1、Guide to Estimating Prestress LossReported by Joint ACI-ASCE Committee 423ACI 423.10R-16First PrintingAugust 2016ISBN: 978-1-945487-13-2Guide to Estimating Prestress LossCopyright by the American Concrete Institute, Farmington Hills, MI. All rights reserved. This material may not be reproduced or co
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14、or incorporation by the Architect/Engineer.ACI 423.10R-16 was adopted and published August 2016.Copyright 2016, American Concrete InstituteAll rights reserved including rights of reproduction and use in any form or by any means, including the making of copies by any photo process, or by electronic o
15、r mechanical device, printed, written, or oral, or recording for sound or visual reproduction or for use in any knowledge or retrieval system or device, unless permission in writing is obtained from the copyright proprietors.1ACI 423.10R-16Guide to Estimating Prestress LossesReported by Joint ACI-AS
16、CE Committee 423Carin L. Roberts-Wollmann*, Chair Amy M. Reineke Trygestad, SecretaryTheresa M. Ahlborn*Robert W. BarnesFlorian G. BarthAsit N. BaxiRoger J. BeckerKenneth B. BondyCharles W. DolanJames P. DonnellyPierre EsselinckMartin J. FraduaWilliam L. GambleHarry A. GleichShawn P. GrossPawan R. G
17、uptaWilliam M. HaleH. R. Trey Hamilton IIICarol HayekMohammad IqbalDonald P. KlineLarry B. KrauserJason J. KrohnMark E. MooreTheodore L. NeffSami H. RizkallaJames RogersBruce W. RussellDavid H. SandersThomas C. SchaefferMorris SchupackRichard W. StoneMiroslav F. VejvodaJeffery S. VolzH. Carl WalkerZ
18、uming XiaPaul Zia*Co-chairs of subcommittee responsible for preparation of report.Subcommittee members.DeceasedConsulting MembersRobert N. Bruce Jr.Ned H. BurnsChunsheng “Steve” CaidSteven R. CloseHenry J. Cronin Jr.Ward N. Marianos Jr.Hani MelhemAntoine E. NaamanThomas E. NehilAndrea J. SchokkerThi
19、s guide is intended for estimation of prestress losses in concrete structures. Methods presented include lump sum, simplified approaches addressing individual source of loss, and additional estimation methods. They address losses in pretensioned and post-tensioned members, including bonded, unbonded
20、, and external tendons. Note that these estimation methods have not been evalu-ated for relative merits. A discussion of the variability of prestress losses caused by the variability in concrete properties is also presented. Several example problems are included.Keywords: creep; friction; post-tensi
21、oning; prestress loss; prestressed concrete; relaxation; shrinkage.CONTENTSCHAPTER 1INTRODUCTION, p. 21.1Introduction, p. 21.2Scope, p. 21.3Historical development, p. 31.4Guide organization and use, p. 3CHAPTER 2NOTATION AND DEFINITIONS, p. 42.1Notation, p. 42.2Definitions, p. 7CHAPTER 3LUMP-SUM MET
22、HOD, p. 73.1Scope, p. 73.2Historical code requirements, p. 73.3Industry practice, p. 83.4Measured losses, p. 8American Concrete Institute Copyrighted Material www.concrete.org2 GUIDE TO ESTIMATING PRESTRESS LOSS (ACI 423.10R-16)CHAPTER 4INITIAL LOSSES, p. 124.1Scope, p. 124.2Pretensioning losses bef
23、ore transfer, p. 134.3Elastic shortening losses in pretensioned members, p. 164.4Post-tensioning losses during tensioning and transfer, p. 184.5Elastic shortening loss in post-tensioned members, p. 214.6Elastic gain under superimposed loads, p. 22CHAPTER 5LONG-TERM LOSSES: SIMPLIFIED METHOD, p. 225.
24、1Scope, p. 225.2Creep of concrete ( fpCR), p. 235.3Concrete shrinkage ( fpSH), p. 235.5AASHTO LRFD approximate estimate of time-dependent losses, p. 25CHAPTER 6LONG-TERM LOSSES: DETAILED METHODS, p. 256.1Scope, p. 256.2Creep and shrinkage models, p. 256.3Age-adjusted effective modulus approaches, p.
25、 266.4Incremental time-step method, p. 306.5Computer programs, p. 316.6Effects of deck temperature during casting of composite deck or topping, p. 31CHAPTER 7VARIABILITY OF LOSS CALCULATIONS, p. 327.1Objective, p. 327.2Scope, p. 327.3Contributions to prestress loss, p. 327.4Modulus of elasticity, p.
26、 337.5Creep, p. 357.6Variational analysis, p. 357.7Shrinkage case study, p. 367.8Self-consolidating concrete, p. 367.9Conclusions, p. 37CHAPTER 8EXAMPLES, p. 388.1Pretensioned double-tee beam, p. 388.2Post-tensioned slab with unbonded tendons, p. 488.3Post-tensioned beam with bonded tendons, p. 528.
27、4Example with heat of hydration during casting, p. 57CHAPTER 9REFERENCES, p. 61Authored documents, p. 61CHAPTER 1INTRODUCTION1.1IntroductionEstimating prestress loss at any given time during the life of a prestressed concrete member is a complex issue. In preten-sioned and post-tensioned members, ap
28、plying prestressing force causes shortening of the concrete member that, in turn, causes a loss of tendon stress. Over time, concrete creep, concrete shrinkage, and steel relaxation result in additional reductions of tendon stress. In post-tensioned members, losses occur during the stressing operati
29、on due to friction between the tendon and sheathing or duct, which is caused by the intended and unintended tendon curvature. There are also losses due to seating of the wedges or nuts as the jacking force is transferred into the anchorage device. These and other sources of prestress loss are examin
30、ed by the licensed design professional to get an estimate of the total prestress loss and resulting effective prestressing force.Losses have inherent variability due to variations of mate-rial properties and environmental and curing conditions. Some losses may affect others. Time-dependent concrete
31、properties are particularly difficult to estimate accurately, so losses due to creep and shrinkage are expected to be variable. Friction between the tendon and sheathing or duct, move-ment of wedges within the anchorage device, and modulus of elasticity of concrete are also variables. The variabilit
32、y within each component and the interdependence among the components make it understandable that studies comparing measured prestress losses to predictions have shown that accurate and consistent calculation of prestress loss is diffi-cult to achieve.The best effort to calculate prestress loss is on
33、ly an esti-mate and, therefore, the licensed design professional should consider the consequences of actual losses being higher or lower than the estimated value. Estimation of prestress loss is an important factor for evaluating the serviceability of all types of prestressed members and the calcula
34、tion of flexural strength of members with unbonded tendons. The estimation of prestress loss, however, is not a significant factor in deter-mination of flexural strength of bonded prestressed members. When computing the shear strength of prestressed members with little or no transverse reinforcement
35、, a conservative estimate of the effective prestressing force is warranted.1.2ScopeACI 318-11 requires that the design of prestressed concrete members allow for prestress loss; however, the required level of detail for calculating losses is unspecified. The fric-tion loss provisions for post-tension
36、ed construction that first appeared in ACI 318-63 were removed from ACI 318-11. Although ACI 318-11 Commentary indicates that the lump sum method is obsolete, the licensed design professionals requirement to choose a method to compute losses remains. This guide is intended to aid the designer in thi
37、s choice by providing an overview of the various methods available.Many participants in the design and construction process need information on prestress losses. The licensed design professional, precasters, and post-tensioners all need an understanding of, and method to estimate, aspects of losses.
38、 To which entity is responsible for calculation of each type of loss has to be clearly defined in the contract documents.Total losses, fpT, are losses due to friction and seating fpFS, elastic shortening fpES, creep of concrete fpCR, shrinkage of concrete fpSH, and relaxation of tendons fpRE. This c
39、an be expressed as Eq. (1.2)American Concrete Institute Copyrighted Material www.concrete.orgGUIDE TO ESTIMATING PRESTRESS LOSS (ACI 423.10R-16) 3fpT= fpFS+ fpES+ fpCR+ fpSH+ fpRE(1.2)This guide presents background information and methods to calculate each type of loss.Following the introduction and
40、 a list of notation and defi-nitions, Chapter 3 includes a historical account of the lump sum method, currently recommended values for preliminary design, and a summary of losses that have been measured in field and laboratory studies.Chapter 4 discusses the different types of initial losses and add
41、resses the differences between pretensioned and post-tensioned members.Chapter 5 presents a simplified approach to estimate long-term losses due to creep, shrinkage, and relaxation for pretensioned and post-tensioned concrete members.Detailed approaches to estimate long-term losses are presented in
42、Chapter 6, which also addresses changes in prestressing force caused by differential shrinkage and hydration of the concrete deck in composite members. The approaches can be used for pretensioned or post-tensioned members.Chapter 7 discusses the variability of prestress loss calcu-lations caused by
43、concrete material properties, including compressive strength at transfer, modulus of elasticity, and creep and shrinkage.Chapter 8 presents example problems and compares solu-tions from different methods.1.3Historical developmentThe concept of prestressing concrete dates back to the late 1800s (Naam
44、an 2012). The performance of early prestressed concrete structures was adversely affected by time-dependent strains in the concretefor example, creep and shrinkage, which were nearly as large as the initial steel strain due to prestressing. Before 1940, the initial steel strain induced by prestressi
45、ng was limited by the low yield strength of steel. French engineer Eugene Freyssinet recognized the significance of prestress losses and the need for steels with high yield strength for prestressed applications. By 1945, higher strength steel became available, making it possible to produce the initi
46、al prestressing strain large enough so that the time-dependent strains developed in the concrete would not overcome the initial prestressing strain. As a result, the remaining prestressing force in the steel would be suffi-ciently large to be effective.Prestress losses were first addressed by ACI 31
47、8 in 1963. Although the provisions catalogued the different causes of prestress loss, they only provided specific instruction on determining friction losses. These code provisions were based on an earlier committee publication that provided similar, slightly more detailed guidance on prestress loss
48、(ACI-ASCE Committee 323 1958).In the 1970s, the Precast/Prestressed Concrete Institute (PCI Committee on Prestress Losses 1975) and Zia et al. (1979) provided more detailed methods to estimate prestress losses. Since the 1970s, others have developed methods to estimate prestress losses (Tadros et al
49、. 2003; Seguirant and Anderson 1985; Youakim et al. 2007; Garber et al. 2013). Gilbert and Ranzi (2011) and Branson (1977) provide general approaches to the calculation of a variety of time-dependent effects in concrete structures, including prestress losses. Computer programs have been developed to perform the tedious calculations required for stepwise analyses of prestress loss. However, due to the inherent uncertainties associated with material properties, construction practices, and in-servi
