1、Report on Indirect Method to Obtain Stress-Strain Response of Fiber-Reinforced Concrete (FRC)Reported by ACI Committee 544ACI 544.8R-16First PrintingMarch 2016ISBN: 978-1-942727-72-9Report on Indirect Method to Obtain Stress-Strain Response of Fiber-Reinforced Concrete (FRC)Copyright by the American
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11、committee reports are gathered together in the annually revised ACI Manual of Concrete Practice (MCP).American Concrete Institute38800 Country Club DriveFarmington Hills, MI 48331Phone: +1.248.848.3700Fax: +1.248.848.3701www.concrete.orgDevelopment of proper design procedures for fiber-reinforced co
12、ncrete (FRC) materials requires use of material tensile and compressive stress strains that reflect the contribution of fibers to the post-cracking behavior. While uniaxial tension tests provide the most fundamental material properties, conducting closed-loop tension tests are difficult to accomplis
13、h; therefore, methods based on indirect measurement of tensile properties using flexural tests are typically used.This report presents the methodologies that are used for data reduction and presentation of the flexural test results in terms of an equivalent tensile stress-strain response for FRC mat
14、erials. Existing methods for estimating uniaxial tensile stress-strain response of strain-softening and hardening FRCs from flexural beam-test data are introduced. Different approaches applied to beam tests based on elastic equivalent, curve fitting, or back-calcu-lation of flexural data are introdu
15、ced. These are divided into two general categories: elastic equivalent approach or inverse analysis method. In the elastic equivalent approach, a summary of available test methods by various code agencies are presented.Using back-calculation methods, tools based on the finite element method and anal
16、ytical closed-form solutions are presented. An approach is presented that uses closed-form moment-curvature relationships and obtains load-deflection responses for a beam of three- or four-point loading. The method is used to obtain equiva-lent parametric tensile stress and strain relationships for
17、a variety of FRC materials. The methods are compared against the available residual strength and also elastically equivalent residual strengths obtained by different specimen geometries.Results for a range of FRC materials studied show the back-calculated post-peak residual tensile strength is appro
18、ximately 30 to 37 percent of the elastically equivalent flexural residual strength for specimens with different fiber types and volume fractions.Keywords: fiber-reinforced concrete; inverse analysis; tensile stress-strain diagram.Barzin Mobasher*, ChairNeven Krstulovic-Opara*, SecretaryClifford N. M
19、acDonald, Membership SecretaryACI 544.8R-16Report on Indirect Method to Obtain Stress-Strain Response of Fiber-Reinforced Concrete (FRC)Reported by ACI Committee 544Corina-Maria AldeaEmmanuel K. AttiogbeNemkumar BanthiaJoaquim Oliveira Barros*Gordon B. BatsonPeter H. BischoffJean-Philippe CharronXav
20、ier DestreeAshish DubeyMahmut EkenelLiberato FerraraGregor D. FischerDean P. ForgeronAntonio GallovichRishi GuptaGeorge C. HoffJohn JonesDavid A. LangeMaria Lopez de MurphyMichael A. MahoneyBruno MassicotteChristian MeyerJames MilliganNicholas C. Mitchell Jr.Gerald H. MortonAntoine E. Naaman*Jeffrey
21、 L. NovakGiovanni A. PlizzariMax L. PorterVenkataswamy RamakrishnanKlaus Alexander RiederPierre RossiSurendra P. ShahFlavio de Andrade SilvaKay WilleRobert C. ZellersLihe ZhangConsulting MembersP.N. BalaguruHiram Price Ball Jr.Arnon BenturAndrzej M. BrandtJames I. DanielSidney FreedmanMelvyn A. Gali
22、natHenry J. MalloyAntoine E. Naaman*Members of the subcommittee that authored this report.Chair of the task group that drafted this report.Deceased.ACI Committee Reports, Guides, and Commentaries are intended for guidance in planning, designing, executing, and inspecting construction. This document
23、is intended for the use of individuals who are competent to evaluate the significance and limitations of its content and recommendations and who will accept responsibility for the application of the material it contains. The American Concrete Institute disclaims any and all responsibility for the st
24、ated principles. The Institute shall not be liable for any loss or damage arising therefrom.Reference to this document shall not be made in contract documents. If items found in this document are desired by the Architect/Engineer to be a part of the contract documents, they shall be restated in mand
25、atory language for incorporation by the Architect/Engineer.ACI 544.8R-16 was adopted and published March 2016.Copyright 2016, American Concrete Institute.All 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
26、by electronic or mechanical device, printed, written, or oral, or recording for sound or visual reproduc-tion or for use in any knowledge or retrieval system or device, unless permission in writing is obtained from the copyright proprietors.1CONTENTSCHAPTER 1INTRODUCTION AND SCOPE, p. 21.1Introducti
27、on, p. 21.2Scope, p. 3CHAPTER 2NOTATION AND DEFINITIONS, p. 32.1Notation, p. 32.2Definitions, p. 4CHAPTER 3TENSILE AND FLEXURAL TESTING AND MECHANICAL PROPERTIES, p. 43.1Tension and flexural testing, p. 43.2Strain softening and hardening, p. 43.3Deflection softening and hardening, p. 53.4Equivalent
28、tensile stress-strain responses, p. 63.5Inverse analysis methods, p. 6CHAPTER 4TEST METHODS, p. 64.1Test and specimen types, p. 64.2Stress-strain diagrams, p. 74.3Stress-strain diagram in RILEM approach, p. 74.4Flexural tensile strength ft,fland residual flexural tensile strengths fR,1and fR,4, p. 7
29、4.5Relationship between uniaxial tensile stress and flexural strength, p. 84.6Tensile stress-strain diagrams and strain values 1, 2, and 3, p. 8CHAPTER 5STRESS-STRAIN CURVES BY BACK-CALCULATION APPROACH, p. 105.1Parametric stress-strain curves, p. 105.2Back-calculation of flexural test data, p. 125.
30、3Comparison with averaged residual strength results, p. 125.4Comparison with RILEM and JCI methods, p. 13CHAPTER 6CONCLUSIONS, p. 13CHAPTER 7REFERENCES, p. 14Authored documents, p. 14APPENDIX ASPREADSHEET-BASED INVERSE ANALYSIS PROCEDURES, p. 16A.1Simplified strain-softening/hardening fiber-rein-for
31、ced concrete model, p. 16A.2Derivation of moment-curvature diagram, p. 17A.3Derivation of nominal flexural strength, p. 17A.4Simplified moment curvature diagram, p. 19A.5Load-deflection response, p. 20A.6Example: Three-point bending test, p. 21CHAPTER 1INTRODUCTION AND SCOPE1.1IntroductionThis repor
32、t provides guidelines for obtaining uniaxial stress-strain curves of fiber-reinforced concrete (FRC) from beam test data. In many FRC systems, the contribution of fibers is apparent after the concrete cracks and the fibers that bridge such cracks start to debond and pullout, thus resisting its openi
33、ng and generating a force that transfers the loads across the crack. The magnitude of load carried by the fibers depends on the opening of the crack width; it can be normal-ized with respect to the cracked area and referred to as a residual strength. The role that fibers play in bridging a main tens
34、ile crack is therefore characterized as resisting crack opening, also referred to as bridging force and is represented as an average effective stress and described by a tensile stress-crack width relationship. A majority of FRC mixtures exhibit a distinct stress-crack width relationship that can als
35、o be integrated with the initial elastic response of the composite into a combined nonlinear stress-strain response.The stress-crack width relationship can be represented as an equivalent stress-strain response by assuming a character-istic length parameter to smear the crack width into a nominal st
36、rain distribution. If mechanical tests that only focus on the tensile strength (ASTM C496/C496M) or flexural strength (ASTM C78/C78M) of the FRC are conducted, this contri-bution, herein referred to as residual strength, is either inac-curate, not reported, or reported in terms of parameters that ma
37、y not be useful for design or analysis. Furthermore, accu-rate measurements of tension tests that capture the post-peak response are difficult to conduct; therefore, many agencies use flexural tests as an indication of tensile response.While the tension test theoretically shows the true mate-rial be
38、havior and the flexural test represents a structural response, a flexural test is often used as a means of property measurement. The difference between the tension and flex-ural test results of many FRC materials is that in a tension test, the post-peak tensile stress-crack width response does not i
39、nfluence the maximum load obtained by the member. In a flexural test, however, the maximum load can be directly related to the residual stress levels such that the overall behavior can be affected by the post-peak response.An alternative method is to calculate post-cracking behavior using the experi
40、mental flexural results and reduce them into a set of material parameters that are in compliance with the model assumptions. This topic is the subject of this report. The testing methodologies are discussed in detail in committee reports such as ACI 544.3R. The present report addresses procedures to
41、 obtain an effective tensile stress-strain curve from the experimental results.Many structural systems that use FRC, such as structural floors or indeterminate structures, can exhibit an increase in strength values in proportion to the residual strength, which is a direct contribution of fibers; how
42、ever, this parameter is only measured in a qualitative way using flexural tests such as ASTM C1609/C1609M.To develop and apply design procedures for FRC mate-rials, simplified equations are needed to account for the fibers contribution to the tensile response, especially after cracking has occurred.
43、 This report addresses methods to compute the stress transfer after cracking is initiated in a concrete section.American Concrete Institute Copyrighted Material www.concrete.org2 INDIRECT METHOD TO OBTAIN STRESS-STRAIN RESPONSE OF FIBER-REINFORCED CONCRETE (ACI 544.8R-16)1.2ScopeThis report presents
44、 existing methods for estimating characteristic tensile stress-strain or tensile stress crack width response of strain-softening fiber-reinforced concrete (FRC) using flexural beam test data. Methods are proposed for strain-softening FRCs that do not exhibit distributed or parallel microcracking whe
45、n tested in flexural loading condi-tions, and strain-softening FRCs that do exhibit distributed or parallel microcracking when tested in flexural loading conditions.A set of definitions for an equivalent stress-strain diagram (Naaman and Reinhardt 2006; Noghabai 1998) are presented first and followe
46、d by calculation procedures for obtaining flexural tensile and residual flexural strengths from beam test data. Specific coefficient values for notched beams (RILEM TC 162-TDF 2003) and third-point beams (NBN B 15 238:1992) are validated. Because the coefficient values are not directly reported for
47、beam types tested per ASTM C1609/C1609M and ASTM C1399/C1399M, this report proposes an approach to do so and compares the results with other methods. The relationship is presented in terms of parameter-based stress coefficients that are determined using a step-by-step inverse analysis procedure in A
48、ppendix A. The report concludes with the relationship between the parameters that define the stress-strain diagram and the experimental flexural residual strengths.The proposed approach has several drawbacks, as it is for a one-dimensional material behavior model, and yields an effective stress-stra
49、in response based on the model assump-tions of trilinear tension and bilinear compression. Further-more, because the results of back-calculation are size- and geometry-dependent, the procedure is presented for test data obtained from ASTM C1609/C1609M specimens. Other geometries and specimen dimensions may need to be corre-lated with standard-sized specimens. The method can be applied to any size specimen and the results can be used for comparative basis. Different beam sizes may yield different stress-strain values because of the size effec
