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25 Wheel Load Distribution close attention to details such as tendon spacing and tie back reinforcement. The following paragraphs summarize the ref- Wheel load distribution has been the subject of many of erences reviewed on the subject. the analytical studies cited earlier. Other studies are discussed in the following paragraphs. Beaupre, R. J., et al. (1988) Deviation Saddle Behavior and Design for Externally Post-Tensioned Bridges, Research Re- Song, S. T., Y. H. Chai, and S. E. Hida (2001) "Live Load Dis- port 365-2. Center for Transportation Research, University tribution in Multi-Cell Box-Girder Bridges and its Compar- of Texas at Austin, Austin, Texas. ison with the AASHTO LRFD Bridge Design Specifications," Final Report to Caltrans for Contract Number 59A0148. This report is the second in a series outlining a major This report presents the results of a series of analyses done study of the behavior of post-tensioned concrete box-girder on box-girder bridges with normal and skewed supports and bridges with post-tensioning tendons external to the con- straight and curved geometry. The analysis models included crete section. It presents the results of an experimental pro- 3-D finite element as well as grillage and single line of elements gram in which ten very accurately sealed reinforced concrete for superstructure. The goal of the project was to evaluate the models of typical tendon deviators were tested. Detailed LRFD live load distribution factors for box-girder bridges. instrumentation led to a very good understanding of the However, the modeling techniques used and verified for this behavior of the various patterns of reinforcement in the project can be used as guidelines for NCHRP Project 12-71. deviators. The models included two very different patterns of detailing, several arrangements of tendon inclinations, Zokaie, T., K. D. Mish, and R. A. Imbsen (1993) "Distribu- and both normal and epoxy-coated reinforcement. tion of Wheel Loads on Highway Bridges," Phase 3, Final The report evaluates the results with respect to both Report to NCHRP 12-26 (2). simplified conventional analysis methods and strut-and- tie models. The results provide the basis for deviator de- This report presents a computer program (LDFac) devel- sign recommendations and several examples are presented to oped for modeling bridge superstructure with straight or illustrate the practical use of these recommendations. skewed supports and obtaining live load distribution factors. Although this computer program did not consider curved Caltrans (1996) Bridge Memo to Designers Manual, Memo geometry specifically, the modeling process and load place- 11-31 Curved Post-Tensioned Bridges, California Depart- ment guidelines may be used for analysis of curved bridges as ment of Transportation, Sacramento, California well. One of the key issues discussed in this report is the mod- eling of distortion of box-girders in a grillage analysis via an Memo 11-31 addresses the design of curved post- equivalent shear deformation parameter. tensioned concrete box-girders for lateral prestress forces. The force effects considered are tendon confinement and Zokaie, T., T. A. Osterkamp, and R. A. Imbsen (1991) "Dis- web regional transverse bending. The lateral prestress force, tribution of Wheel Loads on Highway Bridges," Final Report F, is determined by dividing the jacking force (Pj) per girder to NCHRP 12-26 (1). by the horizontal radius (R) of the web. A standard detail for tendon confinement (see Figure 3-1) is required for all This report presents a series of guidelines for analysis of webs with a Pj/R > 100 kN per m or a horizontal radius (R) various bridge types. The guidelines include calculation of of 250 m or less. The regional transverse bending moment equivalent section property parameters to be used in plate in the web is taken as Mu = 0.20Fhc where hc is the clear dis- and grillage analyses, as well as guidelines for setting the tance between the top and bottom slabs. This assumes the boundary conditions. Although the research did not specifi- web to act as a simple beam spanning the top and bottom cally consider curved bridge geometry, many of the guide- slabs with a concentrated load, F, acting at mid-height of lines for modeling and analysis using common analysis tools the web. The resulting simple beam moment is reduced 20% are applicable to modeling that will be needed in NCHRP for continuity. The load factor is taken as 1.0. The design of Project 12-71 global analysis studies. stirrup reinforcement does not combine regional transverse bending and shear requirements. Graphs are provided to check webs for containment of tendons and adequate stir- Tendon Breakout and Deviation Saddles rup reinforcement to resist regional transverse bending. Prestress tendon breakout in curved bridges has occurred A review of the 405/55 failure has led to the identification on bridges over the years. It is evident from observing the of several issues related to the Caltrans Memo to Designers reasons for these failures that they can be prevented through 11-31. These are discussed below.
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26 Figure 3-1. Caltrans detail A.
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27 Figure 3-1. (continued). Cordtz, K. (2004) Design of Curved Post-Tensioned Bridges have been encountered in both Europe and the United States. for Lateral Prestress Forces, David Evans and Associates, Cracking is attributed in a broad sense to the following fac- Inc., Roseville, California. tors: inadequate flexural and shear capacity, non-consideration of thermal stresses, insufficient attention to stresses devel- This document presents the internal guidelines of David oped by curvature of tendons, improper or inappropriate Evans and Associates, Inc., for the design of horizontally curved construction techniques, lack of quality workmanship to post-tensioned concrete box-girders for lateral prestress forces. meet the tolerances necessary for problem free structures, and The primary focus is on the regional beam action of the webs understrength materials. It is noted that in general the cause and local slab action of the cover concrete over the tendons. The of cracking can be attributed to the superposition of stresses document provides a discussion of the actions on curved of multiple effects. post-tensioned girders, identifies those actions not completely The article discusses the pullout of horizontal curved ten- addressed in current design codes and guidelines, and recom- dons that occurred on several cast-in-place post-tensioned mends design procedures that reflect current best practice. concrete box-girder bridges. In two of these structures, there Local slab action of the concrete cover over the tendons has was a combination of relatively sharp horizontal curvature, been identified as the major cause of failure in several curved thin concrete cover over the tendons, and the bundling of post-tensioned bridges that did not have duct or web ties. For a large-sized tendons close together. Podolny divides the web without duct or web ties, the cover concrete is the only el- analysis of the failures of these bridges in three separate ement restraining the lateral prestress force. The cover concrete actions: acts as a plain concrete beam to restrain the lateral prestress force. The local slab is subject to lateral shear and bending from the lateral prestress force. Specific requirements for local lateral 1. The global or overall girder action of the bridge together shear are given in AASHTO LRFD 184.108.40.206.1 "In-Plane Force with its supporting piers and abutments. Effects." No specific design methodology for local flexure is 2. Regional beam action of each web supported at the top given by AASHTO. The document provides interim recom- and bottom flanges as a beam. 3. Local slab action of the concrete cover over the tendons. mendations for the tensile stresses in the cover concrete. Where duct ties are required, the document recommends the use of a rational method for design such as a strut and tie model. It appears that for both of these bridges, local slab action of The vertical reinforcement in the web is subjected to the concrete cover over the tendons was the primary cause of combined global shear and regional transverse bending due the failure, but the regional beam action could have been a to regional beam action. No specific design methodology for contributory cause and could, by itself, have overstressed these combined actions is given by AASHTO. The docu- some of the stirrups. The global action had a very small effect ment provides interim recommendations for the design of on these failures. the stirrups. A flowchart is presented that outlines the recommended Seible, F., Dameron, R., and Hansen, B. (2003), Structural procedures. Numerous worked examples are also provided. Evaluation of the 405-55 HOV Connector and the Curved Girder Cracking/Spalling Problems. StD&A, San Diego, Podolny, W., Jr. (1985), "The Cause of Cracking in Post- California. Tensioned Concrete Box-girder Bridges and Retrofit Pro- cedures," Journal of the Prestressed Concrete Institute, This document is a detailed (70 pages, including illustra- March-April 1985. tions) project report on results of structural evaluation of the 405-55 HOV Connector's curved girder cracking/spalling This article discusses the types of problems that lead to problems. The report provides background on the observed cracking in post-tensioned concrete box-girder bridges and cracking and spalling (caused by horizontal breakout of web