National Academies Press: OpenBook

Strand Debonding for Pretensioned Girders (2017)

Chapter: Front Matter

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Suggested Citation:"Front Matter." National Academies of Sciences, Engineering, and Medicine. 2017. Strand Debonding for Pretensioned Girders. Washington, DC: The National Academies Press. doi: 10.17226/24813.
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Suggested Citation:"Front Matter." National Academies of Sciences, Engineering, and Medicine. 2017. Strand Debonding for Pretensioned Girders. Washington, DC: The National Academies Press. doi: 10.17226/24813.
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Suggested Citation:"Front Matter." National Academies of Sciences, Engineering, and Medicine. 2017. Strand Debonding for Pretensioned Girders. Washington, DC: The National Academies Press. doi: 10.17226/24813.
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Suggested Citation:"Front Matter." National Academies of Sciences, Engineering, and Medicine. 2017. Strand Debonding for Pretensioned Girders. Washington, DC: The National Academies Press. doi: 10.17226/24813.
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Suggested Citation:"Front Matter." National Academies of Sciences, Engineering, and Medicine. 2017. Strand Debonding for Pretensioned Girders. Washington, DC: The National Academies Press. doi: 10.17226/24813.
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Suggested Citation:"Front Matter." National Academies of Sciences, Engineering, and Medicine. 2017. Strand Debonding for Pretensioned Girders. Washington, DC: The National Academies Press. doi: 10.17226/24813.
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Suggested Citation:"Front Matter." National Academies of Sciences, Engineering, and Medicine. 2017. Strand Debonding for Pretensioned Girders. Washington, DC: The National Academies Press. doi: 10.17226/24813.
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Suggested Citation:"Front Matter." National Academies of Sciences, Engineering, and Medicine. 2017. Strand Debonding for Pretensioned Girders. Washington, DC: The National Academies Press. doi: 10.17226/24813.
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Suggested Citation:"Front Matter." National Academies of Sciences, Engineering, and Medicine. 2017. Strand Debonding for Pretensioned Girders. Washington, DC: The National Academies Press. doi: 10.17226/24813.
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Suggested Citation:"Front Matter." National Academies of Sciences, Engineering, and Medicine. 2017. Strand Debonding for Pretensioned Girders. Washington, DC: The National Academies Press. doi: 10.17226/24813.
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Suggested Citation:"Front Matter." National Academies of Sciences, Engineering, and Medicine. 2017. Strand Debonding for Pretensioned Girders. Washington, DC: The National Academies Press. doi: 10.17226/24813.
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Suggested Citation:"Front Matter." National Academies of Sciences, Engineering, and Medicine. 2017. Strand Debonding for Pretensioned Girders. Washington, DC: The National Academies Press. doi: 10.17226/24813.
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2017 N A T I O N A L C O O P E R A T I V E H I G H W A Y R E S E A R C H P R O G R A M NCHRP RESEARCH REPORT 849 Strand Debonding for Pretensioned Girders Bahram M. Shahrooz Richard A. Miller University of CinCinnati Cincinnati, OH Kent A. Harries Qiang Yu University of PittsbUrgh Pittsburgh, PA Henry G. Russell henry g. rUssell, inC. Glenview, IL Subscriber Categories Bridges and Other Structures Research sponsored by the American Association of State Highway and Transportation Officials in cooperation with the Federal Highway Administration

NATIONAL COOPERATIVE HIGHWAY RESEARCH PROGRAM Systematic, well-designed research is the most effective way to solve many problems facing highway administrators and engineers. Often, highway problems are of local interest and can best be studied by highway departments individually or in cooperation with their state universities and others. However, the accelerating growth of highway transportation results in increasingly complex problems of wide inter- est to highway authorities. These problems are best studied through a coordinated program of cooperative research. Recognizing this need, the leadership of the American Association of State Highway and Transportation Officials (AASHTO) in 1962 ini- tiated an objective national highway research program using modern scientific techniques—the National Cooperative Highway Research Program (NCHRP). NCHRP is supported on a continuing basis by funds from participating member states of AASHTO and receives the full cooperation and support of the Federal Highway Administration, United States Department of Transportation. The Transportation Research Board (TRB) of the National Academies of Sciences, Engineering, and Medicine was requested by AASHTO to administer the research program because of TRB’s recognized objectivity and understanding of modern research practices. TRB is uniquely suited for this purpose for many reasons: TRB maintains an extensive com- mittee structure from which authorities on any highway transportation subject may be drawn; TRB possesses avenues of communications and cooperation with federal, state, and local governmental agencies, univer- sities, and industry; TRB’s relationship to the Academies is an insurance of objectivity; and TRB maintains a full-time staff of specialists in high- way transportation matters to bring the findings of research directly to those in a position to use them. The program is developed on the basis of research needs identified by chief administrators and other staff of the highway and transporta- tion departments and by committees of AASHTO. Topics of the highest merit are selected by the AASHTO Standing Committee on Research (SCOR), and each year SCOR’s recommendations are proposed to the AASHTO Board of Directors and the Academies. Research projects to address these topics are defined by NCHRP, and qualified research agencies are selected from submitted proposals. Administration and surveillance of research contracts are the responsibilities of the Acad- emies and TRB. The needs for highway research are many, and NCHRP can make significant contributions to solving highway transportation problems of mutual concern to many responsible groups. The program, however, is intended to complement, rather than to substitute for or duplicate, other highway research programs. Published research reports of the NATIONAL COOPERATIVE HIGHWAY RESEARCH PROGRAM are available from Transportation Research Board Business Office 500 Fifth Street, NW Washington, DC 20001 and can be ordered through the Internet by going to http://www.national-academies.org and then searching for TRB Printed in the United States of America NCHRP RESEARCH REPORT 849 Project 12-91 ISSN 2572-3766 (Print) ISSN 2572-3774 (Online) ISBN 978-0-309-44640-2 Library of Congress Control Number 2017941011 © 2017 National Academy of Sciences. All rights reserved. COPYRIGHT INFORMATION Authors herein are responsible for the authenticity of their materials and for obtaining written permissions from publishers or persons who own the copyright to any previously published or copyrighted material used herein. Cooperative Research Programs (CRP) grants permission to reproduce material in this publication for classroom and not-for-profit purposes. Permission is given with the understanding that none of the material will be used to imply TRB, AASHTO, FAA, FHWA, FMCSA, FRA, FTA, Office of the Assistant Secretary for Research and Technology, PHMSA, or TDC endorsement of a particular product, method, or practice. It is expected that those reproducing the material in this document for educational and not-for-profit uses will give appropriate acknowledgment of the source of any reprinted or reproduced material. For other uses of the material, request permission from CRP. NOTICE The research report was reviewed by the technical panel and accepted for publication according to procedures established and overseen by the Transportation Research Board and approved by the National Academies of Sciences, Engineering, and Medicine. The opinions and conclusions expressed or implied in this report are those of the researchers who performed the research and are not necessarily those of the Transportation Research Board; the National Academies of Sciences, Engineering, and Medicine; or the program sponsors. The Transportation Research Board; the National Academies of Sciences, Engineering, and Medicine; and the sponsors of the National Cooperative Highway Research Program do not endorse products or manufacturers. Trade or manufacturers’ names appear herein solely because they are considered essential to the object of the report.

The National Academy of Sciences was established in 1863 by an Act of Congress, signed by President Lincoln, as a private, non- governmental institution to advise the nation on issues related to science and technology. Members are elected by their peers for outstanding contributions to research. Dr. Marcia McNutt is president. The National Academy of Engineering was established in 1964 under the charter of the National Academy of Sciences to bring the practices of engineering to advising the nation. Members are elected by their peers for extraordinary contributions to engineering. Dr. C. D. Mote, Jr., is president. The National Academy of Medicine (formerly the Institute of Medicine) was established in 1970 under the charter of the National Academy of Sciences to advise the nation on medical and health issues. Members are elected by their peers for distinguished contributions to medicine and health. Dr. Victor J. Dzau is president. The three Academies work together as the National Academies of Sciences, Engineering, and Medicine to provide independent, objective analysis and advice to the nation and conduct other activities to solve complex problems and inform public policy decisions. The Academies also encourage education and research, recognize outstanding contributions to knowledge, and increase public understanding in matters of science, engineering, and medicine. Learn more about the National Academies of Sciences, Engineering, and Medicine at www.national-academies.org. The Transportation Research Board is one of seven major programs of the National Academies of Sciences, Engineering, and Medicine. The mission of the Transportation Research Board is to increase the benefits that transportation contributes to society by providing leadership in transportation innovation and progress through research and information exchange, conducted within a setting that is objective, interdisciplinary, and multimodal. The Board’s varied committees, task forces, and panels annually engage about 7,000 engineers, scientists, and other transportation researchers and practitioners from the public and private sectors and academia, all of whom contribute their expertise in the public interest. The program is supported by state transportation departments, federal agencies including the component administrations of the U.S. Department of Transportation, and other organizations and individuals interested in the development of transportation. Learn more about the Transportation Research Board at www.TRB.org.

C O O P E R A T I V E R E S E A R C H P R O G R A M S CRP STAFF FOR NCHRP RESEARCH REPORT 849 Christopher J. Hedges, Director, Cooperative Research Programs Lori L. Sundstrom, Deputy Director, Cooperative Research Programs Waseem Dekelbab, Senior Program Officer Gary A. Jenkins, Senior Program Assistant Eileen P. Delaney, Director of Publications Scott E. Hitchcock, Editor NCHRP PROJECT 12-91 PANEL Field of Design—Area of Bridges Bijan Khaleghi, Washington State DOT, Tumwater, WA (Chair) Upul Bandara Attanayake, Western Michigan University, Kalamazoo, MI Fouad A. H. Jaber, Nebraska Department of Roads, Lincoln, NE Edmund H. Newton, Retired, South Dartmouth, MA William N. Nickas, Precast/Prestressed Concrete Institute, Tallahassee, FL Taya Retterer, Texas DOT, Austin, TX Joshua James Sletten, Parsons Brinckerhoff, Murray, UT Julius F. J. Volgyi, Jr., Retired, Richmond, VA Benjamin A. Graybeal, FHWA Liaison Stephen F. Maher, TRB Liaison

This report provides proposed revisions to the current debonding provisions found within the AASHTO LRFD Bridge Design Specifications with detailed examples of the application of the proposed revisions. The proposed revisions are based on comprehensive analytical and testing programs for investigating the effects of end anchorages, beam sections, end- diaphragm details, concrete strengths up to 15 ksi, and strand sizes. The material in this report will be of immediate interest to highway design engineers. Strand debonding is an alternative for reducing stresses in the end regions of pretensioned concrete beams. The AASHTO LRFD Bridge Design Specifications currently limit the amount of partial debonding to twenty-five percent of the total strand area within a pretensioned girder. The limit was imposed in recognition of the detrimental effects that excessive debond- ing can have on shear performance. Nevertheless, several states allow significantly higher percentages of debonding (up to seventy-five percent) to be used routinely in design. These higher percentages are based on successful past practices that have not been challenged. It is clear that unless the experimental evidence provides sufficient clarity, a consensus agreement among bridge owners will continue to be difficult to achieve. A comprehensive study of partial debonding effects on the performance of pretensioned girders was therefore needed. Review of the various debonding practices used throughout the United States and existing test data allowed focused experimental research on the critical parameters. The research was designed to produce definitive recommendations regarding the number and configuration of debonded strands within commonly used cross-sectional shapes (i.e., I-, U-, and box beams). Final statements regarding the integral role of strand anchorage in the service and strength performance of pretensioned beams should be well- substantiated and ultimately highlight the importance of a unified approach to strand debonding. Research was performed under NCHRP Project 12-91 by the University of Cincinnati to develop a proposed revision to the current debonding provisions found within the AASHTO LRFD Bridge Design Specifications and the AASHTO LRFD Bridge Construction Specifica- tions. The proposed revisions consider service and strength limit states for strand debonding within pretensioned flexural superstructure members (i.e., I-, U-, and box beams). A number of deliverables, provided as appendices, are not published but are available on the TRB project website (www.trb.org, search for “NCHRP 12-91”). These appendices are titled as follows: • Appendix A—Survey • Appendix B—Design Case Studies F O R E W O R D By Waseem Dekelbab Staff Officer Transportation Research Board

• Appendix C—Finite Element Modeling • Appendix D—Summaries of Individual FEM Simulations • Appendix E—Specimen Details and Fabrication Photographs • Appendix F—Material Properties and Mix Designs • Appendix G—Internal and External Instrumentation • Appendix H—Overview of Design Calculations • Appendix I—AASHTO Bridge Committee Agenda Item • Appendix J—Example of Proposed Changes

xi Notations 1 Chapter 1 Background 1 1.1 Introduction 2 1.2 Objectives of Research Program 2 1.3 Review of State of the Art and Practice 2 1.3.1 Longitudinal Reinforcement Requirements Associated with Shear Capacity 3 1.3.1.1 AASHTO LRFD Article 5.8.3.5: Longitudinal Reinforcement 4 1.3.2 Extant Experimental Studies 7 1.3.2.1 Synthesis of Past Experimental Studies 7 1.3.3 Past Analytical Studies 8 1.3.3.1 Synthesis of Past Analytical Studies 8 1.4 Current Practice for Debonding Strand 8 1.4.1 State Amended Specifications 9 1.4.2 Survey of Current Practice 11 Chapter 2 Analytical Research Approach and Findings 11 2.1 Research Approach 11 2.2 Evaluation of Current AASHTO Limits on Strand Debonding 12 2.2.1 Shahawy et al. (1993) 15 2.2.2 Russell et al. (2003) 15 2.3 Design Case Studies 15 2.3.1 Determination of Maximum Girder Span 16 2.3.1.1 STRENGTH I 16 2.3.1.2 SERVICE I (AASHTO LRFD Articles 3.4.1 and 5.9.4.2.1) 17 2.3.1.3 SERVICE III (AASHTO LRFD Articles 3.4.1 and 5.9.4.2.2) 17 2.3.1.4 Minimum Girder Span Length 17 2.3.2 Debonding Ratio 18 2.3.3 Summary of Design Parameter Study 21 2.4 Finite Element Method Modeling 22 2.4.1 Development and Validation of 3D-FEM Model 22 2.4.1.1 Material Models 23 2.4.1.2 Structural Modeling 23 2.4.2 FEM Parametric Study 24 2.4.2.1 Modeling Parameters 24 2.4.2.1.1 Concrete Strength 24 2.4.2.1.2 Prestressing Strand 25 2.4.2.1.3 Partial Debonding 25 2.4.2.1.4 Shear Reinforcement 25 2.4.2.1.5 Boundary Conditions 25 2.4.2.1.6 Applied Loads C O N T E N T S

26 2.4.2.1.7 Modeling Steps 26 2.4.2.1.8 Model Conventions 26 2.4.2.2 Simulation Summary 26 2.4.2.2.1 Prestress Transfer 29 2.4.2.2.2 SERVICE I Limit State 29 2.4.2.2.3 STRENGTH I Limit State 30 2.4.2.2.4 Ultimate Capacity 31 2.4.2.2.5 Performance of Different Girder Cross Sections 31 2.5 Strut-and-Tie Modeling of End Regions 32 2.5.1 Motivating Example 32 2.5.2 STM of Prestressed Girder End Region 34 2.5.3 Illustrative Examples 42 2.5.4 Validation by Experimental Results 43 2.5.5 Summary of End Region Behavior 43 2.5.6 Extension of Bulbed Girder Results and Discussion of Other Girder Shapes 44 2.6 Evaluation of the Effects of Skewed Girder Ends 44 2.6.1 Mechanistic Modeling 46 2.6.2 Washington State Girder Examples 46 2.6.2.1 Nonlinear Finite Element Modeling of Girders G2 and G5 50 2.7 Introduction of Debonded Strands at One Section 52 Chapter 3 Experimental Research Approach, Findings, and Associated Analytical Simulations 52 3.1 Research Approach 52 3.2 Design and Detailing of Test Specimens 53 3.3 Material Properties 54 3.4 Transfer Length 59 3.5 Testing Program 59 3.5.1 Test Setup 61 3.5.2 Instrumentation 62 3.5.3 Test Results and Discussions 62 3.5.3.1 Capacity, Stiffness, and Failure Mode 64 3.5.3.2 Crack Patterns 70 3.5.3.3 Shear Deformation 70 3.5.3.4 Shear Resistance from Transverse Reinforcement 72 3.5.3.5 Apparent Strand Slip 76 3.5.3.6 Contribution of Longitudinal Reinforcement 76 3.6 Summary 78 3.7 Modeling of Test Specimens 78 3.7.1 FEM Simulation of Test Girders 78 3.7.2 Utilization of Calibrated Analytical FEM Platform 78 3.7.2.1 Transfer Length 78 3.7.2.2 Further Evaluation of Longitudinal Strains at Release in Texas U-40 86 3.7.2.3 STM Simulation of Test Girders 89 3.8 Web Cracking 90 3.8.1 Calculation of Principal Tensile Stress 90 3.8.2 AASHTO LRFD Specifications Article 5.8.5 92 3.8.3 AASHTO LRFD Specifications Article 5.8.3.4.3 94 3.8.4 Evaluation of Data for AASHTO BI-36 Test Girder

96 Chapter 4 Conclusions and Suggestions 96 4.1 Conclusions 96 4.2 Suggested Detailing Guidelines for Prestressed Girders Having Debonded Strands 98 4.3 Suggestions Regarding Transverse Tension Ties at STRENGTH I Ultimate Limit State 99 4.4 Web Shear Cracking 100 4.5 Suggestions for Future Research 101 References 103 Appendices Note: Photographs, figures, and tables in this report may have been converted from color to grayscale for printing. The electronic version of the report (posted on the web at www.trb.org) retains the color versions.

N O T a T i O N S a = shear span (in.) A = Ramberg-Osgood function parameter Abulb = area of the bottom bulb (flange) Abulb,transformed = area of the transformed bulb section Ac = gross area of precast girder alone (in.2) Ae,g = “effective” gross area of the concrete section (in.2) Ae,transformed = “effective” area of the transformed section (in.2) Ag = gross area of precast girder alone (in.2) Agirder = area of precast girder alone (in.2) Anc = area of the non-composite section Ap = area of one prestressing steel strand (in.2) Aps = area of prestressing steel (in.2); area of one prestressing strand (in.2) As = area of nonprestressed tension reinforcement (in.2) Agross = gross cross-sectional area Atransformed = area of the transformed section Av = area of shear reinforcement (in.2) B = Ramberg-Osgood function parameter B2 = girder dimension (PCI 2011) B3 = girder dimension (PCI 2011) bb = bearing width (in.) bv = width of web (in.) C = Ramberg-Osgood function parameter cb = (bb/2)(1 – nf /Nw)(required location of resultant of portion of shear force dis- tributed to flange outstands to ensure uniform bearing pressure across the bearing pad) D5 = girder dimension (PCI 2011) D6 = girder dimension (PCI 2011) DC = weight of supported structure (kip) DW = superimposed dead load (kip) d = distance from compressive face to centroid of reinforcement (in.) db = nominal diameter of reinforcing bar, wire, or prestressing strand (in.) dc = distance to critical section (in.) de = effective depth from extreme compression fiber to the centroid of the tensile force in the tensile reinforcement (in.) dr = debonding ratio dv = effective shear depth (in.) Ec = modulus of elasticity for concrete (ksi) Ep = modulus of elasticity for prestressing strands (ksi) Es = modulus of elasticity for mild steel (ksi) Esh = modulus of elasticity for strain hardening portion of stress-strain curve (ksi)

e = eccentricity of the prestressing strands eg = eccentricity of the prestressing strands measured to the centroid of the gross concrete section (in.) egirder = average eccentricity of precast girder alone (in.) etransformed = eccentricity of the prestressing strands measured to the centroid of the trans- formed section (in.) fc = compressive stress in concrete (ksi) fc,transformed = concrete stress calculated using transformed section properties fc,g = concrete stress calculated using gross section properties f ′c = specified compressive strength of concrete for use in design (ksi) f ′c,girder = specified compressive strength of girder concrete for use in design (ksi) f ′c,slab = specified compressive strength of slab concrete for use in design (ksi) f ′ci = concrete compressive strength at prestress transfer (ksi) fpc = normal stress in the web fpi = initial prestress at transfer (ksi) fpLT = average stress in prestressing steel after long-term losses (ksi) fpe = effective stress in the prestressing steel after losses (ksi) fps = average stress in prestressing steel at nominal flexural resistance (ksi) fpu = ultimate strength of prestressing strand (ksi) fss = steel stress (ksi) ft = tensile stress in concrete (ksi) fu = ultimate strength of reinforcing bar (ksi) fvy = yield strength of transverse reinforcement fv = stress in shear reinforcement fy = specified minimum yield strength of reinforcing bar (ksi); yield strength of reinforcing bar (ksi) h = overall depth of a member (in.) H = overall depth of a member (in.) hb = depth of bulb or bottom flange (in.) Ic = moment of inertia of the composite section (in.4) Ig = moment of inertia of the gross concrete section (in.4) IM = impact loads (kip) Inc = moment of inertia of the non-composite section (in.4) Itransformed = moment of inertia of the transformed section (in.4) K1 = correction factor for source of aggregate ld = development length (in.) ldebond = debonded length L = span length (in. or ft) Lbearing = length of bearing pad Li = development length of bonded strand at i for beam with skew angle (in.) LL = live load (kip) LLlane = live load due to distributed lane load (ksf) LLtruck = live load due to HS-93 axel loads (kip) Lmin = minimum girder span based on the least of LSERVICE I, LSERVICE III, and LSTRENGTH I (ft) LSERVICE I = maximum girder span as determined by Service I load combination (ft) LSERVICE III = maximum girder span as determined by Service III load combination (ft) LSTRENGTH I = maximum girder span as determined by Strength I load combination (ft) Lt = strand transfer length (ft or in.) M = bending moment Mbarrier wall = total bending moment due to barrier wall (kip-in.) MDC = total bending moment due to weight of supported structure Mdnc = moment due to external loads applied only to the non-composite section (kip-in.) MDW = total bending moment due to superimposed dead load (kip-in.) Mgirder = total bending moment due to weight of girder (kip-in.)

ML = moment due to external loads applied only to the composite section (kip-in.) MLL = total bending moment due to live load (kip-in.) Mn = nominal flexural resistance (kip-in.) Mo = moment about point o Mslab = total bending moment due to weight of slab (kip-in.) Msw = moment due to the self-weight of the concrete section only (kip-in.) Mtotal = total bending moment applied in an experimental setting (kip-in.) Mu = applied factored bending moment at section (kip-in.) MWS = total bending moment due to wind (kip-in.) N = number of strands Nmax = maximum number of strands that may be located in the bulb or lower flange Nt = property of the section geometry and concrete strength at prestress transfer only Nu = applied factored axial force at section taken as positive if tensile (kip) Nw = number of bonded strands at a section nf = number of bonded strands in one side of the outer portion of bulb. The outer portion of bulb is defined as that extending beyond projection of web width, B3. Strands aligned with the edge of web are assumed to fall in the outer portion of bulb. ni = number of bonded strands in vertical group i P = concentrated applied load (kip); effective prestressing force (kip) Ppe = effective prestressing force after all losses (kip) Pi = force associated with each vertical group of ni bonded strands at location i (kip) Q = force effect in associated units Qc = first moment of inertia of the area above y taken about the neutral axis of the noncomposite section (in.3) Qnc = first moment of inertia of the area above y taken about the neutral axis of the composite section (in.3) S = girder spacing (ft) Sbottom of girder = section modulus to bottom of girder alone (in.3) Sbottom of girder, composite = section modulus to bottom of composite girder (in.3) Stop of girder = section modulus to top of girder alone (in.3) Stop of girder, composite = section modulus to top of composite girder (in.3) s = average spacing between mild shear reinforcement T = tensile force in the longitudinal reinforcement (kip) t = composite slab thickness (in.); tension factor for horizontal tie caused by shear strut at support tf = flange thickness ts = thickness of slab tw = thickness of web v = shear stress in concrete Vc = nominal shear resistance provided by tensile stresses in the concrete (kip) Vci = nominal shear resistance provided by concrete when inclined cracking results from combined shear and moment (kip) Vcw = nominal shear resistance provided by concrete when inclined cracking results from excessive principal tensions in web (kip) Vdesign = design shear Vdnc = shear force applied to the non-composite section only (kip) Vexp = experimentally reported shear values at failure (kip) VL = shear force applied to the composite section (kip) Vn = nominal shear resistance of the section considered (kip) Vp = component in the direction of the applied shear of the effective prestressing force (kip) Vs = shear resistance provided by shear reinforcement (kip) Vshear = total shear resistance (kip)

VT@dc = tensile force in longitudinal steel due to shear at the critical section (kip) VT@support = tensile force in longitudinal steel due to shear at the support (kip) Vtotal = total shear load applied in an experimental setting (kip) Vu = applied factored shear force at section (kip) wc = unit weight of concrete (kcf) wmax = widest crack observed during testing of specimen xf = distance from end of beam where the entire girder cross section resists the pre- stressing force xp = horizontal distance to girder centerline of centroid of nf strands in outer portion of bulb y = vertical distance from the bottom of the section to the point where the stress is calculated ybc = vertical distance from the bottom of the section to the composite neutral axis ybnc = vertical distance from the bottom of the section to the non-composite neutral axis yc,g = distance to the centroid of the gross concrete section from the bottom of the girder yc,transformed = distance to the centroid of the transformed section from the bottom of the girder yi = vertical distance from soffit to prestress strand layer i yp = vertical distance from bottom of girder to centroid of nf strands in outer portion of bulb a = over capacity factor = Qn/Qu; horizontal tie force fraction; angle of inclination of transverse reinforcement to longitudinal reinforcement (degrees) b = factor relating effect of longitudinal strain on the shear capacity of concrete, as indicated by the ability of diagonally cracked concrete to transmit tension e = strain (in./in.) ec = concrete longitudinal strain ef = failure strain in mild reinforcement (in./in.) es = net longitudinal tensile strain at the centroid of the longitudinal reinforce- ment (in./in.) esh = strain in mild reinforcement corresponding to the beginning of strain harden- ing (in./in.) eu = ultimate strain in mild reinforcement (in./in.) ey = yield strain in mild reinforcement (in./in.) q = angle of inclination of diagonal compressive stresses (degree); skew angle (degree) k = multiplier for strand development ϕ = resistance factor; diameter (in.) ff = flexure strength reduction factor fv = shear strength reduction factor r = reinforcement ratio = Aps/Ag n = shear stress rc = unit weight of concrete

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TRB's National Cooperative Highway Research Program (NCHRP) Research Report 849: Strand Debonding for Pretensioned Girders provides proposed revisions to the current debonding provisions found within the American Association of State Highway and Transportation Officials (AASHTO) Load and Resistance Factor Design (LRFD) Bridge Design Specifications with detailed examples of the application of the proposed revisions. The proposed revisions are based on comprehensive analytical and testing programs for investigating the effects of end anchorages, beam sections, end-diaphragm details, concrete strengths up to 15 ksi, and strand sizes.

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