses of different cables under indirect excitations were first calculated and compared, afterwards the influence of cable length and design stress to the resonant responses and the importance of external and parametric excitations were further studied. Analysis of results show that all of the FRP cables measuring 575 m in length possess lower resonant responses compared with steel cables, while the hybrid FRP cable with smart dampers exhibits even lower responses than the other FRP cables. Moreover, the external excitation induced resonance will become critical for some kinds of FRP cables with increasing cable length. A method on adjusting design stresses mitigates this critical resonance and benefits vibration control of FRP cables. In addition, parametric excitation plays a more important role in resonant responses for short-length cables in comparison to external excitation, whereas both parametric and external excitations are critically important for long-length cables.

Modal damping evaluation of hybrid FRP cable with smart dampers for long-span cable-stayed bridges

The paper presents a theoretical evaluation on modal damping of hybrid fiber reinforced polymer (FRP) cable with smart damper design in long-span cable-stayed bridge. The principles and design consideration of smart dampers were first clarified. Based on the energy principle, the theoretical equations of modal damping were derived for in-plane and out-of-plane vibrations, respectively. The parameters that influence the damping effect were further analyzed. Finally, an example of hybrid basalt and carbon FRP cable with smart dampers was selected to evaluate damping ratio in terms of the equations derived in the paper. The results show that (1) the smart dampers with discontinuous distribution benefit not only static and dynamic behavior of a cable but also optimization of damping; (2) the gap width, bonding, length and modulus of each smart damper can be optimized to obtain maximum of potential damping; (3) an example of smart damper designed hybrid FRP cable demonstrates its effectiveness for mitigating large magnitude of in-plane vibration, while more dominant damping effect is observed for suppressing out-of-plane vibration.

Evaluation of FRP and hybrid FRP cables for super long-span cable-stayed bridges

Abstract This paper evaluates the safety factors, the applicable lengths, and relative cost of FRP (fiber reinforced polymer) and hybrid FRP cables that are potentially suitable for cable-stayed bridges with a super long-span of between 1000 m and 10,000 m. Following previous studies on 1000-m scale cable-stayed bridges with FRP cables, two kinds of hybrid FRP cables – the previously discussed hybrid basalt and carbon FRP (B/CFRP) cable and the newly-developed basalt and steel-wire FRP (B/SFRP) cable – as well as conventional steel cable, CFRP cable, and BFRP cable are further investigated focusing on their promise in meeting potential requirements for super long-span bridges. Some major results are as follows: (1) a three-stage model for determining safety factors of cables with different kinds and lengths is proposed; (2) a threshold of λ2 is suggested to achieve both high material and stiffness utilization efficiency, based on which the applicable lengths for different kinds of cables were evaluated; and (3) hybrid B/SFRP cables and BFRP cables are comparable in cost to steel cables within a 3000 m span, while hybrid B/CFRP cables and CFRP cables demonstrate a superior performance/cost ratio over a longer span.