Nonlinear Analysis of Pretensioned Bridge Girder Ends to Understand and Control Cracking at Prestress Release

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ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (818 download)

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Book Synopsis Nonlinear Analysis of Pretensioned Bridge Girder Ends to Understand and Control Cracking at Prestress Release by :

Download or read book Nonlinear Analysis of Pretensioned Bridge Girder Ends to Understand and Control Cracking at Prestress Release written by and published by . This book was released on 2012 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hundreds of prestressed concrete girders are used each year for building bridges. Prestressed concrete girders are preferred due to their effective span to depth ratios, and higher durability characteristics. The prestress transfer from the prestressing strands to concrete takes place at the girder ends. Characteristic cracks form in this end region during or immediately after detensioning. These cracks are more severe for the heavily prestressed deep bulb tee girders with thin webs, creating durability concerns. The problem can be structurally hazardous if cracks form paths for corrosion agents to reach the steel strands. Cracks in the bottom flange closer to the strands can easily form such paths. This research primarily focused on the analyses of nonlinear prestressed girder end regions to understand and recommend control methods for girder end cracking. The behavior of the pretensioned girder ends was simulated using nonlinear finite element analysis. The accuracy of the models was ensured by including the concrete nonlinearity, strain softening and stress redistribution upon cracking. The finite element modeling techniques were verified by test data. The principal tensile strain patterns correlating with cracking were used to explain the reasons behind each type of crack. Potential solutions to control end cracking were examined via finite element models. The impact of end zone reinforcement pattern, debonding of strands, strand cutting order, draped strand pattern, and lifting of the girder on the cracks were evaluated. The reduction in principal tensile strains associated with cracking was quantified for each crack control method. The analysis results showed that debonding strands can effectively control cracking. Other methods improve the end zone strains however are not sufficient to eliminate cracking alone. Combining the solutions involving debonding, extra reinforcing in the web, and a controlled sequence of strand detensioning should lead to elimination of end cracking.

De-bonding Strands as an Anchorage Zone Crack Control Method for Pretensioned Concrete Bulb-tee Bridge Girders Using Nonlinear Finite Element Analysis

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ISBN 13 :
Total Pages : 202 pages
Book Rating : 4.:/5 (959 download)

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Book Synopsis De-bonding Strands as an Anchorage Zone Crack Control Method for Pretensioned Concrete Bulb-tee Bridge Girders Using Nonlinear Finite Element Analysis by : Emre Kizilarslan

Download or read book De-bonding Strands as an Anchorage Zone Crack Control Method for Pretensioned Concrete Bulb-tee Bridge Girders Using Nonlinear Finite Element Analysis written by Emre Kizilarslan and published by . This book was released on 2016 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: Wisconsin bulb tee pretensioned concrete girders have being used for bridges. Their effective spans to depth ratios and higher durability have made prestressed concrete girders desirable. However, cracks were observed at the anchorage zones of these girders because of the demand. To satisfy demand, these girders are heavily prestressed. Cracks initiate during detensioning of pretensioned strands and grow more while transporting them to the resting beds. These cracks create durability concerns as cracks lead aggressive salty water to the steel strands, endangering structures' stability. Especially, cracks in the bottom flange closer to the strands are main concerns in this research. This research primarily focused on the analyses of prestressed girder ends with modelling with nonlinear material properties to understand and recommend control methods for girder end cracking. The end zone behavior of the pretensioned girder was modelled using nonlinear material properties. The concrete nonlinearity, strain softening and stress redistribution upon cracking were also included in the behavior and the verification of tests were done by real tests on these girders. Finally, the reasons for cracks were explained by examining the principal tensile strain directions. The results of previous study showed that debonding strands can effectively control cracking. In this thesis, only debonding for cracking control method, therefore, was tested on 72W with 48 strands and 54W with 42 strands WI girders to see the real effect of debonding on anchorage zone cracks. After getting good results from tests and verifying them with Finite Element Analysis models, exact debonding percentages for other girders to eliminate cracks were presented by giving results of FEA models built for each of them.

Evaluation and Repair Procedures for Precast/prestressed Concrete Girders with Longitudinal Cracking in the Web

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Publisher : Transportation Research Board
ISBN 13 : 0309118352
Total Pages : 76 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Evaluation and Repair Procedures for Precast/prestressed Concrete Girders with Longitudinal Cracking in the Web by : Maher K. Tadros

Download or read book Evaluation and Repair Procedures for Precast/prestressed Concrete Girders with Longitudinal Cracking in the Web written by Maher K. Tadros and published by Transportation Research Board. This book was released on 2010 with total page 76 pages. Available in PDF, EPUB and Kindle. Book excerpt: This report establishes a user's manual for the acceptance, repair, or rejection of precast/prestressed concrete girders with longitudinal web cracking. The report also proposes revisions to the AASHTO LRFD Bridge Design Specifications and provides recommendations to develop improved crack control reinforcement details for use in new girders. The material in this report will be of immediate interest to bridge engineers.

Finite Element Analysis of Deep Wide-flanged Pre-stressed Girders to Understand and Control End Cracking

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ISBN 13 :
Total Pages : 134 pages
Book Rating : 4.:/5 (891 download)

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Book Synopsis Finite Element Analysis of Deep Wide-flanged Pre-stressed Girders to Understand and Control End Cracking by : Michael G. Oliva

Download or read book Finite Element Analysis of Deep Wide-flanged Pre-stressed Girders to Understand and Control End Cracking written by Michael G. Oliva and published by . This book was released on 2011 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Issues in Structural and Materials Engineering: 2013 Edition

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Publisher : ScholarlyEditions
ISBN 13 : 1490110836
Total Pages : 1153 pages
Book Rating : 4.4/5 (91 download)

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Book Synopsis Issues in Structural and Materials Engineering: 2013 Edition by :

Download or read book Issues in Structural and Materials Engineering: 2013 Edition written by and published by ScholarlyEditions. This book was released on 2013-05-01 with total page 1153 pages. Available in PDF, EPUB and Kindle. Book excerpt: Issues in Structural and Materials Engineering: 2013 Edition is a ScholarlyEditions™ book that delivers timely, authoritative, and comprehensive information about Computer Engineering. The editors have built Issues in Structural and Materials Engineering: 2013 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Computer Engineering in this book to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Structural and Materials Engineering: 2013 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.

Nonlinear Analysis of Prestressed Concrete Box Girder Bridges Under Flexure

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ISBN 13 :
Total Pages : 9 pages
Book Rating : 4.:/5 (614 download)

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Book Synopsis Nonlinear Analysis of Prestressed Concrete Box Girder Bridges Under Flexure by :

Download or read book Nonlinear Analysis of Prestressed Concrete Box Girder Bridges Under Flexure written by and published by . This book was released on 1989 with total page 9 pages. Available in PDF, EPUB and Kindle. Book excerpt:

End-region Behavior of Precast, Prestressed Concrete I-girders Employing 0.7-inch Diameter Prestressing Strands

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ISBN 13 :
Total Pages : 352 pages
Book Rating : 4.:/5 (15 download)

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Book Synopsis End-region Behavior of Precast, Prestressed Concrete I-girders Employing 0.7-inch Diameter Prestressing Strands by : Jessica Lauren Salazar

Download or read book End-region Behavior of Precast, Prestressed Concrete I-girders Employing 0.7-inch Diameter Prestressing Strands written by Jessica Lauren Salazar and published by . This book was released on 2016 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Pretensioned concrete girders are currently fabricated using 0.5- or 0.6-in. diameter prestressing strands. In recent years, however, it has become of interest to employ larger-diameter 0.7-in. diameter strands to reduce the number of strands and improve the efficiency of pretensioned concrete members. Such a transition requires a considerable initial investment that needs to be justified based on the benefits obtained. Furthermore, the use of 0.7-in. strands would increase the stresses within the end-region of pretensioned elements, which could lead to undesirable cracking and impact the serviceability of the girders. The work presented in this thesis consists of 1) a comprehensive parametric investigation to evaluate the benefits and limitations of using 0.7-in. strands in pretensioned bridge girders, and 2) a full-scale experimental study to investigate the behavior of pretensioned concrete girders with 0.7-in. strands at the time of prestress transfer. The parametric investigation was accomplished by designing thousands of bridge girders with different span lengths, concrete release strengths, and transverse spacings. The results showed that the most noticeable benefit of 0.7-in. strands over 0.6-in. strands was a reduction of up to 35 percent in the number of strands. However, the difference in the total weight of prestressing steel was insignificant. Increasing the release strength of concrete, at least to 7.5 ksi, was found essential to observe benefits in design aspects other than the number of strands. The experimental investigation involved the fabrication of two Tx46 and two Tx70 specimens at the Ferguson Structural Engineering Laboratory. All specimens employed 0.7-in. strands on a 2- by 2-in. grid and the standard detailing currently used for girders with smaller-diameter strands. The observed crack widths in the specimens upon prestress transfer did not exceed those typically observed in Tx-girders with smaller-diameter strands. Therefore, the use of 0.7-in. strands does not seem to trigger a need to modify the end-region detailing in Tx-girders. However, noticeably greater bursting and spalling forces were observed in the end regions of the specimens compared to the demands predicted by AASHTO LRFD provisions. The measured 24-hour transfer length from the specimens also exceeded estimates by AASHTO LRFD and ACI 318-14 provisions.

Prestress Losses in Pretensioned High-strength Concrete Bridge Girders

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Publisher : Transportation Research Board
ISBN 13 : 030908766X
Total Pages : 73 pages
Book Rating : 4.3/5 (9 download)

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Book Synopsis Prestress Losses in Pretensioned High-strength Concrete Bridge Girders by : Maher K. Tadros

Download or read book Prestress Losses in Pretensioned High-strength Concrete Bridge Girders written by Maher K. Tadros and published by Transportation Research Board. This book was released on 2003 with total page 73 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The HCM includes three printed volumes (Volumes 1-3) that can be purchased from the Transportation Research Board in print and electronic formats. Volume 4 is a free online resource that supports the rest of the manual. It includes: Supplemental chapters 25-38, providing additional details of the methodologies described in the Volume 1-3 chapters, example problems, and other resources; A technical reference library providing access to a significant portion of the research supporting HCM methods; Two applications guides demonstrating how the HCM can be applied to planning-level analysis and a variety of traffic operations applications; Interpretations, updates, and errata for the HCM (as they are developed);A discussion forum allowing HCM users to ask questions and collaborate on HCM-related matters; and Notifications of chapter updates, active discussions, and more via an optional e-mail notification feature."--Publisher.

Experimental and Analytical Investigations of the Thermal Behavior of Prestressed Concrete Bridge Girders Including Imperfections

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ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (68 download)

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Book Synopsis Experimental and Analytical Investigations of the Thermal Behavior of Prestressed Concrete Bridge Girders Including Imperfections by : Jonghang Lee

Download or read book Experimental and Analytical Investigations of the Thermal Behavior of Prestressed Concrete Bridge Girders Including Imperfections written by Jonghang Lee and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: An experimental and analytical study was conducted on a BT-63 prestressed concrete girder to investigate the thermal effects on the girder. A 2D finite element heat transfer analysis model was then developed which accounted for heat conduction, convection, radiation, and irradiation. The solar radiation was predicted using the location and geometry of the girder, variations in the solar position, and the shadow from the top flange on other girder surfaces. The girder temperatures obtained from the 2D heat transfer analysis matched well with the measurements. Using the temperatures from the 2D heat transfer analysis, a 3D solid finite element analysis was performed assuming the temperatures constant along the length of the girder. The maximum vertical displacement due to measured environmental conditions was found to be 0.29 inches and the maximum lateral displacement was found to be 0.57 inches. Using the proposed numerical approach, extremes in thermal effects including seasonal variations and bridge orientations were investigated around the United States to propose vertical and transverse thermal gradients which could then be used in the design of I-shaped prestressed concrete bridge girders. A simple beam model was developed to calculate the vertical and lateral thermal deformations which were shown to be within 6% of the 3D finite element analyses results. Finally, equations were developed to predict the maximum thermal vertical and lateral displacements for four AASHTO-PCI standard girders. To analyze the combined effects of thermal response, initial sweep, and bearing support slope on a 100-foot long BT-63 prestressed concrete girder, a 3D finite element sequential analysis procedure was developed which accounted for the changes in the geometry and stress state of the girder in each construction stage. The final construction stage then exposed the girder to thermal effects and performed a geometric nonlinear analysis which also considered the nonlinear behavior of the elastomeric bearing pads. This solution detected an instability under the following conditions: support slope of 5¡©6 and initial sweep of 4.5 inches.

12th PhD Symposium in Prague Czech Rep

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Publisher : FIB - Féd. Int. du Béton
ISBN 13 : 8001064018
Total Pages : 1312 pages
Book Rating : 4.0/5 (1 download)

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Book Synopsis 12th PhD Symposium in Prague Czech Rep by : FIB – International Federation for Structural Concrete

Download or read book 12th PhD Symposium in Prague Czech Rep written by FIB – International Federation for Structural Concrete and published by FIB - Féd. Int. du Béton. This book was released on 2018-08-01 with total page 1312 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Control of Horizontal Cracking in the Ends of Pretensioned Prestressed Concrete Girders

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ISBN 13 :
Total Pages : 19 pages
Book Rating : 4.:/5 (454 download)

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Book Synopsis Control of Horizontal Cracking in the Ends of Pretensioned Prestressed Concrete Girders by : W.T. Marshall

Download or read book Control of Horizontal Cracking in the Ends of Pretensioned Prestressed Concrete Girders written by W.T. Marshall and published by . This book was released on 1962 with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Model of Strain-related Prestress Losses in Pretensioned Simply Supported Bridge Girders

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ISBN 13 :
Total Pages : 608 pages
Book Rating : 4.:/5 (882 download)

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Book Synopsis Model of Strain-related Prestress Losses in Pretensioned Simply Supported Bridge Girders by : José Manuel Gallardo Méndez

Download or read book Model of Strain-related Prestress Losses in Pretensioned Simply Supported Bridge Girders written by José Manuel Gallardo Méndez and published by . This book was released on 2014 with total page 608 pages. Available in PDF, EPUB and Kindle. Book excerpt: Prestressed concrete construction relies on the application of compressive stresses to concrete elements. The prestressing force is typically applied through the tensioning of strands that react against the concrete and induce compression in the concrete. Loss of prestress is the decrease of this pre-applied stress. The conservative estimation of the prestress losses is imperative to prevent undesired cracking of the prestressed element under service loads. A large fraction of the prestress losses is a consequence of concrete deformations. This fraction of the losses can be identified as strain-related losses, and these occur due to instantaneous elastic shortening, and time-dependent creep and shrinkage. Creep and shrinkage of concrete depend on many factors that are extremely variable within concrete structures. The time-dependent behavior of concrete is not well-understood, but recent findings in the topics of concrete creep and shrinkage provide a better understanding of the underlying mechanisms affecting the nature of these two phenomena. However, current design practices and prestress loss estimation methods do not reflect the state-of-the-art knowledge regarding creep and shrinkage. The main objective of this dissertation was the study and estimation of strain-related prestress losses in simply supported pretensioned bridge girders. Simply supported pretensioned girders are widely designed, produced and frequently used in bridge construction. Due to this common use, pretensioned concrete bridge girders has become fairly standardized elements, which results in a reduced variability in the behavior of pretensioned bridge girders, as compare to that of less standardized concrete structures. Hence, a simplified method was calibrated to estimate prestress losses within pretensioned girders to an adequate level of accuracy. To achieve an acceptable accuracy experimental data from the monitoring of pretensioned simply supported girders was used for the calibration of the method. The accuracy of this simplified method is comparable to that achievable using more elaborate methods developed for generic concrete structures.

Flexural and Shear Response of Deteriorated Prestressed Concrete Girders Taken from a Decommissioned Bridge in Alberta

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ISBN 13 :
Total Pages : 112 pages
Book Rating : 4.:/5 (131 download)

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Book Synopsis Flexural and Shear Response of Deteriorated Prestressed Concrete Girders Taken from a Decommissioned Bridge in Alberta by : Zhaohan Wu

Download or read book Flexural and Shear Response of Deteriorated Prestressed Concrete Girders Taken from a Decommissioned Bridge in Alberta written by Zhaohan Wu and published by . This book was released on 2021 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: Prestressed concrete (PC) bridges are a major component of North America's transportation network. As this network ages, the response of deteriorated PC bridge girders is of interest since rehabilitation and repairs are constrained by limited infrastructure budgets. Bridges are often evaluated using a largely qualitative rating system which results in differences in opinions between evaluators. As part of a larger initiative to develop reliability-based bridge management tools for deteriorated structures, this thesis presents results and analysis from a series of full-scale destructive tests on a 28-year old PC bridge removed from service near Barrhead, Alberta. There are many studies on PC girders, but these studies are limited to non-deteriorated systems, systems with accelerated deterioration (corrosion, debonding), non-destructive testing, and normal density concrete. The impact of deterioration on semi-lightweight PC girders subject to real-world environmental effects is rarely studied. Destructive testing was carried out on four 11 m single span, semi-lightweight PC voided slab girders taken from a decommissioned bridge with different types and degrees of deterioration. Both flexural and shear testing was conducted to provide insight on the deteriorated behaviour of the girders. Four-point bending was used for flexural test. Shear tests were conducted using three-point bending with different shear spans (1.0 m and 1.5 m). Modifications on some girders simulated further damage. Flexure tests indicated that all girders resisted the design factored load based on CSA S6:19 but no girders satisfied live load deflection limits of span/800. Deterioration significantly affected the flexural strength of the girders with a 23% decrease in strength for the most deteriorated girder relative to the baseline girder. More concerning, corrosion led to undesirable strand rupture failure prior to yielding which greatly reduced failure deflection. Material tests confirmed that strand corrosion greatly affected the strength and ductility of the strands. Shear tests showed that shear span-to-depth ratio affected failure mode. All specimens with 1.0 m load scheme failed by strut crushing. For 1.5 m load scheme, girders in fair condition failed by shear compression. However, when stirrups were corroded, diagonal tension failure occurred leading to excessive yielding and wide cracks. Anchorage failure may occur when anchorage is inadequate leading to sudden failure from reinforcement or strand pull out. All girders performed well above design ULS loadings; deterioration did not greatly impact the peak load for the tested girders. However, deterioration affected events leading up to failure. Struts formed at a 29% lower load for 1.0 m load scheme and 32% lower load for 1.5 m load scheme due to induced prestressed strand loss, but the ultimate load only decreased by 9.6% and 9.9% for 1.0 and 1.5 m respectively. Anchorage failure resulted in the lowest peak load and sudden unexpected failure away from load point. Corrosion that leads to anchorage issues, such as end cracking, needs to be carefully examined by bridge inspectors. After testing, forensic investigation found the average as-built concrete strength was 51% larger than the design value; four extra 25M bars were also discovered that were not included in the stock drawings for this bridge. These bars were initially added for camber control but served as a major backup system since corrosion was much more present in the strands. With updated material properties, CSA S6:19 accurately predicted the baseline girder capacity within 5% of the test value for flexure. CSA S6:19's sectional approach based on MCFT was conservative in predicting the shear capacity of the girders for both load schemes due to the assumption of plane sections remaining plane. Considering both flexural and shear results, it was concluded that the deteriorated PC girders were flexure dominant and safely resisted the design load at the time of testing.

Control of Horizontal Cracking in the Ends of Pretensioned Prestressed Concrete Girders

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Publisher :
ISBN 13 :
Total Pages : 19 pages
Book Rating : 4.:/5 (454 download)

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Book Synopsis Control of Horizontal Cracking in the Ends of Pretensioned Prestressed Concrete Girders by : William Thomas Marshall

Download or read book Control of Horizontal Cracking in the Ends of Pretensioned Prestressed Concrete Girders written by William Thomas Marshall and published by . This book was released on 1962 with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Computational Modeling of Prestress Transfer, End-region Cracks and Shear Behavior in Prestressed Concrete I-girders Employing Large-diameter Strands

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ISBN 13 :
Total Pages : 190 pages
Book Rating : 4.:/5 (112 download)

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Book Synopsis Computational Modeling of Prestress Transfer, End-region Cracks and Shear Behavior in Prestressed Concrete I-girders Employing Large-diameter Strands by : Roya Alirezaei Abyaneh

Download or read book Computational Modeling of Prestress Transfer, End-region Cracks and Shear Behavior in Prestressed Concrete I-girders Employing Large-diameter Strands written by Roya Alirezaei Abyaneh and published by . This book was released on 2016 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: Prestressed concrete girders are commonly fabricated with 0.5-in. (12.7-mm) or 0.6-in. (15.2-mm) diameter prestressing strands. Recent interest in the use of larger (0.7-in. (17.8-mm) diameter) strands has been driven by potential benefits associated with reduction of the required number of strands and fabrication time, or potential increases in the workable range of prestressed concrete girders (i.e., greater capacities and span capabilities). A limited number of experiments on full-scale specimens with 0.7-in. (17.8-mm) diameter strands have shown that the load-carrying capacity and strand transfer length of specimens with 0.7-in. (17.8-mm) diameter strands can be conservatively estimated using existing AASHTO LRFD provisions. However, performance at prestress transfer requires further investigation to ensure that application of the strands with standard 2-in. (50-mm) spacing and conventional concrete release strength does not increase the end-region cracking that is characteristic of prestressed girders. It must be verified that the development of such cracks does not stimulate anchorage-driven or premature shear failures prior to yielding of the shear reinforcement. Previous research lacks in monitoring of reinforcement stresses and evaluation of end-region cracking which has long been a durability concern. A reliable finite element model that captures the behavior of the specimen at prestress transfer with consideration of performance from construction stages, over the course of the service life, and up to the ultimate limit state can provide key insight into the suitability of using of 0.7-in. (17.8-mm) diameter strands. Further, it could serve as an economical tool for the investigation and proposal of efficient end-region reinforcing details to reduce concrete cracking and enhance durability. Finite element analyses of prestressed I-girder end-regions encompassing cracking and long-term creep- and shrinkage-induced damage, especially in girders fabricated with large diameter strands, have been limited. This research program assessed the limitations of 0.7-in. (17.8-mm) diameter strands at prestress transfer up to limit state response and investigated measures for enhancing the serviceability of the girders through finite element analyses using the commercial software, ATENA 3D. The finite element study was complemented with a full-scale experimental program which was used to validate the numerical results. This paper lays out a validated procedure for modeling the construction stages of prestressed girders and load testing. The model was then used as a tool for investigating alternative end-region reinforcement details for improved end-region serviceability. The most promising options are presented for consideration in further experimental studies and future implementation

Effect of Vertical Pre-release Cracks on Prestressed Bridge Girders

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Publisher :
ISBN 13 :
Total Pages : 676 pages
Book Rating : 4.:/5 (626 download)

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Book Synopsis Effect of Vertical Pre-release Cracks on Prestressed Bridge Girders by : Eray Baran

Download or read book Effect of Vertical Pre-release Cracks on Prestressed Bridge Girders written by Eray Baran and published by . This book was released on 2003 with total page 676 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Effects of Vertical Pre-release Cracks on Prestressed Bridge Girders

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Publisher :
ISBN 13 :
Total Pages : 148 pages
Book Rating : 4.:/5 (55 download)

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Book Synopsis Effects of Vertical Pre-release Cracks on Prestressed Bridge Girders by : Eray Baran

Download or read book Effects of Vertical Pre-release Cracks on Prestressed Bridge Girders written by Eray Baran and published by . This book was released on 2003 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: