External Tendons Research Articles

Effective Repair Grouting Methods and Materials for Filling Voids in External Posttensioned Tendons

Recent inspections of segmental posttensioned (PT) bridges reported the presence of large voids in ducts that contain PT strands. Corrosion of the strands was observed in these voids, which are believed to be a result of poor grouting. Corrosion of the PT strands can result in structural failure. Controversy exists on how best to protect PT tendons from corrosion; filling these voids with grout is one option. An optimized grouting procedure for repairing these voids is needed to protect the strands from corrosive environments. This research investigates three grouting methods for efficiently repairing the voids in PT duct systems: vacuum grouting (VG), pressure grouting (PG), and pressure–vacuum grouting (PVG). Each method is evaluated for filling capability, filling performance, and economic feasibility. Also, three prepackaged grouts for repair are assessed in this research to propose the most suitable material for repairing voids in the PT ducts. The results indicate that the PG and PVG methods are more constructible and likely to be more economical than the VG method. However, the PVG and VG methods seem to be more effective than the PG method in filling the voids. As a result of these tests, the PVG method is recommended for filling voids in tendons. The results also show that Classes C-1 and C-2 grouts have better filling capability than Class C-3 grout.

Numerical investigation of inelastic buckling of steel–concrete composite beams prestressed with external tendons

The ultimate resistance of a continuous composite beam is governed by either distortional lateral buckling or local buckling, or an interactive mode of the two which is sharply different from the torsional buckling mode in a bare steel beam. A finite element model is developed and based on the proposed FE model, inelastic finite element analysis of composite beams in negative bending is investigated, considering the initial geometric imperfection and the residual stress patterns and the FE results are found agree well with the test results. Parametrical analysis is carried out on the prestressed composite beams with external tendons in negative bending. Factors that influence load carrying performance and buckling moment resistance of prestressed composite beams are analyzed, such as initial geometric imperfection, residual stress in steel beams, force ratio, which is defined as the extent of prestressing force and negative reinforcement in the beams, as well as the slenderness ratios of web, flange, and beams. By varying cross-section parameters, 25 groups of composite beams under negative uniform bending with initial geometric imperfection, residual stress as well as different force ratios, 200 beams in total are studied by means of the FE method. The computed buckling moment ratios are drawn against the modified slenderness proposed by the authors and compared with the Chinese Codified steel column design curve. It is demonstrated that the tentative design method based on the Chinese Codified design curve can be used in assessment of buckling strength of composite beams in a term of the modified slenderness defined.

A direct design approach for strengthening simple-span beams with external posttensioning

This paper presents the analytical formulation to establish equations for the direct determination of the increase in load-carrying capacity of simple-span beams strengthened by external post-tensioned tendons. Two sets of equations--refined equations and simplified equations--are proposed. By using these equations, the tendon configuration in terms of its profile, area, and eccentricities can be determined for the strengthening of simple-span beams to carry a specified additional load. A design example is given in the appendix to illustrate the application of the method.

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

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.

Strengthening an in-service reinforcement concrete bridge with prestressed CFRP bar

Carbon fiber reinforced polymer (CFRP) bars were prestressed for the structural strengthening of 8 T-shaped reinforced concrete (RC) beams of a 21-year-old bridge in China. The ultimate bearing capacity of the existing bridge after retrofit was discussed on the basis of concrete structures theory. The flexural strengths of RC beams strengthened with CFRP bars were controlled by the failure of concrete in compression and a prestressing method was applied in the retrofit. The field construction processes of strengthening with CFRP bars—including grouting cracks, cutting groove, grouting epoxy and embedding CFRP bars, surface treating, banding with the U-type CFRP sheets, releasing external prestressed steel tendons—were introduced in detail. In order to evaluate the effectiveness of this strengthening method, field tests using vehicles as live load were applied before and after the retrofit. The test results of deflection and concrete strain of the T-shaped beams with and without strengthening show that the capacity of the repaired bridge, including the bending strength and stiffness, is enhanced. The measurements of crack width also indicate that this strengthening method can enhance the durability of bridges. Therefore, the proposed strengthening technology is feasible and effective.

A comparative study of continuous steel–concrete composite beams prestressed with external tendons: Experimental investigation

A comparative study of prestressed continuous steel–concrete composite beams is carried out based on an experimental investigation. Four full-scale continuous composite beams were tested, among which two were two-span beams and two were three-span beams. One of the two-span beams was a conventional non-prestressed composite beam, and the other was a composite beam prestressed with external tendons in both the positive and negative moment regions. One of the three-span composite beams was non-prestressed, and the other was prestressed only in the negative moment regions with external high-strength tendons. The cracking behaviors, distortional lateral and local buckling as well as the load carrying capacity of the beams were investigated experimentally. Full plasticity was developed at the mid-span section of each beam; however, the maximum moments attained at the internal supports were governed by local buckling, which is related to the slenderness of the composite section. It is found that in hogging moment regions, the ultimate moment resistance of a composite beam prestressed with external tendons is governed by either distortional lateral buckling or local buckling, or an interactive mode composed of distortional lateral and local buckling. The results show that exerting prestressing on a continuous composite beam with external tendons increases the degree of the internal force and moment redistribution in the beam. A design proposal based on moment redistribution to evaluate the load carrying capacity of continuous composite beams with external tendons is proposed.

Experimental study of moment redistribution and load carrying capacity of externally prestressed continuous composite beams

A comparative experimental study of prestressed continuous steel-concrete composite beams was carried out. Two continuous composite beams were tested, one of which was plain continuous steel-concrete composite beam, while the other was a composite beam prestressed with external tendons. Cracking behavior and the load carrying capacity of the beams were investigated experimentally. Full plasticity was developed in the mid-span section each beam, the maximum moments attained at the internal support sections however were governed by local buckling which was related to the slenderness of composite section. It was found that in hogging moment regions, the ultimate resistance of an externally prestressed composite beam would be governed by either distortional lateral buckling or local buckling, or interactive mode of these two buckling patterns. The results show that exerting prestressing on a continuous composite beam with external tendons will increase the extent of internal force and moment redistribution in the beam. The influences of local and distortional buckling on the behaviors of the composite continuous beams are discussed. The Moment redistribution and the load carrying capacity of the prestressed continuous composite beams are evaluated, and it is found that at the ultimate state, the moment redistribution in the prestrssed continuous composite beams is greater than that in non-prestressed composite beams.

In situ estimation of tendon material properties: Differences between muscles of the feline hindlimb

Recent experiments to characterize the short-range stiffness (SRS)–force relationship in several cat hindlimb muscles suggested that the there are differences in the tendon elastic moduli across muscles [Cui, L., Perreault, E.J., Maas, H., Sandercock, T.G., 2008. Modeling short-range stiffness of feline lower hindlimb muscles. J. Biomech. 41 (9), 1945–1952.]. Those conclusions were inferred from whole muscle experiments and a computational model of SRS. The present study sought to directly measure tendon elasticity, the material property most relevant to SRS, during physiological loading to confirm the previous modeling results. Measurements were made from the medial gastrocnemius (MG), tibialis anterior (TA) and extensor digitorum longus (EDL) muscles during loading. For the latter, the model indicated a substantially different elastic modulus than for MG and TA. For each muscle, the stress–strain relationship of the external tendon was measured in situ during the loading phase of isometric contractions conducted at optimum length. Young's moduli were assessed at equal strain levels (1%, 2% and 3%), as well as at peak strain. The stress–strain relationship was significantly different between EDL and MG/TA, but not between MG and TA. EDL had a more apparent toe region (i.e., lower Young's modulus at 1% strain), followed by a more rapid increase in the slope of the stress–strain curve (i.e., higher Young's modulus at 2% and 3% strain). Young's modulus at peak strain also was significantly higher in EDL compared to MG/TA, whereas no significant difference was found between MG and TA. These results indicate that during natural loading, tendon Young's moduli can vary considerably across muscles. This creates challenges to estimating muscle behavior in biomechanical models for which direct measures of tendon properties are not available.

Numerical Analysis of Continuous Beams Prestressed with External Tendons

This paper presents a numerical model conceived to simulate the behavior up to collapse of continuous concrete beams prestressed with bonded or external tendons. Its most valuable feature is the ability to automatically determine the most suitable extent of each load increment according to the actual stiffness of all the segments that form the discretized beam. A crucial problem of nonlinear structural analysis is numerical evaluation of the rotation capacity of plastic hinges, especially when dealing with concrete beams prestressed with external tendons, which is a technology nowadays increasingly adopted in new continuous bridges and in the rehabilitation or strengthening of old or damaged structures. This problem is discussed in depth and a simple rule, which differs from those usually discussed in the scientific literature, is adopted to subdivide the beam into discrete elements. The effectiveness of the numerical model is tested by comparing its numerical output with the outcomes of 14 experimental tests. This comparison looks promising since the mean value of the error on load carrying capacity is only 0.1%, with a 2.4% standard deviation.

Effect of Torsion on Externally Prestressed Segmental Concrete Bridge with Shear Key

Externally Prestressed Segmental (EPS) concrete box sections are widely used in the construction of bridge structures today. EPS concept has become an attractive tool for rehabilitation and strengthening of existing bridges which have insufficient strength and/or excessive deflection and cracking. Problem statement: EPS bridges are affected by combined stresses (bending, shear, normal, and torsional) at the joint interface between the segments. However, very limited researchers studied this type of bridges under combined stresses. Approach: This paper presented an experimental investigation of the structural behaviour of EPS bridge with shear key under torsion. Four beams were tested, each containing three segments that were presetressed using two external tendons. A parametric study of two different external tendon layouts as well as different levels of torsional force applied by different load eccentricities was conducted. Results: The effect of torsion was evaluated in terms of vertical deflections, concrete and tendon strains, failure loads and failure mechanisms. It was concluded that torsion has a significant effect in the structural behaviour of external prestressed segmental box girder beams. Torsion not only alters failure load of the beam but also changes the type of failure mechanism. It was also investigated that harp tendon layout results in better structural behaviour in term of deflection and tendon strain as compared with the straight tendon. Recommendations: It recommended including the effect of joint (flat and shear key) type as well as the effect of tendon layout under torsion to obtain comprehensive behavior of EPS bridge.

Research on Internal and External Tendon System of Composite Box Girder Bridge with Corrugated Steel Webs

AbstractA 3D finite element model of an internal and external tendon concrete simple-supported composite box girder bridge with corrugated steel webs was established by means of the composite element method. The mechanical behaviors of the structure with different internal and external tendon parameters were analyzed, including the arrangement of the internal and external tendon, the tensile force, the position of the anchorage point and the distance of the diversion point. The conclusions show that the normal stresses of the sections between two diversion points in the mid-span only depend on the tensile force, while those between the anchorage point and the diversion point change with the parameters. It is suggested the reasonable ratio of the external tendon to be 30%∼40% for this bridge, and the prestressing force should be no less than 60% of characteristic value of tensile strength. The conclusions provide a reference for the design of internal and external tendons of composite box girder bridge wit...

Strengthening the Röslautal Bridge Using Innovative Techniques, Germany

The Röslautal Bridge is a pre-stressed concrete box girder bridge situated in Germany close to the Czech border. It routes the European highway E48 heading to Prague over the valley of the Röslau creek. The continuously increasing heavy trans-European traffic required an additional third lane on the bridge deck. Elevated traffic loads required strengthening of the bridge, but due to its important role traffic had to be maintained on one lane throughout the construction period. The stringent limits in time and the impact on traffic imposed by the road authorities were met by applying innovative techniques. The box girders are strengthened with external post-tensioning tendons deviated at additional diaphragms cast with self-compacting concrete. Additional flexural capacity for cantilever slabs is provided by arranging carbon fibre reinforced polymer (CFRP) strips bonded in slits which are cut in the top surface of the deck slab. Since the mechanical properties of cold-curing epoxy adhesives are dependent on temperature, the thermal effects during construction and service life had to be evaluated. This article summarises the thermo-mechanical behaviour of epoxies, the consequences on design, and the accompanying monitoring program set up to assess long-time performance and strengthening efficiency. The Röslautal Bridge demonstrates that the use of innovative techniques generates aesthetical, logistical and economical advantages but requires a deep understanding of the applied methods.

Behaviors of Concrete Beam Prestressed with External CFRP Tendons

The purpose of present paper is to study the flexural behaviors of concrete T-beams prestressed with external carbon fiber reinforced polymer(CFRP) tendons. Tests were carried out on 5 beams under four-point load, of which four beams were reinforced with hybrid both external CFRP tendons and internal steel rebars and another one only reinforced with internal steel rebars. Such parameters as the different initial loading states at external CFRP tendon jacking and different jacking stress in tendon were considered in experiment. A program was developed to predict the behaviors of those beams prestressed with externally prestressed tendons and the parametric study was conducted using the program. The predicted results from the program were in good agreement with the test results. Such parameters as jacking stress, elastic modulus of external tendons, configuration of deviators and ratio of span to effective depth of beam were chosen as primary analytical factors for the study on the flexural behaviors of beams prestressed with external tendons. The initial loading state on the beam before tendon jacking has no significant influence on the ultimate loading capacity and deflection.

Experimental and theoretical studies on composite steel–concrete box beams with external tendons

Composite steel–concrete box beams with and without external tendons were tested to their ultimate strength. The effects of external tendons on structural performance of composite steel–concrete beams were investigated in detail. Experimental results proved that, due to the action of external prestressing tendons, the ultimate strength of a composite steel–concrete box beam increased by 27.72%, the elastic limit of a composite steel–concrete box beam increased by 29.17%, the stiffness of a composite steel–concrete box beam increased by 54.15% at the failure state, and the deflection ductility of a composite steel–concrete box beam increased by 18.00%. The equation for estimating the stress in external prestressing tendons is established according to the relationship between the stress in external tendons, and the maximum compressive strain of concrete slab. Based on experimental results, a theoretical model for predicting the flexural resistance of composite steel–concrete box beam with external tendons is proposed. The spatial integral method, which adopts the actual stress distribution, is more rational than the conventional equilibrium rectangular stress block model, and is adopted to calculate the interior force on sections. The calculated flexural resistance based on proposed equations has a high level of accuracy, when compared with test results. Experimental and theoretical studies have demonstrated that the composite steel–concrete box beam with external tendons is a promising innovative structure that combines the merits of composite steel–concrete box beams and external prestressing tendons.

Finite element formulation for geometric and material nonlinear analysis of beams prestressed with external slipping tendons

In this paper a finite element formulation of a geometric and material nonlinear analytical model for externally prestressed beams is illustrated. Differently from existing methods starting from the linear theory and then including the tendon eccentricity variation, the analytical model adopted is based on a nonlinear kinematical theory. Thus a complete description of the nonlinear interactions between tendon and beam is given. The interactions between axial and flexural fields of the beam are also included. The numerically simulated response is verified by comparison with experimental tests available for concrete beams and steel–concrete composite beams prestressed with external 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.

Ring Avulsion Injury with Rupture of Both Digital Arteries Despite a Completely Intact Skin Envelope

A rare case of ring avulsion injury with avulsion of both digital arteries yet without external soft tissue, tendon or skeletal injury in a 29 year-old man is reported.

PSC I합성 거더의 휨 거동 및 외부 강선 보강효과에 관한 실험 연구

For the evaluation of the load carrying capacity of the deteriorated PSC I girder bridge in service load state and the verification of the grade to the reinforcement effect of actual bridge strengthened by external prestressing tendons, the field test using vehicles is applied widely. Because this teat was executed in elastic range, the investigation of the characteristics of behavior caused by live load is only available. And it is impossible to estimate load carrying capacity in limit state and nonlinear behavior after that a crack is appeared. In this study, the 27-year-old prestressed concrete girder bridge is used and various load tests are performed, so we evaluate the behavior characteristics of the bridge in service load state and ultimate load state, and estimate the load carrying capacity of bridge. In addition, the artificial damages are induced from cutting internal tendons, and external tendons is added to strengthen it as much as vanished internal tendons. Next we compare the damage state with the strengthening state. In case of the application of external prestressing method to PSC I girder bridge, the present experiment result may decide more exactly the load carrying capacity of actual bridge, the amount for reinforcement, and the standard of quality control etc. at reinforcement work.

A STUDY ON FLEXURAL BEHAVIOR OF PRESTRESSED CONCRETE SIMPLE BEAMS WITH EXTERNAL TENDONS UNDER STATIC LOADS

Using a verified finite element algorithm, non-linear analysis of externally prestressed concrete beams was carried out to investigate the flexural behavior of such beams under static loads. The behavior of such beams is represented by; change of tendon’s eccentricity, load deflection diagram, the relations of load and stress in external tendons, effective depth of beam, and bond strain reduction factor. The parameters affecting the behavior of such beams include: span to depth ratio, distance between loads to span ratio, distance between deviators to span ratio, the ratio of prestressing index and reinforcement index strength and tensile and compressive reinforcement ratios. The strain variation in an external tendon was investigated on the basis of the deformation compatibility of beam. The proposed method for the numerical analysis can satisfactorily predict the behavior of externally prestressed concrete beams up to the ultimate loading stage. The stress increase in an external tendon depends mainly on the overall deformation of beam. The behavior of externally prestressed concrete beams is different than that of bonded prestressed beams due to the second order effect of tendon’s eccentricity. This point is clearly investigated in the current study. From the obtained results, a model was proposed to estimate both of the bond strain reduction factor ( R ) and effective depth reduction factor (K) considering the effect of the parameters affecting the behavior of such beams. Based on numerical analyses, a model was proposed to calculate the flexural strength of externally prestressed concrete beams considering the parameters of the study.