Unbonded Tendons Research Articles

포스트텐션 휨부재에서 비부착긴장재의 극한응력

It is quite difficult to predict the flexural strength of post-tensioned members with unbonded tendons (unbonded posttensioned members, UPT members) because of debonding behavior between concrete and prestressing tendons, which is different from that with bonded tendons. Despite many previous researches, our understanding on the flexural strength of UPT members is still insufficient, and thus, national codes use different methods to calculate the strength, which quite often give very different results. Therefore, this paper reviews various existing methods, and aims at proposing an improved rational strength model for UPT flexural members having better accuracy. Additionally, a database containing a large number of test data on UPT flexural members has been established and used for verification of the proposed flexural strength model. The analysis results show that the proposed method provides much better accuracy than many existing methods including the rigid-body model that utilizes the assumption of concentrated deformation and plastic hinge length, and that it also gives proper consideration on the effects of primary parameters such as reinforcement ratio, loading pattern, concrete strength, etc. Especially, the proposed method also well predicts the ultimate stress of unbonded tendons of over-reinforced members, which are often possible in construction fields, and high strength concrete members.

강선량 및 긴장력에 따른 외부 강선을 가진 PSC 보의 휨거동 실험

Dept. of Civil Engineering, Kunsan National University, Jeonbuk 573-701, KoreaABSTRACT Recently, the externally prestressed unbonded concrete structures are increasingly being built. The mechanicalbehavior of prestressed concrete beams with external unbonded tendon is different from that of normal bonded PSC beams in thatthe slip of tendons at deviators and the change of tendon eccentricity occurs as external loads are applied in external unbondedPSC beams. The purpose of the present paper is therefore to evaluate the flexural behavior by performing static flexural test accord-ing to tendon area and tendon force. From experimental results, before flexural cracking, there was no difference between externalmembers and bonded members. However, after cracking, yielding load of reinforcement, ultimate load, and the tendon stress ofexternal members was lower than that of bonded members. For the relationship of load-tendon stress, the increasing of tendon st rainwas inversely proportional to the initial tendon force. However, even if the initial tendon force was large, the tendon strain withsmall effective stress was smaller than that with large effective stress. The concrete compressive strain was proportional to t he effec-tive stress of external tendon. From the comparison between test results and codes, the ACI-318 could not consider the effect oftendon force or effective stress, and especially the results of ACI-318 were very small, so it was very conservative. And theAASHTO 1994 could be influenced on the tendon area, initial force and effective stress, but as it was made on the basis of internalunbonded tendon, its results were much larger than the test results. For this reason, the new correct predict equation of externaltendon stress will be needed.Keywords : prestressed concrete, external unbonded tendon, tendon area, tendon force

Flexural behavior of steel I-beam prestressed with externally unbonded tendons

The external post-tensioning technique has been commonly used in the construction field because it facilitates the analysis of structures and is widely applicable for many types of structures. In this paper, the flexural behavior and strengthening effect of a bridge were studied using a steel I-beam that had been externally prestressed with unbonded tendons. Eleven steel beams were fabricated and tested in terms of the tendon type, the amount of tendon or prestressing force, the installation of a deviator, and the embedment of a draped tendon. The results show that the externally prestressing method creates a stiffer steel beam when the proper amount of prestressing force is applied and when detail techniques are appropriately combined.The experimental results were compared to a theoretical solution in order to verify whether the external post-tensioning method is useful for strengthening a steel bridge and whether it is applicable in the construction field.

Estimation of ultimate stress in external FRP tendons

In a prestressed concrete beam with external tendons, the tendon stress depends on the member deformation, and it cannot be determined from section analysis alone as in the bonded case. Previous work has been mainly on the ultimate stress in unbonded steel tendons, with little on unbonded fibre-reinforced polymer (FRP) tendons. To account for the relative slip between the unbonded tendon and concrete, the ratio of the equivalent plastic hinge length to the neutral axis depth is analysed using available test results. It is found that this ratio for unbonded partially prestressed concrete (UPPC) beams with external FRP tendons can also be treated as a constant as for those with unbonded steel tendons. A simple method for evaluation of the ultimate stress in either steel or FRP external tendons is therefore proposed. After suitable modifications, the equations currently adopted by various design codes can still be used to predict the ultimate stress in external FRP tendons of UPPC beams.

프리캐스트 세그먼트 PSC 교각의 성능평가를 위한 지진해석

The purpose of this study is to investigate the seismic behavior of precast segmental PSC bridge columns. For the analysis of reinforced concrete structures, a computer program named RCAHEST (Reinforced Concrete Analysis in Higher Evaluation System Technology) is used. To represent the interaction between tendon and concrete of a prestressed concrete member, a bonded or unbonded tendon element based on the finite element method is used. A joint element is modified to predict the inelastic behaviors of segmental joints. The solution of the equations of motion is obtained by numerical integration using Hilber-Hughes-Taylor (HHT) algorithm. The proposed numerical method gives a realistic prediction of seismic behavior throughout the input ground motions for numerical examples.

외부강선으로 보강되는 PSC I 합성거더의 해석 기법

Korea Expressway Transportation & Technology Institute, Whasung 461-703, KoreaABSTRACT This paper presents an analytical prediction of Nonlinear characteristics of prestressed concrete bridges by strength-ened of externally tendon considering construction sequence, using unbonded tendon element and beam-column element based onflexibility method. Unbonded tendon model can represent unbounded tendon behavior in concrete of PSC structures and it can dealwith the prestressing transfer of posttensioned structures and calculate prestressed concrete structures more efficiently. This tendonmodel made up the several nodes and segment, therefore a real tendon of same geometry in the prestressed concrete structure canbe simulated the one element. The beam-column element was developed with reinforced concrete material nonlinearities which arebased on the smeared crack concept. The fiber hysteresis rule of beam-column element is derived from the uniaxial constitutiverelations of concrete and reinforcing steel fibers. The formulation of beam-column element is based on flexibility. Beam-columnelement and unbonded tendon element were be involved in A computer program, named RCAHEST (Reinforced Concrete Analysisin Higher Evaluation System Technology), that were used the analysis of RC and PSC structures. The proposed numerical methodfor prestressed concrete structures by strengthened of externally tendon is verified by comparison with reliable experimental results.Keywords : externally tendon, construction sequence, unbonded tendon element, fiber beam-column element, PSC structure

Effect of overloading on fatigue performance of reinforced concrete beams strengthened with externally post-tensioned carbon-fibre-reinforced polymer tendons

This paper presents the results of an experimental and analytical study of the fatigue performance of reinforced concrete beams strengthened with externally post-tensioned carbon-fibre-reinforced polymer (CFRP) tendons. Two loading conditions prior to strengthening the beams were investigated: in-service loading and overloading. A total of 18 beams were tested to failure: three under monotonic loading and fifteen under fatigue loads. The CFRP tendons were post-tensioned to 40% of their ultimate capacity. The results demonstrated that overloading the beams had no discernable effect on the fatigue life of the strengthened beams. The strain-reduction approach for unbonded steel tendons was modified to account for using CFRP tendons and for the permanent deformations resulting from the overloading process. The loading history of the beams prior to and after post-tensioning was incorporated into a strain-life fatigue model to predict the fatigue life of the strengthened beams.

Experimental Study on Behaviors of Unbonded Prestressed Concrete Beams Reinforced with CFRP Tendons

In order to research behaviors of unbonded prestressed concrete beams reinforced with CFRP tendons, static load experiments on 4 partially prestressed simple beams with unbonded CFRP tendons and 9 two spans partially prestressed concrete continuous beams with unbonded CFRP tendons were performed. Based on the experiment results of simple beams, the law of ultimate stress increment in unbonded CFRP tendons in simple beams was obtained. Based on the experiment results of continuous beams, the law of stress increment in unbonded CFRP tendons in continuous beams was obtained at serviceability state and at strength limit state of bending capacity. The calculation formula of length of equivalent plastic hinge for this kind of continuous beam was presented. The calculation formulas of moment modification coefficient with composite reinforcement index for intermediate support as variable and relative plastic rotation for intermediate support as variable were given respectively.

Avaliação "in loco" das perdas de protensão de cordoalhas engraxadas em lajes planas

Este trabalho apresenta os resultados de um estudo sobre as perdas de protensão, medidas "in loco", de cordoalhas engraxadas em lajes planas. Essas lajes planas, com 17 centímetros de espessura e 350 m2 de área, fazem parte de um edifício para fins hoteleiros de 16 pavimentos. As forças de protensão foram medidas por células de carga colocadas nas proximidades da ancoragem ativa e da ancoragem passiva. As medidas de forças foram feitas desde a protensão até idades de 170 dias após esse instante. Os resultados revelam um coeficiente de atrito μ igual a 0,0528 bastante próximo ao valor apresentado pela norma brasileira NBR 6118: 0,05. Nas perdas pela acomodação da ancoragem os valores apurados foram bastante similares e em termos médios, essa perda correspondeu a 5,17% da força inicial de protensão. Os valores de força medidos mostram também que a perda de tensão na cordoalha, próximo à ancoragem passiva, é menor em relação à perda na ancoragem ativa. Até a idade de 170 dias, verificou-se uma perda média de 14% da força inicial de protensão.

Deformability of concrete beams with unbonded FRP tendons

As fibre-reinforced polymer (FRP) behaves linearly until it ruptures without any yielding, the ductility and deformability of prestressed concrete beams with FRP tendons are of prime concern. This paper describes a comparative study of five existing deformability indices for unbonded partially prestressed concrete (UPPC) beams with FRP tendons. A numerical method has been developed to predict the full-range response of prestressed concrete beams with bonded and/or unbonded FRP tendons under loading, and the results agree well with experimental results reported in the technical literature. The results show that the deformability index defined as the ratio of the product of moment and deflection at ultimate to the corresponding value at cracking is consistently decreasing with the increase of combined reinforcement ratio. In addition, this index is sensitive to changes of factors that may influence the deformability of UPPC beams with FRP tendons. The present investigation also indicates that, when the ratio of neutral axis depth to the depth to FRP tendons at the critical section at ultimate is greater than 0.3, the beam would fail by crushing of concrete, which is the more favourable failure mode compared to the rupture of tendons.

Behaviour of partially prestressed beams with external tendons

The behaviour of prestressed concrete structures with unbonded tendons differs significantly from that of those with bonded tendons after the working stage. To assess the safety of such structures, it is necessary to carry out full-range analysis with particular attention to the post-peak behaviour. This paper reports the initial findings of experimental investigations. A number of simply supported externally prestressed concrete beams with either steel or aramid fibre-reinforced polymer tendons are tested to failure, so as to study the effect of external prestressing on the ductility. The specimens tested all have T-sections prestressed by two external tendons with one on each side. In the experiments, different factors are taken into consideration. They include the level of prestressing force, area of non-prestressed steel reinforcement and partial prestressing ratio and so on. It is found that friction may vary significantly when a beam is subjected to large deformations. Comprehensive analysis of internal forces in selected specimens has been carried out. While the tendons play a key role in supporting loads during the initial stage of loading, their contribution decreases with further loading. At the same time, the role of bottom non-prestressed reinforcement increases and remains predominant after the apparent yielding of the specimen.

Tendon Stress in Unbonded Posttensioned Masonry Walls at Nominal In-Plane Strength

Accurate estimation of stress in unbonded tendons at the nominal strength limit state is essential for calculating the in-plane flexural strength of posttensioned masonry walls. These walls gain their lateral strength and desirable seismic properties through the utilization of vertical unbonded posttensioning. Unlike walls with bonded tendons where the tendon stress can be found through strain compatibility with the surrounding masonry, the stress in unbonded tendons results from wall deformation between the two tendon anchorages. International masonry codes, including ASCE 5-05 (Masonry Standards Joint Committee), provide varying equations for calculating tendon stress at the nominal strength limit state but in no case have these equations been verified for in-plane loading. A finite-element model validated against large-scale in-plane structural testing of posttensioned concrete masonry walls is used to demonstrate the accuracy of existing code equations. A revised equation is then shown to provide a more accurate prediction of tendon stress for walls loaded in-plane and is recommended for inclusion in future masonry code revisions.

Effect of prestressing on the first flexural natural frequency of beams

In this paper the effect of prestressing force on the first flexural natural frequency of beams is studied. Finite element technique is used to model the beam-tendon system, and the prestressing force is applied in the form of initial tension in the tendon. It is shown that the effect of prestressing force on the first natural frequency depends on bonded and unbonded nature of the tendon, and also on the eccentricity of tendon. For the beams with bonded tendon, the prestressing force does not have any appreciable effect on the first flexural natural frequency. However, for the beams with unbonded tendon, the first natural frequency significantly changes with the prestressing force and eccentricity of the tendon. If the eccentricity of tendon is small, then the first natural frequency decreases with the prestressing force and if the eccentricity is large, then the first flexural natural frequency increases with the prestressing force. Results of the present study clearly indicate that the first natural frequency can not be used as an easy indicator for detecting the loss of prestressing force, as has been attempted in some of the past studies.

Determination of the Cable Factor for Deviated Tendon Bundles

This article illustrates how the cable factor of deviated bundle tendons and accordingly the pressure between prestressing steel elements and ducts can be accurately determined. The knowledge of the maximum pressure between single tendons and the duct of a tendon bundle is important both to estimate the danger of fatigue fracture of the prestressing steel due to fretting corrosion when using corrugated steel ducts and to estimate the imprints into polyethylene (PE) ducts of unbonded tendons. PE ducts serve as corrosion protection sheathing for tendons. Especially for unbonded tendons, it is necessary to limit the wear of ducts to ensure the corrosion protection of the steel, the durability of the tendon and the tensioned structure. The remaining thickness of PE ducts after loading has to fulfill certain requirements (e.g.according to the guideline for European Technical Approval of Post-Tensioning Kits for Prestressing of Structures, ETAG 013 Ed. June 2002). In the past, graphical methods were applied as well as costly and time-consuming simulations of the arrangement of strands or wires in a duct with the help of small-scale samples. For configurations other than the ones tested or for a greater number of wires in a duct these results cannot be used. That is why two numerical approaches of how to arrange single tendons in a duct were developed. After finding a stable arrangement of the tendons it is possible to determine the cable factors and thus the maximum transverse loading by the help of a twodimensional (2D) truss calculation. Additionally, two simplified approaches for estimating the maximum cable factors are presented. They reduce the calculation effort to different extents. The first approach is based on hydrostatic analogy. The second one is a simplified method that allows for a quick estimation with the help of the relevant parameters. When using PE ducts for bonded post-tensioning fatigue fracture due to fretting occurs at the contacts between single tendons. A simplified model quantifying the maximum inner cable factor is presented for the first time. With the help of the tools presented, the curvature design of deviated tendons and the formulation of restrictions in codes can be reconsidered. In addition to this, they can contribute to a qualified assessment of the durability and efficiency of existing post-tensioning systems or to their development.

Rational Approach for Predicting Stress in Beams with Unbonded Tendons

Estimating the tendon stress in concrete beams prestressed with unbonded tendons is challenging due to the lack of strain compatibility between the tendon and the surrounding concrete. This paper presents a rational approach for predicting the flexural response of beams prestressed with unbonded tendons. The proposed methodology considers the beam and tendon as a trussed beam system that allows for the rational use of equilibrium and compatibility equations as well as the law of conservation of energy to predict the overall behavior at various load levels. The methodology was validated using results from tests performed on 25 high-strength concrete beams as well as test data available in the literature. Various parameters such as area of reinforcing steel, concrete strength, area of prestressing steel, effective prestress, and span-depth ratio were considered. Results from the experimental study include deflection and strain in prestressing strands, reinforcing steel, and concrete. Based on the analytical study, an equation for predicting the stress at ultimate was derived. Experimental results confirm the accuracy of the proposed methodology and equation.

スティールキャップを有するアンボンドＰＣａＰＣ柱・梁圧着接合による卜型試験体の繰返し載荷実験

Experimental results of new precast concrete beam-column connections constructed by post-tensioning precast beams to precast columns using unbonded tendons are presented. The connections consist of precast beams which has steel cap at its ends and precast columns which has steel band at the connection region. The steel cap and steel band are used to reduce damage in the plastic hinge region of precast beams. Four test specimens were subjected to reversed cyclic loading and comparisons were made between the behavior of presented precast concrete specimens and conventional precast concrete specimen.

Seismic Performance of Self-Centering Structural Walls Incorporating Energy Dissipators

This paper presents elements of seismic design for jointed precast cantilever wall units designed to rock about their foundation. Gravity loading and prestressed unbonded tendons provide the restoring force in these walls. Lateral displacements eventually result in a separation gap forming only at the wall-foundation beam connection. The gap reduces the wall stiffness and results in nonlinear response. Design of these walls is made with the explicit objective of ensuring a self-centering response. That is, the wall returns to its pre-earthquake position upon unloading from a large displacement excursion. The integrity of the walls is maintained because no plastic hinges form and there are no residual postearthquake displacements. Energy dissipators, in the way of longitudinal mild steel reinforcement crossing the joint between the walls and the foundation, are incorporated into these walls to add significant energy dissipation capacity while preserving the self-centering response. This paper also describe...

Experimental Behavior of Reinforced Concrete Beams Strengthened with Prestressed CFRP Shear Straps

One promising means of increasing the capacity of existing shear-deficient beams is to strengthen the structure using external prestressed carbon fiber reinforced polymer (CFRP) straps. In this system, layers of CFRP tape are wrapped around a beam to form a strap that acts like a discrete unbonded vertical prestressing tendon. Experiments were undertaken to investigate the influence of the strap spacing, the strap stiffness, the initial strap prestress level and/or any preexisting damage on the strengthened behavior, and mode of failure. An unstrengthened control beam was tested and failed in shear. In contrast, all of the strengthened beams showed a significant increase in their ultimate load capacity with several of the strengthened beams failing in flexure. A number of different failure modes were noted and initial guidelines on the design parameters that influence the propensity for a particular failure mode were developed.

Corrosion-Related Failure of Post Stressed Tendons

The structure and placement of unbonded post stressed tendons is discussed briefly, together with regard to possible problems relating to ingress of water between the outer polyethylene sheath and inner stressed steel strand. Premature corrosion and failure of some tendons after fourteen years service in a floor slab are examined via optical and scanning electron microscopy (SEM) and related to conditions occurring within the tendons. Water penetration caused localized crevice corrosion of individual wires in the strand via formation of oxygen concentration cells, consistent with in-situ pH measurements of the water environment in the tendon. Initially, such corrosion propagated as cracks transverse to the axis of the individual wires. Subsequent hydrolysis reactions within the crevices/cracks produced local pH conditions conducive to hydrogen embrittlement and crack propagation along the wire axis, consistent with cracking observed under hydrogen charging conditions.

Design and construction of the Metrolink Finback Bridge

The Manchester to Oldham line of the proposed Metrolink Phase 3 passes through the new Central Park business park utilising the existing track bed of a disused and dismantled heavy rail route. To the east of Thorp Road Bridge the new Metrolink route crosses the existing four tracks of the Manchester to Leeds Trans-Pennine railway. A post-tensioned concrete finback bridge has been provided to carry the new twin Metrolink tracks over the existing heavy rail route. In order to minimise disruption to the operational railway, the Finback Bridge was constructed in a position alongside and roughly parallel to the existing railway. Once the construction was substantially complete, the 6250 t bridge was rotated in plan through 21° to its final position during a weekend possession. The site constraints resulted in a reverse-curved horizontal alignment with the consequential requirement to cater for significant torsion in the design of the deck. The deck solution was a box section finback bridge with varying fin height and fin wall thickness. The bottom slab of the box was extended to cantilever outside the central fin to support the Metrolink tracks. The superstructure incorporates two types of post-tensioning; internal bonded tendons in the deck slab of the main span and external unbonded tendons located inside the fin.