External Tendons Research Articles

Experimental Study on Behaviour of Concrete Box Girder Prestressed with External CFRP Tendons

AbstractA concrete thin-walled box girder prestressed with external CFRP tendons has been made, and tested in the course of CFRP tendons tensing until concrete cracking. Prestressing loss and some behaviors under uniform load such as stress and strain distribution, effective width coefficient of compressive top flange, deflection, crack patterns at mid-section, and stress variety of CFRP tendons have been studied. Experiments show that the box girder perform well against cracking and deformation, with effective width coefficient of compressive top flange increased by less than 5% due to concrete cracking. The reliable experimental basis will be helpful to the application of externally prestressed CFRP tendons in concrete box girder.

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.

Strut–tie analysis of beams with external tendons

Strengthening of concrete beams by means of external tendons has been increasingly used. Analysis of such beams is more difficult than that of beams with internal bonded tendons because the stress in external tendons depends on the deformations of the whole beam. In the current paper, a simple model based on the strut-and-tie method is presented to predict the capacity of simply supported externally prestressed concrete beams subjected to equal concentrated loads at third-points. The model defines the struts and ties that form a load transfer mechanism in the beams. It predicts the ultimate loads the beam can carry and the force in the tendons at failure using the section method and equilibrium equations. When comparing the results obtained using the proposed model with others in the literature, the model was found to be conservative. The proposed model is intended to help designers in the inspection and structural assessment of beams.

Strengthening of RC Continuous Beams by External Prestressing

This paper presents the test results on 12 two-span continuous T-beams strengthened using different external tendon types and profiles and subjected to third-point loadings. Test results indicated that an increase in ultimate strength with sufficient ductility could be achieved using short tendons located over the critical sections. Such a strengthening scheme led to a more ductile beam behavior compared to those with continuous tendons over both spans or with draped tendons within each span. Parabolic tendons anchored beyond the interior support however effectively strengthened the negative moment region with improved ductility at ultimate limit state. Furthermore, beams strengthened with carbon fiber-reinforced polymers tendons showed similar response to those with steel tendons, while beams subjected to unsymmetrical loading suffered from larger deflections and lower ultimate load compared to those subjected to symmetrical loading. Theoretical predictions based on the concept of bond reduction coefficients were found to agree with the test results. Finally, a parametric study was carried out to establish design charts that can be used for the strengthening of continuous beams. A design example is presented to illustrate the use of the charts.

Simplified Method for Failure Analysis of Concrete Beams Prestressed with External Tendons

The flexural strength of externally prestressed beams depends on the tendon stress at failure. If the tendon is free to slip at the deviators its stress will depend on the global deformation of the whole structure. Thus the tendon stress at failure, and consequently, the flexural strength cannot be evaluated by a local analysis of the critical sections, but a nonlinear analysis of the whole beam-tendon structural system is required. In the past, simplified formulas were proposed to calculate the tendon stress increment at failure avoiding the need for a nonlinear analysis of the entire structure. Some of these formulas have been adopted as code recommendations. Some approaches however do not seem to be consistent with the actual behavior of externally prestressed beams and in some cases excessively high increments of stress are recommended. On the other hand, other approaches appear to be too conservative. In this work a new simplified and rational method of analysis based on shape functions approximating deformations is proposed to study the tendon stress increment and consequently the flexural strength of externally prestressed concrete beams. The proposed simplified method reduces the analysis of externally prestressed structures from a global structure problem to an easier section problem.

SIMPLIFIED TRUSS MODEL FOR EXTERNALLY PRESTRESSED CONCRETE BEAMS

The parametric study using FEM and the experiment of T-beams prestressed with external tendons have been performed to investigate the factors thought to influence on the shear mechanism of externally prestressed concrete beams. The effects of prestressing force and stirrup can be observed as important factors to the failure mechanism. The simplified truss model, having a small number of degrees of freedom, has been modified and proposed by adapting the formulation to predict the angle of concentrated stress flow and the thickness of diagonal compression members for evaluating the shear carrying capacity of externally prestressed concrete beams. The predicted results show the good agreement with experimental results.

Calculation of loading-induced tendon slip in beams prestressed with external tendons. Part II: Numerical analysis

In this paper, a computing method for the tendon slip based on the force equilibrium condition at deviators was proposed. The proposed method for the evaluation of tendon slip was presented in a general form by taking into account all possibilities of tendon slip at deviators, and several factors found to be important that affect the tendon slip, such as effects of the slippage at two adjacent deviators, friction, change of tendon angles during the applied load, etc. The validation of the proposed method was verified by comparing with the experimental results. The predicted results showed a close agreement with the experimental observation.

Calculation of loading-induced tendon slip in beams prestressed with external tendons. Part I: Experiment

This study consists of two parts, in which both experimental and numerical studies on externally prestressed concrete beams were investigated. In Part I, three identical beams of T-shaped section prestressed with external tendons have been tested to failure to investigate the effects of geometry of the applied load on flexural behavior of externally prestressed concrete beams. The tendon slip at deviators was also monitored in order to examine the evolution of stress in the external tendons. Test results were presented with emphasis on the effects of geometry of applied load and tendon slip at deviators.

Vibrational Tension Measurement of External Tendons in Segmental Posttensioned Bridges

A rapid and economical vibrational tension measurement method is presented to detect distress in external tendons used in segmental posttensioned bridges. This method provides a complementary technique to traditional inspection methods currently employed in the field. The natural frequency and overtones produced by an impact excitation are measured and used to determine the tendon segment’s tension and flexural stiffness using a differential equation describing a stiff string with clamped-clamped boundary conditions. The flexural stiffness is not negligible in tendons of this type causing the vibration modes to be inharmonically related. This method provides consistent (typically within 1%) and reasonably accurate (typically within 10%) estimates of tendon tension. Accuracy can be improved by lessening uncertainty in input constants such as the tendon mass and tendon length. Application examples from several in-service bridges have shown that detection of corrosion damage, improper tensioning, and force d...

Behavior of composite beams prestressed with external tendons: Experimental study

The paper deals with the failure mechanisms and behavior of composite steel–concrete beams prestressed with external tendons and subjected to positive bending. Experimental tests were carried out on beams with straight and draped tendons as well as on a non-prestressed beam. Six simply supported beams subjected to a positive static bending moment were tested up to failure. The influence of shear connection flexibility was taken into account and slip was measured along the beam axis. Concurrently, push-out specimens were made and tested to determine shear force vs. slip curves. It was found that at the same eccentricity of tendons (draped or straight without saddle points) the tendon shape has no significant effect on the behavior and ultimate resistance of composite steel–concrete beams. It is also shown that steel–concrete bond cohesion can significantly influence the behavior of the shear connection in composite beams. This influence is comparable with the design shear resistance of a single stud connector.

Stress at Ultimate in Unbonded Post Tensioning Tendons for Simply Supported Beams: A State-of-the-Art Review

An in depth State-of-Art Review is done on the topic, Stress at Ultimate in Unbonded Post tensioning Tendons. Simply supported members are used for discussion. Prediction equations proposed to compute the stress in tendons at ultimate, fps are reviewed. Six data sets are used to analyse the prediction equations and the results discussed. In addition, the parameter Δ fps is compared with plastic hinge length on the basis of Δ fps is directly related to the plastic hinge formation that occurs from yielding of nonprestressing steel to the concrete crushing in the extreme compressive fiber. Acceptable trend is obtained from the comparison. Further, stress in external tendons are reviewed and discussed based on the review of internal unbonded tendons.

Finite element modeling of concrete beams prestressed with external tendons

In this study, a numerical model based on the finite element method incorporating an arc-length solution algorithm for materially and geometrically nonlinear analysis of concrete beams prestressed with external tendons is established. The second-order effects are taken into account. The effects of external tendons are expressed by equivalent nodal loads of the beam element and therefore analysis of externally prestressed concrete beams can be conducted with the ordinary bonded concrete beams. The section tangent stiffness matrix is derived by the layered approach, and then the nonlinear beam flexural theory is utilized to determine the element tangent stiffness matrix. An updated normal plane arc-length solution algorithm is used to trace the nonlinear response of the beams from zero loads up to ultimate loads. This algorithm can deal well with the changes of response during loading, so that the possible limit points on the load–deflection response prior to the ultimate limit state can be easily passed. Results predicted by the analysis are in good agreement with the experimental data.

Accurate cable force determination using ambient vibration measurements

Knowledge of the tensile forces in cables of bridges or in external tendons is required for regular inspection and safety assessments. Force determination by lift-off tests with hydraulic jacks can result in considerable expenditure as well as the danger of damage. However, alternatively conducted vibration measurements have shown that, due to improper identification of natural frequencies or the use of over-simple force–frequency relationships, accuracies achieved up to now are sometimes not achieved. For high cable forces and short cables, errors of up to ±10% could be realized. Fast and accurate methods for assessing cable forces are thus required. The main target of this paper is the presentation of a practical applicable procedure to determine cable forces in civil engineering constructions by means of vibration measurements. By taking into account the identified natural frequencies, the bending stiffness and the boundary conditions, accuracy in the range of ±1% may be achieved.

SLIP PHENOMENON AT DEVATORS IN BEAMS PRESTRESSED WITH EXTERNAL TENDONS

Three identical beams of T-shaped section prestressed with external tendons have been tested to failure to investigate the effects of geometry of the applied load on flexural bebavior of externally prestressed concrete beams. The tendon slip at deviators was also monitored in order to examine the evolution of stress in the external tendons. Test results were presented with emphasis on the effects of geometry of applied load and tendon slip at deviators. For the evaluation of tendon slip, a method of calculation of tendon slip was proposed. The validation of the proposed method was verified by comparing with the experimental results. The predicted results showed a close agreement with the experimental observation.

PREDICTION OF TENDON STRESS AND FLEXURAL STRENGTH OF EXTERNALLY PRESTRESSED CONCRETE BEAMS

The experiment and nonlinear FE analysis of concrete beams prestressed with external tendons were performed to investigate the flexural strength, the tendon stress, and to propose the equation for evaluating the tendon stress. Several parameters were examined in order to evaluate the significance of influential parameters. The analytical results were validated with the experimental investigations carried out in this study. From the parametric study, it indicates that the span-to-depth ratio has less significant effect on the tendon stress. However, the geometry of applied load must be taken into account for evaluating the tendon stress. Finally, the design equations to predict the tendon stress of such beams were proposed.

Analysis of concrete beams prestressed and post-tensioned with externally unbonded carbon fiber reinforced polymer tendons

Fiber reinforced polymer (FRP) tendons are being increasingly used nowadays in prestressing and (or) post-tensioning concrete structures. However, designers are faced with lack of practical analysis procedure that leads to proper evaluation of their structural performance, especially when bonded prestressing is combined with unbonded post-tensioning. This paper presents an analytical procedure for these beams. It examines the load–defelction characteristics and proceeds to estimate the ultimate load carrying capacity by taking into consideration the change of stress that occurs in the externally unbonded tendons during different stages of loading. The analytical procedure uses the concept of effective moment of inertia of concrete beams. The equations used are developed by ACI Committee 440, the Intelligent Sensing for Innovative Structures (ISIS) Canada Research Network, and the Comité Euro-International du Béton - Fédération International de la Précontrainte (CEB-FIP), for calculating the deflection of beams reinforced with carbon fiber reinforced polymer (CFRP) tendons. Finite element analyses have been conducted to verify the proposed analytical method. Two experimental programs were used to validate the proposed analytical method. The experimental findings of two box beams reinforced with bonded and unbonded external tendons are compared with finite element analyses and the analytical results. A full-scale test for an internally and externally prestressed double-T beam was undertaken at Construction Technology Laboratories Inc., Skokie, Illinois. The results from this experimental work were used to validate the analytical procedure.Key words: bonded CFRP tendons, concrete, post-tensioning, unbonded CFRP tendons.

Effective width of a concrete slab in steel–concrete composite beams prestressed with external tendons

The finite element method is applied to evaluate the effective width of a concrete slab in composite beams prestressed with external tendons. The beams studied are simply supported, with external prestressed strands straightly and draped arranged. The effective width for the prestressed composite beams evaluated based on the finite element parametric study is compared with that of plain composite beams without prestressing, and code provisions. The influence of the shear connections on the effective width and the shear slips along the beam span, as well as the incremental stresses developed in the prestressed strands, are analyzed. The behaviors of the external prestressed composite beams subject to the shrinkage and creep in the concrete slab are also discussed.

Cable Force Determination for the Danube Channel Bridge in Vienna

The knowledge of tensile forces in cables of cable-stayed bridges or in external tendons is required for regular inspection and safety assessment of these structures. Force determination by lift-off tests with hydraulic jacks is connected with considerable expenditures as well as the danger of damages. But also vibration measurements conducted up to now have shown that the accuracies achieved sometimes were not satisfying. Above all for high cable forces and short cables, errors of up to ± 10% could be determined. Therefore fast, accurate and non-destructive methods for assessing cable forces are required. Main target of this paper is the presentation of a recently developed, accurate and practically applicable procedure to determine cable forces for civil engineering constructions by means of vibration measurements. By taking into account the identified natural frequencies, the bending stiffness as well as the boundary conditions an accuracy in the range of ± 1% may be achieved. The application of the described method is shown on one selected cable stayed bridge crossing the Danube-Channel in Vienna.

Stress Variation of External Tendons under Live Load in Prestressed Concrete Bridges

By using a computer program especially developed for externally prestressed concrete bridges, the stress variation of external tendons under live load in several typical spans of externally prestressed concrete box-girder bridges is analysed. The influence of span-to-depth ratio, the level of bonding between external tendons and the structure, and the spacing between deviators on externally prestressed concrete simply-supported bridges is discussed. The influence of the construction method, the ratio of external tendons to internal tendons, the number of continuous spans, and the layout of external tendons on externally prestressed concrete continuous bridges is investigated. The comparison of results between externally prestressed concrete bridges to similar conventional internally prestressed concrete bridges is also made.

Factors affecting the external prestressing stress in externally strengthened prestressed concrete beams

The wide use of external prestressing system to strengthen reinforced and prestressed concrete members requires the full understanding of the behaviour of the strengthened members. At ultimate the stress in the external prestressing tendons need to be known in order to calculate the ultimate strength of the strengthened member. Several factors that can influence the increase in the ultimate stress in steel external prestressing tendons have been studied and well understood while the effect of these factors on tendons made from fibre reinforced plastics needs more research. This research was carried out to study the effect of several factors on the increase in the ultimate stress in external Parafil ropes as well as external steel tendons. These factors were related to the external prestressing system, internal prestressed and ordinary bonded steel, beam geometry and material properties. Also, the accuracy of equations proposed by the Eurocode (EC2), ACI318 and BS8110 to calculate the ultimate stress in external steel and FRP prestressing tendons was examined. The experimental and the analytical results showed that the studied factors have the same effect on both steel (up to yield) and Parafil ropes though this effect is greater in case of steel tendons. Also, factors such as tendon profile (straight or deviated), high strength of the concrete, effective tendon depth, number of deviators should be taken into consideration when calculating the ultimate stress in the external tendons.