Application of Wigner-Ville Transform to Evaluate Tensile Forces in Seven-Wire Prestressing Strands

Seven-wire steel strands are widely used in various types of prestressed concrete structures. When a strand is subjected to a tensile force, the traveling time of the stress wave will be affected due to the elongation of the strand together with the changes in wave velocities. In this paper, the Wigner-Ville transform technique was used to analyze the measured stress waves in order to identify the arrival time of each frequency component. A numerical calculation considering the elastic waveguide theory and the acoustoelastic effect was conducted. A commonly used 12.7-mm (1/2 in.) diameter seven-wire prestressing strand (Grade 270) was tested. Tensile force up to 142 kN (32 kips) was applied to the strand. The results indicate that evaluation of the tensile force in the strand can be accomplished by measuring the traveling time of a single-frequency component of the propagating stress wave. The Wigner-Ville transform technique can efficiently identify the arrival time of each frequency component of the stress-wave signals with reasonable accuracy. The numerical and experimental results correlate well with each other. Results of this study present a technique that can provide an efficient nondestructive measurement of stress retension levels in long post-tensioned steel strands.     

Use of Interwire Ultrasonic Leakage to Quantify Loss of Prestress in Multiwire Tendons

This paper presents a technique developed on the basis of ultrasonic guided waves to monitor prestress levels in multiwire prestressing strands. The transducer layout identified for stress measurement is composed of an ultrasound excitation provided by a piezoelectric element bonded on a peripheral wire. Ultrasound detection is performed on the central and peripheral wires at the strand’s end. The ultrasonic feature used for stress monitoring is the interwire leakage between the peripheral and the central wire, occurring across the strand anchorage. A semianalytical finite-element analysis is first used to predict modal and forced wave solutions in seven-wire strands as a function of the applied prestress level. The numerical analysis accounts for the changing interwire contact as a function of applied loads and predicts the attenuation occurring in loaded strand when the wave travels across the anchorage. Results of load monitoring in free strands during laboratory tests are then presented. Finally, a statistical approach is used to enhance the sensitivity of the technique to stress level in the strands. The study presented focuses on unbonded tendons. However, the final goal of the research is to monitor prestress loss in bonded tendons that are found in the majority of the bridges built in California.     

Effects of Temperature Variations on Precast, Prestressed Concrete Bridge Girders

The monitoring of a precast, prestressed girder bridge during fabrication and service provided the opportunity to observe temperature variations and to evaluate the accuracy of calculated strains and cambers. The use of high curing temperatures during fabrication affects the level of prestress because the strand length is fixed during the heating, the coefficients of thermal expansion of steel and concrete differ, and the concrete temperature distribution may not be uniform. For the girders discussed here, these effects combined to reduce the calculated prestressing stress from the original design values at release by 3 to 7%, to reduce the initial camber by 26 to 40%, and to increase the bottom tension stress in service by 12 to 27%. The main effect of applying the standard service temperature profiles to the bridge was to increase the bottom stress by 60% of the allowable tension stress. These effects can be compensated for by increasing the amount of prestressing steel, but in highly stressed girders, such an increase leads to increased prestress losses (requiring yet more strands) and higher concrete strength requirements at release.     

Theoretical Analysis of Transfer Lengths in Pretensioned Prestressed Concrete Members

The realistic design of pretensioned prestressed concrete members requires adequate determination of transfer length for prestress forces. The purpose of the present paper is to propose a rational theory, which can evaluate the transfer lengths realistically for arbitrary designed pretensioned members. The theory considers the prestressing steel as a solid cylinder and the surrounding concrete as a hollow cylinder. The compatibility condition is then imposed at the steel–concrete interface with an appropriate equilibrium equation. The possible cracking of surrounding concrete in a radial direction due to expansive pressure after prestress transfer has been considered by employing an appropriate tensile stress–crack width relation. The equilibrium equations are solved for each successive segment in longitudinal direction and the strain buildup curves from the end of pretensioned members are obtained, which provides the basis for the determination of transfer length. Comprehensive tests were conducted to measure the transfer lengths for various design variables, including the concrete strength, strand diameter, cover thickness, and strand spacing. The measured values of transfer lengths were compared with the calculated ones and the comparison indicates that the theoretical prediction exhibits good correlation with test data. The proposed theory allows more realistic prediction of transfer lengths for rational design of actual pretensioned prestressed concrete members.     

Flexural Strengthening of RC Beams with Prestressed CFRP Sheets: Development of Nonmetallic Anchor Systems

This paper presents a novel anchoring technique for strengthening reinforced concrete beams with prestressed carbon fiber- reinforced polymer (CFRP) sheets. Permanent steel anchors are commonly used for the application of prestressed CFRP sheets. The steel anchors are, however, susceptible to corrosion and may not blend into the aesthetics of the original structure. As a result, it may be preferable to remove the steel anchors after transferring the required prestress to the structure with minimal losses of sustained prestress. A technique for replacing the steel anchors with nonmetallic anchors is investigated and reported herein. Nine doubly reinforced concrete beams are tested with various types of nonmetallic anchor systems such as nonanchored U-wraps, mechanically anchored U-wraps, and CFRP sheet-anchored U-wraps. The developed nonmetallic anchorages successfully transfer the sustained prestress in the CFRP sheets with insignificant prestress losses. A closed-form solution for the transfer of prestress is developed and compared to the experimental results.     

Fatigue Strength of Repaired Prestressed Composite Beams

Composite steel-concrete bridges constitute a major portion of the national bridge inventory. Many of these structures are approaching or have passed their service lives and are in need of repair and rehabilitation. External prestressing by means of high-strength bars or cables attached to the steel beams has been used as an effective technique for upgrading the load carrying capacity of composite steel-concrete girders. While several researchers have investigated the static behavior of prestressed composite beams, few have reported on the fatigue strength of this structural system. The writers present the results of the experimental and analytical study of ten composite girders that were prestressed with seven-wire strands and then fatigue tested to failure. Three methods of extending the fatigue life of cracks were then explored: (1) drilling a hole at the crack tip and installing a high-strength bolt; (2) splicing the web at the cracked section; and (3) increasing the prestressing force of the tendon. The efficacy of the three methods is compared.     

Strength-Fatigue Behavior of Fiber Reinforced Polymer Strengthened Prestressed Concrete T-Beams

Strengthening concrete girders with fiber-reinforced polymers (FRP) is becoming an increasingly common practice as more research investigations are favorably qualifying the technique. However, important behavioral aspects, such as fatigue in prestressed concrete beams, are yet to be adequately evaluated. An experimental program was conducted to test five pretensioned, prestressed concrete T beams designed for specific prestressing strand stress ranges under live-load conditions. The experimental testing consisted of precracking the beams, strengthening them with carbon FRP, and mechanically loading them to study the effect of increasing the live load on strand fatigue. The beams were either loaded monotonically to ultimate capacity or cyclically fatigued and then loaded monotonically to failure. All the beams were monotonically loaded past their cracking moment at midspan prior to strengthening, to simulate girders in the field. Beam 1 was tested as a control specimen under static loading up to failure. Beams 2 and 3 were strengthened with carbon FRP to have a design stress range of 124 MPa (18 ksi) under service load condition. Beams 4 and 5 were strengthened to have a higher stress range of 248 MPa (36 ksi). For all the strengthened beams, the failure mode observed was FRP rupture. The results favorably qualify the application of FRP strengthening to increase the live load of concrete beams prestressed with straight strands.     

Flexural Performance of Carbon Fiber-Reinforced Polymer Prestressed Concrete Side-by-Side Box Beam Bridge

The effect of varying transverse posttensioning levels and arrangements on the load response of a one-half scale 30° skewed seven box beam bridge model was investigated. The effective span of the bridge model was 9.45?m (31?ft) with a width of 3.35?m (11?ft) and depth of 355.6?mm (14?in.). The bridge model was prestressed and reinforced with carbon fiber composite cables (CFCCs). CFCCs were also used as shear reinforcement. The bridge model was provided with five transverse diaphragms equally spaced along the length of the bridge. The experimental investigation included load and strain distribution tests and a flexural ultimate load test. The load and strain distribution tests were conducted on the bridge model with and without full-depth longitudinal cracks at the shear-key locations. The investigation showed that the application of an adequate transverse posttensioning force was successful in restoring the load distribution of the bridge model with full-depth longitudinal deck cracks to that of the case without deck cracks. The ultimate load and the associated compression-controlled failure mode of the bridge model agreed well with that predicted according to ACI 440.4R-04 and numerical analysis. The behavior of the bonded pretensioned and reinforced CFCC strands was linear elastic and remained intact throughout the collapse of the bridge model. The unbonded transverse posttensioned CFCC strand also remained intact.     

Use of Glass-Fiber-Reinforced Polymer Tendons for Stress-Laminating Timber Bridge Decks

Researchers at the University of Maine led an effort in the mid-1990s to develop and use glass-fiber-reinforced polymer (GFRP) tendons, instead of the commonly used steel-threaded bars, for stress-laminating timber bridge decks. The GFRP tendons are 12.7 mm (0.5 in.) in diameter and consist of seven-wire strands similar in construction to steel prestressing strands. Because the modulus of elasticity of the GFRP tendons is approximately 1/9 that of steel, they are not as susceptible to loss of prestress as steel bars and may not have to be restressed during the life of deck. In 1997, researchers obtained funding to design, construct, and monitor a stress-laminated timber bridge located in Milbridge, Maine, utilizing the new GFRP tendons. The bridge was constructed from preservative treated No. 2 and better eastern hemlock laminations and is 4.88 m (16 ft) long, 7.75 m (25 ft, 6 in.) wide, and 350 mm (14 in.) deep. Based on 4.25 years of field monitoring the tendon forces and moisture content, the GFRP tendons have maintained an adequate prestress level without having to be restressed.     

Behavior of Prestressed Concrete Strengthened with Various CFRP Systems Subjected to Fatigue Loading

Many prestressed concrete bridges are in need of upgrades to increase their posted capacities. The use of carbon fiber-reinforced polymer (CFRP) materials is gaining credibility as a strengthening option for reinforced concrete, yet few studies have been undertaken to determine their effectiveness for strengthening prestressed concrete. The effect of the CFRP strengthening on the induced fatigue stress ratio in the prestressing strand during service loading conditions is not well defined. This paper explores the fatigue behavior of prestressed concrete bridge girders strengthened with CFRP through examining the behavior of seven decommissioned 9.14?m (30?ft) girders strengthened with various CFRP systems including near-surface-mounted bars and strips, and externally bonded strips and sheets. Various levels of strengthening, prestressing configurations, and fatigue loading range are examined. The experimental results are used to provide recommendations on the effectiveness of each strengthening configuration. Test results show that CFRP strengthening can reduce crack widths, crack spacing, and the induced stress ratio in the prestressing strands under service loading conditions. It is recommended to keep the prestressing strand stress ratio under the increased service loading below the value of 5% for straight prestressing strands, and 3% for harped prestressing strands. A design example is presented to illustrate the proposed design guidelines in determining the level of CFRP strengthening. The design considers the behavior of the strengthened girder at various service and ultimate limit states.     

Posttensioned Anchorage Zone Enhancement with Fiber-Reinforced Concrete

The secondary spiral and skin reinforcement in the anchorage zone of prestressed posttensioned girders causes congestion and poses difficulty in the placement of concrete. It is also labor intensive to produce and place secondary anchorage reinforcement. The objective of this study was to determine the feasibility of reducing the secondary reinforcement with steel fibers for posttensioned anchor zones. The AASHTO Special Anchorage Device Acceptance Test was performed in this study. Variations of spiral and skin reinforcement, with concrete strengths ranging from 37.9?MPa (5,500?psi)?to?52?MPa (7,500?psi), were utilized to investigate the performance of the two types of steel fibers with various amounts. The experimental results indicated that 1% hooked-end steel fibers could eliminate all secondary reinforcement for a minimum concrete strength of 40.7?MPa (5,900?psi). Lower volumes of steel fibers may also be used to reduce secondary reinforcements.     

Comparison of Prestress Losses for a Prestress Concrete Bridge Made with High-Performance Concrete

Five prestressed concrete girders made with high-performance concrete were instrumented using vibrating-wire strain gages. Their behavior was monitored for three years from the time of casting. The measured change in concrete strain at the centroid of the prestressing strands was used to evaluate changes in prestress. The total measured prestress loss was as large as 28% of the total jacking stress. Due to the higher stresses, this loss is larger than would be expected for a girder made with conventional-strength concrete. The observed values of prestress losses were compared with values calculated using the recommended AASHTO LRFD and NCHRP 18-07 procedures. The AASHTO LRFD method overpredicted the average prestress losses for the highly stressed Span 2 girders by 20% while the NCHRP method underpredicted the average losses by 16%. The NCHRP method was found to be more inclusive and adaptable to regional construction. The calculated NCHRP Span 2 losses were found to be within 10% of the average measured losses when the elastic shortening losses were calculated based on measured data and differential shrinkage was calculated based on continuous beams.     

CFRP Tendons for the Repair of Posttensioned, Unbonded Concrete Buildings

The deterioration attributable to corrosion of concrete structures reinforced with unbonded, posttensioned tendons is a costly problem. Recent research has shown composite materials such as fiber-reinforced polymers (FRP) to be suitable alternatives to steel because they provide similar strength without susceptibility to electrochemical corrosion. Carbon-FRP (CFRP) in particular has great promise for prestressed applications because it shows resistance to corrosion in environments that might be encountered in concrete and experiences less relaxation than steel. This paper outlines the testing and implementation of a posttensioned system that uses CFRP tendons to replace corroded, unbonded posttensioned steel tendons. This system was then implemented in a parking garage in downtown Toronto. To the writers’ knowledge, this is the first example of an unbonded, posttensioned tendon replacement using FRP tendons. The system used split-wedge anchors designed specifically for CFRP tendons. The dead end was anchored by directly bonding the tendon to the concrete slab. The CFRP tendon was successfully inserted in the opening created by the removal of the corroded tendon and stressed. Although the system was shown to be feasible, the current anchorage configuration results in load losses of up to 60% during the transfer. Changing the orientation of the anchor was found to reduce the load loss to an acceptable range of 1–9%.     

Mechanical Model for Unbonded Seven-Wire Tendon with Symmetric Wire Breaks

A mechanical model for unbonded seven-wire tendons with broken wires that accounts for the effects of interwire friction and contact forces between the tendon and surrounding concrete is derived. The model is an essential tool for predicting the response, and reliability, of unbonded posttensioned concrete structures containing corroded tendons with broken wires. For the case where the broken wires are symmetrically arranged around the tendon cross section, the model predicts: (1) the strain variation with distance from the break in the broken and unbroken wires; (2) the affected length, where strains in the broken wires are less than those in the unbroken wires; and (3) the prestress force remaining after wire breaks occur. The affected length has practical significance because techniques used in practice to detect wire breaks will fail if performed outside the affected length. Experimental data obtained using a novel strongback beam confirm the response predicted by the model and indicate the coefficient of interwire friction is 0.164 for uncorroded tendons.     

浅谈后张法有粘结预应力梁施工工艺

本文旨在更有效地利用高强钢材,弥补混凝土与钢筋拉应变之间的差距,把预应力运用到钢筋混凝土结构中去。亦即在外荷载作用到构件上之前,预选建立有内应力的混凝土,通过对预应力筋进行张拉、锚固、放松,借助钢筋的弹性回缩,使受拉区混凝土事先获得预压应力。当构件承受由外荷载产生的拉力时,首先抵消混凝土中已有的预压力,然后随荷载增加,才能使混凝土受拉而后出现裂缝,因而延迟了构件裂缝的出现和开展。     

Long-Term Deflection and Cracking Behavior of Concrete Beams Prestressed with Carbon Fiber-Reinforced Polymer Tendons

This paper discusses the experimental result on the long-term deflection and cracking behavior of concrete beams prestressed with carbon fiber-reinforced polymer (CFRP) tendons, under sustained long-term service load, including cracked and uncracked sections. Six full-scale beams were cast and tested. The experimental parameters included the level of prestress, the level of sustained service loading, and concrete strengths. The experimental results showed that the performance of concrete beams prestressed with CFRP tendons meets the serviceability criteria in terms of deflection and cracking. The test results also showed that the long-term performance of concrete beams prestressed with CFRP tendons was comparable to those prestressed with steel tendons. Furthermore, the test results showed that with the increase of concrete strength, the serviceability performance also improved with concrete beams prestressed with CFRP tendons.     

Fatigue Performance of Tension Steel Plates Strengthened with Prestressed CFRP Laminates

An experimental and analytical study was conducted to investigate the fatigue behavior of tension steel plates strengthened with prestressed carbon-fiber-reinforced polymer (CFRP) laminates. A simple fracture mechanics model was proposed to predict the fatigue life of reinforced specimens. Double-edge-notched specimens were precracked by fatigue loading and then strengthened by CFRP laminates at different prestressing levels. The effects of the applied stress range, CFRP stiffness, and prestressing level on the crack growth were investigated. Experimental results show that the increase of the prestressing level extends the fatigue life of a damaged steel plate to a large amount. The CFRP with the highest prestressing level performed best, prolonging fatigue life by as much as four times under 25% higher fatigue loading. Theoretically, predicted results were in a reasonable agreement with the experimental results. A parametric analysis was also performed to investigate the effects of the applied stress range and the prestressing level on the debonding behavior of the adhesive and on the secondary crack propagation.     

Investigation of Damaged 12-Year Old Prestressed Concrete Box Beams

An investigation was conducted of unexpected damage to a pair of three-span continuous-spread prestressed box beam bridges after 12 years of service. Routine inspection had revealed cracks in the box beams near the piers and abutments. An investigation was conducted to assess the condition of the beams in the bridges as well as their as-built properties and remaining strength. The investigation showed that the beams were built in accordance with the design drawings and specifications. One beam was tested under a combination of flexure and shear. These tests showed that the effective prestress was lower than standard design estimates. Measurable slip of the strands initiated as shear or flexure-shear cracks developed; however, the bond strength was sufficient for the strands to fail by fracture. The measured ultimate strength exceeded the analytical estimates by 7 to 9%. The conclusion of the investigation is that the cracks in the beams developed from a combination of conditions created by the design, detailing, and production of the beams.     

Ductility and Cracking Behavior of Prestressed Concrete Beams Strengthened with Prestressed CFRP Sheets

This paper investigates the flexure of prestressed concrete beams strengthened with prestressed carbon fiber-reinforced polymer (CFRP) sheets, focusing on ductility and cracking behavior. Structural ductility of a beam strengthened with CFRP sheets is critical, considering the abrupt and brittle failure of CFRP sheets themselves. Cracking may also affect serviceability of a strengthened beam, and may be especially important for durability. Midscale prestressed concrete beams (L = 3.6?m) are constructed and a significant loss of prestress is simulated by reducing the reinforcement ratio to observe the strengthening effects. A nonlinear iterative analytical model, including tension of concrete, is developed and a nonlinear finite-element analysis is conducted to predict the flexural behavior of tested beams. The prestressed CFRP sheets result in less localized damage in the strengthened beam and the level of the prestress in the sheets significantly contributes to the ductility and cracking behavior of the strengthened beams. Consequently, the recommended level of prestress to the CFRP sheets is 20% of the ultimate design strain with adequate anchorages.     

Mechanical Model for Unbonded Seven-Wire Tendon with Single Broken Wire

This paper presents the derivation and experimental validation of a mechanical model for unbonded seven-wire prestressing tendons with a single broken outer wire. The model has practical significance because corrosion of these tendons typically causes a single outer wire to fail first. The tendency for the tendon to deflect toward the broken wire causes strains in the unbroken wires to be unequal at any cross section. As a result, the strains in the two wires adjacent to the broken wire increase significantly due to the wire break. Equations are presented for: (1) the strains along the lengths of the broken and unbroken wires; (2) the affected length, where the broken wire can be detected because its strain is less than the strains in the unbroken wires; and (3) the prestress force remaining after the break occurs. Experimental data obtained from tests of seven-wire tendons performed on an 18.3?m (60?ft) long strongback beam validate the model.