Application of LRFD Bridge Design Specifications to High-Strength Structural Concrete: Shear Provisions (2007)

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20 This chapter presents the experimental and analytical research program and then summarizes the detailed findings of this work. Because the findings are presented in significant detail in this chapter, it is anticipated that some readers may not wish to review all 10 sections of the chapter. Therefore, they are encouraged to first review the description of the contents of Chapter 2 that is presented in the next few para- graphs before selecting which sections of Chapter 2 to read. The key observations presented in Chapter 2 that pertain to the extension of the LRFD specifications to HSC are sum- marized in Chapter 3 prior to the presentation in that chap- ter of the proposed changes to the LRFD specifications. Section 2.1 summarizes a review of experiences with the use of HSC in design and construction practice, identifies barriers in the LRFD specifications for use of HSC, and then discusses possibilities for extension of provisions with existing data. Section 2.2 presents a large experimental database of shear test results on reinforced and prestressed concrete beams. Mea- sured test strengths are compared with the calculated shear capacity using the LRFD Sectional Design Model to assess the influence of concrete strength on the safety of these provisions and to identify areas of potential concern. This database is also examined to assess where additional experimental research is required for the extension of provisions. The next several sections of Chapter 2 present the experi- mental research program and the primary results. Section 2.3 presents a summary of the test program, design details, mate- rial properties, and test set-up and instrumentation layout. Sec- tion 2.4 presents the measured strengths and compares those strengths with the shear strengths calculated using the LRFD Sectional Design Model Article 5.8.3, the AASHTO Standard Specifications, and several other relevant codes and formulas. Critical mechanisms of resistance and modes of failure are also discussed. Section 2.5 presents the measured cracking strengths, patterns, angles, and widths for all test members. Sec- tion 2.6 presents the measured reinforcement strains in the stir- rups and longitudinal deformed bars. It also presents measured longitudinal strains at mid-depth and compares these with the development of longitudinal strain at mid-depth, εx, as calcu- lated using the LRFD specifications. It also presents the meas- ured shear strains and a formula for predicting shear straining. The remaining sections in Chapter 2 examine in some depth the measured response of the test girders. In Section 2.7, the detailed test data is used to assess the total force carried by the stirrups and concrete.Section 2.8 presents the results of the inter- face shear transfer experiments.Section 2.9 examines the behav- ior of end regions, and Section 2.10 presents the behavior of the girders predicted using nonlinear finite element analyses and compares this behavior with the measured response. While Chapter 2 presents a topic-by-topic summary of the results, each of the first 10 appendices to this report provide detailed descriptions of the objectives, design, testing, and measured behavior of the experiments on each of the 10 test girders. Appendix 11 presents a discussion on evaluating effective shear depths and on the method that was used for measuring crack patterns. 2.1 Collection, Analysis, and Use of Existing HSC Information In this section, the work completed in Tasks 1 through 3, which led to defining the objectives and scope of the subse- quent large-scale research program, is presented. The descrip- tion consists of the following three subsections: 2.1.1 Review Experience with Use of HSC; 2.1.2 Identify Barriers to Use of HSC in LRFD Section 5; and 2.1.3 Extend Provisions with Existing Information. 2.1.1 Review Experience with Use of HSC (Results from Task 1) Task 1 was to review relevant practice, performance data, research findings, and other information related to the C H A P T E R 2 Findings

21 behavior and design of reinforced and prestressed HSC structures. This information was assembled from the techni- cal literature and from the unpublished experiences of engi- neers, bridge owners, and others. Information on actual field performance was of particular interest. In November 1999, the FHWA and many state DOTs jointly initiated a 3-year study entitled “Compilation and Evaluation of Results from High Performance Concrete (HPC) Bridge Projects.” The study was conducted under Contract DTFH61-00-C-00009 by Henry G. Russell, Inc., with Henry G. Russell as the principal investigator. The HPC bridge program included the construction of demonstration bridges. in each of the FHWA regions and dissemination of the technology and results at showcase workshops. Eighteen bridges in 13 states were included in the national program. Since the program’s inception, several states that were not a part of the program at the beginning have implemented the use of HPC in various bridge elements. All available information was collected and compiled as part of the FHWA study (22), and then used on NCHRP Proj- ect 12-56. Data from 19 HPC bridges are included in two for- mats: summary tables and detailed information on individual bridges. The complete information is provided in Section A12.1 of Appendix 12. 2.1.2 Identify Barriers to Use of HSC in LRFD Section 5 (Results from Task 2) Article 5.4.2.1 of the LRFD specifications limits the appli- cability of the specifications to concrete compressive strengths of 10 ksi (70 MPa) or less unless physical tests are made to establish the relationship between concrete strength and other properties. With the greater usage of high-strength concrete and its economical and technical advantages, consideration needs to be given to raising the limit above 10 ksi (70 MPa). The objective of work performed in Task 2 was to identify all provisions in Section 5 of the LRFD specifications that directly or indirectly have the potential for preventing the extension of the specifications in their current form to high-strength con- crete. Details of the work completed in Task 2 to meet that objective are provided in Section A12.2 of Appendix 12. 2.1.3 Extend Provisions with Existing Information (Results from Task 3) In Task 2, provisions in Section 5 of the LRFD specifica- tions that are potential barriers to the use of HSC in design practice were also identified. For barriers where sufficient information existed to support a change, proposed revisions were developed and submitted to the AASHTO Committee T-10. Section A12.3 of Appendix 12 provides a summary of the changes with respect to HSC that have been made in the LRFD specifications since the results from the FHWA project, as reported in Task 2, were completed. Revisions through the 2006 Interim Revision are included. Section A12.3 of Appen- dix 12 also contains an assessment of the articles that cannot be changed based on existing information. 2.2 Development and Analysis of Shear Database 2.2.1 Presentation of Shear Database A large database was collected from shear tests conducted on reinforced and prestressed concrete members. The data- base consists of tabularized information on the material, geometry, and test data from each experiment. A total of 1,874 test results were extracted from the literature and used to examine the influence of HSC on the merits and limita- tions of the Sectional Design Model in the LRFD specifica- tions. A description of the reinforced and prestressed concrete databases is given in Appendix 13. Based on a review of the characteristics of tested members, the following differences between the types of members tested in laboratories and the types of members designed in practice are noted: • Members in the field are typically slender (L/d > 10) and support distributed loads, while members tested in labora- tories are typically stocky and support one or two point loads. • Members in the field are often large and continuous and contain flanges, while members tested in laboratories are typically small, simply supported, rectangular members. • Members in the field typically contain shear reinforcement, while the majority of members tested in laboratories do not contain shear reinforcement. • Members in the field are designed to fail in flexure, while members in laboratories are overreinforced in flexure, often to extreme limits, in the regions of shear failure. • Members in the field need to be designed for shear over their entire length, while members in laboratories are typ- ically designed to fail in shear near supports. Despite the very large amount of research that has been conducted to evaluate the shear behavior of members, the sig- nificant differences between the characteristics of members designed for the field and members tested in laboratories clearly indicates that the accuracy of code provisions cannot be solely evaluated by their ability to predict the strength of laboratory test structures. Nevertheless, an assessment of the LRFD Sectional Design Model was conducted using existing test data to identify concerns with its extension to HSC and where additional research is required. In these assessments,

22 no limit was placed on the value of the compressive cylinder strength, f c´, so as to evaluate where changes were required before this limit could be raised or eliminated. 2.2.2 Influence of Concrete Compressive Strength Figure 11 plots the ultimate shear stress at failure versus the concrete cylinder strength for the 1,287-member RC database. Different marker types are used to characterize the different levels of shear reinforcement. This figure illustrates that there is very limited data for members designed for high shear stresses, particularly when considering that the LRFD specifi- cations allow members to be designed for shear stresses up to 0.25f c´. Figure 12 presents a similar plot for PC members. This plot illustrates that there are few test results for members cast with very high-strength concretes. To assess whether the limit on f c´ in the LRFD Sectional Design Model can be removed or to what extent it can be raised, the shear strength ratio (Vtest/VLRFD) was plotted versus the compressive cylinder strength for the 1,287-member RC database, as shown in Figure 13. In calculating the design capacity of members using the LRFD Sectional Design Model, the maximum aggregate size was reduced to zero when f c´ was greater than 10.0 ksi, as has been done in the CSA Code for members cast with concretes that have a compressive strength greater than 10 ksi (70 MPa). The results illustrate that the LRFD specifications are just as accurate and conservative for members cast with concrete strengths above 10.0 ksi as they are for members cast with concrete strengths less than 10.0 ksi. The LRFD specifications typically underestimate the capacity of tested members. While there is significant scatter in the predictive capability of this method for members without shear reinforcement, it should be noted that the LRFD specifications have been found in other comparisons (23) to provide more accurate and uniform estimates of the shear capacity of mem- bers without shear reinforcement than either the ACI 318-05 or AASHTO Standard Specifications methods. For members with shear reinforcement, the shear strength ratios (Vtest/VLRFD) range from about 0.70 to 2, with a general upward trend with increasing concrete strength until f c´ = 10 ksi. To assess the impact on calculated strengths of the assump- tions made in the derivation of the Sectional Design Model from the MCFT,a similar plot to that of Figure 13 was prepared, Figure 11. Ultimate shear stress (vtest) at failure versus the concrete compressive strength (f’c) of reinforced concrete members. Figure 12. Ultimate shear stress (vtest) at failure versus the concrete compressive strength (f’c) of prestressed concrete members. Figure 13. Shear strength ratio (Vtest / VLRFD) versus the concrete compressive strength (f’c ) of reinforced concrete members. 0 200 400 600 800 1000 1200 1400 1600 1800 2000 0 5000 10000 15000 20000 f'c (psi) v te st (p si) members without Av members with at least minAv members with Av but less than minAv large, lightly reinforced members without Av 0 500 1000 1500 2000 2500 0 3000 6000 9000 12000 15000 f'c (psi) v te st (p si) members without Av members with at least minAv members with Av but less than minAv 0 0.5 1 1.5 2 2.5 3 0 5000 10000 15000 20000 f'c (psi) Vt es t/V LR FD members without Av members with at least minAv members with Av but less than minAv large, lightly reinforced members without Av

but the capacity of the members was determined using program Response 2000 (R2K) (24). R2K is a computer analysis/design tool based on the MCFT and developed by Dr.Evan Bentz of the University of Toronto. It uses a multilayer analysis approach for determining the distribution of shear stress over the depth of a member, uses more accurate constitutive relationships for the compressive response of HSC, and calculates crack spacing based on the levels of shear and longitudinal reinforcement pro- vided. Figure 14 illustrates that the LRFD Sectional Design Model gives somewhat more conservative estimates of strength than does R2K and that the predictions given by this analysis tool are somewhat less scattered. A similar set of plots was prepared for examining the influ- ence of concrete compressive strength on the shear strength ratio for members in the PC databank. See Figures 15 and 16. Because there are a very limited number of test results for PC members cast with concrete strengths above 10 ksi, it is diffi- cult to identify a trend from the results of this analysis. The particularly unconservative results that appear in the lower right corner of Figures 15 and 16 are two prestressed I-beam test results reported by J. Jacob and B. Russell at the Trans- portation Research Board 78th Annual Meeting in 1999. Those beams were cast with a concrete strength of about 12 ksi and used welded wire fabric for shear reinforcement. The authors of this paper reported that substantial strand slip, of up to 0.38 inch, had occurred prior to failure and that this event may have precipitated the failure of these girders. When the shear strength ratio was calculated using R2K, as shown in Figure 16, there was less scatter than when the LRFD spec- ifications were used, as shown in Figure 15. This is particu- larly true for the PC members that did not contain shear reinforcement. The HSC PC members with the noticeably different shear stress ratio for the two predictions are part of the “CW series” beams reported by Elzanaty et al. in 1986 (25). These 18-inch deep beams did not contain shear rein- forcement, and the webs were only 2 inches thick. Since the majority of the test data is from tests on small members, it is useful to specifically examine the effectiveness of the LRFD specifications for large HSC members. There- fore, Figures 17 and 18 present the shear strength ratio versus beam depth for RC members and versus beam height for PC members, respectively, and different marker types are used to demarcate ranges in concrete strengths. 23 0 0.5 1 1.5 2 2.5 3 0 5000 10000 15000 20000 f'c (psi) Vt es t/V R 2K members without Av members with at least minAv members with Av but less than minAv large, lightly reinforced members without Av 0 0.5 1 1.5 2 2.5 3 0 3000 6000 9000 12000 15000 f'c (psi) Vt es t/V LR FD members without Av members with at least minAv members with Av but less than minAv 0 0.5 1 1.5 2 2.5 3 0 3000 6000 9000 12000 15000 f'c (psi) Vt es t/V R 2K Vt es t/V R 2K members without Av members with at least minAv members with Av but less than minAv Figure 14. Shear strength ratio (Vtest / VR2K) versus the concrete compressive strength (f’c ) of reinforced concrete members. Figure 15. Shear strength ratio (Vtest / VLRFD) versus the concrete compressive strength (f’c ) of prestressed concrete members. Figure 16. Shear strength ratio (Vtest / VR2K) versus the concrete compressive strength (f’c ) of prestressed concrete members.

24 2.2.3 Maximum Shear Strength Limitation The maximum nominal shear resistance permitted in the LRFD specification is 0.25f c´ plus the vertical component of inclined prestressing. This is a significant increase over what is permitted in the AASHTO Standard Specifications, and thus it is useful to examine existing test data to assess the safety of this increased limit. Figures 19 and 20 present the distribution of test data as a function of concrete compressive strength. It is apparent from Figure 19 that, for RC members, while there is very little data to evaluate the extreme upper limit, there are a significant number of test results for HSC members that support relatively large shear stresses. For PC members, there is data for members cast with normal- to modestly high-strength concrete that illustrates that shear stresses up to twice the limit used in the LRFD specifications can be supported. To assess the safety and accuracy of the LRFD specifica- tions and the program R2K for calculating the capacity of members designed for high shear stresses, shear strength ratios are plotted versus f c´ for these members in Figures 21 through 24. For RC members with heavy stirrups, both the LRFD specifications and the R2K predictions give good results. However, the predicted strengths of the PC members were unconservative for some deep members with large amounts of shear reinforcement. 0 0.5 1 1.5 2 2.5 3 0 10 20 30 40 50 depth, d (in) Vt es t/V LR FD f'c<5 ksi f'c=5~8 ksi f'c=8~12 ksi f'c=12~19 ksi 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0 10 20 30 40 50 60 height, h (in) Vt es t/V LR FD f'c<4 ksi 4<f'c<7 ksi 7<f'c<10 ksi 10<f'c<13 ksi Figure 17. Shear strength ratio (Vtest / VLRFD) versus the member depth (d) of reinforced concrete members. Figure 18. Shear strength ratio (Vtest / VLRFD) versus the member height (h) of prestressed concrete members. Figure 19. Examination of maximum shear strength limitations for reinforced concrete members. 0 500 1000 1500 2000 2500 3000 3500 4000 0 3000 6000 9000 12000 15000 f'c (psi) v te st (p si) rhov > 1.4%, a/d<2.4 1.0 < rhov < 1.4%, a/d>2.4 rhov > 1.4%, a/d>2.4 0.6 < rhov < 1.0%, a/d<2.4 1.0 < rhov < 1.4%, a/d<2.4 0.6 < rhov < 1.0%, a/d>2.4 LRFD limit Figure 20. Examination of maximum shear strength limitations for prestressed concrete members. 0 500 1000 1500 2000 2500 3000 0 5000 10000 15000 20000 f'c (psi) v te st (p si) rhov > 1.4%, a/d<2.4 1.0 < rhov < 1.4%, a/d>2.4 rhov > 1.4%, a/d>2.4 0.6 < rhov < 1.0%, a/d<2.4 1.0 < rhov < 1.4%, a/d<2.4 0.6 < rhov < 1.0%, a/d>2.4 LRFD limit

2.2.4 Minimum Shear Reinforcement Requirements The primary roles of minimum reinforcement are to restrain the growth of inclined cracks, to improve ductility, and to ensure that the concrete contribution to shear resistance (Vc) is maintained up until at least yield of the shear reinforcement. In the LRFD specifications, the minimum amount of shear reinforcement is given by Equation 18. and if vu (Vu/bvdv) < 0.125, then smax = 0.8dv or 24.0 inches, while if vu ≥ 0.125, then smax = 0.4dv or 12.0 inches. Figure 25 plots the shear strength ratio for a segment of the RC test results with very light amounts of shear rein- forcement (ρvfy = 30–150 psi) versus the spacing ratio (stir- rup spacing divided by beam depth [s/d]). Different marker types are used to identify the strength (ρvfy) of the shear reinforcement that was provided in each test. Furthermore, if the reinforcing details for a test beam did not satisfy code requirements (i.e., less than minimum reinforcement or A f b s f f v y v v y c= ≥ρ 0 0316 1. ´ ( ) (in square inches 8) 25 0 0.5 1 1.5 2 0 5000 10000 15000 20000 f'c (psi) Vt es t/V LR FD rhov > 1.4%, a/d<2.4 1.0 < rhov < 1.4%, a/d>2.4 rhov > 1.4%, a/d>2.4 0.6 < rhov < 1.0%, a/d<2.4 1.0 < rhov < 1.4%, a/d<2.4 0.6 < rhov < 1.0%, a/d>2.4 Figure 21. LRFD prediction of reinforced concrete members with heavy amount of shear reinforcement. 0 0.5 1 1.5 2 0 5000 10000 15000 20000 f'c (psi) Vt es t/V R 2K rhov > 1.4%, a/d<2.4 1.0 < rhov < 1.4%, a/d>2.4 rhov > 1.4%, a/d>2.4 0.6 < rhov < 1.0%, a/d<2.4 1.0 < rhov < 1.4%, a/d<2.4 0.6 < rhov < 1.0%, a/d>2.4 Figure 22. MCFT prediction of reinforced members with heavy amount of shear reinforcement. 0 0.5 1 1.5 2 0 3000 6000 9000 12000 15000 f'c (psi) Vt es t/V LR FD rhov > 1.4%, a/d<2.4 1.0 < rhov < 1.4%, a/d>2.4 rhov > 1.4%, a/d>2.4 0.6 < rhov < 1.0%, a/d<2.4 1.0 < rhov < 1.4%, a/d<2.4 0.6 < rhov < 1.0%, a/d>2.4 Figure 23. LRFD prediction of prestressed concrete members with heavy amount of shear reinforcement. 0 0.5 1 1.5 2 0 3000 6000 9000 12000 15000 f'c (psi) Vt es t/V R 2K rhov > 1.4%, a/d<2.4 1.0 < rhov < 1.4%, a/d>2.4 rhov > 1.4%, a/d>2.4 0.6 < rhov < 1.0%, a/d<2.4 1.0 < rhov < 1.4%, a/d<2.4 0.6 < rhov < 1.0%, a/d>2.4 Figure 24. MCFT prediction of prestressed concrete members with heavy amount of shear reinforcement.

26 too large a spacing of stirrups), then a circle is drawn around the marker for this test result. One measure of assessing the suitability of the minimum shear reinforce- ment requirement is to count the number of markers with- out circles below which the shear strength ratio was less than 1.0. The LRFD has seven code-satisfying test results having a ratio of less than 1.0, but most of them are rea- sonably close to 1.0. In Figure 26, the predictions from R2K are somewhat better because in only three of the members, which satisfied the LRFD specifications, is the shear stress ratio less than 1.0. Figures 27 and 28 examine the suitability of the minimum shear reinforcement requirements of the LRFD specifications for PC members that are lightly reinforced in shear. As illus- trated, in only a few cases was the strength ratio slightly less than 1.0. Both RC and PC test data in Figures 25 through 28 indicate that the minimum reinforcement requirements used in the LRFD specifications are reasonable and appropriate. They also illustrate that increasing the amounts of minimum shear reinforcement has a marginal influence on the shear strength ratio (Vtest/VLRFD). Furthermore, they also result in the rather 0 0.5 1 1.5 2 0 0.2 0.4 0.6 0.8 1 1.2 s/d Vt es t/V LR FD rhovfy = 30-60 psi rhovfy = 90-120 psi rhovfy = 60-90 psi rhovfy = 120-150 psi Figure 25. Influence of shear reinforcement details on shear strength ratio (Vtest / VLRFD) for reinforced concrete members. 0 0.5 1 1.5 2 0 0.2 0.4 0.6 0.8 1 1.2 s/d Vt es t/V R 2K rhovfy = 30-60 psi rhovfy = 90-120 psi rhovfy = 60-90 psi rhovfy =120-150 psi 0 0.5 1 1.5 2 0 0.2 0.4 0.6 0.8 1 1.2 s/d Vt es t/V LR FD rhovfy = 30-60 psi rhovfy = 90-120 psi rhovfy = 60-90 psi rhovfy = 120-150 psi 0 0.5 1 1.5 2 0 0.2 0.4 0.6 0.8 1 1.2 s/d Vt es t/V R 2K rhovfy = 30-60 psi rhovfy = 90-120 psi rhovfy = 60-90 psi rhovfy = 120-150 psi Figure 26. Influence of shear reinforcement details on shear strength ratio (Vtest / VR2K) for reinforced concrete members. Figure 27. Influence of shear reinforcement details on shear strength ratio (Vtest / VLRFD) for prestressed concrete members. Figure 28. Influence of shear reinforcement details on shear strength ratio (Vtest / VR2K) for prestressed concrete members.

unexpected observation that the s/d ratio has little to no effect on the shear strength ratio. 2.2.5 Size Effect in Shear It is now generally accepted that for members without shear reinforcement, the ultimate shear stress decreases as the depth of the member increases. Figure 29 is used to illustrate this effect over the full range in shear design stress levels and concrete strength levels. This depth effect is confirmed by the test data because the strength ratios for the deepest range of members (20 to 40 inches) plot closer to the bottom of the figure, while the strength ratios for the least deep members (less than 10 inches) generally plot toward the top of the fig- ure. It is also interesting to observe that members having more than 2 percent of longitudinal reinforcement generally failed at higher shear stresses than members with lower lon- gitudinal reinforcement levels. In Figure 30, a similar plot was created to determine whether similar trends would be seen in PC members. The lack of data across a range in depths makes it difficult to iden- tify a trend or lack of a trend. Figure 30 does show that the PC members having more than 2 percent of longitudinal rein- forcement have somewhat higher shear failure stress levels than members having less than 2 percent of longitudinal reinforcement. Many international codes use the depth as a parameter for reducing the limiting shear stress as the depth of the member increases. In the LRFD specifications, a size effect for members without shear reinforcement is made by using the lesser of the overall depth or the distance between layers of longitudinal reinforcement in the tables for selecting the parameter β that controls the concrete contribution to shear resistance. The basis for this approach is that (a) crack spacing is proportional to the distance between layers of crack control reinforcement and (b) crack widths, which influence the aggregate interlock mechanism, are roughly in proportion to crack spacing for any given level of longitudinal strain. In members with minimum shear reinforcement, such as the majority of prestressed mem- bers, the LRFD method assumes a crack spacing of 12 inches and thereby predicts that there is no size effect in shear. Figures 31 through 34 show the influence of f c´, depth, and longitudinal reinforcement ratio on the shear strength ratio. The results reinforce similar trends that have already been identified. 27 0 100 200 300 400 500 600 700 800 0 5000 10000 15000 f'c (psi) v u te st (p si) d<10 in, rho<2.0% d = 10~20 in, rho>2.0% d<10 in, rho>2.0% d = 20~40 in, rho<2.0% d = 10~20 in, rho<2.0% d = 20~40 in, rho>2.0% 0 200 400 600 800 1000 1200 1400 0 2000 4000 6000 8000 10000 12000 f'c (psi) v u te st (p si) h<10 in, rho<2.0% h = 10~20 in, rho>2.0% h<10 in, rho>2.0% h = 20~32 in, rho<2.0% h = 10~20 in, rho<2.0% h = 20~32 in, rho>2.0% 0 0.5 1 1.5 2 2.5 3 0 5000 10000 15000 f'c (psi) Vt es t/V LR FD d<10 in, rho<2.0% d = 10~20 in, rho>2.0% d<10 in, rho>2.0% d = 20~40 in, rho<2.0% d = 10~20 in, rho<2.0% d = 20~40 in, rho>2.0% Figure 29. Influence of member size for reinforced concrete members without shear reinforcement. Figure 30. Influence of member size for prestressed concrete members without shear reinforcement. Figure 31. Influence of member size on shear strength ratio (Vtest / VLRFD) for reinforced concrete members.

28 2.2.6 Influence of Longitudinal Reinforcement Ratio Figures 35 and 36 illustrate that the LRFD and R2K pre- dictions become more conservative as the amount of longi- tudinal reinforcement in RC members increases. A similar effect is observed for PC members in Figures 37 and 38. 2.2.7 Summary of Research Needs The analysis presented in this section illustrates that the LRFD Sectional Design Model and the Response 2000 design/analysis tool provide conservative estimates of capacity in most cases. It further indicates that the LRFD specifications are equally conservative and accurate at predicting the strength of members cast with HSC as those cast with normal strength. However, the considerable scatter in the experimental test results over the entire range of possible concrete compressive strengths indicates that these tools do not accurately account for all influencing factors. This is a concern when coupled with the recognition that members tested in laboratories do not well represent what is built in the field.As summarized at the begin- ning of this section, there is comparatively little experimental test data on large members, uniformly loaded members, 0 0.5 1 1.5 2 2.5 3 0 5000 10000 15000 f'c (psi) Vt es t/V R 2K d<10 in, rho<2.0% d = 10~20 in, rho>2.0% d<10 in, rho>2.0% d = 20~40 in, rho<2.0% d = 10~20 in, rho<2.0% d = 20~40 in, rho>2.0% 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0 2000 4000 6000 8000 10000 12000 f'c (psi) Vt es t/V LR FD h<10 in, rho<2.0% h = 10~20 in, rho>2.0% h<10 in, rho>2.0% h = 20~32 in, rho<2.0% h = 10~20 in, rho<2.0% h = 20~32 in, rho>2.0% 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0 2000 4000 6000 8000 10000 12000 f'c (psi) Vt es t/V R 2K h<10 in, rho<2.0% h = 10~20 in, rho>2.0% h<10 in, rho>2.0% h = 20~32 in, rho<2.0% h = 10~20 in, rho<2.0% h = 20~32 in, rho>2.0% 0 0.5 1 1.5 2 2.5 3 0 1 2 3 4 5 6 7 ρl (%) Vt es t/V LR FD d<10 in, f'c<8 ksi d = 10~20 in, f'c>8 ksi d<10 in, f'c>8 ksi d = 20~40 in, f'c<8 ksi d = 10~20 in, f'c<8 ksi d = 20~40 in, f'c>8 ksi Figure 32. Influence of member size on shear strength ratio (Vtest / VR2K) for reinforced concrete members. Figure 33. Influence of member size on shear strength ratio (Vtest / VLRFD) for prestressed concrete members. Figure 34. Influence of member size on shear strength ratio (Vtest / VR2K) for prestressed concrete members. Figure 35. Influence of longitudinal reinforcement ratio on shear strength ratio (Vtest / VLRFD) of reinforced concrete members without shear reinforcement.

continuous members, members for which shear is critical away from the support, and prestressed members cast with HSC. While the experimental test results did not identify any alarming trends, the new aspects of the LRFD specifications in combination with a lack of specific test data to validate this method for HSC members indicates a significant need for experimental research. As discussed in Chapter 1, the LRFD design issues that are particularly important to validate for HSC members include the upper shear design stress limit, the method for calculating the contribution of shear reinforce- ment, the design of end regions by the Sectional Design Model, minimum shear reinforcement requirements, and the capacity/demand on longitudinal tension reinforcement in support regions. To evaluate the significance of these design issues, the decision was made to test HSC prestressed bulb-tee girders that were subjected to uniformly distributed loads. This member type and test configuration were selected because HSC is particularly beneficial for this commonly used product and there is very little existing test data for this type of member. The LRFD provisions that were primarily examined by these tests include • Article 5.8.2.5, Minimum Transverse Reinforcement; • Article 5.8.4.1, General in Interface Shear Transfer—Shear Friction; • Article 5.8.3.3 Nominal Shear Resistance; and • Article 5.8.3.4 Determination of β and θ. Information relevant for the extension of the following provisions was also collected during NCHRP Project 12-56: • Article 5.6.3.3.3, Limiting Compressive Stress In Strut; • Article 5.8.2.8, Design and Detailing Requirements; • Article 5.4.2.7, Tensile Strength; • Article 5.9.5.4,Refined Estimates of Time-Dependent Losses; and • Article 5.11.2, Development of Reinforcement. 2.3 Description of Experimental Research Program This section describes the large-scale testing program on 63-inch deep bulb-tee girders. It presents an overview of the test program, material properties, the fabrication process, 29 0 0.5 1 1.5 2 2.5 3 0 1 2 3 4 5 6 7 ρl (%) Vt es t/V R 2K d<10 in, f'c<8 ksi d = 10~20 in, f'c>8 ksi d<10 in, f'c>8 ksi d = 20~40 in, f'c<8 ksi d = 10~20 in, f'c<8 ksi d = 20~40 in, f'c>8 ksi 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0 2 4 6 8 10 ρl (%) Vt es t/V LR FD h<10 in, f'c<8 ksi h = 10~20 in, f'c>8 kis h<10 in, f'c>8 ksi h = 20~32 in, f'c<8 ksi h = 10~20 in, f'c<8 ksi h = 20~32 in, f'c>8 ksi Figure 36. Influence of longitudinal reinforcement ratio on shear strength ratio (Vtest / VR2K) of reinforced concrete members without shear reinforcement. Figure 37. Influence of longitudinal reinforcement ratio on shear strength ratio (Vtest / VLRFD) of prestressed concrete members without shear reinforcement. 0 2 4 6 8 10 0.0 0.5 1.0 1.5 2.0 2.5 3.0 ρl (%) Vt es t/V R 2K h<10 in, f'c<8 ksi h = 10~20 in, f'c>8 kis h<10 in, f'c>8 ksi h = 20~32 in, f'c<8 ksi h = 10~20 in, f'c<8 ksi h = 20~32 in, f'c>8 ksi Figure 38. Influence of longitudinal reinforcement ratio on shear strength ratio (Vtest / VR2K) of prestressed concrete members without shear reinforcement.

30 the experimental test set-up, and associated shear friction tests. 2.3.1 Overview of Test Program on 63-Inch Deep Bulb-Tee Girders The overall objective of the experimental testing program was to generate the additional test data necessary to increase the limit on the compressive strength of concrete in the shear provisions of the AASHTO LRFD Bridge Design Specifications, specifically including the provisions of the Sectional Design Model (S5.8.3). Based on a review of existing test data, an experimental program was designed to study the overall per- formance of full-scale bridge members as well as to gather the level of detailed experimental test data on the performance of these members that was considered necessary to assess and validate the individual elements of the Sectional Design Model and other LRFD shear provisions. Twenty experiments on ten 63-inch deep and 52-foot long bulb-tee girders were planned. Each simply supported mem- ber was designed to span 50 feet and to carry a uniformly dis- tributed load over the central 44 feet of its length. A 10-inch deep composite slab was cast on each girder. The overall geometry of the test girders is shown in Figure 39. The primary variables in this study were girder concrete strength (ranging from 10 ksi to 18 ksi), maximum shear design stress (700 psi to 2,500 psi), strand anchorage details (straight, unbonded, and draped), and end reinforcement details (bar size, spacing, and level of confinement). The range of vari- ables in the experiments was selected in part to investigate the limits of resistance associated with different modes of shear failure. These modes included yielding and rupture of the shear reinforcement, localized diagonal crushing with stirrup yield, localized diagonal crushing without stirrup yield, shear failure at the interface between the base of the web and the bottom bulb, distributed diagonal crushing, and failure initi- ated by strand slip. Each half of each girder (designated as East [E] and West [W]) was designed to be different so as to obtain two test results from each girder. This action was accomplished by reconstructing and strengthening the half of the girder that failed first and then reloading the girder until the second half failed. Each test girder was designed to satisfy all requirements of the LRFD specifications but with no limit on f c´ used in any of the design calculations. In accordance with the LRFD specifi- cations, the first critical section for shear design was taken to be at 0.5dvcotθ1 from the inside face of the bearing plate above the end support. Based on the shear force for this girder Figure 39. Geometry of 63-inch bulb-tee girders with slabs. 6" 4½ " 3½ " 2" 45 " 42" 10 " Sl ab 10" 2" 3/4" Chamfer 26" 2" 63 " G ird er73 " 6" (a) Geometry of test cross sections (b) Front elevation view 9'' 12''Span Length = 50 ft Total Length = 52 ft mid-span West End of Girder East End of Girder 9'' 12''

section, shear reinforcement was selected to provide adequate shear capacity for that section. Then the same quantity of shear reinforcement was used over a length of dvcotθ1 from that sec- tion and toward the center of the beam. The next section designed for shear was then taken at dvcotθ1 + 0.5dvcotθ2 from the inside face of the support, and the shear reinforcement required to provide the necessary resistance at that section was then used over a length dvcotθ2 from that section and towards the center of the beam. This design approach was repeated for subsequent shear regions as necessary. The effect of following this methodology, given in the LRFD specifications, is that these test beams were theoretically just as likely to fail in shear in the regions of lower shear and higher moment away from the support as they were to fail at sections with higher shear and lower moment adjacent to the support. A summary of the design characteristics for each of the girders, including the number of prestressing strands and the amount of shear rein- forcement, is shown in Table 3. The reinforcing details for each of the 10 girders are presented in Figures 40 and 41. Note that the factor of safety against flexural failure ranged from 1.1 to 1.4. It was expected that those factors would be high enough to ensure a shear failure but not so high to be unrealistic. A com- plete summary of the design of each member is presented in the associated appendix for each girder. 31 Table 3. Summary of experimental research program on 63-inch bulb-tee girders. Number of Strand ( 0.6” ) Shear Reinforcement Tes t Specimen f 'c , (ksi) b w , (in) d p a, (in) Designe d v / f 'c bottom to p p b , (%) f pe , (ksi) v f y e, (psi) Sect.3c Sect.1c Sect.2c G1E 10.0 6 68.50 0.12 32-straight 2 1.70 134.5 389 2-#4 @12” 2-#4 @24” - G1W 10.0 6 68.50 a 0.11 26-straight + 6-draped 2 1.70 b 134.5 389 2-#4 @12” 2-#4 @24” - G2E 10.0 6 67.32 0.18 38-straight 2 2.05 125.9 745 2-#5 @11” 2-#5 @17” 2-#4 @22” G2W 10.0 6 67.32 a 0.17 32-straight + 6-draped 2 2.05 b 125.9 745 2-#5 @11” 2-#5 @17” 2-#4 @22” G3E 14.0 6 67.67 0.12 42-straight 2 2.26 116.4 565 2-#4 @8 ” 2-#4 @12” 2-#4 @24” G3W 14.0 6 67.67 0.12 42-straight 2 2.26 116.4 565 2-#4 @8 ” 2-#4 @12” 2-#4 @24” G4E 14.0 6 67.67 0.17 42-straight 2 2.26 116.4 1113 2-#5 @6 ” 2-#5 @10” 2-#5 @24” G4W 14.0 6 67.67 0.17 42-straight 2 2.26 116.4 1113 2-#5 @6 ” 2-#5 @10” 2-#5 @24” G5E 18.0 6 70.00 0.05 24-straight - 1.25 141.6 169 2-D11 @20” d - - G5W 18.0 6 70.00 0.05 24-straight - 1.25 141.6 140 2-#3 @20” - - G6E 18.0 6 67.67 0.10 42-straight 2 2.26 123.4 557 2-#5 @12” 2-#5 @20” 2-#3 @24” G6W 18.0 6 67.67 a 0.08 42-straight (18 debonded) 2 2.26 b 123.4 557 2-#5 @12” 2-#5 @20” 2-#3 @24” G7E 14.0 6 67.67 0.12 42-straight 2 2.26 116.4 577 2-#4 @8 2-#4 @1 2 2-#4 @2 4 G7W 14.0 6 67.67 0.04 42-straight 2 2.26 116.4 119 2-#4 @8 2-#3 @2 3 - G8E 14.0 6 67.67 0.12 42-straight 2 2.26 116.4 577 2-#4 @8 2-#4 @1 2 2-#4 @2 4 G8W 14.0 6 67.67 0.12 42-straight 2 2.26 116.4 577 2-#4 @8 2-#4 @1 2 2-#4 @2 4 G9E 8.0 6 66.88 0.25 34-straight 2 1.85 131.4 1040 2-#5 @6.5 2-#4 @7.5 2-#4 @2 4 G9W 8.0 6 66.88 a >0.25 26-straight + 8-draped 2 1.85 b 131.4 1690 2-#5 @4 2-#4 @7.5 2-#4 @2 4 G10E 16.0 6 66.88 0.12 34-straight (8-debonded) 2 1.85 138.1 751 2-#5 @9 2-#4 @1 0 2-#4 @2 2 G10W 16.0 6 66.88 a 0.12 26-straight + 8-draped 2 1.85 b 138.1 751 2-#5 @9 2-#4 @1 0 2-#4 @2 2 a) d p : effective depth at mi d-span. b) p : longitudinal reinforcement ratio based on effective depth at mid-span. c) For the location of each section, see drawing of each specim en. d) Two layers of WWR were used (20 20-D11 D11). e) v f y : stirrup strength at the first critical section except G7W (section 2 in flexure-shear region).

32 Section 1: 2-#4@12"2-#5 @2" 26 straight strands + 6 draped strands 32 straight strands midspan 1'Section 2: 2-#4@24" Section 1: 2-#4@12" 2-#3@5"2" 2-#3@5" 2"Holddown Point (5 ft from midspan) 2-#4@12" 2-#4@12" (top only) (top only) (bottom cage reinf.) (bottom cage reinf.) draped strands (West End only) # of top strands: 2 #8 bars at East End only (55" long) W es t E nd Ea st E nd (a) Girder 1 Section 1: 2-#5@11"2-#5 @2" 32 straight strands + 6 draped strands 38 straight strands 1'Section 2: 2-#5@17" 2-#3@5"2" Section 3: 2-#4@22" 2-#4@11" midspan (top only) (top only) (bottom cage reinf.) (bottom cage reinf.) Section 2: 2-#5@17" Section 1: 2-#5@11" 2-#4@11" 2-#3@5"Holddown Point (5 ft from midspan) 2" draped strands (West End only) # of top strands: 2 W es t E nd Ea st En d (b) Girder 2 2-#5 @2" 42 straight bottom strands midspan 2-#3@5"2" 2" 2-#4@8" Section 3: 2-#4@24" 2-#4@16" 2-#3@5" Section 2: 2-#4@12" Section 1: 2-#4@8" (top only) 1' (bottom cage reinf.) (bottom cage reinf.) W es t E nd Ea st En d Section 2: 2-#4@12" 2-#4@8"2-#4@16" (top only) Section 1: 2-#4@8" 2-#4 short bars 2-#3 bars(10' long) # of top strands: 2 Strand Pattern φ3.5" spiral bars at West End only (20" long)φ3.5" spiral bars φ3.5" spiral bars # of bottom strands: 42 Strand Pattern φ3.5" spiral bars at West End only (20" long) # of bottom strands: 42 (c) Girder 3 42 straight bottom strands 2" 2" 2-#5@12"2-#5@6" Section 1: 2-#5@6" Section 2: Section 3: 2-#5@10" 1' midspan 7"- 5/8" Hilti Rod PL¾" x 20" x 30' (top only) (top only) 1' W es t E nd Ea st En d # of top strands: 2 2-#5@24" 2-#5@24" Section 2: 2-#5@10" " Section 1: 2-#5@6" 2-#5@6"2-#5@12" 2-#3@5" (bottom cage reinf.) 2-#3@5" (bottom cage reinf.)2-#5 short bars 2-#3 bars (10' long) 2-#5 @2" (d) Girder 4 Section 1: 2 Layers of 20x20-D11xD11 (WWR) 24 straight bottom strands midspan2-#3@5"2" 2" 2-#5 @2.5" Section 1: 2-#3@20" 2-#3@10" 20" (bottom cage reinf.) (top only) 2-#3@10"(top only) 2-#3@5" (bottom cage reinf.) Total Length = 52 ft # of top strands: 0 # of bottom strands: 24 #7 bars at both ends (55" long) Strand Pattern 1' W es t E nd Ea st E nd (e) Girder 5 # of bottom strands: 32 Strand Pattern #8 bars at East End only (55" long) # of bottom strands: 38 Strand Pattern Figure 40. Summary of reinforcing layout in bulb-tee girders.

33 2-#5 @2" 42 straight bottom strands (16 bottom strands and 2 top strands debonded at West End) midspan2-#3@5"2" 2" 1' 24"2-#5@12" 24" Section 2: 2-#5@20"Section 1: 2-#5@12" Section 3: 2-#3 (bottom cage reinf.) (top only) (bottom cage reinf.) Strand Pattern 2 top strands - 10ft 18 strands debonded at West End only debonded length: 2ft 4ft 6ft 8ft 10ft 2ft 4ft 6ft 8ft 10ft 10ft 9ft 8ft W es t E nd Ea st E nd 20"20" Section 2: 2-#5@20" Section 1: 2-#5@12" 2-#5@12"(top only) 2-#3@5" (f) Girder 6 42 straight bottom strands + 2 straight top strands midspan2" 2" 30"Desinged Failure Region(Transition Zone) # of top strands: 2 Strand Pattern # of bottom strands: 42 2-#5 @2" Section 1: 2-#4@8" 2-#4@8" 2-#4@16" (top only) 2-#3@5" (bottom cage reinf.) Section 2: 2-#3@23" Section 3 2-#4@24" Section 2: 2-#4@12" Section 1: 2-#4@8" 2-#4@8"2-#4@16" (top only) 1' 2-#3@5" (bottom cage reinf.) W es t E nd Ea st E nd (g) Girder 7 42 straight bottom strands + 2 straight top strands midspan2" 2" Section 3: 2-#4@24"Section 1: 2-#4@8" Separation plate (30 degree) # of top strands: 2 # of bottom strands: 42 Strand Pattern 2-#4@8" 2-#4@16" (top only) Section 2: 2-#4@12" Section 1: 2-#4@8"Section 2: 2-#4@12" 2-#4@16" 2-#4@8" (top only) 2-#3@5" (bottom cage reinf.) 2-#3@5" (bottom cage reinf.) 2-#5 @2" 1' Seperation plate W es t E nd Ea st E nd (h) Girder 8 34 bottom strands (10 draped) + 2 straight top strands + (6 - φ1.25'' Dywidag bars) midspan2" 2" Section 2: 2-#4@7.5"Section 1: 2-#5@4" 2-#5 @2" 13" Section 3: 2-#4@24" Section 3: 2-#4@24" 2-#5@6.5"2-#3@7.5" (top only) Section 2: 2-#4@7.5" Section 1: 2-#5@6.5" (top only) 2-#3@7.5" (top only) 1' 2-#3@5" (bottom cage reinf.) 2-#3@5" (bottom cage reinf.) Holddown Point (10 ft from midspan) 4'6" 4' 4'6" 150ksi Dywidag bars (each bar: 35' long)Strands 26' 4'6" 4'6" 4' W es t E nd Ea st E nd draped strands (West End only) Strand Pattern Dywidag bars φ1.25" Dywidag layout (Plan View) Dywidag layout (Plan View) (i) Girder 9 Total Length = 52 ft midspan2" 2" Section 2: 2-#4@10" Section 1: 2-#5@9" 18" Section 3: 2-#4@22" Draping Point 2-#5@9" 34 bottom strands ( 10 draped) + 2 straight top strands + (6 - φ1.25'' Dywidag bars) (top only) Section 3: 2-#4@22" Section 2: 2-#4@10" Section 1: 2-#5@9" 2-#5@9" (top only) 1' 2-#3@5" (bottom cage reinf.) 2-#3@5" (bottom cage reinf.) 2' 150ksi Dywidag bars (each bar: 35' long)Strands 22' 6'6" 6'6"6'6" 6'6" 2' Holddown Point (10 ft from midspan) 2-#5 @2" W es t E nd Ea st E nd draped (West) Dywidag bars 12ft9ft6ft 3ft Debonding (East) ( j) Girder 10 φ1.25" Figure 40. (Continued).

34 As described above, the testing program was designed to investigate the design and behavior of HSC prestressed gird- ers that exhibited different modes of resistance and failure. This was accomplished by designing the girders using a range of concrete strengths and shear demand levels, with different end reinforcement details. In the remainder of this section, a brief summary of the design details for each girder is presented. Girders 1 and 2 were designed using a specified concrete strength of 10 ksi to support shear stresses, vu, at the first critical section (0.5dvcotθ1 from the inside face of the sup- port) of 0.12f c´ (1.2 ksi) and 0.17f c´ (1.7 ksi), respectively. From the standpoint of the LRFD shear design provisions, which permit designs with maximum shear stresses of 0.25f c´, these girders can be said to have been designed to support moderate and moderately high shear design stress levels, respectively. However, from the perspective of the AASHTO Standard Specifications, the designs corre- sponded to shear design stresses of 12 and 17 , which are near and beyond, respectively, the maximum shear design stress permitted by those specifications. Each end of each girder contained the same quantity of shear reinforcement, but different longitudinal reinforcement details. At the first critical section in Girder 1, double- legged #4 bars at 12-inch centers were used (ρvfy = 389 psi). At the first critical section in Girder 2, double-legged #5 bars at 11-inch centers were used (ρvfy = 745 psi). Thirty- four 0.6-inch diameter, seven-wire strands were used in Girder 1, and forty 0.6-inch diameter, seven-wire strands were used in Girder 2. At the east end of both of these mem- bers, the strands were straight and bonded through to the end of the beam, while at the west end of these members, six strands were draped starting 5 feet from mid-span, as shown in Figures 40(a) and (b). The angle of the six draped strands was about 11 degrees for G1W and about 10 degrees f c´f c´ for G2W. Two stressed top strands were provided in each beam to keep the top tensile stresses within the LRFD spec- ified limit. Four #8 deformed bars were placed at the east ends of both girders to provide longitudinal tensile strength at the inside face of the support. Girders 3 and 4 were designed using a specified concrete strength of 14 ksi and were designed for shear stresses of 0.12f c´ (1.68 ksi) and 0.17f c´ (2.38 ksi), respectively, at the first critical shear section from the support. These shear stresses were very large relative to the commonly used maximum shear stress level, which is approximately psi, or 0.93 ksi. Each end of each girder contained the same quantity of shear reinforcement, but different end reinforcement details. At the first critical section in Girder 3, double-legged #4 bars at 8-inch centers were used (ρvfy = 565 psi). At the first critical section in Girder 4, double-legged #5 bars at 6-inch centers were used (ρvfy = 1,113 psi). Forty-two straight strands were used in the bottom bulb, and two tensioned prestressing strands were used in the top flange. The west ends of Girder 3 (G3W) and Girder 4 (G4W) were strengthened to reduce the chance of premature failure due to strand slip, diagonal compressive failure, and horizontal shear slip. This strengthening con- sisted of four 20-inch long spirals wrapped around groups of strands, two #3 horizontal bars on 6-inch centers that extended 10 feet from the end of the member, and four pairs of vertical bars (#4 in Girder 3, #5 in Girder 4) at the inside face of the support. See Figures 40(c) and (d). In Girder 4, a 0.75-inch thick, 20-inch wide, and 30-feet long plate was added under the bottom flange to provide the additional flexural reinforcement that was calculated to be necessary to avoid a flexural failure. Girder 5 was designed with a specified concrete strength of 18 ksi and was reinforced with only slightly more than the minimum required amount of shear reinforcement. 12 12 6 000 929f c´ ,= = #4 R1 BAR #5 R2 BAR 5' 8" 4" 1' 4" #3 R3 BAR #4 R4 BAR #5 R5 BAR Front 5' 7" 4" 5" 2" M IN . #5 R11 BAR 5' 7" 4" #3 R6 BAR #4 R7 BAR #5 R8 BAR Side 7" 7" 2' 7" 2" #4 R9 BAR #5 R10 BAR #5 R12 BAR 6" 5' 7" 6" 5' 7" 6" WWR (D11xD11) 1" 18 " 20 " 2" 18 " 8" Figure 41. Shapes of stirrup reinforcement.

By the LRFD specifications, the minimum required amount of shear reinforcement is ρvfy ≥ 0.0316 = 134 psi. On the east half of Girder 5 (G5E), welded wire reinforcement (WWR) was used. The reinforcement consisted of a grid of D11 × D11 bars (area = #3 bar) on 20-inch centers (ρvfy = 169 psi). On the west half of Girder 5 (G5W), deformed bar reinforcement was used that consisted of double-legged #3 bars on 20-inch centers (ρvfy = 140 psi). See Figure 40(e). Twenty-four strands were located in the bottom bulb, and no prestressing strands were used in the top flange. Four #7 deformed bars (55 inches long) were placed at both ends of Girder 5 to provide longitudinal tensile strength at the inside face of the support. Girder 6 was designed using a specified concrete strength of 18 ksi. While each half of the girder was designed using the same pattern of shear reinforcement, the halves differed in how strands were anchored. The shear reinforcement at the first critical section from either support consisted of double-legged #5 bars on 12-inch centers (ρvfy = 557 psi). At the east end of the girder, all strands were bonded, while in the west end, 18 of the 44 strands were debonded. Figure 40(f) shows the reinforcement details and the debonding pattern. The level of debonding slightly exceeded what would be permitted by the LRFD specifications (S5.11.4.3), but this was considered useful to experimentally evaluate performance at this higher level of debonding. Both ends of Girder 6 failed to meet the requirements for longitudinal reinforcement specified in Section 5.8.3.5 of the LRFD specifications. Girder 7 was designed using a specified concrete strength of 14 ksi. The east end was designed to contain the same shear reinforcement as used in Girder 3. At the west end of the member, only the minimum shear reinforcement was included in Section 2 in an effort to induce a failure away from the end region. See Figure 40(g). This region is desig- nated as a “transition”zone because its behavior is somewhere between that of “web-shear” and “flexure-shear.” In the west transition zone, the shear reinforcement consisted of double- legged #3 bars at 23-inch centers (ρvfy = 119 psi), while in the equivalent region on the east side of the member, double- legged #4 bars at 12-inch centers (ρvfy = 384 psi) were pro- vided. Thus, only 31 percent (119 out of 384 psi) of the required strength of shear reinforcement was provided in the west transition region. The member contained 42 bottom and 2 top straight, fully bonded, and stressed 0.6-inch diameter seven-wire strands. Girder 8 was designed on both halves to contain the same amount and distribution of longitudinal and shear rein- forcement as used in the east halves of Girders 3 and 7. Girder 8 was also designed using a specified concrete strength of 14 ksi. Girder 8 differed from Girders 3 and 7 in the use of a diagonal slip plane and side diaphragms. The diagonal slip f c´ plane was inserted near the first critical section at the west end of the girder and was to eliminate, or at least minimize, the shear stress that could be transferred in the web by “interface shear transfer.” This slip plane was created by inserting into the web two aluminum sheets pressed against each other, as shown in Figure 40(h). At the east end of Girder 8, side diaphragms were cast and posttensioned against the web so as to prevent an end region failure and force the failure into a region where there was a uniform field of diagonal compression. The member contained 42 bottom and two top straight, fully bonded, and stressed 0.6-inch diameter seven-wire strands. Girder 9 was designed using a specified concrete strength of 8 ksi. The east end was designed for a shear stress equal to the maximum LRFD limit of 0.25f c´. The corresponding shear reinforcement consisted of double-legged #5 bars at 6.5-inch centers (ρvfy = 1,040 psi). The design of the west end region differed from that in the east in two ways. Approxi- mately 60 percent more shear reinforcement was provided at the first critical section by using double-legged #5 bars at 4-inch centers (ρvfy = 1,690 psi) and by draping eight of the strands in a splayed manner such that they were close to uni- formly distributed over the height of the web at the west end of the member. See Figure 40(i). Girder 9 contained 34 bot- tom and two top straight and fully bonded 0.6-inch diameter strands. Additionally, six 1.25-inch diameter, high- strength (150 ksi) unstressed posttensioning bars were placed over the majority of the length of the member to pro- vide the additional flexural capacity calculated as necessary to produce a shear failure. Girder 10 was designed using a specified concrete strength of 16 ksi. It was designed for a shear stress ratio (v/f c´) of 0.12. It contained the same quantity of shear reinforcement in both halves of the member. At the first critical section, this rein- forcement consisted of double-legged #5 bars on 9-inch cen- ters (ρvfy = 751 psi). Thirty-four bottom and two top 0.6-inch diameter strands were used. At the east end, eight strands were debonded, while at the west end, eight strands were draped and splayed out over the depth of the web, as was done at the west end of Girder 9. See Figure 40(j). Six 1.25-inch diameter high- strength (150-ksi) unstressed bars were also placed in the bottom flange. 2.3.2 Material Properties A variety of material tests were conducted to measure the mechanical properties of the concrete and the steel reinforcement. This section provides a summary of these properties. The concrete mix designs are presented in Table 4, the measured concrete strength properties at the time of the test are listed in Table 5, the concrete compressive stress- strain responses are plotted in Figure 42, and the strength 35

36 properties of the reinforcement are summarized in Table 6. Additional information about the materials used in this study follows. Concrete The concrete mix designs, as presented in Table 4, were devel- oped at Wiss, Janney, Elstner Associates, Inc. (WJE), using aggregate supplies available from the precaster, Prestress Engineering Cooperation (PEC), and a Traprock aggregate imported from Wisconsin. After several batch plant trials, the mix designs were adjusted to obtain the target concrete strengths. Target strengths were as listed in Table 3. With the exception of Girders 6 and 10, the concrete strengths achieved were close to or in excess of the target strengths. The shortfalls in strengths were considered to be associated with difficulties in very accurately measuring the moisture content in the aggre- gates. With these very dry mixes, a small error in moisture content can have a significant effect on the water-cement ratio and thus the final compressive strength. Property G1 & G2 G3 & G4 G5 & G6 G7 & G8 G9 G10 Type I Cement Weight (lbs/yd3) - - 1,050 1,050 Type III Cement Weight (lbs/yd3) 750 1,030 - 1,030 700 Fly Ash Weight (lbs/yd3) - - - Silica Fume Weight (lbs/yd3) - 125 150 125 150 Water Weight (lbs/yd3) 210 300 264 300 280 264 Sand Weight (lbs/yd3) 1,328 777 858 777 1,180 858 Coarse Aggregate (3/4” max) Weight (lbs/yd3) 1,880 - - - 1,786 Coarse Aggregate (1/2” max) Weight (lbs/yd3) - 1,820 - 1,820 Coarse Aggregate (3/8” max) Weight (lbs/yd3) - - 1,820 - 1,820 Retarder (100XR) Weight - - 4 oz/ 100 lbs 20 oz/ yard 4 oz/100 lbs Super Plasticizer (MB 300FC) Weight - as needed 15-18 oz/100 lbs as needed 175 oz/yard 15-18 oz/ 100 lbs water/cementitious mat. ratio 0.28 0.24 0.25 0.24 0.40 0.25 Note: 1 in = 25.4 mm, 1 ksi = 6.895 MPa, 1 lb/yd3 = 432 kg/m3. Girder Deck Specimen Strength(ksi) Strain* ( 610 ) Split Tensile (psi) Modulus of Rupture (psi) Strength (ksi) Girder 1 12.1 3,000 867 991 4.5 Girder 2 12.6 2,600 811 991 8.6 Girder 3 15.9 3,300 766 1,090 3.6 Girder 4 16.3 3,400 766 1,090 6.3 Girder 5 17.8 3,500 894 1,190 6.1 Girder 6 12.7 2,800 823 1,190 9.2 Girder 7 12.5 3,200 706 720 4.5 Girder 8 13.3 3,200 706 720 7.0 Girder 9 9.6 2,400 686 1,080 6.0 Girder 10 10.6 2,600 765 1,180 5.4 *Strain value at peak stress. Table 4. Summary of concrete mix designs. Table 5. Summary of concrete strength properties.

The concrete compressive strengths finally achieved are shown in Table 5. These strength values are used in all subsequent calculations, including the evaluation of the LRFD-calculated shear design strength of the girders. This distribution of delivered strengths, coupled with the exper- imental measurements presented in the remaining subsec- tions of Chapter 2 and other available test data, were considered to be sufficient to support the proposed changes to design specifications that are presented in Chapter 3. The volume of concrete in each girder was approximately 10 cubic yards. Because the precaster, PEC, used a 2-cubic- yard pan mixer, six batches were required to cast each girder and the associated material test samples. Two girders were often cast one after another using the same mix design. Deck slabs were cast after the girders were delivered to the New- mark Laboratory at the University of Illinois using concrete with a 5-ksi design strength. As shown in Table 5, with the exception of Girders 1, 3, and 7, this strength was also 37 0 2000 4000 6000 8000 10000 12000 14000 16000 18000 0 0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004 Strain Co m pr es siv e St re ss (p si) Girder 1 Girder 2 Girder 3 Girder 4 Girder 5 Girder 6 Girder 7 Girder 8 Girder 9 Girder 10 Girder 10 Girder 9 Girder 1 Girder 3 Girder 5 Girder 4 Girder 6 Girder 7 Girder 8 Girder 2 (a) Transverse Reinforcement Specimen G1 G2 G3 G4 G5 Bar #4 #5 #4 #5 #4 #5 #4 #5 #3 WWR Nominal Area (in2) 0.20 0.31 0.20 0.31 0.20 0.31 0.20 0.31 0.11 0.11 Yield Strength, fy (ksi) 70.0 79.3 70.0 79.3 67.8 64.6 67.8 64.6 76.5 92.2 Tensile Strength, fu (ksi) 109.0 119.0 109.0 119.0 106.1 101.8 106.1 101.8 112.5 106.1 Specimen G6 G7 G8 G9 G10 Bar #5 #3 #4 #4 #5 #4 #5 #4 #5 Nominal Area (in2) 0.31 0.11 0.20 0.20 0.31 0.20 0.31 0.20 0.31 Yield Strength, fy (ksi) 64.7 74.5 69.2 69.2 68.4 67.9 65.4 67.9 65.4 Tensile Strength, fu (ksi) 102.0 109.5 107.8 107.8 107.4 (b) Prestressing Strands Beam Girder 1 Girder 2 Girder 3 Girder 4 Girder 5 Effective Stress, fpe (ksi) 159.7 150.2 154.9 153.7 174.7 Prestressing Loss* (%) 21.1 25.8 23.5 24.1 13.7 Beam Girder 6 Girder 7 Girder 8 Girder 9 Girder 10 Effective Stress, fpe (ksi) 167.6 167.0 158.5 166.5 173.7 Prestressing Loss* (%) 17.2 17.5 21.7 17.8 14.2 *The prestressing loss was calculated based on measurements at the time of testing. Table 6. Summary of steel reinforcement properties. Figure 42. Concrete compressive stress-strain relationships.

38 achieved. Since these girders failed well before their flexural capacity was reached, the lower-than-specified strength for the deck slabs was considered to have no significant effect on the project outcome. Compression Strength Tests: From each of the six con- crete batches used in casting a single girder, seven 4-inch diameter cylinders were cast. The initial cylinder tests were conducted using cylinder testing machines available at WJE and the University of Illinois and were made in accordance with ASTM C 39. However, there were larger-than-expected variations in the cylinder strengths, and some of the cylinders for the very high-strength mix failed under lower stresses than seemed to be realistic. The variations were considered to be due to the sensitivity of the test results to the cylinder end preparation methods, as has been the experience of produc- ers of very high-strength concretes. To address this difficulty, Prairie Materials Group out of Chicago was retained to pre- pare the cylinder ends and test many of the very high-strength concretes. In parallel, end preparation techniques were improved at the University of Illinois by using a rock saw to cut thin, (3/16-inch thick) strips off the ends of cylinders per- pendicular to their axes. This enabled the measuring of cylin- der strengths in excess of 16 ksi in the University of Illinois testing machines. Tensile Strength Tests: The results of the split cylinder and modulus of rupture (MOR) tests are also reported in Table 5. The MOR tests were made under third-point loading and using an 18-inch span. As shown in Figure 43, failure cracks in the MOR tests passed through the aggregates, and the resultant surfaces were relatively smooth. Reinforcement Seven-wire, low-relaxation prestressing strands with a diameter of 0.6 inch, an area of 0.218 square inch, and a specified ultimate tensile strength of 270 ksi were used for all girders. The number of strands and the strand pattern for each beam is presented in Figure 40. In the original designs, the anticipated prestressing loss was calculated in accordance with the provisions of the LRFD specifications. Anticipated losses ranged from 39 percent to 42 percent depending on the number of strands and the concrete compressive strength. The actual prestressing loss at the time of testing was determined from displacement measurements of the change in distance between targets mounted on the bottom bulb of the girder at the level of the centroid of the pre- stressing steel. The measured prestressing losses ranged from about 15 percent to 25 percent, and these measured values were used in calculating nominal capacities of the girders. The displacement targets also permitted determination of the transfer lengths for the strands. Detailed results are pre- sented in the Appendices. All transverse reinforcements were ASTM A 615 Grade 60 deformed steel bars except for the deformed welded wire fab- ric used as shear reinforcement in the east end of Girder 5. The welded wire reinforcement conformed to ASTM A 496. The structural properties of the transverse reinforcement are listed in Table 6, and the shapes of the various transverse reinforcements used in the girders are shown in Figure 41. The yield strength of the welded wire reinforcement was determined in accordance with ASTM A 497 requirements where the yield strength is measured at a strain of 0.5 per- cent. All shear reinforcements were double legged, with a loop extending out of the top flange of the girder to provide horizontal shear resistance between the girder and the deck slab. Additional short double-legged stirrups were placed in the end zone of each girder to provide the additional hori- zontal shear resistance required by LRFD specifications for end regions of the girder-to-slab interface. All girders also had between four and six No. 5 stirrups at each end to con- trol spalling stresses caused by release of the prestressing strands and to provide confinement for the concrete over the support per LRFD requirements. Deformed longitudinal bars were used in the top flange of the girders and deck slab. No. 7, No. 8, or No. 9 bars were used in the top flange of the girders to control tension cracks due to prestressing. No. 6 bars were used as com- pression reinforcement in the deck slab. In all girders, con- finement reinforcement was also placed around the prestressing steel in the bottom flange for a distance of 100 inches from each end of each girder. This confinement rein- forcement consisted of No. 3 bars placed at 6-inch spacing. In Girders 9 and 10, large 1.25-inch diameter high-strength deformed bars were used to provide additional flexural capacity. The locations for all reinforcements are shown in Figure 40.Figure 43. Tested specimens.

2.3.3 Fabrication of Test Girders All test beams were fabricated at Prestress Engineering Coop- eration (PEC) in Blackstone, Illinois. That plant was located about 100 miles from the University of Illinois.After the stirrup and confinement cage reinforcements were fabricated at PEC, selected bars were brought to the University of Illinois labora- tory, electrical resistance strain gages were attached to the cages, and then the reinforcements were delivered back to PEC for insertion into the girders. In the prestressing operation, a load cell was used to measure the prestressing force in the strands. After the strands were pulled, University of Illinois researchers attached electrical resistance strain gages onto selected strands near the ends of the girders. The reinforcement cage and one side of the form were then placed in their final position. Prepa- ration of the reinforcement cage was completed outside the stressing bed, and then, once completed and checked, the rein- forcement cage was moved into the bed and anchored to one side of the form. See Figure 44. After a final check for all rein- forcement details, pictures were taken and the other side of the steel form was put into place. Each girder required approximately 10 cubic yards of con- crete that was prepared into 6 batches. Four vibrators (two form vibrators and two immersion vibrators) were used to consolidate the concrete as it was placed. After casting, the top surface was intentionally roughened to satisfy the require- ments of the LRFD specifications. See Figure 45. After casting and the initial set, a soaker hose was placed on top of the girder and a tarp was placed over the girder to prevent excess drying of the concrete. After removal of the formwork and before release of the strands, aluminum targets were placed on the end anchorage zone and in the middle of each girder for the measurement of the effects of strand release using a Whittemore gage. The strands were released a few days after casting the gird- ers and when the measured concrete compressive strengths were at about the required level for strand release. The strain in the end reinforcement, strands, and the surface deformation of the bottom flange at release were measured. The 4-inch by 8-inch cylinders, the modulus of rupture beams, the fracture beams, and the shear friction specimens were cast alongside the girders, as shown in Figure 46. These specimens were kept with the test girders to ensure similar conditions for curing. The girders were transported by truck from PEC to New- mark Laboratory, as shown in Figure 47. All material test 39 Figure 44. Placement of reinforcement. Figure 46. Material test specimens. Figure 45. Roughening of surface of top flanges.

40 specimens were delivered to the Newmark Laboratory at the same time. As shown in Figure 48, a 10-inch deep and 42-inch wide deck slab with a design concrete compressive strength of 5,000 psi was then cast on the top of the girder. A detachable and reusable formwork were created and used for casting the deck slab. 2.3.4 Test Set-Up A reaction structure, shown in Figures 49 and 50, was cre- ated to support the ends of the girders, and a loading from the jacks was placed on top of the girder of up to 60 kips per linear foot. The reaction structure consisted of six W12 × 65 steel columns fastened to the Newmark Laboratory strong floor at regular 9-foot intervals along the length of each side of the test specimen. The overall height of the columns was 15 feet 4 inches.Six pairs of W18 × 119 steel sections were used as trans- verse beams to span across the test specimen between each pair of columns. A W27 × 146 section 50 feet long served as a lon- gitudinal reaction beam that resisted the loading from the indi- vidual hydraulic jacks. To avoid possible cracking of the strong floor in the Newmark Laboratory due to the end reaction forces that could exceed 1 million pounds, abutments at either end of the test specimen were designed as simply supported beams that distributed the loading directly to the top of the web walls located under the top flange of the strong floor. Each abutment was made from two W27 × 146 steel sec- tions 14 feet long. The steel sections of the abutments were Figure 47. Transportation of test girders to Newmark Laboratory. Figure 48. Casting of top deck.

welded together at the flanges to make a box section. An additional 1-inch thick steel plate was added to the top and bottom flange in the middle portion of the section to increase the moment capacity near mid-span. The insides of the box sections were reinforced in flexure and shear and then filled with concrete to increase shear capacity and pro- vide lateral and torsional rigidity. The abutments were designed to support a 1,500-kip load at mid-span that caused a 4,500 kip-ft bending moment. The transverse beams spanning between the columns across the test speci- men were 9 feet long and designed as simply supported to resist 550 kips of load and a 1,200 kip-ft bending moment at mid-span. A combination of twenty-two 100-ton, single-acting hydraulic jacks and twenty-two 60-ton, double-acting hydraulic jacks were used for imposing the uniformly dis- tributed load, as shown in Figure 51. A linear variable dis- placement transducer (LVDT) was attached to the centermost double-acting jack to measure the extension of its piston. During the test, a servo controller was used to reg- ulate the pressures that controlled the movement of this cen- ter point jack as measured by the LVDT. Through a series of 12 manifolds, the same high and low pressures that were used to control the force in the centermost double-acting jack were then distributed to all double-acting jacks. The actions of the single-acting jacks were controlled by a single pressure value that was regulated by hand so as to keep the force in those jacks close to a selected fixed proportion of the total load. With this system, a center point displacement con- trolled test was conducted in which a uniformly distributed load was achieved by having each pair of alternating single- and double-acting jacks apply the same force. The average jack spacing was one jack per foot, with 22 jacks on each side of mid-span. For the majority of the tests, this meant that a uniformly distributed load was applied over the central 44 feet of the length of the girder. For a 41 Figure 49. Front elevation view of reaction structure. Figure 50. Test set-up. Plow Phigh Dp Oil Displacement-Control PinOil Load-ControlO Lo ad w Displacement Displacement-Control Load-Control Midspan Figure 51. Load control system. W18 x119 W12 x 65 W27 x146 Support Plates 2-W27 x146 (welded) Strong Floor Concrete Filling Loading Jacks West End of Test Beam Test Beam East End of Test Beam Span Length = 50 ft Total Length = 52 ft 4' 4' 12''12'' 9''

42 variety of different reasons, ranging from concern over the effectiveness of the repair to the first failed region of the girder, to concern over the possibility of a flexural failure, the pattern of loading was modified on a several occasions. Figure 52 summarizes the actual patterns of distributed loading used for each girder. 2.3.5 Instrumentation Traditional and advanced measurement systems were used to gather detailed data on the displacement, straining, and cracking of the test girders. This data was subsequently used to assess the overall stiffness of the test girders, the contribu- tion of the stirrups to shear resistance, and the behavior of the complicated end regions of the test girders. The types of measurement systems used during the experiments and the location of these measurements are now described. Linear Variable Displacement Transducer (LVDT) Measurements Vertical deflections were measured using LVDTs at five loca- tions, including mid-span, quarter points, and immediately inside of the face of the supports. These locations are labeled as V1 through V5 in Figure 53. Longitudinal deformations of the top flange and bottom flange at mid-span, and of the bot- tom bulb at both ends of girder, were measured. Those loca- tions are shown as H1 through H4 in Figure 53. These measurements were taken to calculate the curvature at mid- span, the development of flexural cracking, and the loss in pre- stressing or the development of cracking at member ends. Web-shear strains were measured at multiple locations using displacement transducers, as also shown in Figure 53. In most cases, three LVDTs (ED1, 2, 3 or WD1, 2, 3) were located at 3 feet from the support, and another three LVDTs (ED4, 5, 6 or WD4, 5, 6) were located at 6 feet from the support. Initial shear cracking was expected at approximately 3 feet from the sup- port, and the critical section for shear design was about 6 feet from the support. Finally, LVDTs were mounted on end strands to monitor the slip between individual strands and the end of the test girder. See S1 and S2 in Figure 53. Strain Gages on Reinforcement Electrical resistance strain gages were used to measure strains in the shear reinforcement, in the end bursting rein- forcement, and in the reinforcement of the bottom bulb con- finement cages and a few selected prestressing strands. Because the test beams were designed so that they were as likely to fail in shear in regions of low shear and high moment as they were to fail in regions of high shear and low moment, a large number of stirrups were gauged over the entire length of the girder. In each girder, four strain gages were placed on each of 16 to 20 stirrups. The density of this grid of gages was selected deliberately so that a reasonably accurate measure- ment was made of the contribution of the shear reinforce- ment to the shear capacity over the entire length of the member. Strain gages were also placed on the bursting rein- forcement located at the ends of the girders to assess the demands placed on this special purpose reinforcement. The locations of the strain gages on the vertical transverse rein- forcement for each girder are given in Figure 54. Strain gages were also placed on deformed bar longitudinal reinforcement that was used at the end of the members to satisfyFigure 52. Typical loading pattern. Span Length = 50 ft Total Length = 52 ft a b c w Loading Pattern Load Specimen a (ft) b (ft) c (ft) w (kips/ft) G1E 3.0 44.0 3.0 26.03 G1W 3.0 44.0 3.0 30.09 G2E 3.0 44.0 3.0 33.79 G2W 3.0 44.0 3.0 38.74 G3E 3.0 44.0 3.0 35.68 G3W 3.0 44.0 3.0 38.82 G4E 3.0 44.0 3.0 42.74 G4W 3.0 44.0 3.0 42.74 G5E 3.0 44.0 3.0 23.70 G5W 3.0 44.0 3.0 19.90 G6E 15.0 32.0 3.0 38.32 G6W 3.0 44.0 3.0 27.85 G7E 3.0 44.0 3.0 33.47 G7W 11.0 28.0 11.0 44.76 G8E 13.0 28.0 9.0 43.73 G8W 3.0 34.0 13.0 32.70 G9E 3.0 44.0 3.0 32.80 G9W 3.0 4.0 26.0 10.0 21.0 36.0 37.19 22.32 G10E 3.0 44.0 3.0 33.93 G10W 3.0 43.0 4.0 42.85

43 Figure 53. Displacement transducers (LVDTs). V1V2V3V4V5 S2 H3 S1 ED1 ED2 ED3 H2 H4 WD4 WD5 WD6WD3 WD2 WD1 H1 27"Longitudinal deformation 21" 27"285" 285" 136½" 154½" 154½" 136½" 21"Vertical displacement 70" 175"Web deformation 36" 343" 33 " 4" Ea st (a) Girder 1 V1V2V3V4V5 S2 H3 S1 ED1 ED2 ED3 H2 H4 WD4 WD5 WD6WD3 WD2 WD1 H1 27"Longitudinal deformation 21" 27"285" 285" 136½" 154½" 154½" 136½" 21"Vertical displacement 70" 160"Web deformation 50" 321" 33 " 4" 2½ " Ea st (b) Girder 2 V1V2V3V4V5 S2 H3 S1 ED1 ED2 ED3 H2 H4 WD4 WD5 WD6WD3 WD2 WD1 H1 27"Longitudinal deformation 21" 27"285" 285" 136½" 154½" 154½" 136½" 21"Vertical displacement 48" 48"Web deformation 36" 456" 33 " 4" 2½ " Ea stED6ED5 ED4 36" (c) Girder 3, Girder 4, Girder 5, and Girder 6, Girder 9 and Girder 10 V1V2V3V4V5 S2 H3 S1 ED1 ED2 ED3 H2 H4 WD4 WD5 WD6WD3 WD2 WD1 H1 27"Longitudinal deformation 21" 27"285" 285" 136½" 154½" 154½" 136½" 21"Vertical displacement 175" 48"Web deformation 36" 329" 33 " 4" 2½ " Ea stED6 ED5 ED4 36" (d) Girder 7 V1V2V3V4V5 S2 H3 S1 ED1 ED2 ED3 H2 H4 WD3 WD2 WD1 H1 27"Longitudinal deformation 21" 27"285" 285" 136½" 154½" 154½" 136½" 21"Vertical displacement 48" 48"Web deformation 492" 33 " 4" 2½ " Ea stED6ED5 ED4 36" (e) Girder 8 2½ "

44 3 2 1 4 3 2 1 midspan 4 Girder 6 midspan 4 3 2 1 4 3 2 1 Girder 7 Figure 54. Stirrup strain gages. 4 3 2 1 4 3 2 1 midspan Girder 1 4 3 2 1 4 3 2 1 midspan Girder 2 4 3 2 1 4 3 2 1 midspan Girder 3 4 3 2 1 3 2 1 midspan 4 Girder 4 midspan 4 3 2 1 4 3 2 1 Girder 5

the longitudinal reinforcement capacity requirements of the LRFD specifications.Four strain gages were used at the east ends of Girders 1 and 2, in which four No. 8 deformed bars were required. Six strain gages were used at the west end of Girders 3 and 4, while four strain gages were used on the deformed bar longitudinal reinforcement used in Girder 5. The locations for all longitudinal gages are provided in the appendices. Confinement reinforcement was used, as required by the LRFD specifications, around the prestressing steel in the bottom flange for 100 inches from the end of each girder. The locations of the strain gages on the confinement re- inforcement are shown in Figure 55. Four strain gages (Gages 1 through 4) were attached to longitudinal bars, and six strain gages (Gages 5 through 10) were placed on trans- verse bars. The change in strain in the longitudinal rein- forcement was used to assess the loss in prestressing force due to the demands of shear and flexure, while the strain in the transverse reinforcement was used to evaluate the mag- nitude of the confinement pressure on the prestressing strands. 45 midspan 4 3 2 1 4 3 2 1 Girder 8 midspan 4 3 2 1 4 3 2 1 Girder 9 midspan 4 3 2 1 4 3 2 1 Girder 10 Figure 54. (Continued). 6 " 24" 5" 20 spa cings@ 5"=100 " 5 " 1 2 3 4 5 6 7 8 9 10 Figure 55. Strain gages on confinement reinforcement.

46 Strain Gages on Concrete Beginning with Girder 5, 2-inch long concrete surface strain gages were used on the ends of the girders to measure the diagonal compressive strain in the web and the loss in pre- compression strain in the bottom bulb. The number of gages used on Girders 5 to 10 ranged from 22 to 58. Figure 56 shows the location of the strain gages used on the ends of Girder 4. The locations of the concrete strain gages for each girder are presented in the appendices. The strain gage locations were selected based on the crack patterns of previously tested gird- ers. However, because crack patterns were not exactly the same from girder to girder, it was occasionally necessary to attach additional strain gages in better positions relative to the shear cracking when crack patterns were determined. It should be noted that the concrete strains obtained from these gages did not include initial strains due to prestressing. Whittemore Gage Readings A portable displacement measurement system known as a Whittemore gage was used to measure changes in deforma- tion along the length of the bottom bulb. See Figure 57. x 1 2 3 4 5 6 7 8 9 y (a) Whittemore gage targets (b) Whittemore gage reading Figure 56. Concrete surface strain gages. Figure 57. Whittemore gage and transfer length measurements.

Displacement measurements over 10-inch gage lengths were determined using targets glued to the girder at 5-inch centers along the bottom bulb at both ends and in the middle of the girder. These targets were attached after the forms were removed and before strands were detensioned. Measure- ments were taken before strand release, after strand release, at periodic intervals, and before testing to assess transfer length, prestressing loss, and the distribution of strains prior to testing. Krypton’s RODYM and K-600 Dynamic Measurement Machine The Krypton Dynamic Measurement Machine is able to measure the position of up to 256 small (8-gram and 5/16- inch diameter) light emitting diode (LED) markers in three- dimensional space to an accuracy of ±0.0008 inch (±0.02 millimeter) at a sampling rate of up to 3,000 individual read- ings per second. The Krypton system consists of a portable housing containing three 2,048-CCD (charge-coupled device) line-element cameras. The camera system has an effective measurement volume of 600 cubic feet. Figure 58 shows a grid of LED targets on the surface of the test beam and the K-600 camera system. The data acquisition system reports the time-stamped position of each marker in three- dimensional space to a resolution of 0.00004 inch (0.001 mil- limeter). Measurements were made using the Krypton system to assess the directions of principal straining in the members, the contributions of shear reinforcement, the magnitude of the diagonal compressive straining in the web, and the over- all distribution of straining and deformations in the complex end regions of the girders. Zurich Gage Measurement System The Zurich gage measurement system is analogous to an electronic Whittemore or Demac gage. As illustrated in Figures 59 and 60, the Zurich gage system consists of an LVDT rigidly clamped to, and within, an aluminum channel. The LVDT plunger is attached to a linear bearing. There are two measurement legs that terminate with tapered ends into which a spherical ball is mounted. One leg extends from the aluminum channel and the other leg extends from the linear bearing. The distance between these legs when the linear bearing is at mid-stroke is 10 inches, and the LVDT has a range of ±0.5 inch. There is a second Zurich gage measure- ment device in which the legs are spaced at inches when the linear bearing is at mid-stroke. These two devices were used to measure the horizontal, vertical, and diagonal distances between targets on a 10-inch grid over the surface of the web of the test girder at selected load stages. See Figure 61. Because the resolution of this system was not suf- ficient to measure small strains and because it took about 14 14 10 2. ( ) 47 (a) Krypton camera (b) Krypton LED markers 10" (254 mm) Housing for Portable Transducer Fixed Leg SlidingLeg LVDT Target To DAQ System Test Specimen LVDT ROD Target DAQ = data acquisition system. Figure 58. Krypton K-600 Dynamic Measurement Machine. Figure 59. Components of a Zurich gage.

48 90 minutes for a full set of readings, at some load stages only a partial set of readings was taken. 2.3.6 Test Procedure A combination of twenty-two 100-ton, single-acting hydraulic jacks and twenty-two 60-ton, double-acting hydraulic jacks were used for imposing the uniformly dis- tributed load. Using the laboratory’s 3,000-psi pump, the twenty-two 100-ton jacks could exert a total loading of 1,320 kips, which corresponded to a shear stress of 1,884 psi at the inside face of the support. Using the same pump, the twenty- two 60-ton jacks could be used to exert a total loading of 792 kips, which corresponded to a shear stress of 1,130 psi. In combination, a total shear stress of 3,014 psi could be applied to the girder at the inside face of the support. This cor- responds to a maximum load of 48 kips per foot over the 44-foot length of the distributed loading. After the girder was positioned underneath the reaction frame and the deck was cast, a series of loading plates were placed on top of the girder. The hydraulic jacks were lowered into position, and a 60-ton load cell was placed between the piston of each jack and the steel reaction beam. Next, the girder was painted using a whitewash, and a 10-inch square grid was drawn on the web. The instrumentation was then attached, including concrete surface strain gages, LVDTs, Figure 60. Zurich gage measurements. Figure 61. Location of LED markers and Zurich gage targets. 9" 12" Span Length = 50 ft Total Length = 52 ft C L 27" 31 spacings @ 10" 2" 25 spacings @ 5" Krypton Markers Zurich Gage Targets 8 sp ac ing @ 5" 4 sp ac in g@ 10 " 2½ " 2½ "17 ½ " South North Krypton Markers Zurich Gage Targets Krypton Markers Zurich Gage Targets Kr yp to n M ar ke rs Zu ric h G ag e T a rg et s 10 ½ "

Krypton’s LED markers, and Zurich gage targets. All instru- mentation devices and strain gage wires were then connected to the signal conditioning equipment. Four different data acquisition systems were used in the experiments. One National Instruments (NI) signal condi- tioning and data acquisition system was used to record the data from the strain gages on the reinforcement, the data from the LVDTs, and the data from the load cells. With that system, a complete set of readings was taken every second during testing. A second NI system was used to record the concrete surface strain gage measurements in which readings were taken as quickly as 100 times per second as failure approached. A third NI system was used to record the Zurich gage readings. One of these three NI data acquisition systems and a load controller is shown in Figure 62. The Krypton camera measurements were recorded by dedicated software and data acquisition programs. A pretest was completed 1 or 2 days ahead of the actual loading to check for hydraulic leaks in the loading system. This check was critical because the system had more than 200 points where leakage was possible. Prior to the first day of testing, all initial measurement readings were zeroed, and shunt-calibrations were performed on the strain gages. In addition, two full sets of Zurich readings were taken, with each involving the taking and recording of 1,058 indi- vidual readings. This activity required a three-person crew, with one person at the data acquisition computer and each of the other two holding one of the two Zurich gages (10 and 14.14 inches). All three people were connected on wire- less headsets. On the day of testing, the loading was increased until first the diagonal cracking, “load stage 1,” occurred. At that point, the displacement at mid-span was held constant, cracks were marked, and a complete set of measurements was taken. Sub- sequent “load stages” were taken at points of significant addi- tional cracking, when local damage was observed, or after there had been a significant increase in applied load or deformation. During each of these load stages, Zurich gage readings were taken, cracks were marked, crack widths were measured, and pictures were taken.After one end of the girder failed, the load- ing was removed. The failed regions were then repaired by removing all loose concrete from the failed region, adding rein- forcement on either side of the web, casting a 10- to 15-foot long repair on either side of the web using self-compacting concrete, and then vertically posttensioning this region of the girder using posttensioning bars placed 2 feet apart on centers. See Figure 63.After the girder was repaired, it could be reloaded until failure occurred at the other end. 49 Figure 62. Data acquisition system. (a) Failed end region before repair (b) Failed end region after repair Figure 63. Repair of failed end region.

50 2.3.7 Data Processing and Reduction After testing on an individual girder was completed, the data was postprocessed and reduced using a combination of commercial and locally written tools. The volume of test data was very large. Over 300 MB of numerical data and 700 MB of pictures and video were acquired for each girder. The multiplicity of measurement sources increased the difficulty of data reduction, synchro- nization, and review. To better understand the test data, an integral visualization system named GrdVis was developed that enabled the results from multiple data sources to be displayed simultaneously and provided a convenient and complete environment for data analysis. Figure 64 shows a screen shot of the user interface. GrdVis has three windows: a visualization window, a data window, and an output window. The visualization window displays the structural elements and instrumentation, the data window displays data curves, and the output window shows numerical results. GrdVis also provides many operations for exploring, manipulating, and analyzing the mixed data. Data collected from the Krypton system was reported as three-dimensional position data versus time for each LED target placed on the specimen. This information was also very dense, with files consisting up to 298 columns of data with more than 40,000 rows. A program called DIAdem, developed by NI, was used to extract useful information from the raw Krypton displacement data. Scripts were created in DIAdem to calculate the strain between targets and to present various strain distributions along the length or height of the girder. These strain distributions were then imported into the GrdVis software. In this data processing and reduction, it was necessary to synchronize the time of acquisition of the data from the mul- tiple measurement sources as well as develop a protocol for what assumptions to employ in merging together data from multiple days of testing. The latter issue was important because there was likely some shift in the strains and defor- mations of the girder from the time that failure occurred at one end of the girder to after the repair was completed and the girder was reloaded. The procedure used in data merging is described below. The first step of data merging was to establish a point of zero deformation and strain at the start of a test.When a test spanned over multiple days, values were checked and adjusted as neces- sary so that the original values from the start of testing were Figure 64. Girder visualization program.

used. After data merging, a data cleaning operation was applied to improve the quality of data, such as detecting and removing errors and inconsistencies. Data reduction was the last step, in which the number of data points in the array was reduced to around 2,000 per channel. This number was sufficient to produce an accurate and detailed envelope (unloading and reloading parts removed) for each instrument reading. A semi- automatic approach was taken to ensure that the reduced data sufficiently captured all relevant aspects of girder behavior. The procedures employed above are considered to provide the best possible documentation of the response of the test girders. 2.3.8 Shear Friction Experiments As discussed in Chapter 1, one of the primary motivations for this project was a concern that the smooth cracks that occur in HSC could lead to a breakdown in the aggregate interlock, or interface shear transfer mechanism, and subse- quently lower shear strengths. This was considered to be of particular concern for shear design provisions derived from the MCFT, because that procedure assumes that interface shear transfer is the primary source of the concrete contribu- tion to shear resistance. While the large-scale girder tests pro- vided an overall evaluation of the performance of the LRFD specifications, it was also considered useful to directly evalu- ate the interface shear transfer mechanisms for the materials and reinforcement arrangements used in the experimental testing program. Figure 65 illustrates the idealized segment of the girder for which the interface shear friction resistance was evaluated and the reinforcement details for a typical test spec- imen used to represent that segment. The complete interface shear transfer testing program and results are presented in Section 2.9. 51 Figure 65. Shear friction test. (a) Segment of web idealized in shear friction experiments (b) Reinforcement in a shear friction experiment dvcotθ 9" D V θ

52 2.4 Measured and Code-Calculated Strengths Plus Modes of Failure Section 2.4.1 presents the measured capacities of the test girders and compares these capacities with the shear capaci- ties calculated using the LRFD Sectional Design Model. From this comparison, observations are drawn about the extension of these provisions to high-strength structural concrete. Section 2.4.2 compares the measured capacities with those calculated by other codes of practice, including the AASHTO Standard Specifications, the new provisions in the Canadian Standards Association, and the proposed LRFD Simplified Design Provisions that were developed in NCHRP Project 12-61 and that are described in NCHRP Report 549. Section 2.4.3 examines the impact of using the staggered shear design methods on the safety of the Sectional Design Model. Section 2.4.4 discusses the modes of failure and conditions at the point of failure for the test girders and examines the significance of these observations for use of the Sectional Design Model. Finally, Section 2.4.5 presents the overall load-deformation response of the test girders. 2.4.1 Measured Strengths and Comparisons with LRFD Sectional Design Model As discussed in Section 2.3, the objective of the test series was to evaluate the shear performance of girders made with con- crete design strengths ranging from 10 ksi to 18 ksi, designed for different shear stress levels (from a minimum shear stress to a shear stress greater than or equal to 0.25f c´) and with dif- ferent end reinforcement conditions (straight strands, draped strands, bonded and debonded strands, and different amounts of deformed bar reinforcement). The objective was to test gird- ers that would demonstrate a range of different types of behav- ior and failure mechanisms, including yielding of the shear reinforcement, local diagonal crushing, distributed diagonal crushing, shear slip at interfaces, and strand slip. Section 2.3.1, Table 3, and Figure 40 present the shear design procedures and reinforcement used in each of the 10 girders. The following list provides a brief summary of some of the key characteristics and objectives of each test. The abbreviations used in this description are as follows: S = straight strands; Dr = some draped strands; B = bonded strands; Db = some debonded strands; and E = Enhanced end region reinforcement consist- ing of distributed vertical and horizontal reinforcement. • Girder 1: f c´ = 12.1 ksi; vu =1.21 ksi = 0.10f c´; east (S,B); west (Dr,B); examine behavior of HSC girder designed for mod- erately high shear stresses and having draped strands. • Girder 2: f c´ = 12.6 ksi; vu = 1.89 ksi = 0.15f c´; east (S,B); west (Dr,B); examine behavior of HSC girder designed for high shear stresses and having draped strands. • Girder 3: f c´ = 15.9 ksi; vu = 1.59 ksi = 0.10f c´; east (S); west (S,E); examine behavior of very high-strength concrete girder designed for moderately high shear stresses and hav- ing added distributed reinforcement and improved strand anchorage in end regions. • Girder 4: f c´ = 16.3 ksi; vu = 2.45 ksi = 0.15f c´; east (S); west (S,E); examine behavior of very high-strength concrete girder designed for high shear stresses and using distrib- uted reinforcement and improved strand anchorage in end regions. • Girder 5: f c´ = 17.8 ksi; vu = 0.89 ksi = 0.05f c´; east (S); west (S); examine behavior of very high-strength concrete girder, with minimum shear reinforcement throughout its length, with welded wire reinforcement used on the east half and regular deformed bars used in the west half of the girder. • Girder 6: f c´ = 12.7 ksi; vu = 1.65 ksi = 0.13f c´; east (S); west (S,Db); examine behavior of girder with a large number of debonded strands. • Girder 7: f c´ = 12.5 ksi; vu = 1.63 ksi = 0.13f c´; east (S); west (S); at east end examine behavior of a girder with shear reinforcement the same as for Girder 3E, providing for duplicate test; and at west end examine behavior of a tran- sition region by underdesigning this region for shear in comparison with the shear design for rest of girder. • Girder 8: f c´ = 13.3 ksi; vu = 1.60 ksi = 0.12f c´; east (S); west (S); at east end examine behavior of girder with externally strengthened end region that forces failure in beam region away from support; and at west end examine behavior when interface shear transfer is minimal as a result of inserting two aluminum plates in the web to form a slip plane. • Girder 9: f c´ = 9.6 ksi; vu = 2.40 ksi = 0.25f c´; east (S); west (Dr); east end examine behavior of girder designed for close to maximum permissible shear design stress of 0.25f c´; west end examine behavior of girder heavily overdesigned for shear with eight draped strands uniformly distributed over height of the web at member end. • Girder 10: f c´ = 10.6 ksi; vu = 1.70 ksi = 0.16f c´; east (S); west (Dr); east end examine behavior of girder with eight strands debonded; west end examine behavior of girder with eight draped strands distributed over the height of the web at the member end. The calculated strength of the test girders by the LRFD Sectional Design Model is presented in Table 7. No limit on the compressive strength of the concrete was used in cal- culating nominal capacities. In making these calculations, measured material properties and prestressing losses were used. Column 3 lists the distance, x, from the center of the support to the critical design section for shear in the first design region (dvcotθ). Column 4 lists the shear design

stress ratio (v/f c´) at section x. Column 5 lists the effective depth at the critical section (dv). Column 6 lists the longi- tudinal strain at mid-depth (εx), as calculated using Equa- tions 15 or 16. Columns 7 and 8 list the values of β and θ, respectively, as derived from Table 5.8.3.4.2-1 of the LRFD specifications. Columns 9 through 14 list the stirrup yield strength (fyv), the shear reinforcement ratio (Av/s), and the contributions to shear resistance of the concrete (Vc), the shear reinforcement (Vs), the prestressing (Vp), and the sum of those resistances which is the nominal shear resist- ance (Vn), respectively. In Column 2, the distributed load- ing (wn) that would produce this Vn at the critical section is listed as the calculated LRFD shear capacity of the mem- ber. That capacity is expressed in terms of a uniformly dis- tributed load. All girders except 7 and 8 have listed only one calculated capacity for failure of the east (E) end and only one for failure of the west (W) end. For the west end of Girder 7, the LRFD shear capacity is listed at the loca- tion 0.5dvcotθ from the center of the support (G7W). For the east end of Girder 8, a 5-foot long diaphragm was cast against the very end of the member on both sides of the web and laterally posttensioned to the web in order to ensure a failure away from this region and in a part of the member where essentially flexural behavior only was expected. Therefore, the shear capacity is also listed for the location 0.5dvcotθ from the inner face of the diaphragm (G8EB). In the second-to-last column of Table 7, the ratio of the measured-to-calculated capacity for each girder is given. The mean of these ratios is 1.11 with a coefficient of varia- tion of 0.10. It should be noted that the results from Girder 4 and 9W are not failure loads. Girder 4 failed in flexure at a load that was considered to be within 10 percent of the shear failure load, while Girder 9W was considered, from its behavior, to be within a few percentage points of its failure load. Justification for this conclusion is provided later. From a review of these strength ratios, and considering the range of experiments that were conducted in this study, the following observations can be made about the LRFD specifications: • The LRFD Sectional Design Model provides relatively accurate estimates for the shear capacity of members cast with concrete strengths ranging from 10 ksi through 18 ksi, regardless of whether draped or debonded strands are used. • A slight exception to the foregoing observation is that the LRFD specifications become slightly unconservative for members designed to resist shear stresses exceeding v = 0.2f c´. This unconservatism is due to the funneling into the support of the diagonal compressive stresses above the sup- port. That funneling leads to local diagonal crushing and very high shear stresses at the interface between the bottom bulb and the base of the web. Failure was observed to occur 53 Table 7. Measured and calculated shear strength for LRFD procedure. Girde r En d n w (kips/ft) x (ft ) ' c f v v d (in) x ( 3 10 ) yv f (kips ) s A v (in) c V (kips ) s V (kips ) p V (kips ) n V (kips ) LRFD Test LRFD Test G1E 24.47 6.36 0.102 61.7 -0.046 2.98 23.2 70.0 0.40/12 121.0 335.2 0 456.2 1.06 1.06 G1W 24.70 5.94 0.096 62.0 0.005 2.91 24.9 70.0 0.40/12 118.9 311.5 40.5 470.9 1.22 1.22 G2E 35.08 5.68 0.148 60.6 0.000 2.67 25.5 79.3 0.62/11 109.0 568.8 0 677.8 0.96 0.96 G2W 33.56 5.25 0.135 61.7 0.067 2.56 27.8 79.3 0.62/11 106.3 523.0 33.6 662.9 1.15 1.15 G3E 31.98 6.16 0.104 60.9 0.043 2.87 23.7 67.8 0.40/8 132.1 470.3 0 602.4 1.12 1.12 G3W 31.98 6.16 0.104 60.9 0.043 2.87 23.7 67.8 0.40/8 132.1 470.3 0 602.4 1.21 1.21 G4E 43.43 5.05 0.146 60.9 0.018 2.53 28.5 64.6 0.62/6 118.0 748.4 0 866.5 0.98 # 0.98 # G4W 43.43 5.05 0.146 60.9 0.018 2.53 28.5 64.6 0.62/6 118.0 748.4 0 866.5 0.98 # 0.98 # G5E 19.31 6.94 0.052 63.0 -0.003 3.75 21.8 92.2 0.22/20 189.0 159.7 0 348.7 1.23 1.23 G5W 17.80 6.94 0.048 63.0 -0.019 3.75 21.8 76.5 0.22/20 189.0 132.5 0 321.5 1.12 1.12 G6E 34.88 6.16 0.125 60.9 -0.044 2.87 23.7 64.7 0.62/12 118.1 463.8 0 581.9 1.10 0.97 ** G6W 27.67 5.64 0.113 61.3 0.126 2.74 25.9 64.7 0.62/12 113.5 422.2 0 535.7 1.01 0.99 ** G7E 30.69 6.02 0.128 60.9 -0.075 2.78 24.2 69.2 0.40/8 113.5 468.9 0 582.4 1.09 1.05 ** G7W 41.60 6.02 0.128 60.9 -0.096 2.78 24.2 69.2 0.40/8 113.5 468.9 0 582.4 1.08 1.04 ** G8EB† 37.39 9.78 0.110 60.9 -0.006 2.87 23.7 69.2 0.40/8,12 120.9 415.2 0 536.1 1.17 1.16 ** G8W 34.85 6.16 0.124 60.9 -0.050 2.87 23.7 69.2 0.40/8 120.9 480.0 0 600.9 0.94 0.93 ** G9E 36.15 4.72 0.211 60.2 -0.004 2.34 30.0 65.4 0.62/6.5 82.7 650.4 0 733.1 0.91 0.91 G9W 40.97 4.13 0.250 58.0 0.499 1.70 32.8 65.4 0.62/4 58.0 912.9 40.4 876.6 * 0.91 # 0.91 # G10E 28.90 4.89 0.153 59.6 0.234 2.52 28.8 65.4 0.62/9 92.7 488.5 0 581.2 1.17 1.16 ** G10W 31.89 5.02 0.160 58.3 -0.007 2.54 27.6 65.4 0.62/9 91.2 501.5 42.2 634.9 1.34 1.27 ** Averag e 1 .11 1.09 CO V 0 .10 0.10 * Controlled by p v w ' c n V d b f . V 25 0 . # No shear failure in this region; strength ratio not used in statistical calculations. ** Specified f c used when m easured strength less than the specified f c . † B = beam or Bernoulli region.

54 in these situations before yielding occurred in a band of reinforcement that formed the critical shear plane. This local crushing effect in the web above a support is some- what analogous to the web crippling effect that has long been a design consideration for the same location in steel beams. • Design of the end regions of a beam—including consider- ation of the consequences of using draped strands, debonded strands, and added deformed bar longitudinal reinforcement—has a significant effect on the overall shear strength of girders. The use of draped strands, particularly strands that are draped over the depth of the web of the girder in its end region, can significantly improve the shear capacity of the end region. The sensitivity of the strength ratios to the concrete cylin- der compressive strength was evaluated by adding a final col- umn, Column 16, to Table 7. Column 16 lists the calculated LRFD capacity when that capacity is evaluated using the specified compressive strength of the concrete for those gird- ers where the measured concrete strength was less than that specified. As illustrated by a comparison of the last two columns, because Vc is typically much less than Vs for shear designs in accordance with the LRFD specifications, the strength ratios are only slightly affected. The overall mean of these new strength ratios is 1.09, with a coefficient of varia- tion of 0.10. Thus, if the measured strength of the concrete would have always been at least equal to that specified, then the overall conclusions about the accuracy and safety of the shear design provisions of the LRFD specifications for HSC remain unaltered. 2.4.2 Evaluation of Other Shear Design Provisions The measured strength of each test girder was also com- pared with its nominal capacity calculated using the AASHTO Standard Specifications, the computer program Response 2000 (24), the Canadian Standard Association A23.3-04 provisions, and the proposed simplified design pro- visions that were developed as part of NCHRP Project 12-61. The basis, and the governing shear equations, for each of these four procedures are briefly summarized below. The measured strengths and the strengths predicted by those four procedures, together with the LRFD predictions, are listed in Table 8. AASHTO Standard Specifications The AASHTO Standard Specifications method for calcu- lating the shear strength of prestressed concrete members is essentially the same as the detailed method of ACI 318 (26). The components of resistance are from the contribution of the concrete, the shear reinforcement, and the vertical Table 8. Measured and calculated shear strengths for differing evaluation methods. Calculated Load (kips/ft) Test/Calculation Ratio Girde r En d Tes t (kips/ft) LRFD STD R2K CSA PROP LRFD STD R2K CSA PROP G1E 26.03 24.47 19.92 23.14 24.18 21.84 1.06 1.31 1.12 1.08 1.19 G1W 30.09 24.70 23.17 23.71 25.24 25.19 1.22 1.30 1.27 1.19 1.19 G2E 33.79 35.08 26.34 36.90 34.65 32.57 0.96 1.28 0.92 0.98 1.04 G2W 38.74 33.56 29.58 37.57 34.22 36.55 1.15 1.31 1.03 1.13 1.06 G3E 35.68 31.98 25.81 29.68 31.73 29.61 1.12 1.38 1.20 1.12 1.21 G3W 38.82 31.98 25.81 29.68 31.73 29.61 1.21 1.50 1.31 1.22 1.31 G4 E # 42.74 43.43 33.41 43.28 44.07 45.81 0.98 1.28 0.99 0.97 0.93 G4 W # 42.74 43.43 33.41 43.28 44.07 45.81 0.98 1.28 0.99 0.97 0.93 G5E 23.70 19.31 15.47 21.86 18.95 11.63 1.23 1.53 1.08 1.25 2.04 G5W 19.91 17.80 14.90 21.70 18.11 10.92 1.12 1.34 0.92 1.10 1.82 G6E 38.32 34.88 25.59 34.29 34.27 30.15 1.10 1.50 1.12 1.12 1.27 G6W 27.85 27.67 20.59 29.95 28.07 20.13 1.01 1.35 0.93 0.99 1.38 G7E 33.47 30.69 24.12 28.41 31.38 28.57 1.09 1.39 1.18 1.07 1.17 G7W 44.76 41.60 37.18 37.51 45.01 40.94 1.08 1.20 1.19 0.99 1.09 G8EB† 43.73 37.39 33.29 37.86 36.70 32.41 1.17 1.31 1.16 1.19 1.35 G8W 32.70 34.85 24.96 31.46 34.38 28.22 0.94 1.31 1.04 0.95 1.16 G9E 32.80 36.15 26.14 37.83 36.82 31.03 0.91 1.25 0.87 0.89 1.06 G9 W # 37.19 (22.32) 40.97 (24.59) 27.19 (16.32) 48.14 (28.89) 39.94 (23.97) 31.53 (18.92) 0.91 1.37 0.77 0.93 1.18 G10E 33.93 28.90 24.59 31.56 28.15 29.79 1.17 1.38 1.08 1.21 1.14 G10W 42.85 31.89 27.73 34.85 33.27 34.41 1.34 1.55 1.23 1.29 1.25 Averag e 1 .11 1.36 1.10 1.10 1.28 CO V 0 .10 0.07 0.12 0.10 0.21 # No shear failure in this region; strength ratio not used in statistical calculations. † B = beam or Bernoulli region. STD = AASHTO Standard Specifications. PROP = proposed provisions.

component of the prestressing force—Vc,Vs, and Vp, respec- tively. The Vc term is the lesser of the shear forces estimated to cause web-shear cracking (as calculated in Equation 19) and those estimated to cause flexure-shear cracking (as calculated in Equation 20). The contribution of shear reinforcement to capacity, Vs, is calculated using the 45-degree truss analogy (as calculated in Equation 21), with a limitation of (in inches and psi). In the calculated strengths for AASHTO Standard Specifications presented in Table 8, no limitation on Vs is imposed. where: d = distance from extreme compressive fiber to cen- troid of the prestressing force, or to centroid of neg- ative moment reinforcement for precast girder bridges made continuous; Vd = shear force at section due to unfactored dead load; Vi = factored shear force at section due to externally applied loads occurring simultaneously with Mmax; (in inches and psi): moment causing flexural cracking at section due to externally applied loads; Mmax = maximum factored moment at section due to externally applied loads; and fpc = compressive stress in concrete (after allowance for all prestress losses) at the centroid of the cross sec- tion resisting externally applied loads or at the junc- tion of web and flange when the centroid lies within the flange. (In a composite member, fps is the result- ant compressive stress at the centroid of the com- posite section, or at the junction of web and flange when the centroid lies within the flange, due to both prestress and moments resisted by the precast member acting alone.) Computer Program Response 2000 (24) The computer program Response 2000 (R2K) is a sectional design and analysis tool for predicting the response of a M I y f f fcr t c pe d= + −( ´ )6 V f b d d h ci c w≥ ( ) ≥ 1 7 0 8 . ´ . in inches and psi and ; V A f d s s v y = ( )21 V f b ds c w≤ 8 ´ V f b d V V M M ci c w d i cr = +0 6. ´ max + in inches and psi( ) ( )20 V f f b d Vcw c pc w p= +( ) +3 5 0 3. ´ . in inches and psi( ) ( )19 reinforced or prestressed concrete section to the actions of shear, moment, and axial load, including the effects of prestressing. The calculations assume that plane sections remain plane and use an equivalent dual-section analysis method in conjunction with the modified compression field theory for evaluating the distribution of shear stresses over the depth of a member. The program is as complete an implementation of the MCFT as is possible for a member in which a linear variation in longitudi- nal strains is assumed over the depth of a member.The program was used to predict the capacities for the girders at each of the critical sections identified in Table 7. The calculation required inputting into the R2K program the appropriate material prop- erties, level of prestressing (including accounting for losses),and the moment-to-shear ratio at the critical shear section,and then solving for the complete shear versus shear strain response. In using this program, the ultimate strength of the stirrups was taken as the yield strength of the stirrups. Canadian Standards Association (CSA A23.3-04) Design of Concrete Structures The MCFT is the basis for the general shear provisions of the both the CSA and the LRFD specifications. In previous versions of the CSA code, values for β and θ were selected from tables, as is presently done in the LRFD Sectional Design Model. In order to simplify the CSA shear design procedure, equations were introduced for β and θ in the 2004 CSA spec- ifications in which these parameters were made, for members with minimum or more shear reinforcement, a function of the longitudinal strain at mid-depth, εx, only. In addition, the equation for evaluating εx was simplified by taking θ equal to 30 degrees for evaluations of the demand of shear on the lon- gitudinal reinforcement requirements. These simplifications eliminated the need for iteration in shear design. In this approach, the nominal strength is calculated by Equation 22 and the concrete contribution and transverse reinforcement contributions calculated by Equations 23 and 24, respectively. where: p = strength reduction factor for prestress and in inches and psi. The values of β and θ are directly determined from the lon- gitudinal strain, at mid-depth, as computed from Equations 25 or 26. V A f d s s v y v = ( )cot ( ) θ 24 V f b dc c w v= β ´ ( )23 V V V V f b d Vn c s p p c w v p p= + + ≤ +φ φ0 25 22. ´ ( ) 55

56 where: Mf = ultimate moment = factored moment at the section, Nf = factored axial force, and Vf = factored shear force. When εx is negative, it is either taken as zero or recalculated by changing he denominator of Equation 25 such that the equation becomes: However,εx shall not be taken as less than 0.2 × 10−3.For mem- bers having at least minimum transverse reinforcement,with the longitudinal strain, εx, computed from Equation 25 or 26, the angle of the diagonal compression field, θ, is calculated as: and the coefficient, β, is obtained from Equation 28. NCHRP Report 549 (7) recommended that Table 5.8.3.4.2-1 of the LRFD specifications be replaced with equations similar to the foregoing for β and θ. The iteration procedure is then completely removed in this method, and there are trade-offs made between simplicity, generality, and accuracy. Collins and Rahal (23) reported that this approach had been checked against a database of 413 large reinforced and prestressed concrete beams. The average shear capacity ratio was Vtest/ Vprediction 1.16, with a coefficient of variation of 0.169 and a 1-percent fractile value of Vtest/Vprediction of 0.77. AASHTO Simplified Shear Design Provisions The second recommendation from NCHRP Report 549 was the addition of an alternative or simplified set of shear design relationships that would be applicable to both reinforced and prestressed concrete members containing at least the mini- mum required amount of shear reinforcement and not sub- jected to a net axial tension. The recommendation has been incorporated into the fourth edition of the LRFD specifica- tions. These recommendations are a modified version of the AASHTO Standard Specifications. The expression for web- shear cracking strength was modified so that it was applicable to both nonprestressed and prestressed members. Thus, when the decompression stress fpc is equal to zero, then the web-shear cracking stress is equal to 2 (in psi units). The expression for flexure-shear cracking was kept virtually unchanged, while f c´ β ε = +( ) ( ) 4 8 1 1 500 28. , x θ ε= + ( )29 7 000 27, x ε φ x f v f f p p p po s s p p c c M d N V V A f E A E A E A = + + − − + + / .0 5 2 t( ) ( )26 ε φ x f v f f p p p po s s p p M d N V V A f E A E A = + + − − +( ) / . ( 0 5 2 25) the contribution of the shear reinforcement was evaluated using a variable angle truss model. The angle used for calculat- ing the contribution of the transverse reinforcement to shear resistance was evaluated from Mohr’s circle of stress consider- ing the effect of the decompression stress, fpc. When there was no decompression stress, as in nonprestressed members, the angle of cracking is 45 degrees and cotθ equals unity. With increasing levels of decompression stress, the angle of cracking becomes flatter, cotθ increases, and the contributions of the shear reinforcement to shear capacity increase. A limit of 1.8 was imposed on cotθ, which is equivalent to limiting θ to 29 degrees. The other differences from the AASHTO Standard Specifications were that dv rather than d was used for the shear depth, the LRFD required that minimum shear reinforcement limit be applied, and the limit on Vs was replaced with the LRFD maximum allowable design shear stress. These provi- sions are shown below in both ksi and psi units. Note that coef- ficients were selected so that they would be simpler in the LRFD ksi unit system. where stress is in ksi units, which is equivalent to where stress is in psi units. where stress is in ksi units, which is equivalent to where stress is in psi units. The 0.06 coefficient establishes a uniform minimum Vc contribution over the length of the member independent of whether a web-shear or flexure-shear region is being designed. The coefficient of 0.06 (in ksi units) is also very close to the traditional coefficient of 1.7 (in psi units) when it is considered that dv = 0.9d. when Vcw < Vci where stress is in ksi units, which is equivalent to: where stress is in psi units. cot . . . ( )θ = + ≤1 0 0 095 1 8 34 f f pc c´ cot . . ( )θ = + ≤1 0 3 1 8 33 f f pc c´ V f b d V V M M f b dci c v v d i cr c v v= + + ≥0 632 1 9 32. . ( max ´ ´ ) V f b d V V M M f b dci c v v d i cr c v v= + + ≥0 02 0 06 31. . ( max ´ ´ ) V f f b d Vcw c pc v v p= + +( . ´ . ) ( )1 9 0 30 30 V f f b d Vcw c pc v v p= + +( . ´ . ) ( )0 06 0 30 29

Comparison of Measured Strengths with Shear Design Provisions The measured strengths of the test girders are compared with the calculated capacities of the LRFD specifications and the four methods described above (AASHTO Standard Spec- ifications, the computer program Response 2000, CSA A23.3- 04, and Simplified Proposed Specifications), plus the LRFD Sectional Design Model in Table 8. In these calculations, no limit was placed on the value of f c´, and the LRFD maximum shear strength limitation was imposed. The shear strength limitation was not imposed upon the R2K prediction because it directly evaluates the diagonal compression stress and checks against available compressive capacity. Table 8 shows the measured distributed loading in kips per foot at failure and the distributed loading at nominal capacity as calculated by the five methods. That listing is followed by the strength ratios for each of the five methods expressed as the measured strength divided by the calculated nominal capacity. At the bottom of the columns for these strength ratios, the mean strength ratio and the coefficient of variation for these ratios are given. In these calculations, the results from tests G4E, G4W, and G9W were not included because these members did not fail in shear. From an examination of these strength ratios, the following observations are drawn: • All five methods predicted the capacity of the test girders to an acceptable level of accuracy. • The strength ratios from the LRFD and CSA methods pro- duced very similar results, as was expected given that they are both derived from the MCFT and use the longitudinal strain at mid-depth to characterize the condition of the member in shear. • The AASHTO Standard Specifications method was the most conservative and had the lowest coefficient of varia- tion. The ratios of the measured to code-calculated nomi- nal strengths ranged from 1.20 to 1.55. • The program Response 2000 (R2K) had the lowest average strength ratio. Higher strength estimates of Girder 9 were to be expected because R2K assumes that there is a uniform field of diagonal compression, that there is no local crush- ing due to funneling of compressive stresses, and that for Girder 9 the stirrups yielded prior to failure. • The proposed simplified provisions provided a safe esti- mate of the capacity of all test girders that failed in shear. The proposed provisions were particularly conservative at predicting the capacity of Girder 5, which contained mini- mum shear reinforcement only. These provisions are inten- tionally more conservative for lightly reinforced members to guard against serviceability and fatigue problems. The results presented in Table 8 are useful for evaluating whether these other shear design provisions and methods can be used with HSC. However, it should be recognized that this is only one set of comparisons. Extension of the LRFD and other specifications to HSC for all member types requires consideration of all available test results, including those pre- sented in Section 2.2. Caution is urged in drawing too strong a conclusion about the relative accuracy and conservatism of these five methods from the range of tests in this program and those in the experimental databases presented in Section 2.2 because that range is limited. This matter is further discussed in Chapter 4. Additional observations from these girder tests, and of the success of the different methods for calculating nominal capacity, are presented in, and discussed throughout, the remaining sections of Chapter 2. 2.4.3 Impact of Method Selected for Staggered Shear Design on Strength Evaluations The LRFD Sectional Design Model (S5.8.2.3) permits the use of a staggered shear design approach over the entire length of a member. The shear design force permitted in a region is taken as the lowest shear force at the edge of that region. This concept and its consequences are illustrated in Figure 66. The justification for the LRFD approach is that the design force for a region should only consider the force that needs to be carried across the diagonal crack that spans that region, as illustrated in Figure 66(b). One difficulty with using the staggered shear design approach of LRFD is that the designer needs to evaluate the angle θ before determining the location of the shear design force, Vu, to be used in the design. Since θ is a function of εx and εx is a function of Vu, the design becomes awkwardly iter- ative. Consequently, the contractor used the approach shown in Figure 66(a) when designing the test girders. In order to evaluate the safety of using a staggered shear design method over the entire length of the girder, it is useful to reeval- uate the capacity of the test girders using only the load that occurs to the right of section (2), as shown in Figure 67. The revised strength ratios are presented in Table 9, where the shear force under the test load wu was computed at section (2) and then was compared with the calculated shear strength from above evaluation methods. Note that the locations of section (2) were different in these methods and that the test load wu is shown in the second column of Table 8.From Table 9, the following obser- vations are made about the staggered shear design approach: • The use of a staggered shear design method over the length of the girder leads to a lower ratio of the measured capac- ity to calculated capacity than when a region is designed for the shear force at the center of that region. • The strength ratios calculated using the LRFD, R2K, CSA and proposed methods had very similar mean values of 57

58 around 0.78. That the mean value is less than 1.0 suggests that the use of the staggered shear design method over the entire length of a member leads to unconservative results. • The strength ratio from the AASHTO Standard Specifica- tions was still conservative at 1.19. The lesser impact of the staggered shear design concept for the AASHTO Standard Specifications is in large part due to the much shorter length of the shear design region when the angle of diago- nal compression is taken as 45 degrees and due to the stocky aspect ratio of the test girders. Sh ea r Location Design Span Design Span Vu Vr Design Section Design Section dvcotθ2dvcotθ 0.5dvcotθ2 dvcotθ2dvcotθ 0.5dvcotθ 0.5dvcotθ20.5dvcotθ Sh ea r Location Design Span Design Span Vu Vr Design Section Design Section (a) Designing a region for shear at center of region (b) Staggered shear design for calculating shear design force Figure 66. Staggered shear design concept. Sh ea r Location (1) (2) VTest,1 VTest,2VLRFD Design Span dvcotθ 0.5dvcotθ 0.5dvcotθ Design Span dvcotθ2 0.5dvcotθ2 0.5dvcotθ2 Figure 67. Locations for evaluating design shear force in test girders. Test/Calculation Ratio Girder End LRFD STD R2K CSA PROP G1E 0.72 1.12 0.76 0.68 0.75 G1W 0.86 1.12 0.90 0.81 0.81 G2E 0.70 1.10 0.67 0.68 0.72 G2W 0.87 1.13 0.78 0.84 0.79 G3E 0.77 1.19 0.83 0.74 0.78 G3W 0.84 1.29 0.91 0.80 0.85 G4E# 0.75 1.10 0.76 0.73 0.71 G4W# 0.75 1.10 0.76 0.73 0.71 G5E 0.78 1.32 0.69 0.73 1.12 G5W 0.71 1.15 0.58 0.64 1.00 G6E 0.72 1.26 0.73 0.69 0.77 G6W 0.73 1.16 0.67 0.70 0.93 G7E 0.77 1.19 0.83 0.71 0.78 G7W 1.02 1.20 1.14 0.95 1.04 G8EB 0.70 1.22 0.69 0.67 0.76 G8W 0.62 1.11 0.69 0.60 0.71 G9E 0.71 1.08 0.68 0.70 0.84 G9W# 0.65 1.09 0.55 0.71 0.78 G10E 0.91 1.19 0.83 0.92 0.87 G10W 1.03 1.33 0.94 0.97 0.94 Average 0.79 1.19 0.78 0.75 0.85 COV 0.15 0.06 0.17 0.15 0.14 # No shear failure in this region; strength ratio not used in statistical calculations. STD = AASHTO Standard Specifications. PROP = proposed provisions. Table 9. Shear strength ratios for critical section at dvcot from face of support.

2.4.4 Modes of Failure and Condition of Members at Ultimate Limit State The values of the design parameters selected for the tests were intended to facilitate the evaluation of different mecha- nisms of shear resistance. The events that could precipitate shear failure included stirrup yielding, stirrup rupturing, strands slipping, local crushing of concrete along the line of diagonal compression as it funnels to the support, distributed crushing across a band of diagonal compression, or shear slip along a crack or between the web and bottom bulb. Each of these events was exhibited in this experimental research pro- gram, as illustrated in Figure 68. The modes of failure for all of the test girders are described in Figures 69(a) through 69(t). Each of these figures consists of two text boxes and selected photographs. In the left text box 59 (a) Low v/f ′c, stirrups yield and rupture (b) Moderate v/f ′c, stirrups yielding (c) Moderate v/f ′c, local crushing (d) Moderate to high v/f ′c, brittle compression/shear failure (e) Horizontal shear slip (f) Crushing of diagonal compression field Figure 68. Typical failure modes.

60 G1E Concrete: f ′c = 12.1 ksi, f ′c,deck = 4.5 ksi Stirrup: 2-#4@12, ρv f y = 389 psi Strand: 32-straight on bottom, 2-straight on top Failure Load: 26.03 kips/ft Loading pattern: (3,44,3)ft Support Reaction R: 573 kips R(first crack)/R(failure) = 57% R(first stirrup yield)/R(failure) = 65% average stirrup strain at failure = 2.0εy strand slip prior to failure: minor shear slip along cracks: significant localized crushing: significant Test/LRFD = 1.06 failure manner: explosive (a) Failure Mode of G1E G2E Concrete: f ′c = 12.6 ksi, f ′c,deck = 8.6 ksi Stirrup: 2-#5@11, ρv f y = 745 psi Strand: 38-straight on the bottom half; 2- straight on the top Failure Load: 33.79 kips/ft Loading pattern: (3,44,3)ft Support Reaction R: 743 kips R(first crack)/R(failure) = 55% R(first stirrup yield)/R(failure) = 82% average stirrup strain at failure = 1.1εy strand slip prior to failure: 0.02 inch shear slip along cracks: significant localized crushing: significant horizontal sliding after failure: 2.5 inches Test/LRFD = 0.96 failure manner: explosive (c) Failure Mode of G2E Figure 69. Failure Modes. G1W Concrete: f ′c = 12.1 ksi, f ′c,deck = 4.5 ksi Stirrup: 2-#4@12, ρv f y = 389 psi Strand: 26-straight and 6-draped on the bottom half; 2-straight on top Failure Load: 30.09 kips/ft Loading pattern: (3,44,3)ft Support Reaction R: 662 kips R(first crack)/R(failure) = 60% R(first stirrup yield)/R(failure) = 71% average stirrup strain at failure = 2.3εy strand slip prior to failure: 0.08 inch shear slip along cracks: significant localized crushing: significant Test/LRFD = 1.22 failure manner: explosive (b) Failure Mode of G1W

61 G2W Concrete: f ′c = 12.6 ksi, f ′c,deck = 8.6 ksi Stirrup: 2-#5@11, ρv f y = 745 psi Strand: 32-straight and 6-draped on the bottom half; 2-straight on the top Failure Load: 38.73 kips/ft Loading pattern: (3,44,3)ft Support Reaction R: 852 kips R(first crack)/R(failure) = 56% R(first stirrup yield)/R(failure) = 61% average stirrup strain at failure = 2.1εy strand slip prior to failure: 0.025 inch shear slip: minor localized crushing: significant Test/LRFD = 1.15 failure manner: very explosive with 10- inch high web segment totally crushed. (d) Failure Mode of G2W G3E Concrete: f ′c = 15.9 ksi, f ′c,deck = 3.6 ksi Stirrup: 2-#4@8, ρvf y = 565 psi Strand: 42-straight on the bottom; 2- straight on the top Failure Load: 35.68 kips/ft Loading pattern: (3,44,3)ft Support Reaction R: 785 kips R(first crack)/R(failure) = 45% R(first stirrup yield)/R(failure) = 50% average stirrup strain at failure = 2.3εy strand slip prior to failure: none shear slip along cracks: significant localized crushing: significant horizontal sliding after failure: 4 inches Test/LRFD = 1.12 failure manner: very explosive (e) Failure Mode of G3E G3W Concrete: f ′c = 15.9 ksi, f ′c,deck = 3.6 ksi Stirrup: 2-#4@8, ρvf y = 565 psi Strand: 42-straight on the bottom; 2- straight on the top Enhancement: Additional 10-foot long #3 horizontal skin bars; Four pairs of #4 vertical bars in the bottom web near support; Four 20-inch long spirals wrapped around groups of strands; Failure Load: 38.82 kips/ft Loading pattern: (3,44,3)ft Support Reaction R: 854 kips R(first crack)/R(failure) = 39% R(first stirrup yield)/R(failure) = 41% average stirrup strain at failure = 2.7εy strand slip prior to failure: none shear slip along cracks: significant localized crushing: significant horizontal sliding after failure: minor Test/LRFD = 1.21 failure manner: very explosive (f) Failure Mode of G3W Figure 69. (Continued).

62 G4E Concrete: f ′c = 16.3 ksi, f ′c,deck = 6.3 ksi Stirrup: 2-#5@6, ρvf y = 1,113 psi Strand: 42-straight on the bottom; 2- straight on the top Failure Load: 42.73 kips/ft Loading pattern: (3,44,3)ft Support Reaction R: 940 kips R(first crack)/R(failure) = 33% R(first stirrup yield)/R(failure) = 100% average stirrup strain at failure = 0.9εy strand slip prior to failure: none shear slip along cracks: small localized crushing: none Test/LRFD = 0.98 failure manner: No shear failure (g) Failure Mode of G4E G4W Concrete: f ′c = 16.3 ksi, f ′c,deck = 6.3 ksi Stirrup: 2-#5@6, ρvf y = 1113 psi Strand: 42-straight on the bottom; 2- straight on the top Enhancement: Additional 10-foot long #3 horizontal skin bars; Four pairs of #5 vertical bars in the bottom web near support; Four 20-inch long spirals wrapped around groups of strands; Test Load: 42.73 kips/ft Loading pattern: (3,44,3)ft Support Reaction R: 940 kips R(first crack)/R(failure) = 36% R(first stirrup yield)/R(failure) = 100% average stirrup strain at failure = 0.9εy strand slip prior to failure: none shear slip along cracks: small localized crushing: none Test/LRFD = 0.98 failure manner: No shear failure (h) Failure Mode of G4W G5E Concrete: f ′c = 17.8 ksi, f ′c,deck = 6.1 ksi Stirrup: 2-#3@20, ρvf y = 169 psi, Welded-wire reinforcement were used Strand: 24-straight on the bottom Test Load: 23.70 kips/ft Loading pattern: (3,44,3)ft Support Reaction R: 521 kips R(first crack)/R(failure) = 71% R(first stirrup yield)/R(failure) = 71% average stirrup strain at failure = 3εy stirrups fractured strand slip prior to failure: 0.02 inch shear slip along cracks: significant the bottom bulb flange: broken horizontal sliding after failure: 4.5 inches Test/LRFD = 1.23 failure manner: very explosive (i) Failure Mode of G5E Figure 69. (Continued).

63 G5W Concrete: f ′c = 17.8 ksi, f ′c,deck = 6.1 ksi Stirrup: 2-#3@20, ρvf y = 140 psi Strand: 24-straight on the bottom Test Load: 19.91 kips/ft Loading pattern: (3,44,3)ft Support Reaction R: 438 kips R(first crack)/R(failure) = 61% R(first stirrup yield)/R(failure) = 73% average stirrup strain at failure = 2εy strand slip prior to failure: none. Local crushing: significant horizontal sliding found along a preexisting crack. Test/LRFD = 1.12 failure manner: brittle ( j) Failure Mode of G5W G6E Concrete: f ′c = 12.7 ksi, f ′c,deck = 9.2 ksi Stirrup: 2-#5@12, ρvf y = 557 psi Strand: 42-straight on the bottom, 2- straight on the top Test Load: 38.32 kips/ft Loading pattern: (15,32,3)ft Support Reaction R: 760 kips R(first crack)/R(failure) = 47% R(first stirrup yield)/R(failure) = 77% average stirrup strain at failure = 1.7εy strand slip prior to failure: none shear slip along cracks: significant localized crushing: significant horizontal sliding after failure: 2.0 inches Test/LRFD = 1.1 failure manner: explosive (k) Failure Mode of G6E G6W Concrete: f ′c = 12.7 ksi, f ′c,deck = 9.2 ksi Stirrup: 2-#5@12, ρvf y = 557 psi Strand: 42-straight (16-debonded) on the bottom, 2-straight on the top (2 debonded) Failure Load: 27.85 kips/ft Loading pattern: (3,44,3)ft Support Reaction: 613 kips R(first crack)/R(failure) = 60% R(first stirrup yield)/R(failure) = 100% average stirrup strain at failure = 1.6εy strand slip prior to failure: 0.5 inch shear slip along cracks: significant localized crushing: significant horizontal sliding after failure: 1.0 inch Test/LRFD = 1.01 failure manner: brittle (l) Failure Mode of G6W Figure 69. (Continued).

64 Figure 69. (Continued). G7W Concrete: f ′c = 12.5 ksi, f ′c,deck = 4.5 ksi Stirrup: 2-#4@8, ρv f y = 557 psi (end) 2-#3@23, ρv fy = 119 psi (transition) Strand: 42-straight on the bottom, 2- straight on the top Enhancement: all strands were anchored to a steel plate; A 5-foot long diaphragm was cast Test Load: 44.75 kips/ft Loading pattern: (11,28,11)ft Support Reaction R: 627 kips R(first crack)/R(failure) = 66% R(first stirrup yield)/R(failure) = 95% average stirrup strain at failure = 2.6εy strand slip prior to failure: none shear slip along cracks: significant localized crushing: significant horizontal sliding after failure: minor Test/LRFD = 1.08 failure manner: brittle (n) Failure Mode of G7W G7E Concrete: f ′c = 12.5 ksi, f ′c,deck = 4.5 ksi Stirrup: 2-#4@8, ρvf y = 557 psi Strand: 42-straight on the bottom, 2- straight on the top Test Load: 33.47 kips/ft Loading pattern: (3,44,3)ft Support Reaction: 736 kips R(first crack)/R(failure) = 54% R(first stirrup yield)/R(failure) = 93% average stirrup strain at failure = 1.2εy strand slip prior to failure: none shear slip along cracks: minor localized crushing: minor Test/LRFD = 1.09 failure manner: loading stopped before explosive failure formed. (m) Failure Mode of G7E G8E Concrete: f ′c = 13.3 ksi, f ′c,deck = 7.0 ksi Stirrup: 2-#4@8, ρvf y = 557 psi Strand: 42-straight on the bottom, 2- straight on the top; Enhancement: all strands were anchored; 5-foot long diaphragms were cast on either side with lateral post- tensioning. Failure Load: 43.72 kips/ft Loading pattern: (13,28,9)ft Support Reaction R: 661 kips R(first crack)/R(failure) = 48% R(first stirrup yield)/R(failure) = 62% average stirrup strain at failure = 1.8εy strand slip prior to failure: none shear slip along cracks: small localized crushing: significant Test/LRFD = 1.17 failure manner: brittle, distributed crushing across a bond of diagonal compression before the diaphragms (o) Failure Mode of G8E

65 G8W Concrete: f ′c = 13.3 ksi, f ′c,deck = 7.0 ksi Stirrup: 2-#4@8, ρvf y = 557 psi Strand: 42-straight on the bottom, 2- straight on the top; Enhancement: two aluminum plates were installed Failure Load: 32.70 kips/ft Loading pattern: (3,34,13)ft Support Reaction: 667.1 kips R(first crack)/R(failure) = 52% R(first stirrup yield)/R(failure) = 82% average stirrup strain at failure = 0.95εy strand slip prior to failure: none shear slip along cracks: significant along plates localized crushing: significant Test/LRFD = 0.94 failure manner: the loading was halted after failure was deemed imminent. (p) Failure Mode of G8W G9W Concrete: f ′c = 9.6 ksi, f ′c,deck = 6.0 ksi Stirrup: 2-#5@4, ρvf y = 1690 psi Strand: 24-straight and 10-draped on the bottom, 2-straight on the top Test Load: 37.20 kips/ft, 22.32 kips/ft Loading pattern: (3,26,21)ft /(4, 10,36)ft Support Reaction: 840.7 kips R(first crack)/R(failure) = 57% Stirrup didn’t yield at failure; average stirrup strain at failure = 0.5εy strand slip prior to failure: none shear slip along cracks: none localized crushing: significant Test/LRFD = 0.91 failure manner: test load was stopped when local crushed was observed, which suggested the loading was within a few percent of the failure. (r) Failure Mode of G9W G9E Concrete: f ′c = 9.6 ksi, f ′c,deck = 6.0 ksi Stirrup: 2-#5@6.5, ρvf y = 1040 psi Strand: 34-straight on the bottom, 2- straight on the top Failure Load: 32.80 kips/ft Loading pattern: (3,44,3)ft Support Reaction: 722 kips R(first crack)/R(failure) = 49% Stirrup didn’t yield at failure; average stirrup strain at failure = 0.7εy strand slip prior to failure: 0.013 inch shear slip along cracks: none localized crushing: significant horizontal sliding after failure: 4.0 inches Test/LRFD = 0.91 failure manner: explosive, concrete crushed along the interface of web and bottom bulb. (q) Failure Mode of G9E Figure 69. (Continued).

66 is presented material strengths, reinforcement details, and whether the loads are failure or ultimate loads. In the right text box, the condition of the structure just prior to failure and the mode of failure are described. This description includes • The ratio of the support reaction force at first shear crack- ing to the support reaction force at failure/ultimate— R(first crack)/R(failure); • The equivalent reaction ratio for first stirrup yield—R(first stirrup yield)/R(failure); • The average stirrup strain at peak loading; • Whether or not slip had occurred of strands or along shear cracks; and • A brief description of the type of failure. At the bottom of each summary, several images are used to describe the condition of the structure immediately before and/or just after failure. Table 10 is then used to summarize and compare the conditions at the end of each girder immediately prior to failure or at the ultimate sustained load. Table 10 lists in turn: (1) the reaction force at ultimate load; (2) the compressive state in the web above the reaction; (3) whether or not the stir- rups yielded and the extent of the yielding; (4) the magnitude of strand slip; (5) the web-shear crack spacing, maximum web- shear crack width, and the shear-slip condition along shear cracks; and (6) the magnitude of the slip between the bottom bulb and the web of the member after failure. From the descrip- tion and summary provided in Figure 69 and Table 10, the fol- lowing should be noted: G10E Concrete: f ′c = 10.6 ksi, f ′c,deck = 5.4 ksi Stirrup: 2-#5@9, ρvf y = 751 psi Strand: 34-straight (8-debonded) on the bottom, 2-straight on the top Test Load: 33.93 kips/ft Loading pattern: (3,44,3)ft Support Reaction: 747 kips R(first crack)/R(failure) = 46% R(first stirrup yield)/R(failure) = 92%; average stirrup strain at failure = 1.3εy strand slip prior to failure: 0.01 inch shear slip along cracks: significant localized crushing: significant Test/LRFD = 1.17 failure manner: test load was halted to prevent a brittle failure when local crushing was observed near the support; failure was considered imminent (s) Failure Mode of G10E G10W Concrete: f ′c = 10.6 ksi, f ′c,deck = 5.4 ksi Stirrup: 2-#5@9, ρvf y = 751 psi Strand: 24-straight and 10-draped on the bottom, 2-straight on the top Test Load: 42.85 kips/ft Loading pattern: (3,43,4)ft Support Reaction: 940 kips R(first crack)/R(failure) = 46% R(first stirrup yield)/R(failure) = 87%; average stirrup strain at failure = 1.7εy strand slip prior to failure: none shear slip along cracks: minor localized crushing: significant horizontal sliding after failure: minor Test/LRFD = 1.34 failure manner: very explosive, with concrete in the bottom web near support totally crushed over 10 inches height. (t) Failure Mode of G10W Figure 69. (Continued).

• The top flange was never damaged in any test. • The bottom bulb remained intact in all girders except for G5E, where the bottom bulb failed in shear after rupture of the shear reinforcement. For most girders, the bottom bulb looked completely unharmed at failure, except for narrow flexural cracks. • In most cases, the girders failed after significant local crushing was observed in the web just above and inside of the support. Associated with this local crushing were also significant shear stresses between the bottom bulb and web. These led to flatter cracks as well as localized crushing and slip along shear cracks. • In many cases, the girders supported considerable additional load after stirrup yielding and before failure. • In about one-third of the tests, some strand slip was observed prior to failure. • The direction of shear slip along diagonal cracks in the web- shear zone was almost always in the direction opposite to what would be expected if interface shear transfer contributes to the concrete contribution to shear resistance. Figure 70(a) illustrates the typical shear slip that was observed, and it is opposite to what is needed to produce the shear stress on the crack, shown in Figure 70(b). • The different events that led to failure in this testing pro- gram included the following: – Stirrup yield and rupture, – Stirrup yield and localized crushing near support, – Stirrup yield and distributed diagonal crushing over wide band of the web, – Stirrups that did not yield before localized crushing above the support, and – Stirrup yield followed by strand slip and localized crushing near support. The localized crushing that is observed near the support occurs in a region that also has very large shear stresses. 67 Table 10. Conditions at failure of girders. V Vd Vs Vcz Vag C T (a) Shear slip in experimental test Shear Slip (b) Shear resistance components Figure 70. Typical shear slip in girder test. We b-Shear Cracks En d Reactio n Forc e (kips ) Condition of We b Concrete Above Support Max. Stirrup Strain Strand Slip (in) Spacin g (in) Wi dth (mm) Shear Slip Bulb-Web Interface Slidin g (in) G1E 572.7 We b base crush 3.2 y 0.08 5.8 1.0 Large Yes G1W 662.0 We b base crush 3.7 y 0.07 3.7 1.0 Small Yes G2E 743.4 We b base crush 2.0 y 0.02 5.1 0.60 Yes 2.5 G2W 852.1 We b base crush 3.5 y 0.025 4.2 0.80 No Yes G3E 785.0 We b base crush 4.0 y No 4.7 0.55 Yes 4.0 G3W 854.0 We b base crush 4.0 y No 4.3 0.50 Yes Yes G4E 940.1 Good 1.0 y No 3.5 0.55 Small No G4W 940.1 Good 1.0 y No 3.1 0.30 Small No G5E 521.4 Bulb broken Fracture 0.02 5.7 >5.0 Yes 4.5 G5W 438.0 Sign 5.0 y No 6.1 2.5 Yes No G6E 760.3 We b base crush 3.1 y No 5.0 1.0 Yes 2.0 G6W 612.7 We b base crush 3.7 y 0.5 5.8 0.70 Yes 1.0 G7E 736.3 Sign 1.7 y No 4.6 0.90 Yes No G7W 626.5 We b base crush 3.7 y No 3.8 1.2 Yes Yes G8E 661.0 Field crushing 2.5 y No 4.0 1.5 Yes No G8W 667.1 Sign 1.7 y No 4.8 1.2 Yes No G9E 721.6 We b base crush 0.8 y 0.013 4.1 0.50 No 4.0 G9W 840.7 Sign 0.6 y No 3.1 0.30 No No G10E 746.5 Sign 1.7 y 0.01 3.9 1.0 Yes No G10W 939.7 We b base crush 2.4 y No 4.3 0.55 Yes Yes Sign: Modest local crushing or significant cracking in web or bottom bulb that typifies the initiation of failure.

68 This was evident in the direction of cracking and level of damage. Therefore, in many cases, it is appropriate to con- sider that the localized crushing failure was actually a failure induced by a combination of both high local compressive and shear stresses. This is discussed further in Appendix 11. Also presented in Appendix 11 is a discussion the defini- tion of the effective depth d. • The types of failures ranged from relatively ductile shear failures to very brittle and explosive shear failures. The most brittle and explosive failures were observed in mem- bers that failed due to local crushing and concrete com- pression shear failures between the bottom bulb and the girder web. In these members, the sudden loss of compres- sive and horizontal shear capacity resulted in an explosive failure of the web coupled with a large horizontal shearing between the bottom bulb and the web, as described for many of the failures presented in Figure 69. The more duc- tile shear failures were observed in members with light shear reinforcement (G5E), in which large numbers of strands were debonded (G6W), and in which failure occurred away from end regions (G8E). 2.4.5 Load-Deformation Response of Test Girders To complete this presentation of the overall strength and mode of failure of the test girders, it is also useful to present the measured load versus center point displacement relationships for all of the test girders. These results are given in Figure 71, in which the plots from 10 girders have been organized into two groups in accordance with the number of strands used in the girders. Girders 1, 2, 5, 9 and 10 are grouped in Figure 71(a), and their strands numbers are 32(G1), 38(G2), 24(G5), 34(G9) and 34(G10). The load-versus-displacement response of Gird- ers 3, 4, 6, 7, and 8 are shown in Figure 71(b), and all of these girders contained 42 strands that are each 0.6 inch in diameter. From these plots, the following observations can be made: • The load-deformation response was linear until first shear cracking. • After first shear cracking, there was a very small and almost imperceptible change in overall member stiffness. • The significant change in stiffness occurred at the onset of flexural cracking, and the response became progressively softer as the extent of flexural cracking increased. • The onset of yield of the shear reinforcement had little to no influence on the overall load-deformation response. • All plots have a similar initial elastic slope prior to cracking except Girder 4. A steel plate was attached on the bottom of Girder 4 before the test. That plate increased its elastic modulus, and as a result the girder had a higher initial elas- tic stiffness than the other nine girders. • The number of strands had the most influence on the load for flexural cracking and the subsequent drop in stiffness. 2.5 Cracking This section presents a summary of the measured cracking of the test girders and discusses the significance of these results. It is divided into several subsections, beginning with an introduction in Section 2.5.1 on the relevance of the meas- ured cracking behavior and the methods that were employed to measure and document cracking. Section 2.5.2 describes the development of cracking in a typical girder, and Section 2.5.3 summarizes the measured crack angles and crack spac- ing for all girders. Section 2.5.4 compares measured and predicted web-shear cracking loads and angles, while Sec- tions 2.5.5 and 2.5.6 compare measured and predicted 0 5 10 15 20 25 30 35 40 45 0 1 2 3 4 5 6 7 Vertical Deflection(in) Un ifo rm L oa d (ki ps /ft ) G3 G4 G6 G7 G8 G4 G8 G3 G7 G6 (b) Vertical displacements at middle span point for Girders 3, 4, 6, 7, and 8. 0 1 2 3 4 5 6 7 Vertical Deflection(in) 0 5 10 15 20 25 30 35 40 45 Un ifo rm L oa d (ki ps /ft ) G1 G2 G5 G9 G10 G1 G5 G9 G10 G2 (a) Vertical displacements at middle span point for Girders 1, 2, 5, 9, and 10 Figure 71. Load-deformation response of test girders.

69 flexure-shear and flexural cracking loads, respectively. Section 2.5.7 summarizes the crack widths and their development, and Section 2.5.8 presents the most significant observations on cracking. 2.5.1 Introduction The loads at which cracks occur, the angle of cracking, and the width and spacing of cracks are all important aspects of the behavior of prestressed concrete members. The load at shear cracking is important because this cracking can lead to serviceability problems due to corrosion or fatigue of trans- verse reinforcement. The angle of shear cracking is important for calculating the contribution of shear reinforcement to capacity because this angle is a good indicator of how many stirrups participated in lifting the diagonal compressive force above an inclined crack. The rate of growth of crack widths is important for evaluating the durability of structures in dif- ferent environments. In reviewing the results that are presented in the reminder of Section 2.5, it is useful to consider the following: • In the LRFD Sectional Design Model, the effectiveness of shear reinforcement is proportional to the cotangent of the angle of diagonal compression. Although the angle of diag- onal cracking is not necessarily equivalent to the angle of diagonal compression, it is still an important indicator for assessing the accuracy of the LRFD variable angle truss model. • With the LRFD Sectional Design Model, members can be designed for much higher shear stresses than permitted by the AASHTO Standard Specifications. If members are designed for these higher shear stresses, then shear crack- ing will occur at a lower fraction of the design shear strength. With the phasing out of the AASHTO Standard Specifications shear design provisions, the relationships for evaluating web-shear and flexure-shear cracking strengths will be lost. To evaluate whether these relationships are use- ful for assessing the state of cracking at service loads and whether they should continue to be used for serviceability design considerations, it is useful to examine whether the AASHTO Standard Specifications relationships are effec- tive at predicting the web-shear and flexure-shear cracking strengths for the test girders. • An outcome of NCHRP Project 12-61 was the develop- ment of simplified shear design provisions for structural concrete members that are applicable to members con- taining the minimum required amount of shear reinforce- ment and are not subjected to a net-axial tension. In this method, a variable angle truss model was introduced that uses the calculated angle of diagonal cracking from Mohr’s circle of stress for evaluating cotθ and the contribution of shear reinforcement. The measured crack angles for the test girders are also useful for evaluating the realism of this variable angle truss model. During each test, the loading was paused at several “load stages” so that discrete measurements could be taken, cracks could be marked and measured, and pictures could be taken. Cracks occurred and propagated with increasing load. Pic- tures for each loading stage were taken to record crack devel- opment. Each girder test was divided into many load stages, and hence there were several hundreds of pictures taken per test. It was necessary to find a way to extract the crack infor- mation stored in those pictures in an automated manner in order to produce crack drawings in an efficient and accurate manner. A crack recording method based on digital close- range photogrammetry was developed to track the develop- ment of cracking in the girders. Crack patterns were created, and then crack angles and spacing were computed for each girder test. This method is fully described in Appendix 11. 2.5.2 Crack Development and Patterns The development of cracking, as measured during the 13 load stages in Girder 1, is presented in Figure 72. This pattern of development is quite similar to what was recorded for each of the test girders; full crack patterns for each test girder are presented in the appendices. Prior to loading, and when the girders were delivered to the testing laboratory, diagonal cracks were present in the ends of most members, as shown for the extreme ends of Girder 1 in Figure 72(a). These initial cracks were predicted by the finite element analyses that are reported in Section 2.10 and are due to the tensile stresses caused by anchoring of the strands in the bottom bulb. These initial cracks did not propagate further during the loading, typically decreased in width with loading, and should be ignored as far as NCHRP Project 12-56 objectives are concerned. The first cracks to occur in all members were web-shear cracks in the end region of the members, as shown for the east and west ends of Girder 1 in Figures 72(a) and 72(b). Nearly all these first cracks, and most other web-shear cracks, occurred with a significantly loud popping sound. Thus, it was possible to pause the loading immediately after first cracking and after other significant cracking developments. Under increasing load, additional web-shear cracks occurred, typically further from the support, as shown at the east end of Girder 1 in Figures 72(a) through 72(f). It was unusual to first have the first web-shear crack occur some distance from the support and then have subsequent cracks form closer to the support, as apparent for the west end of Girder 1 in Figures 72(c) through 72(e). In this case, the development of

70 cracking close to the support was undoubtedly suppressed by the six draped strands that ran from 0.4L from the west sup- port to the top of the web. The onset of flexural cracking at mid-span is shown in Fig- ure 72(e).As the loading continued beyond this point, shown in Figures 72(e) through 72(h),existing flexural cracks propagated upward while new flexural and shear cracks developed. In the flexural region farther from mid-span, the effect of the shear caused what were initially flexural cracks to grow into flexure- shear cracks. Also during these load increases, the widths of existing cracks increased. The extent of shear cracking over the length of the girder was influenced by the level of prestressing and the magnitude of the design shear stress. For members designed for higher design shear stresses than those for Girder 1, the webs of the girders became heavily cracked over their entire length and the bottom bulbs became cracked to within a few feet of the support. In some of the girders designed for large shear stresses, a close to stable crack pattern developed, after which cracks only widened with increasing load. The majority of the web-shear cracks developed over the full height of the girder at one time and with a very audible sound. By contrast, the development of the flexure and flexure-shear cracks was more progressive and quieter. 2.5.3 Crack Angles and Spacing In this section, the crack angles and the spacing of cracks are summarized for all test girders. As illustrated in Figure 72, it is reasonable to characterize shear cracks as straight lines with one slope (or angle). Using the image analysis methods described in Appendix 11, a least squares procedure was used to find the average angle for each crack. Only the crack pro- files within the web were considered when assessments were made of the angle of best fit for each crack. An example of the making of this crack angle assessment is illustrated in Figure 73 for the east half of Girder 1 (G1E). The longitudinal position of each crack was taken as the point where each crack crossed the centroid line of the composite West End Mid-Span East End (a) Load Stage 1 (Load: 14.71 kips/ft) (b) Load Stage 2 (Load: 18.79 kips/ft) (c) Load Stage 3 (Load: 19.11 kips/ft) (d) Load Stage 4 (Load: 19.96 kips/ft) (e) Load Stage 5 (Load: 21.27 kips/ft) (f) Load Stage 6 (Load: 22.52 kips/ft) (g) Load Stage 7 (Load: 23.67 kips/ft) Figure 72. Crack pattern of Girder 1.

71 section. The shape of the curve for the distribution of angles with distance from the support is close to a parabolic curve. For G1E, the crack angle was approximately 45 degrees near the support. It then decreased to 25 degrees in the first shear design region, went back up to 45 degrees in the flexure-shear cracking zone, and then increased to the finally expected 90 degrees near mid-span, where only flexural cracking occurred. Observations from the other girder tests were similar, as apparent from the crack angle diagrams shown for each girder in Figure 74. In girders designed for higher shear stresses, such as Girders 4 and 9, the cracking was very extensive and the many crack angle data points illustrated a clear parabolic pattern; see Figures 74[4(a), 4(b), 9(a), and 9(b)]. The pattern of cracking was also used to assess the average spacing of cracks. The horizontal spacing Sx, or the horizon- tal distance between any two adjacent cracks, can be com- puted from their positions. Furthermore, the spacing of any two adjacent cracks S can be computed from Sx and from the crack angle θ as S = Sx sinθ. Table 11 lists the average spacing of web-shear and flexure-shear cracks for all the tests. The horizontal spacing of the web-shear cracks was com- puted for the centroidal axis of the composite section, while for flexure-shear cracks the spacing was computed along a line at a height of 23 inches (584 millimeters) from the bot- tom. Table 11 also shows the details of the stirrup layouts. As apparent from the values in the table, there is some, but not (h) Load Stage 8 (Load: 24.56 kips/ft) (i) Load Stage 9 (Load: 26.03 kips/ft) (j) Load Stage 10 (Load: 26.59 kips/ft) (k) Load Stage 11 (Load: 27.44 kips/ft) (l) Load Stage 12 (Load: 28.75 kips/ft) (m) Load Stage 13 (Load: 30.09 kips/ft) Figure 72. (Continued). Centroid axis of Composite section Flexure Shear Web Shear 90 80 70 60 50 40 30 20 10 50100150200250300 0 0 Distance from Support (in) Cr ac k A ng le (d eg ) Figure 73. Crack angle distribution of G1E.

72 Flexure-Shear Web-Shear Web-Shear Flexure-Shear 0 10 20 30 40 50 60 70 80 90 0 50 100 150 200 250 300 Distance From Support (inch) Cr ac k An gl e (de g) 0 10 20 30 40 50 60 70 80 90 Cr ac k An gl e (de g) Flexure-Shear Web-Shear Flexure-Shear Web-Shear (2.a) Crack Angle of G2W 0 10 20 30 40 50 60 70 80 90 0 50 100 150 200 250 300 Distance From Support (inch) Cr ac k An gl e (de g) 0 10 20 30 40 50 60 70 80 90 Cr ac k An gl e (de g) (1.a) Crack Angle of G1W 0 50 100 150 200 250 300 Distance From Support (inch) (1.b) Crack Angle of G1E 0 50 100 150 200 250 300 Distance From Support (inch) (2.b) Crack Angle of G2E Flexure-Shear Web-Shear Flexure-Shear Web-Shear Flexure-Shear Web-Shear Flexure-Shear Web-Shear 0 10 20 30 40 50 60 70 80 90 0 50 100 150 200 250 300 Distance From Support (inch) Cr ac k An gl e (de g) 0 10 20 30 40 50 60 70 80 90 Cr ac k An gl e (de g) (3.a) Crack Angle of G3W 0 50 100 150 200 250 300 Distance From Support (inch) (3.b) Crack Angle of G3E 0 10 20 30 40 50 60 70 80 90 0 50 100 150 200 250 300 Distance From Support (inch) Cr ac k An gl e (de g) 0 10 20 30 40 50 60 70 80 90 Cr ac k An gl e (de g) (4.a) Crack Angle of G4W 0 50 100 150 200 250 300 Distance From Support (inch) (4.b) Crack Angle of G4E Figure 74. Crack angle distribution along centroid axis of composite section.

73 Flexure-Shear Web-Shear Flexure-Shear Web-Shear 0 10 20 30 40 50 60 70 80 90 0 50 100 150 200 250 300 Distance From Support (inch) Cr ac k An gl e (de g) 0 10 20 30 40 50 60 70 80 90 Cr ac k An gl e (de g) (5.a) Crack Angle of G5W 0 50 100 150 200 250 300 Distance From Support (inch) (5.b) Crack Angle of G5E Flexure-Shear Web-Shear Flexure-Shear Web-Shear 0 10 20 30 40 50 60 70 80 90 0 50 100 150 200 250 300 Distance From Support (inch) Cr ac k An gl e (de g) 0 10 20 30 40 50 60 70 80 90 Cr ac k An gl e (de g) (6.a) Crack Angle of G6W 0 50 100 150 200 250 300 Distance From Support (inch) (6.b) Crack Angle of G6E Flexure-Shear Web-Shear Flexure-Shear Web-Shear 0 10 20 30 40 50 60 70 80 90 0 50 100 150 200 250 300 Distance From Support (inch) Cr ac k An gl e (de g) 0 10 20 30 40 50 60 70 80 90 Cr ac k An gl e (de g) (7.a) Crack Angle of G7W 0 50 100 150 200 250 300 Distance From Support (inch) (7.b) Crack Angle of G7E Flexure-Shear Web-Shear Flexure-Shear Web-Shear 0 10 20 30 40 50 60 70 80 90 0 50 100 150 200 250 300 Distance From Support (inch) Cr ac k An gl e (de g) 0 10 20 30 40 50 60 70 80 90 Cr ac k An gl e (de g) (8.a) Crack Angle of G8W 0 50 100 150 200 250 300 Distance From Support (inch) (8.b) Crack Angle of G8E Figure 74. (Continued).

74 Table 11. Average spacing of shear cracks. Figure 74. (Continued). CEB-FIP = Comité Européen du Béton (European Committee for Concrete)–Fédération Internationale de la Précontrainte (International Federation for Prestressing). Web-Shear Cracking Flexure-Shear Cracking Average Spacing Average Spacing Girder End Stirrup Layout Test (in) CEB-FIP (in) Stirrup Layout Test (in) CEB-FIP (in) G1E #4@12 5.82 12.76 #4@24 7.53 17.04 G1W #4@12 3.71 12.71 #4@24 7.26 17.08 G2E #5@11 5.13 11.09 #5@17/#4@22 5.56 13.80 G2W #5@11 4.18 11.09 #5@17/#4@22 4.34 13.76 G3E #4@8 4.70 10.28 #4@12/#4@24 5.40 12.68 G3W #4@8 4.24 8.17 #4@12/#4@24 4.70 12.76 G4E #5@6 3.52 8.26 #5@10/#@24 3.46 10.59 G4W #5@6 3.08 6.73 #5@10/#@24 3.73 10.58 G5E #3@20 5.66 20.69 #3@20 7.17 18.98 G5W #3@20 6.06 20.38 #3@20 7.97 18.03 G6E #5@12 4.95 11.64 #5@20/#3@24 9.21 14.97 G6W #5@12 5.80 11.74 #5@20/#3@24 8.30 14.89 G7E #4@8 4.60 10.28 #4@12/#4@24 5.62 12.66 G7W #4@8 3.78 10.28 #3@23 6.36 19.20 G8E #4@8 3.98 10.27 #4@12/#4@24 7.50 12.69 G8W #4@8 4.81 10.27 #4@12/#4@24 5.47 12.64 G9E #5@6.5 4.09 8.58 #4@7.5/#4@24 4.92 10.08 G9W #5@4 3.08 7.09 #4@7.5/#4@24 4.40 10.31 G10E #5@9 3.90 10.09 #4@10/#4@22 6.36 11.98 G10W #5@9 4.35 10.05 #4@10/#4@22 4.61 13.31 Flexure-Shear Web-Shear Flexure-Shear Web-Shear Flexure-Shear Web-Shear Flexure-Shear Web-Shear 0 10 20 30 40 50 60 70 80 90 0 50 100 150 200 250 300 Distance From Support (inch) Cr a ck A ng le (d eg ) 0 10 20 30 40 50 60 70 80 90 Cr ac k An gl e (de g) (9.a) Crack Angle of G9W 0 50 100 150 200 250 300 Distance From Support (inch) (9.b) Crack Angle of G9E 0 10 20 30 40 50 60 70 80 90 0 50 100 150 200 250 300 Distance From Support (inch) Cr a ck A ng le (d eg ) 0 10 20 30 40 50 60 70 80 90 Cr ac k An gl e (de g) (10.a) Crack Angle of G10W 0 50 100 150 200 250 300 Distance From Support (inch) (10.b) Crack Angle of G10E

75 a strong, correlation between crack spacing and the amount and spacing of shear reinforcement. The same effect is pre- dicted by the CEB-FIP (Comité Européen du Béton [Euro- pean Committee for Concrete]–Fédération Internationale de la Précontrainte FIP [International Federation for Prestress- ing]) model for crack spacing as described below. The CEB-FIB Code (27) expression for the average crack spacing accounts for the influence of several variables in the following manner: where: c = concrete cover, s = maximum spacing between reinforcing bars, db = bar diameter, ρef = effective reinforcement ratio, k1 = coefficient for the bond properties of the bar, and k2 = coefficient to account for the strain gradient. It is suggested that the spacing of the inclined cracks, smθ, be taken as where: smx and smv = spacing of the longitudinal and transverse reinforcement, respectively, and θ = angle of the inclined crack. Table 11 also gives the crack spacing predicted by the CEB- FIP model. The measured and predicted crack spacings are compared in Figure 75. These comparisons illustrate that the average measured spacing was about half of the value pre- dicted by the CEB-FIP procedure. s s s m mx mv θ θ θ = + ⎛ ⎝⎜ ⎞ ⎠⎟1 36 sin cos ( ) s c s k k d m b ef = + +2 10 351 2( ) ( )ρ The length over which flexural cracks occurred and the average spacing for those cracks are listed in Table 12. In this table, Lw and Le are the lengths of the distances from mid- span to the flexural crack that was closest to the west and east supports, respectively; L is the total length of the flexural cracking region; and N is the total number of flexural cracks. The average spacing of the flexural cracks, S, and the coeffi- cient of variation are also presented. The mean of the aver- age spacing is 5.56 inches (141 millimeters), with an average COV of 0.44. The average spacing of flexural cracks depends on the bond properties of the prestressing strands, which were reasonably constant throughout the tests. The largest average crack spacing was in Girder 6 (S = 7.80 inches), for which 10 strands were debonded on the west end of the girder. The girders that were loaded close to their flexural capacity, such as Girder 4, had the smallest average crack spacing, at 4.51 inches. The bottom bulb of Girder 10 was Figure 75. Ratio of the measured and CEB-FIP predicted average shear crack spacing. Girder End Lw (in) Le (in) L (in) Crack Numbers N Average Spacing S (in) COV G1 123.2 125.7 248.9 51 4.98 0.34 G2 220.1 200.3 420.4 93 4.57 0.40 G3 160.5 161.3 321.9 71 4.60 0.40 G4 209.7 232.3 442.0 99 4.51 0.45 G5 122.0 183.3 305.3 56 5.55 0.53 G6 130.0 127.4 257.4 34 7.80 0.52 G7 85.6 151.7 237.3 32 7.65 0.41 G8 135.3 157.8 293.1 59 5.05 0.50 G9 226.5 218.6 445.1 85 5.30 0.39 G10 246.8 245.6 248.9 - - - Average 5.56 0.44 - Not available. Lw and Le = lengths of the distances from mid-span to the flexural crack that was closest to the west and east supports, respectively. L = total length of the flexural cracking region. N = total number of flexural cracks. Table 12. Average spacing of flexural cracks. Test/CEB-FIP 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0 50 100 150 200 250 db /ρef (in) (a) Comparison of average spacing for web-shear cracks 0 50 100 150 200 250 db /ρef (in) (b) Comparison of average spacing for flexure-shear cracks Test/CEB-FIP 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

76 covered by a fiber-reinforced plastic sheet, so no flexure cracks were marked during the test. 2.5.4 Web-Shear Cracking This section compares the loads and the angles of first diago- nal cracking, as well as the angles for the primary web-shear cracks, with the web-shear cracking loads predicted using the AASHTO Standard Specifications and the angles of diagonal compression calculated from the LRFD Sectional Design Model. The occurrence of the first diagonal crack is a significant event in the life of a structure because it signifies the point at which stirrups begin to significantly participate in the response and fatigue concerns must be evaluated.That cracking is also significant because it is often desirable, and sometimes required, that members remain uncracked under service loads in order to ensure durability of the structure. The first load stage was terminated when the first, very audible, web- shear crack occurred. It was also possible to verify the first cracking load by the sudden increased in stirrup strains that occurred. The first diagonal cracking often consisted of two or three diagonal cracks that appeared simultaneously. Figure 76 shows an example of first cracking for the east end of Girder 1(G1E). In this example, the first crack crossed the centroid of the composite section at an angle of 43 degrees. The intersection point was located at Lws = 41.17 inches (1,046 millimeters) from the center of the east support. Table 13 summarizes the measured web-shear cracking loads and the locations of the first web-shear crack from the center of the support for all girder tests. It can be seen that first Test STD Ends LocationLws (in) Load(kips/ft) Vtest (kips) fpc (psi) Vcw (kips) cw test V V G1E 41.17 14.71 317.3 907.4 270.1 1.17 G1W 120.93 18.09 269.9 1086.6 313.8 0.86 G2E 47.03 18.51 390.2 903.8 268.2 1.45 G2W 64.66 21.74 426.4 1103.8 331.2 1.29 G3E 50.05 16.11 335.5 1224.0 328.3 1.02 G3W 71.44 14.96 284.9 1236.4 329.8 0.86 G4E 57.09 14.26 288.6 1036.7 307.7 0.94 G4W 63.33 15.44 304.5 1041.1 308.2 0.99 G5E 40.33 16.80 363.5 528.2 262.7 1.38 G5W 55.60 12.20 248.5 539.3 264.1 0.94 G6E 66.40 16.19 315.1 930.3 273.4 1.15 G6W 31.29 16.70 367.4 452.6 216.1 1.70 G7E 55.55 17.93 365.3 1058.2 287.8 1.27 G7W 48.66 18.90 395.9 1052.8 287.1 1.38 G8E 53.63 14.50 297.7 838.8 266.0 1.12 G8W 59.71 15.71 314.5 844.1 266.7 1.18 G9E 56.03 16.00 325.3 940.7 250.9 1.30 G9W 52.67 21.60 445.2 1100.5 301.2 1.48 G10E 55.34 15.57 317.5 759.3 233.7 1.36 G10W 40.05 19.30 418.0 1091.6 311.4 1.34 Average 1.21 COV 0.19 STD = AASHTO Standard Specifications. Centroid axis of composite section First Web Shear Crack 12 in LWS = 41.17 in Figure 76. Location of first web-shear cracking at east end of Girder 1. Table 13. First web-shear cracks.

77 cracking occurred within less than one girder depth (73 inches, or 1,854 millimeters) from the center of the support for all tests except G1W. In Table 13, the AASHTO Standard Spec- ifications web-shear cracking load is given for each end of each girder, and a comparison is made with the measured cracking load. The mean of the shear strength ratio Vtest/Vcw,STD is 1.21, with COV of 0.19. It is apparent that the AASHTO Standard Specifications expression for Vcw provides a usually conserva- tive and reasonably accurate prediction of the first web-shear cracking strength. Figure 77 shows the ratio of the measured web-shear cracking load to the design shear strength for all the test girders. Ratios range from 0.33 (for G4E) to 0.87 (for G5E). This is useful for assessing whether the member is likely to be cracked in shear under service load levels. To assess the significance or lack of significance of this observation, it is useful to examine the derivation of the AASHTO Standard Specifications expression for web-shear cracking strength, Vcw. Equation 37 was derived from the Mohr’s circle of stress, with the state of stress taken as that at the centroidal axis of the girder and the tensile cracking strength of the concrete taken as approximately 4 where f c´ is in psi units. In this rela- tionship, the cracking stress increases as a linear function of the applied precompression stress fpc. For the calculated value of Vcw presented in Table 13, the full effective prestress force in the given location was used to compute fpc, and d was taken as the distance from the top of the deck to the centroid of the strands in the bottom half of the girder. The value of d was usu- ally larger than 63 inches. Because the first crack occurred close to the support and the prestressing was anchored in the bottom of the member, the actual fpc at mid-depth is expected to be less f c´ V f f b d Vcw c pc w p= + +( . ´ . ) ( )3 5 0 30 37 than that used in the calculations, and yet the expression for Vcw was typically conservative. The apparent contradiction suggests that either the principal tensile stress is higher than 4 or the shear forces carried by the top flange and the bottom bulb are not negligible, or both. Table 14 presents the measured and calculated angles of diagonal cracking. The predicted angle of diagonal cracking was calculated using Mohr’s circle of stress, the full magni- tude of fpc, and Equation 38. where: The predicted angle of diagonal cracking was also calculated from a nonlinear finite element analysis Vector2 (28), as explained in Section 2.10. The mean ratio of θtest/θMohr is 1.21, with a COV of 0.10. The high mean value of 1.29 is to be expected given the likely over- estimation of fpc. The mean ratio of θtest/θVector2 is 1.21, with a COV of 0.09. There is a relatively close correlation between the angles of cracking predicted by the two procedures. For a member with shear reinforcement, the more impor- tant angle of web-shear cracking is not at the end of the girder but at the first shear design span, because it is this latter angle that determines the effectiveness of the shear reinforcement. Figure 78 illustrates that the angle of diagonal cracking for much of this design shear span was reasonably constant. This first design shear span can be said to typically extend from about d distance away from the support to the point where web-shear cracking ends and flexure-shear cracking begins. The average angle for that crack average region was computed f ft c= 4 ´ cot ( )θ = +1 38 f f pc t f c´ 61 % 54 %5 1% 44 % 49 % 53 %71 % 58 % 60 % 51 % 69 %87 % 33 % 47 % 50 %65 % 53 % 73 % 60 % 36 % 0 200 400 600 800 1000 G1 E G1 W G2 E G2 W G3 E G3 W G4 E G4 W G5 E G5 W G6 E G6 W G7 E G7 W G8 E G8 W G9 E G9 W G1 0E G1 0W Test Specimen Su pp or t R ea ct io n (K ips ) LRFD Design Cracking Figure 77. Ratio of the web-shear cracking load to the design shear strength.

78 for each girder end, and results are presented in Table 15. Equation 38 was also used for predicting the cracking angle in the same region. In this case, the use of that equation is more appropriate than for the end region because the full prestressing force must be effective. The mean ratio of cotθtest/cotθMohr for this first shear design span was 1.06, with a COV of 0.16. The predicted angle matches reasonably well and slightly conservatively with that measured except for Girders 5 and 6. It is also useful to compare the measured cracking angles with the LRFD Sectional Design Model’s angle of diagonal compression, as presented in Table 5.8.3.4.2-1 of the second edition (1994) of the LRFD specifications. The mean ratio of cotθtest/cotθLRFD is 0.91, with a COV of 0.08. The average ratio Mohr Circle Vector2 Girder End ' cf (ksi) test (deg) fpc(psi) Mohr (deg) Mohr test fpc (psi) Vector2 (deg) Vector2 test G1E 12.1 43.0 907.4 29.7 1.45 622 32.8 1.31 G1W 12.1 30.0 1,086.6 28.2 1.06 1,108 28.1 1.07 G2E 12.6 38.0 903.8 29.9 1.27 880 30.2 1.26 G2W 12.6 37.0 1,103.8 28.3 1.31 1,194 27.6 1.34 G3E 15.9 38.0 1,224.0 28.4 1.34 950 30.5 1.25 G3W 15.9 28.0 1,236.4 28.3 0.99 1,143 29.0 0.97 G4E 16.3 35.0 1,036.7 29.9 1.17 1,034 29.9 1.17 G4W 16.3 34.0 1,041.1 29.8 1.14 1,109 29.3 1.16 G5E 17.8 43.0 528.2 35.3 1.22 348 37.9 1.14 G5W 17.8 35.0 539.3 35.2 0.99 531 35.3 0.99 G6E 12.7 38.0 930.3 29.7 1.28 1,252 27.2 1.40 G6W 12.7 46.0 452.6 35.2 1.31 397 36.1 1.27 G7E 12.5 32.0 1,058.2 28.6 1.12 1,069 28.5 1.12 G7W 12.5 38.0 1,052.8 28.6 1.33 920 29.8 1.28 G8E 13.3 36.0 838.8 30.8 1.17 1,186 27.9 1.29 G8W 13.3 33.0 844.1 30.7 1.07 1,186 27.9 1.18 G9E 9.6 35.0 940.7 28.5 1.23 982 28.1 1.25 G9W 9.6 35.0 1,100.5 27.1 1.29 1,153 26.7 1.31 G10E 10.6 35.0 759.3 30.7 1.14 883 29.4 1.19 G10W 10.6 35.0 1,091.6 27.6 1.27 1,072 27.8 1.26 Average 1.21 Average 1.21 COV 0.10 COV 0.09 Table 14. Crack angles of first web-shear cracks. 90 80 70 60 50 40 30 20 10 50100150200250300 0 0 Cr ac k A ng le (d eg ) Distance from Support (inch) Centroidal Axis Flexure Shear Web Shear Crack Average Region 63'' Figure 78. Average crack angle of web-shear cracks for G1E. Mohr Circle LRFD Girder End ' cf (ksi) test (deg) Mohr(deg) Mohr test cot cot LRFD (deg) LRFD test cot cot G1E 12.1 26.7 29.2 1.11 23.2 0.85 G1W 12.1 28.4 27.8 0.98 24.9 0.86 G2E 12.6 28.5 29.8 1.05 25.5 0.88 G2W 12.6 30.9 28.2 0.90 27.8 0.88 G3E 15.9 26.1 27.5 1.06 23.7 0.90 G3W 15.9 27.1 27.5 1.02 23.7 0.86 G4E 16.3 28.7 28.8 1.00 28.5 0.99 G4W 16.3 30.7 28.8 0.93 28.5 0.91 G5E 17.8 23.7 33.9 1.53 21.8 0.91 G5W 17.8 25.6 33.9 1.40 21.8 0.83 G6E 12.7 28.2 28.7 1.02 23.7 0.82 G6W 12.7 26.4 32.3 1.27 25.9 0.98 G7E 12.5 25.8 26.8 1.04 24.2 0.93 G7W 12.5 25.5 26.8 1.06 24.2 0.94 G8E 13.3 27.7 28.4 1.03 23.7 0.84 G8W 13.3 28.3 28.4 1.00 23.7 0.82 G9E 9.6 28.5 28.3 0.99 32.8 1.19 G9W 9.6 32.2 27.1 0.81 30.0 0.92 G10E 10.6 29.4 29.2 0.99 28.8 0.98 G10W 10.6 28.3 26.8 0.94 27.6 0.97 Average 1.06 Average 0.91 COV 0.16 COV 0.08 Table 15. Average crack angle for web-shear cracks.

79 of 0.91 suggests that the LRFD specifications are unconserv- ative for estimating the angle of diagonal compression, and therefore for evaluating the contribution of the shear rein- forcement, if the angle of diagonal compression and that of cracking are equivalent. These comparisons of the angles of cracking in the end region of the girder and in the first shear design region beyond that end region demonstrate the appropriateness of the LRFD specifica- tions Article 5.8.1, which require the designer to differentiate between shear design for flexural regions (the first shear design region) and regions near discontinuities.The latter region can be defined as the portion of the girder within one overall girder depth from the centerline of the support, as shown in Figure 78. 2.5.5 Flexure-Shear Cracking This section examines the measured loads for flexure- shear cracking and the angles of those cracks. Consistent with their name, flexure-shear cracks develop from the extension of flexural cracks in regions of high flexure and significant shear. They extended in the region from the end of the web-shear cracking region to near mid-span. The occurrence of flexure-shear cracking is indicated by a rapid change in stirrup strain gage readings. For each half of the girder, the flexure-shear crack that was farthest from mid- span was selected for examination. Figure 79 shows the selected flexure-shear crack for the east end of Girder 1, in which the crack location is reported as the distance, LFS, from the center of the support to the location of the flexural crack from which the flexure-shear crack formed. Table 16 lists the selected flexure-shear crack’s position, its angle, the distrib- uted load at cracking, and the moment and shear forces at the location of the flexural crack from which that selected flexure-shear crack originated. The measured angles for flex- ure-shear cracking range from 30.2 degrees to 60.8 degrees. The occurrence of very steep shear cracks may be of concern if the member is limited by its shear capacity in this region Centroid axis of Composite section LFS = 17.69 ft 12 inSelected Flexure- Shear Crack Figure 79. Location of selected flexure-shear crack for evaluation at G1E. Test STD Girder End Position LFS (ft) Angle (deg) Load (kips/ft) M (k-ft) V (kips) Mcr (k-ft) Vci (kips) M/Mcr V/Vci G1E 17.68 51.3 24.13 6,785.9 176.6 5,628.0 182.2 1.21 0.97 G1W 14.71 46.4 26.34 6,718.2 271.0 5,388.9 255.7 1.25 1.06 G2E 12.46 34.6 26.82 6,151.8 336.3 6,340.3 388.6 0.97 0.87 G2W 12.16 39.0 26.82 6,049.7 344.4 5,996.2 382.6 1.01 0.90 G3E 15.18 39.4 28.634 7,439.4 281.1 6,996.6 306.7 1.06 0.92 G3W 15.96 42.8 28.634 7,649.3 258.9 6,985.8 277.8 1.09 0.93 G4E 10.70 31.3 31.8 6,544.4 454.6 7,270.2 553.0 0.90 0.82 G4W 11.08 30.2 31.04 6,552.6 432.1 7,262.1 526.4 0.90 0.82 G5E 13.39 31.1 16.59 3,991 192.7 5,222.7 299.4 0.76 0.64 G5W 18.57 59.8 19.97 5,737.9 128.4 5,151.2 156.5 1.11 0.82 G6E 14.36 35.8 34.08 6,255.3 288.9 7,892.4 557.9 0.79 0.74 G6W 15.09 39.6 34.09 6,257.1 411.2 5,614.9 413.5 1.11 0.99 G7E 16.06 38.0 31.85 8,537.7 284.8 7,690.8 294.3 1.11 0.97 G7W 13.11 37.0 32.24 7,650.2 383.3 7,738.3 429.0 0.99 0.89 G8E 16.01 39.9 35.5 7,720.8 288 7,535.1 319.7 1.02 0.90 G8W 16.82 36.2 35.5 8,791.6 233.5 7,524.0 237.6 1.17 0.98 G9E 12.05 35.0 23.49 5,265.3 304.2 6,116.3 392.7 0.86 0.77 G9W 13.06 41.4 24.3 5,752.3 290.1 5,992.9 340.2 0.96 0.85 G10E 14.64 46.2 22.87 5,815.6 236.8 5,337.7 254.7 1.09 0.93 G10W 17.38 60.8 22.01 6,139.4 167.7 6,412.8 209.6 0.96 0.80 Average 1.02 0.88 COV 0.13 0.11 Table 16. Flexure-shear cracks.

80 because there will then be fewer stirrups carrying the load than would be calculated by either the AASHTO Standard Specifications or the LRFD specifications. In Table 16, the flexure-shear cracking loads calculated by the AASHTO Standard Specifications are also presented and compared with the measured values. In the AASHTO Stan- dard Specifications, the flexure-shear cracking strength, Vci, is calculated by Equation 39. where: where: I = moment of inertia of the section resisting externally applied factored loads. In this relationship, Vci consists of three terms. The sum of the latter two is the shear force corresponding to flexural cracking, and the first term is the increment in shear force that is expected to lead to the formation of a shear crack from the flexure crack. When computing the flexure-shear strength, the flexural cracking stress is taken as (in psi units). The shear force Vtest for the crack selected for evaluations of the flexure-shear cracking load was computed at the section LFS from the centerline of the adjacent support. (LFS is the dis- tance from the center of the support to the location of the flexural crack.) The mean ratio of the test shear force Vtest to the predicted shear cracking strength Vci is 0.88, with a COV of 0.11. Therefore, the AASHTO Standard Specifications are somewhat unconservative for most of the test results. In the second-to-last column of Table 16, the ratio of the moment at the location of the selected flexure-shear crack (M) to the cal- culated cracking moment (Mcr) for the same location is given. The mean ratio is 1.02, with a COV of 0.13. Since the flexure- shear crack typically formed as the extension of a flexural crack, the flexural cracking strength is reasonably well pre- dicted by using a cracking stress of (in psi units). This result also implies that the unconservatism of the Vci expres- sion of the AASHTO Standard Specifications is the result of an unconservatism in the first term of Equation 39 for beams with depths like those of the test girders. 2.5.6 Flexural Cracking Table 17 compares measured and computed flexural cracking loads. To assess when flexural cracking occurred, a linear variable displacement transducer (LVDT) was attached to the bottom bulb at mid-span to measure the change in displacement over the 6 f c´ 6 f c´ M I y f f fcr t c pe d= + −( / )( ´ ) ( )6 40 V f b d V V M M ci c w d i cr = + +0 6 39. ´ ( ) max central 48 inches of the span.Columns 2 through 4 in this table list the distributed load at first cracking, the average strain measured by the bottom LVDT, and the corresponding cracking moment. Both AASHTO Standard Specifications and LRFD specifi- cations take the modulus of rupture fr as in computing the cracking moment. Table 17 also lists the predicted cracking moment and the predicted horizontal strain increase for cal- culations using the AASHTO Standard Specifications. The pre- dictions were based on the prestressing strains measured before testing and take into account the strain changes in the strands due to the external loading. The average ratio of the measured to predicted cracking strain is 0.73, with a COV of 0.12, and the average ratio of the measured to predicted cracking moment is 0.88, with a COV of 0.06. The comparison shows that the cracking moment prediction fits the test result well, but it also suggests that a better fit would be obtained if the modulus of rupture fr were taken as less than . 2.5.7 Crack Widths This section summarizes measured crack widths. The growth in crack widths is important for a number of reasons. In the LRFD model, the concrete contribution to shear resist- ance is limited by the slip resistance along cracks. This inter- face shear transfer resistance, also referred to as “aggregate interlock,” is a function of the width and smoothness of shear cracks. The expression used in the derivation of the LRFD specifications is shown as Equation 41 (29). According to this expression, the interface transfer resis- tances for crack widths of 0.012, 0.024, and 0.04 inch (0.3, 0.6, and 1.0 millimeter) are 63 percent, 43 percent, and 31 percent, respectively, of the shear slip resistance of a hairline crack of width 0.002 inch (0.05 millimeter). These values were v f w a ci c = + + 2 16 0 31 24 0 63 . ´ . . (in inches and psi) (41) 7 5. ´f c 7 5. ´f c Test AASHTO Standard SpecificationsGirder End Load(kips/ft) Strain ( 610 ) Mcr (k-ft) Strain ( 610 ) Mcr (k-ft) STD Test cr,STD Test,cr M M G1 19.56 661.1 6,024.5 782.6 6,385.8 0.84 0.94 G2 21.56 683.1 6,641.5 757.0 7,157.6 0.90 0.93 G3 23.14 724.9 7,127.1 961.6 7,984.3 0.75 0.89 G4 26.28 667.6 8,094.2 956.9 10,081.0 0.73 0.83 G5 16.75 508.7 5,159.0 696.4 5,734.2 0.73 0.90 G6 23.70 703.4 7,298.5 1,089.6 8,878.4 0.65 0.82 G7 23.27 808.3 7,167.2 1,299.2 8,795.1 0.62 0.81 G8 25.70 802.7 7,915.6 1,244.3 8,662.2 0.65 0.91 G9 20.21 634.3 6,224.7 865.5 6,770.9 0.73 0.92 G10 20.01 777.3 6,163.1 1,094.3 7,307.5 0.71 0.84 Average 0.73 0.88 COV 0.12 0.06 Table 17. Flexure cracks and flexural cracking moment.

81 calculated using a maximum aggregate size of 0.50 inch. It has been suggested that for very high-strength concrete, cracks are so smooth that the aggregate size should be taken as zero in the use of Equation 39. If this is done, then the drop in shear resistance is even more sensitive to crack width, with only 51 percent, 32 percent, and 21 percent of the resistances being available at crack widths 0.012, 0.024, and 0.04 inch (0.3, 0.6, and 1.0 millimeter), respectively, as was available along a hairline crack of width 0.002 inch (0.05 millimeter). Crack width is also important for evaluating the durability of a member. The PCI Bridge Committee guidelines suggested that cracks of up to 0.006 inch (0.15 millimeter) are generally considered acceptable, while once a crack exceeds 0.0012 inch (0.3 millimeter), repair using epoxy grouting techniques are warranted to protect the reinforcement from salt water pen- etration and corrosion. In heavily cracked members, the com- bination of average crack width and crack spacing can be used for assessing the principal tensile strain in the member because the elastic tensile strain in concrete at cracking is very small. During the experiments, crack widths were measured using a crack comparator gage at each load stage. Prefabri- cated crack width markings were then taped beside the asso- ciated cracks, and this information was recorded in pictures. The crack widths were measured in millimeters because of the ready availability of crack comparator gages. This process is illustrated in Figure 80. Table 18 summarizes the development of crack widths with increasing load. At each load stage for each girder, the maximum crack width in the web-shear zone, the flexure- shear zone, and the flexural zone was recorded. Crack widths are given in millimeters. Figure 81 shows the growth of the web-shear cracks with loading. The maximum measured crack width is plotted on the x-axis, while the external test load is plotted on the y-axis. The results from the 20 web- shear regions were classified into five groups according to the different effective stirrup strengths, ρvfyv. The first group (Girders 1 and 5) had low ρvfyv values that ranged from 140 psi to 389 psi, the second group (Girders 3 and 6) and the third group (Girders 7 and 8) had average ρvfyv ranging from 557 to 577 psi. The fourth group (Girders 2 and 10) had moderately high ρvfyv values ranging from 745 to 751 psi. The last group (Girders 4 and 9) had the highest ρvfyv values ranging from 1,040 to 1,113 psi. It can be seen from Figure 81 that once cracking occurred, the maximum crack width reached between 0.3 millimeters and 0.5 millimeters. The low ρvfyv values were associated with the higher maximum crack width values. The measured maximum flexure-shear crack widths are shown in Figure 82. Compared with web-shear crack plots of Figure 81, the plots of Figure 82 show that the flexure- shear cracks opened faster with increasing load once flex- ure-shear cracking had occurred. The maximum crack width for the flexure-shear region of G7W was larger than the maximum flexure-shear crack widths for other girders because of the low amount of stirrup reinforcement in G7W (119 psi). The maximum flexural cracks measured are plotted in Figure 83, with the vertical axis being M for Figure 83(a) and M/Mcr for Figure 83(b), where Mcr was calculated using a tensile fiber cracking stress of (in psi units). As dis- cussed previously, flexural cracking occurred a little earlier than predicted, as apparent from the initial M/Mcr values plotted in Figure 83(b). The plots of Figure 83 show that after flexural cracking occurred, the maximum crack width increased linearly with increasing external moment. 2.5.8 Summary of Primary Observations From the comparison of measured values with (a) crack- ing loads calculated using the AASHTO Standard Specifica- tions, (b) crack angles calculated using Mohr’s circle of stress and angles of diagonal compression calculated using the LRFD specifications, and (c) crack spacings predicted using the CEB-FIP model, some of the key observations are as follows: • Typically, web-shear cracks occurred very suddenly, along straight lines, and with a significantly loud “pop.” • The first web-shear crack usually occurred within a longi- tudinal distance equal to the overall height of the member from the center of the support. This shear cracking was within a region of discontinuity, as defined by Article 5.8.1.2 of the LRFD specifications. These web-shear cracks had angles ranging from 28 degrees to 46 degrees, with an 7 5. ´f c Figure 80. Crack measurement.

82 Girder 1 West Mid East Load (kips/ft) WS (mm) FS (mm) F (mm) FS (mm) WS (mm) 14.71 0.00 0.00 0.00 0.00 0.25 18.79 0.00 0.00 0.00 0.00 0.35 19.11 0.35 0.00 0.00 0.00 0.40 19.96 0.40 0.00 0.00 0.00 0.40 21.17 0.40 0.00 0.05 0.00 0.50 22.52 0.40 0.00 0.05 0.00 0.55 23.67 0.40 0.05 0.10 0.10 0.80 24.56 0.40 0.15 0.15 0.30 1.0 26.03 >0.40 >0.15 >0.15 >0.30 >1.0 26.59 0.50 0.30 0.25 27.44 0.75 0.50 0.25 28.75 1.00 0.55 0.30 30.09 >1.00 >0.55 >0.30 Girder 2 West Mid East Load (kips/ft) WS (mm) FS (mm) F (mm) FS (mm) WS (mm) 18.79 0.00 0.00 0.00 0.00 0.40 21.74 0.30 0.00 0.00 0.00 0.40 25.94 0.40 0.10 0.05 0.10 0.45 28.94 0.40 0.15 0.10 0.20 0.45 30.36 0.50 0.75 0.20 0.60 0.60 33.79 >0.50 >0.75 >0.20 >0.60 >0.60 38.34 0.80 0.85 0.40 38.74 >0.80 >0.85 >0.40 Girder 3 West Mid East Load (kips/ft) WS (mm) FS (mm) F (mm) FS (mm) WS (mm) 14.96 0.20 0.00 0.00 0.00 0.00 16.17 0.30 0.00 0.00 0.00 0.20 18.83 0.30 0.00 0.00 0.00 0.30 22.79 0.30 0.00 0.00 0.00 0.35 26.05 0.30 0.00 0.05 0.00 0.35 29.29 0.35 0.25 0.10 0.25 0.50 32.4 0.45 0.40 0.15 0.40 0.55 35.68 0.45 0.40 0.15 0.40 >0.55 33.23 0.45 0.40 0.15 38.82 0.50 0.45 0.20 Girder 4 West Mid East Load (kips/ft) WS (mm) FS (mm) F (mm) FS (mm) WS (mm) 17.63 0.15 0.00 0.00 0.00 0.15 21.61 0.15 0.00 0.00 0.00 0.25 26.90 0.20 0.00 0.00 0.00 0.30 30.61 0.25 0.05 0.10 0.15 0.30 34.73 0.25 0.25 0.15 0.25 0.35 42.65 0.30 0.80 0.35 0.80 0.55 42.74 0.30 0.80 0.35 0.80 0.55 Girder 5 West Mid East Load (kips/ft) WS (mm) FS (mm) F (mm) FS (mm) WS (mm) 12.20 0.50 0.00 0.00 0.00 0.00 13.10 0.75 0.00 0.00 0.00 0.00 15.40 1.50 0.00 0.00 0.00 0.00 16.80 1.50 0.00 0.00 0.00 0.75 18.20 1.75 0.10 0.15 0.10 1.00 18.70 2.50 0.20 0.15 0.20 1.50 19.90 >2.50 >0.20 >0.15 >0.20 >1.50 20.95 0.30 0.40 2.00 22.07 0.35 0.60 2.50 23.24 0.40 0.70 3.00 23.70 >0.40 >0.70 >5.00 Girder 6 West Mid East Load (kips/ft) WS (mm) FS (mm) F (mm) FS (mm) WS (mm) 17.27 - 0.00 0.00 0.00 - 19.80 0.40 0.00 0.00 0.00 0.40 23.90 - 0.00 0.00 0.00 - 27.40 0.70 0.10 10.00 0.05 0.60 27.85 - - - - - 27.67 >0.70 >0.10 - - - 30.00 0.10 0.10 0.70 29.72 - - 0.70 37.30 0.15 0.15 10 38.32 >0.15 >0.15 >1.0 Girder 7 West Mid East Load (kips/ft) WS (mm) FS (mm) F (mm) FS (mm) WS (mm) 18.10 0.00 0.00 0.00 0.00 0.30 18.90 0.30 0.00 0.00 0.00 0.30 24.40 0.35 0.00 0.00 0.00 0.40 31.23 0.50 0.10 0.15 0.10 0.75 32.27 0.75 0.15 0.15 0.20 0.90 33.47 >0.75 >0.15 >0.15 >0.20 >0.90 36.20 0.75 0.70 0.15 40.57 1.00 1.00 0.15 43.40 1.20 1.00 0.25 44.75 >1.20 >1.00 >0.25 Girder 8 West Mid East Load (kips/ft) WS (mm) FS (mm) F (mm) FS (mm) WS (mm) 14.71 0.00 0.00 0.00 0.00 0.20 18.20 0.30 0.00 0.00 0.00 0.35 21.50 0.35 0.00 0.00 0.00 0.35 23.65 0.40 0.00 0.00 0.00 0.35 26.44 0.60 0.00 0.00 0.00 0.40 27.90 0.70 0.00 0.05 0.00 0.40 32.70 1.20 0.05 0.05 0.00 0.50 35.50 0.15 0.10 0.75 38.60 0.20 0.30 0.75 40.20 0.20 0.40 1.00 43.00 >0.20 0.40 1.50 43.73 >0.20 >0.40 >1.50 Table 18. Maximum crack width at each load stage for each girder.

83 average angle of 36.2 degrees. The closer the crack was to the end of the member, the steeper was the crack angle. • The angle of web-shear diagonal cracking in the first shear design region (a flexural region in the terms of Article 5.8.1.1 of the LRFD specifications) was reasonably constant and substantially flatter than the first web-shear crack. The crack angles ranged from 23 degrees to 32 degrees, with an average angle of 27.8 degrees. • The angle of shear cracking over the length of the member went from close to 45 degrees near the support, to a Girder 9 West Mid East Load (kips/ft) WS (mm) FS (mm) F (mm) FS (mm) WS (mm) 17.90 0.00 0.00 0.00 0.00 0.30 22.12 0.10 0.10 0.10 0.15 0.30 25.80 0.15 0.30 0.15 0.30 0.30 30.80 0.20 0.40 0.20 0.45 0.30 32.80 0.20 0.40 0.30 0.45 0.50 37.19 0.30 0.40 >0.30 Girder 10 West Mid East Load (kips/ft) WS (mm) FS (mm) F (mm) FS (mm) WS (mm) 15.84 0.00 0.00 0.00 0.00 0.30 20.21 0.20 0.00 0.00 0.00 0.40 22.54 0.30 0.15 N/A 0.20 0.45 23.91 0.30 0.15 N/A 0.20 0.45 26.43 0.30 0.30 N/A 0.25 0.50 29.12 0.30 0.30 N/A 0.30 0.50 31.59 0.30 0.30 N/A 0.40 0.75 33.93 0.30 0.30 N/A 0.40 1.00 33.68 0.40 0.75 N/A 36.46 0.50 0.80 N/A 38.56 0.55 1.00 N/A 42.85 >0.55 >1.00 N/A Table 18. (Continued). 0 2 41 3 5 G1E G1W G5E G5W G1W G5EG1E G5W G3E G3W G6E G6W G6W G3E G6E G3W 0 5 10 15 20 25 30 35 40 45 0 0.5 1 1.5 2 Maximum Crack Width (mm) Un ifo rm L oa d (ki p/f t) 0 5 10 15 20 25 30 35 40 45 0 0.5 1 1.5 2 Maximum Crack Width (mm) Un ifo rm L oa d (ki p/f t) 0 5 10 15 20 25 30 35 40 45 0 0.5 1 Maximum Crack Width (mm) Un ifo rm L oa d (ki p/f t) 0 5 10 15 20 25 30 35 40 45 0 0.5 1 1.5 2 Maximum Crack Width (mm) Un ifo rm L oa d (ki p/f t) 0 5 10 15 20 25 30 35 40 45 Maximum Crack Width (mm) Un ifo rm L oa d (ki p/f t) G7E G7W G8E G8W G7W G8E G7E G8W G2E G2W G10E G10W G2W G2E G10E G10W G4E G4W G9E G9W G4W G9E G4EG9W Figure 81. Maximum crack width of the web-shear cracks. Note: A blank cell indicates that no information was possible at that load level because the associated end of the girder had already failed. A dash indicates that the researchers did not take the measurement at that load stage. “N/A” indicates that the information was not available to be taken.

84 constant value in the web-shear region, to an increasing quadratic curve relationship in the flexure-shear region, and to almost 90 degrees at mid-span. • The angle of diagonal cracking could be accurately pre- dicted using Mohr’s circle of stress. • The angle of diagonal cracking in the first shear design region was typically a little steeper than the angle of diag- onal compression calculated from Table 5.8.3.4.2-1 of the LRFD Sectional Design Model. Consequently, the LRFD method may overestimate the contribution of shear rein- forcement unless there are significant shear stresses acting on the faces of the cracks. • The angle of potentially critical flexure-shear cracks can be up to 60 degrees, which suggests that the contribution of G1E G1W G5E G5W G1W G5E G1E G5W G3E G3W G6E G6W G6W G3E G6E G3W G7E G7W G8E G8W G7W G8E G7E G8W G2E G2W G10E G10W G2W G2E G10E G10W G4 E G4W G9E G9W G4W G9E G4E G9W 0 5 10 15 20 25 30 35 40 45 0 0.5 1 Maximum Crack Width (mm) Un ifo rm L oa d (ki p/f t) 0 5 10 15 20 25 30 35 40 45 0 0.5 1 1.5 Maximum Crack Width (mm) Un ifo rm L oa d (ki p/f t) 0 5 10 15 20 25 30 35 40 45 0 0.5 1 1.5 Maximum Crack Width (mm) Un ifo rm L oa d (ki p/f t) 0 5 10 15 20 25 30 35 40 45 0 0.5 1 1.5 Maximum Crack Width (mm) Un ifo rm L oa d (ki p/f t) 0 5 10 15 20 25 30 35 40 45 0 0.5 1 1.5 Maximum Crack Width (mm) Un ifo rm L oa d (ki p/f t) Figure 82. Maximum crack width of the flexure-shear cracks. 0 3000 6000 9000 12000 15000 0 0.2 0.4 0.6 Maximum Crack Width (mm) M om en t a t M id -S pa n (ki p- ft) G1 G2 G3 G4 G5 G6 G7 G8 G9 G9 G1 G5 G6 G2 G7 G4 G8 G3 (a) 0 0.2 0.4 0.6 Maximum Crack Width (mm) (b) 0.0 0.5 1.0 1.5 2.0 M /M cr G1 G2 G3 G4 G5 G6 G7 G8 G9 G9 G1 G5 G6 G2 G7 G4 G8 G3 Figure 83. Maximum crack width of flexure cracks.

85 shear reinforcement by most codes of practice is likely to be overestimated in these regions. • The spacing of shear cracks in the web was on average about half of the values predicted using the CEB-FIP expression for crack spacing. • The AASHTO Standard Specifications provided a reason- ably accurate and somewhat conservative estimate of the web-shear cracking load, Vcw, even when the full value of fpc was used in the calculations. It is to be expected that the longitudinal stress in the concrete at the centroidal axis will be less than fpc because the axial compressive force takes up to the last 30 inches in length of the bottom bulb to be fully transferred into the girder. • First web-shear cracking was observed to occur at between 33 percent and 87 percent of the LRFD shear design stress. Values can be a much lower percentage of the shear design stress than would have been possible with the use of the AASHTO Standard Specifications. The low percentages are possible because the LRFD spec- ifications permit members to be designed for shear stresses up to 0.25f c´. • The AASHTO Standard Specifications marginally over- estimated the flexure-shear cracking loads Vci. • The flexural cracking loads were reasonably well predicted by Mcr when the tensile cracking stress was taken as (in psi units). • Upon initiation of web-shear cracking, the first measured web-shear crack width ranged from 0.3 millimeter to 0.5 millimeter. The initial crack widths were larger for mem- bers with less shear reinforcement. Flexure-shear cracks opened faster than web-shear cracks once flexure-shear cracking occurred. After flexural cracking occurred, the maximum crack width increased linearly with increasing external moment. 2.6 Reinforcement and Other Strains This section summarizes the measured strains in the rein- forcing steel, as well as the longitudinal strains in the concrete at mid-depth and the shear strains. Section 2.6.1 introduces the value and challenge of measuring reinforcement strains. Section 2.6.2 describes the development of stirrup strains in the west half of Girder 3. Sections 2.6.3 and 2.6.4 summarize the measured strains in the web-shear regions and flexure- shear regions, respectively, for all girder tests. Section 2.6.5 presents longitudinal reinforcement strains, and Section 2.6.6 presents strains in the confinement reinforcement. Section 2.6.7 presents the measured longitudinal strains at mid- depth, εx, and compares these values with the development of longitudinal strains as calculated by the general method of the LRFD specifications. Section 2.6.8 presents the shear stress versus shear strain response of the test girders and provides a 7 5. ´f c relationship for predicting shear stiffness that is derived from the test data. Section 2.6.9 compares measured and LRFD- predicted time-dependent losses, and Section 2.6.10 com- pares measured and LRFD-predicted transfer lengths. 2.6.1 Introduction Measuring stirrup strains is useful for identifying when cracking first occurs, for evaluating the contribution of stir- rup reinforcement to capacity, for determining when cracks are rapidly opening, for assessing the strength of the bond between concrete and reinforcement, for evaluating fatigue concerns, and for measuring the magnitude of fracture energy release. One of the challenges to assessing stirrup strains is that these reinforcement strains at crack locations are usually much larger than reinforcement strains between cracks because between cracks, particularly in HSC members, the concrete has the capacity to carry significant tensile stress. Consequently, to accurately assess the strain in an individual stirrup, it is necessary to measure the strain at multiple points over the height of a stirrup. In this research program, strain gages were attached to the stirrups at 6, 17, 28, and 39 inches from the bottom of the 45-inch deep web. The girders were designed for shear by the LRFD specifications so that they were, according to the LRFD design philosophy, just as likely to fail in a region of low shear and high moment as they were in a region of high shear and low moment. Thus, as shown in Figure 54, selected stirrups were gauged over the entire length of the test girder, with between 14 and 20 stirrups being gauged on each girder. Measuring the strains in the longitudinal reinforcement before testing is useful for assessing the level of precompres- sion due to prestressing and for measuring prestressing losses due to shrinkage and creep. During a test, this measuring is also useful for assessing the demands placed on the longitu- dinal tension reinforcement due to flexure and shear. In this program, strains were measured on the longitudinal rein- forcement in the confinement cages and on larger deformed bar reinforcement that was required by the LRFD specifica- tions for some girder designs in order to provide the neces- sary longitudinal tensile capacity. The locations for these gages are shown in Figure 55 and in the appendices. Measuring strains on confinement reinforcement prior to loading is useful for assessing the level of confinement devel- oped following strand release and for determining the con- finement available to help anchor the strands. Measuring strains during testing is useful for helping to identify whether slip is occurring and for correlating behavior with the demands placed on longitudinal tensile reinforcement and other effects. In this research program, 20 gages, 10 on each end, were attached to the confinement reinforcement. The locations for these gages are shown in Figure 55 and in the appendices.

86 2.6.2 Stirrup Reinforcement Strains in the West Half of Girder 3 Figure 84 summarizes the development of strains in the west end of Girder 3. Figure 84(a) shows the locations of the strain gages on Stirrups S2, S3, and so forth through S8, with the four gages on each stirrup numbered sequentially from the bottom to the top of the stirrup. The web-shear and flexure-shear regions for each girder were defined from the measured pattern of cracking. If a given stirrup extended across both web-shear and flexure-shear cracks, then only those gages crossing each pattern or crack were counted as part of that region. The devel- opment of the strains in each stirrup in the web-shear region, Stirrups S2 through S5, is shown in Figure 84(b). From Figures 84(a) and 84(b), the following observations can be made: • Prior to first cracking, the strains in the stirrups were small, less than 30 microstrain, which corresponds to a stress of less than 1 ksi. A large portion of this strain must be due to a Poisson’s effect from the significant diagonal compres- sion in the web of the girder. The strain expected to lead to first cracking, not including strains due to Poisson’s effect, was 60–100 microstrain. • Immediately after occurrence of web-shear cracking, the first web-shear crack was at 14.96 kips/ft, and strains in some gages jumped to very close to the yield strain. • With the development of additional web-shear cracks, sim- ilarly large jumps in stirrup strains were observed. • There was a dramatic variation in strain in some stirrups, with a gage near a crack measuring the yield strain while a gage farther from the same crack measured very little strain. For example, for the gages on Stirrup 3, shortly after first diagonal cracking, one gage measured about 3,500 microstrain (well above yield), while the other three gages were all less than 100 microstrain (less than 5 percent of the yield). • As the magnitude of the strains increased, particularly beyond yield, the ratio of the maximum to minimum strain in a stirrup decreased. • Along a given critical crack line in a field of diagonal crack- ing, where cracks are close to parallel and of similar widths, it is to be expected that the strain in the stirrups across this S1 S2 S3 S4 S5 S6 S7 S8 m2m1 m3 m4 m1m2m3 Web Shear Region Flexure Shear Region S1 S2 S3 S4 S5 S6 S7 S8 S1 S2 S3 S4 S5 S6 S7 S8 w = 14.96 kips/ft w = 18.83 kips/ft S1 S2 S3 S4 S5 S6 S7 S8 S1 S2 S3 S4 S5 S6 S7 S8 w = 26.05 kips/ft w = 29.29 kips/ft S1 S2 S3 S4 S5 S6 S7 S8 S1 S2 S3 S4 S5 S6 S7 S8 w = 35.68 kips/ft w = 38.82 kips/ft (a) Development of Shear Cracking in West End of Girder 3 (G3W) Figure 84. Stirrup reinforcement strain in west end of Girder 3 (G3W).

87 band of cracks should be similar. However, the measure- ments show that this was not always the case, and this result is probably due to differences in the distance from the crack to the closest gage for each of the stirrups that crossed the same crack. • Prior to failure, yielding progressed until it extended over the height of the stirrups in the field of web-shear cracking. Figure 84(c) shows the development of straining in each stirrup in the flexure-shear region. Note that Gage 4 of Stirrup 6 was not considered part of the flexure-shear region. From these figures, the following observations can be made: • Because flexure-shear cracking did not occur until consid- erably later than web-shear cracking in the loading history of the test specimens, the straining of stirrups in the flexure- shear regions occurred much later than in the web-shear regions. For example, in test G3W, flexure-shear cracking did not occur until 28 kips/ft was uniformly distributed. In comparison, web-shear cracking occurred initially at a load of 15 kips/ft. • Prior to flexure-shear cracking, significant compressive strains developed in the flexure-shear reinforcement. The compressive strains were largest in the stirrups that were closest to mid-span, but even some compressive strains were observed in web-shear regions. See Stirrups S4 and S5 in Figure 84(b). The compressive strains were largest in the lower strain gages of a stirrup, with strains ranging from around 100 microstrain to 300 microstrain. This compres- sive straining must have been the result of a release of ten- sile strains caused by Poisson’s effect during prestressing. As the loading increased, the positive bending moment increased and the magnitude of decompression stress decreased with a corresponding decrease in the vertical tensile strain. Because the magnitudes of the strains in the gages were set to zero at the beginning of each test, this reduction in tensile strain is measured as compressive strain. For the purpose of assessing the tensile stress in a given stirrup, it is appropriate to use a strain equal to the total tensile strain due to loading less the maximum com- pressive strain that occurred as the strains caused by pre- stressing were released. Since the magnitudes of these Gage 1 Gage 2 Gage 3 Gage 4 Gage 2 Gage 3 Gage 1 Gage 4 Gage 2 Gage 3 Gage 4 Gage 3 Gage 2 Gage 4 (b) Stirrup Reinforcement Strain in Web-Shear Region of G3W 0 5 10 15 20 25 30 35 40 -500 1500 3500 5500 7500 9500 Strain (x10-6) Un ifo rm Lo ad (ki p/ ft) 0 5 10 15 20 25 30 35 40 Un ifo rm Lo ad (ki p/ ft) Gage 1 Gage 2 Gage 4 Gage 4 Gage 1 Gage 2 Gage 1 Gage 2 Gage 3 Gage 4 Gage 4 Gage 1 Gage 3 Gage 2 Stirrup 2 (S2) 0 5 10 15 20 25 30 35 40 -500 1500 3500 5500 7500 9500 Strain (x10-6) Un ifo rm Lo ad (ki p/ ft) Stirrup 3 (S3) 0 5 10 15 20 25 30 35 40 -500 1500 3500 5500 7500 9500 Strain (x10-6) Un ifo rm Lo ad (ki p/ ft) Stirrup 4 (S4) -500 500 25001500 3500 4500 5500 Strain (x10-6) Stirrup 5 (S5) Figure 84. (Continued).

88 compressive strains are typically small, they were ignored in calculating the stresses in stirrups. • As with the development of web-shear cracking, there was a rapid increase in stirrup strains following the formation of flexure-shear cracking, with strain values approaching the yield strain being measured immediately upon cracking. Unlike the situation for web-shear cracking, the development of a complete pattern of flexure-shear cracks occurred rapidly over a very narrow loading range.Consequently, the measured strains in all gages crossing flexure-shear cracks went from close to zero strain to almost all being close to the yield strain, with an increase in loading of around 10 to15 percent. • Within the flexure-shear region, the farther a stirrup was from mid-span, the larger the shear was, the flatter the flexure-shear crack was, and the larger the magnitude of the stirrup strains was. As shown in Figure 84(c), the strains in Stirrup S6 were much larger than those in Stirrup S8. • While the strains in Stirrup S6 were well beyond the yield strain and cracks were quite large in this region, there were no other significant signs of an impending shear failure. The foregoing observations concerning the behavior of the west half of Girder 3 were reasonably typical of the behavior in many, but not all, of the girder tests. The next two sections present a summary and a discussion of the measured stirrup strains in each of the test girders. 2.6.3 Stirrup Reinforcement Strains in Web-Shear Regions Table 19 and Figure 85 summarize the measured stirrup strains in all 20 web-shear regions. The locations of these gages were shown in Figure 54. Table 19 lists, for each girder and for eight characteristic load levels, the maximum strain in each of the first four gauged stirrups from the inside face of the support (labeled εm1, εm2, εm3, εm4 in relation to their proximity to the sup- port) the overall maximum strain (εm = max(εm1, εm2, εm3, εm4)), and the average maximum strain (εma = ave(εm1, εm2, εm3, εm4)). The eight characteristic load levels provide measured strains immediately before cracking (Crk), at selected load stages for which cracking was measured (CS1 through CS5), 2 minutes 0 5 10 15 20 25 30 35 40 Un ifo rm Lo ad (ki p/ ft) -500 500 25001500 3500 4500 5500 Strain (x10-6) Stirrup 6 (S6) 0 5 10 15 20 25 30 35 40 Un ifo rm Lo ad (ki p/ ft) -500 500 25001500 3500 4500 5500 Strain (x10-6) Stirrup 7 (S7) 0 5 10 15 20 25 30 35 40 Un ifo rm Lo ad (ki p/ ft) -500 500 25001500 3500 Strain (x10-6) Stirrup 8 (S8) Gage 1 Gage 2 Gage 3 Gage 4 Gage 2 Gage 3 Gage 1 Gage 4 Gage 1 Gage 2 Gage 3 Gage 4 Gage 3 Gage 2 Gage 1 Gage 4 Gage 1 Gage 2 Gage 3 Gage 4 Gage 3 Gage 2 Gage 1 Gage 4 (c) Stirrup Reinforcement Strain in Flexure-Shear Region of G3W Figure 84. (Continued).

89 G1W w m1 m2 m3 m4 m ma <Crk 9.00 -44 -4 27 -12 27 -8 CS1 14.71 -61 12 59 -19 59 -2 CS2 19.11 438 1,161 914 1,988 1,988 1,125 CS3 21.17 1,752 2,240 2,294 1,956 2,294 2,060 CS4 24.56 2,424 3,328 3,465 2,861 3,465 3,019 CS5 26.59 3,878 5,537 8,894 4,011 8,894 5,580 2<F 29.83 11,459 11,074 17,126 7,431 17,126 11,773 <Fail 30.09 11,459 11,256 17,654 9,152 17,654 12,380 G1E w m1 m2 m3 m4 m ma <Crk 9.00 -9 37 -11 0 37 4 CS1 14.71 1,630 901 162 64 1,630 689 CS2 18.79 1,398 1,302 595 764 1,398 1,015 CS3 19.96 1,696 2,058 1,411 1,768 2,058 1,734 CS4 21.17 1,959 2,130 1,456 2,183 2,183 1,932 CS5 23.67 2,141 3,462 1,490 2,172 3,462 2,316 2<F 25.90 2,418 5,071 1,629 2,680 5,071 2,949 <Fail 26.03 2,418 5,071 1,657 2,717 5,071 2,966 G2W w m1 m2 m3 m4 m ma <Crk 14.02 61 -20 22 -62 61 0 CS1 18.79 100 -15 64 -75 100 18 CS2 25.94 3,684 2,719 1,873 -61 3,684 2,053 CS3 30.36 4,102 2,969 2,442 2,398 4,102 2,978 CS4 33.79 4,928 3,432 3,529 2,961 4,928 3,713 CS5 38.34 7,953 4,378 4,378 3,579 7,953 5,072 2<F 38.63 9,586 4,783 4,198 4,524 9,586 5,773 <Fail 38.74 12,365 15,317 4,464 3,694 15,317 8,960 G2E w m1 m2 m3 m4 m ma <Crk 14.02 -9 37 -11 0 37 4 CS1 18.79 1,630 901 162 64 1,630 689 CS2 21.74 1,398 1,302 595 764 1,398 1,015 CS3 25.94 1,696 2,058 1,411 1,768 2,058 1,734 CS4 28.94 1,959 2,130 1,456 2,183 2,183 1,932 CS5 30.36 2,141 3,462 1,490 2,172 3,462 2,316 2<F 33.57 2,418 5,071 1,629 2,680 5,071 2,949 <Fail 33.79 2,418 5,071 1,657 2,717 5,071 2,966 G3W w m1 m2 m3 m4 m ma <Crk 6.72 22 5 -10 8 22 6 CS1 14.96 139 1,779 39 66 1,779 506 CS2 18.83 818 3,395 2,323 140 3,395 1,669 CS3 29.29 3,315 4,857 4,077 2,803 4,857 3,763 CS4 32.40 3,983 9,098 7,104 2,798 9,098 5,746 CS5 35.68 7,511 10,039 7,935 3,920 10,039 7,351 2<F 38.63 9,319 10,039 12,457 5,073 12,457 9,222 <Fail 38.82 10,013 9,924 12,648 5,172 12,648 9,439 G3E w m1 m2 m3 m4 m ma <Crk 14.96 36 80 95 32 95 61 CS1 16.17 85 2,207 362 98 2,207 688 CS2 22.79 3,153 2,632 3,210 1,418 3,210 2,603 CS3 26.05 3,919 2,974 3,822 2,205 3,919 3,230 CS4 29.29 4,445 3,474 4,588 2,501 4,588 3,752 CS5 32.40 9,138 4,078 5,513 2,649 9,138 5,345 2<F 35.49 15,006 4,916 7,657 3,332 15,006 7,728 <Fail 35.68 15,173 4,992 8,222 3,407 15,173 7,948 G4W w m1 m2 m3 m4 m ma <Crk 13.25 11 30 2 22 30 16 CS1 17.63 394 610 15 58 610 269 CS2 21.61 690 936 178 415 936 555 CS3 26.90 800 1,078 536 671 1,078 771 CS4 30.61 1,005 1,289 1,161 878 1,289 1,083 CS5 34.73 1,307 1,512 1,327 997 1,512 1,286 2<F 42.04 1,860 1,802 1,666 1,363 1,860 1,673 <Fail 42.65 2,397 2,056 1,877 1,484 2,397 1,953 G4E w m1 m2 m3 m4 m ma <Crk 13.25 -4 54 0 26 54 19 CS1 17.63 878 704 15 64 878 415 CS2 21.61 902 832 203 322 902 565 CS3 26.90 1,121 1,158 654 810 1,158 936 CS4 30.61 1,372 1,401 679 1,277 1,401 1,182 CS5 34.73 1,609 1,617 1,121 1,349 1,617 1,424 2<F 42.04 2,055 1,933 1,473 1,736 2,055 1,799 <Fail 42.65 2,362 2,097 1,556 1,844 2,362 1,965 G5W w m1 m2 m3 m4 m ma <Crk 9.95 32 56 72 24 72 46 CS1 12.20 81 867 336 519 867 451 CS2 13.10 86 911 2,657 407 2,657 1,015 CS3 15.40 90 1,821 10,625 470 10,625 3,252 CS4 16.80 92 3,609 14,021 843 14,021 4,641 CS5 18.20 91 3,609 14,021 1,443 14,021 4,791 2<F 19.66 96 13,997 14,021 14,047 14,047 10,540 <Fail 19.90 99 3,679 14,021 14,032 14,032 7,958 G5E w m1 m2 m3 m4 m ma <Crk 12.20 58 9 0 -3 58 16 CS1 15.40 73 16 0 5 73 23 CS2 16.80 2,513 2,708 24 1,029 2,708 1,569 CS3 18.70 2,393 6,088 7,457 2,473 7,457 4,603 CS4 20.95 2,568 8,412 17,569 3,105 17,569 7,914 CS5 22.07 2,632 8,412 17,574 3,326 17,574 7,986 2<F 23.57 2,950 8,412 17,574 14,133 17,574 10,767 <Fail 23.70 2,950 8,412 17,574 14,037 17,574 10,743 Table 19. Maximum stirrup strains in web-shear regions.

90 G6 W w m 1 m 2 m 3 m 4 m ma <Crk 7.35 79 16 12 8 79 29 CS 1 17.27 587 527 61 38 587 303 CS 2 19.80 591 1,012 61 47 1,012 428 CS 3 23.90 933 1,399 938 380 1,399 912 CS 4 27.40 1,885 2,091 1,381 1,494 2,091 1,713 CS 5 27.85 2,763 2,204 1,472 1,572 2,763 2,003 2<F 27.48 3,056 2,147 1,431 1,543 3,056 2,044 <Fail 27.67 8,232 3,218 1,585 1,592 8,232 3,657 G6 E w m 1 m 2 m 3 m 4 m ma <Crk 7.35 4 7 7 0 7 4 CS 1 17.27 929 542 292 39 929 451 CS 2 23.90 1,331 980 871 1,012 1,331 1,04 8 CS 3 27.40 1,839 1,175 1,073 1,553 1,839 1,41 0 CS 4 30.00 4,784 1,581 1,369 1,668 4,784 2,35 1 CS 5 37.30 6,664 1,902 1,656 1,834 6,664 3,01 4 2<F 38.00 7,010 2,031 1,646 1,850 7,010 3,13 4 <Fail 38.32 7,025 4,785 1,718 1,880 7,025 3,85 2 G7 W w m 1 m 2 m 3 m 4 m ma <Crk 18.10 86 83 75 32 86 69 CS 1 24.40 1,207 1,020 1,220 598 1,220 1,011 CS 2 32.27 3,306 1,917 2,975 1,615 3,306 2,453 CS 3 36.20 4,725 2,201 3,975 1,978 4,725 3,220 CS 4 40.57 6,152 3,627 6,451 2,855 6,451 4,771 CS 5 43.40 6,152 2,452 6,451 6,571 6,571 5,406 2<F 44.50 6,152 4,006 6,451 6,571 6,571 5,795 <Fail 44.76 6,152 2,933 8,824 6,571 8,824 6,120 G7 E w m 1 m 2 m 3 m 4 m ma <Crk 8.70 6 16 3 8 16 8 CS 1 18.10 641 677 426 71 677 454 CS 2 18.90 691 573 501 47 691 453 CS 3 24.40 1,140 1,319 1,047 1,235 1,31 9 1 ,185 CS 4 31.23 3,381 2,495 1,461 1,774 3,38 1 2 ,278 CS 5 32.27 4,165 2,978 1,565 1,864 4,16 5 2 ,643 2<F 32.93 4,165 3,429 1,660 1,932 4,16 5 2 ,796 <Fail 33.47 4,165 3,583 1,739 1,989 4,16 5 2 ,869 G8 W w m1 m2 m3 m4 m ma <Crk 6.05 -23 -3 11 20 20 1 CS 1 14.71 -62 149 100 896 896 271 CS 2 18.20 234 470 1,019 1,763 1,763 872 CS 3 21.50 342 763 1,345 1,790 1,790 1,060 CS 4 26.44 799 1,046 1,534 4,134 4,134 1,878 CS 5 27.90 916 1,138 1,662 4,134 4,134 1,962 2<F 32.36 1,670 1,310 1,810 4,134 4,134 2,231 <Fail 32.70 1,823 1,325 1,825 4,134 4,134 2,277 G8 E w m 1 m 2 m 3 m 4 m ma <Crk 18.20 851 851 670 691 851 766 CS 1 23.65 1,192 1,112 1,015 1,034 1,19 2 1 ,088 CS 2 27.90 1,538 1,451 1,778 1,599 1,77 8 1 ,592 CS 3 35.50 5,860 2,184 2,303 2,969 5,86 0 3 ,329 CS 4 38.60 5,860 4,860 2,523 3,203 5,86 0 4 ,112 CS 5 40.20 5,860 4,502 3,204 3,290 5,86 0 4 ,214 2<F 43.30 5,860 6,853 14,562 4,956 14,562 8,058 <Fail 43.73 5,860 6,853 14,562 6,793 14,562 8,517 G9 W w m 1 m 2 m 3 m 4 m ma <Crk 8.76 -16 17 10 10 17 5 CS 1 17.00 -32 99 28 61 99 39 CS 2 22.12 193 533 362 296 533 346 CS 3 25.80 739 678 547 490 739 614 CS 4 30.80 930 929 692 699 930 812 CS 5 32.80 1,026 1,004 761 735 1,026 882 2<F 36.45 1,225 1,116 816 792 1,225 987 <Fail 37.19 1,384 1,239 899 888 1,384 1,102 G9 E w m 1 m 2 m 3 m 4 m ma <Crk 8.76 6 7 11 5 11 7 CS 1 17.00 820 398 183 126 820 382 CS 2 22.12 1,061 962 419 701 1,06 1 7 86 CS 3 25.80 1,151 1,213 554 803 1,213 930 CS 4 30.80 1,379 1,559 1,355 1,069 1,55 9 1 ,340 CS 5 31.80 1,474 1,612 1,478 1,160 1,61 2 1 ,431 2<F 32.28 1,489 1,658 1,501 1,195 1,65 8 1 ,460 <Fail 32.80 1,657 1,909 1,549 1,239 1,90 9 1 ,588 G10W w m 1 m 2 m 3 m 4 m ma <Crk 15.84 22 41 102 8 102 43 CS 1 22.54 538 1,120 1,273 83 1,273 753 CS 2 26.43 1,157 1,139 1,536 1,057 1,536 1,222 CS 3 29.12 1,272 1,319 1,519 1,126 1,519 1,309 CS 4 33.68 1,674 1,632 1,789 1,501 1,789 1,649 CS 5 38.56 2,573 2,260 2,246 1,726 2,573 2,201 2<F 42.51 2,573 5,319 4,589 2,549 5,319 3,757 <Fail 42.85 2,573 5,520 4,723 2,658 5,520 3,868 G10E w m 1 m 2 m 3 m 4 m ma <Crk 9.65 -14 44 12 2 44 11 CS 1 15.84 400 994 832 41 994 567 CS 2 20.21 958 1,159 1,325 769 1,325 1,05 3 CS 3 23.91 1,354 1,347 1,317 1,192 1,35 4 1 ,303 CS 4 29.12 1,659 1,844 1,890 1,387 1,89 0 1 ,695 CS 5 31.59 1,871 2,482 2,496 1,606 2,49 6 2 ,114 2<F 33.61 2,145 3,467 3,639 1,775 3,63 9 2 ,757 <Fail 33.93 2,279 3,639 3,871 1,805 3,87 1 2 ,898 Table 19. (Continued).

91 0 5 10 15 20 25 30 -2000 0 2000 4000 6000 8000 10000 Strain (x10-6) Un ifo rm L oa d (ki p/f t) 0 5 10 15 20 25 30 -2000 0 2000 4000 6000 8000 10000 Strain (x10-6) Un ifo rm L oa d (ki p/f t) 0 5 10 15 20 25 35 40 30 -2000 0 2000 4000 6000 8000 10000 Strain (x10-6) Un ifo rm L oa d (ki p/f t) 0 5 10 15 20 25 35 40 30 -2000 0 2000 4000 6000 8000 10000 Strain (x10-6) Un ifo rm L oa d (ki p/f t) 0 5 10 15 20 25 35 45 40 30 -2000 0 2000 4000 6000 8000 10000 Strain (x10-6) Un ifo rm L oa d (ki p/f t) 0 5 10 15 20 25 35 45 40 30 -2000 0 2000 4000 6000 8000 10000 Strain (x10-6) Un ifo rm L oa d (ki p/f t) 0 5 10 15 20 25 35 45 40 30 -2000 0 2000 4000 6000 8000 10000 Strain (x10-6) Un ifo rm L oa d (ki p/f t) 0 5 10 15 20 25 35 45 40 30 Un ifo rm L oa d (ki p/f t) 0 5 10 15 20 25 35 45 40 30 -2000 0 2000 4000 6000 8000 10000 Strain (x10-6) -500 0 500 1000 1500 2000 2500 3000 Strain (x10-6) 0 5 10 15 20 25 35 45 40 30 Un ifo rm L oa d (ki p/f t) -500 0 500 1000 1500 2000 2500 3000 Strain (x10-6) Un ifo rm L oa d (ki p/f t) G1E G1W G5E G5W G1W G5E G1E G5W G3E G3W G6E G6W G3W G6E G3E G6W G7E G7W G8E G8W G7W G8E G7E G8W G2E G2W G10E G10W G2W G10E G2E G10W G4E G4W G9E G9W G4W G9E G4E G9W (a) Overall Maximum Strain of Stirrups in Web-Shear Region of Each End G1E G1W G5E G5W G1W G5E G1E G5W G3E G3W G6E G6W G3W G6E G3E G6W G7E G7W G8E G8W G7W G8E G7E G8W G2E G2W G10E G10W G2W G10E G2E G10W G4E G4W G9E G9W G4W G9E G4E G9W (b) Average Maximum Strain of Stirrups in Web-Shear Region of Each End Figure 85. Maximum stirrup strain in web-shear region.

92 before failure (2<F),and for the last measured dataset before fail- ure or peak load (<Fail). Using these selected strain levels, load versus strain envelopes were developed for the overall maximum strain (εm) and the average maximum strain (εma). These envelopes are presented in Figures 85(a) and 85(b), in which the results from the 20 girder tests have been organized into five groups based on the strength of the shear reinforcement pro- vided in the first critical shear design region from the end: Group 1: G1E, G1W, G5E, and G5W; ρvfy = 140 – 389 psi Group 2: G3 and G6; ρvfy = 557 – 577 psi Group 3: G7 and G8; ρvfy = 557 – 577 psi Group 4: G2 and G10; ρvfy = 745 – 751 psi Group 5: G4E(1,113 psi), G4W (1,113 psi), G9E (1,040 psi) and G9W (1,690 psi) Section 2.6.1 presented the primary observations concern- ing the development of strains in the stirrups crossing web- shear cracks. From Table 19 and Figure 85, the following additional observations are made: • For members with the least amount of shear reinforce- ment, ρvfy, the increases in stirrup strains at the onset of web-shear cracking are the largest. Girder 5 contained the least amount of shear reinforcement, and its stirrups yielded at cracking. The east end of Girder 5 failed due to fracture of the stirrups, while the remainder of the mem- ber was in good condition. By contrast, the members with the largest amount of shear reinforcement failed when the maximum stirrup strains were only slightly beyond yield or somewhat less than yield. • The maximum (εm) and the average maximum (εma) web- shear stirrup strain for all girders in the first four groups (ρvfy <1,000 psi) exceeded the yield strain, with many of the strains being several times the yield strain. • The maximum (εm) and the average maximum (εma) web- shear stirrup strains in both ends of Girder 4 (ρvfy = 1,113 psi) were just a little less than the yield strain when this member failed in flexure. • In the east web-shear region of Girder 9 (ρvfy = 1,040 psi), the strains were less than yield when the member failed in diagonal compression. • In the west web-shear region of Girder 9 (ρvfy = 1,690 psi), the maximum stirrup strain was only two-thirds of the yield strain and the average maximum stirrup strain was only one-half of the yield strain when the member was unloaded due to an impending failure of the east end repair. At this time, local crushing was observed, with long diagonal cracks above the west end support. • The maximum web-shear stirrup strains in the ends with draped strands—G1W, G2W, G9W, and G10W—were lower, at the same magnitude of loading, than the maximum web-shear stirrup strains in the east ends of the same gird- ers where the strands were straight. 2.6.4 Stirrup Reinforcement Strains in Flexure-Shear Regions This section discusses the measured stirrup reinforce- ment strains in the flexure-shear regions. Table 20 shows the maximum strain for each girder and for several selected load levels for each of the first three to four gauged stirrups toward the end from mid-span (labeled εm1, εm2, εm3, and εm4 in relation to their proximity to mid-span), the overall maximum strain (εm = max(εm1, εm2, εm3, εm4)), and the aver- age maximum strain (εma = ave(εm1, εm2, εm3, εm4)). The six load stages provide the measured strains immediately before cracking (Crk), at selected load stages in which flex- ure-shear cracking was measured (CS1 through CS3), 2 minutes before failure (2<F), and for the last measured dataset before failure or peak load (<Fail). Using these selected strain levels, load versus strain envelopes were developed for the overall maximum strain (εm) and the average maximum strain (εma). These envelopes are pre- sented in Figures 86(a) and 86(b), in which the results from the 20 girder tests have been organized into five groups based on the strength of the shear reinforcement provided in the flexure-shear region: Group 1: G1E, G1W, G5E, G5W, and G7W; ρvfy < 200 psi (119 psi ~ 194 psi) Group 2: G3 and G6; ρvfy = 334 – 384 psi Group 3: G7E and G8; ρvfy = 453 – 482 psi Group 4: G2 and G10; ρvfy = 745 – 751 psi Group 5: G4E (668 psi), G4W (668 psi), G9E (604 psi), and G9W (604 psi) Section 2.6.1 presented the primary observations concerning the development of strains in the stirrups crossing flexure-shear cracks. From Table 20 and Figure 86, the following additional observations are made: • In general, the strains in the flexure-shear regions were less than the maximum strains in the web-shear regions even though the members were designed to be equally as likely to fail in a web-shear region as they were to fail in a flexure- shear region. • Sometimes, the differences between the states of strain in the web-shear and flexure-shear regions were modest. For example, the development of straining in the web-shear and flexure-shear regions of the west end of Girder 2 was

93 G1W w m1 m2 m3 m4 m ma <Crk 19.96 -14 3 27 21 27 9 CS1 26.59 -69 84 139 272 272 106 CS2 27.44 177 1,597 1,122 303 1,597 800 CS3 28.75 433 2,286 2,529 357 2,529 1,401 2<F 29.83 718 2,863 4,101 3,136 4,101 2,704 <Fail 30.09 803 4,180 4,409 3,489 4,409 3,220 G1E w m1 m2 m3 m4 m ma <Crk 14.71 -10 -13 3 -32 3 -13 CS1 19.96 -5 31 126 -39 126 28 CS2 22.52 -18 75 166 -8 166 54 CS3 24.56 481 199 610 193 610 371 2<F 25.90 1,593 2,606 1,807 4,908 4,908 2,729 <Fail 26.03 1,637 2,631 1,870 295 2,631 1,608 G2W w m1 m2 m3 m4 m ma <Crk 21.74 -30 199 55 0 199 56 CS1 25.94 -111 279 388 0 388 139 CS2 30.36 1,366 1,892 2,463 2,398 2,463 2,030 CS3 33.79 1,667 4,288 3,110 2,961 4,288 3,006 2<F 38.63 2,290 10,849 4,676 4,524 10,849 5,585 <Fail 38.74 2,290 10,849 4,707 3,694 10,849 5,385 G2E w m1 m2 m3 m4 m ma <Crk 18.79 8 -23 -11 64 64 10 CS1 21.74 8 -27 57 764 764 200 CS2 25.94 -33 113 652 1,768 1,768 625 CS3 28.94 2,865 1,608 751 2,183 2,865 1,852 2<F 33.57 3,232 3,160 1,736 2,680 3,232 2,702 <Fail 33.79 3,251 3,180 1,754 2,717 3,251 2,725 G3W w m1 m2 m3 m ma <Crk 1.18 0 0 0 0 0 CS1 26.05 -13 119 -66 119 13 CS2 29.29 1,121 1,030 -67 1,121 695 CS3 32.40 1,534 2,311 3,873 3,873 2,573 2<F 35.68 1,853 2,824 4,756 4,756 3,145 <Fail 38.63 3,146 5,251 11,722 11,722 6,706 G3E w m1 m2 m3 m ma <Crk 14.96 -13 33 0 33 7 CS1 26.05 -29 77 0 77 16 CS2 29.29 506 1,223 0 1,223 576 CS3 32.40 1,852 3,899 2,744 3,899 2,831 2<F 35.49 2,454 3,802 3,221 3,802 3,159 <Fail 35.68 2,501 4,090 3,265 4,090 3,285 G4W w m1 m2 m3 m4 m ma <Crk 17.63 -3 14 4 24 24 10 CS1 26.90 -3 36 54 139 139 57 CS2 30.61 -7 57 71 878 878 250 CS3 34.73 783 1,004 461 997 1,004 811 2<F 42.04 888 1,333 551 1,363 1,363 1,034 <Fail 42.65 1,094 1,700 569 1,484 1,700 1,212 G4E w m1 m2 m3 m4 m ma <Crk 17.63 -5 -4 0 -21 0 -7 CS1 26.90 -8 3 76 -13 76 14 CS2 30.61 359 35 569 286 569 312 CS3 34.73 821 1,054 695 762 1,054 833 2<F 42.04 934 1,317 1,231 1,736 1,736 1,305 <Fail 42.65 1,245 1,641 1,409 1,611 1,641 1,477 G5W w m1 m2 m3 m ma <Crk 12.20 0 -13 20 20 2 CS1 16.80 25 32 275 275 111 CS2 18.20 131 46 1,307 1,307 495 CS3 18.70 162 17 1,557 1,557 579 2<F 19.66 183 27 1,772 1,772 661 <Fail 19.90 230 40 1,896 1,896 722 G5E w m1 m2 m3 m ma <Crk 16.80 -26 57 64 64 32 CS1 18.20 -27 774 73 774 273 CS2 20.95 532 1,965 67 1,965 855 CS3 22.07 1,067 2,450 1,030 2,450 1,516 2<F 23.57 1,810 5,621 4,395 5,621 3,942 <Fail 23.70 1,867 6,852 4,395 6,852 4,371 G6W w m1 m2 m3 m ma <Crk 17.27 0 -3 0 0 -1 CS1 19.80 0 -14 0 0 -5 CS2 23.90 0 -20 0 0 -7 CS3 27.40 0 22 0 22 7 2<F 27.48 0 23 0 23 8 <Fail 27.85 0 25 0 25 8 G6E w m1 m2 m3 m ma <Crk 17.27 -7 0 16 16 3 CS1 23.90 -21 0 72 72 17 CS2 30.00 -33 0 111 111 26 CS3 37.30 23 556 1,020 1,020 533 2<F 38.00 37 680 1,175 1,175 630 <Fail 38.32 60 706 1,221 1,221 662 Table 20. Maximum stirrup strains in flexure-shear regions.

94 quite similar with the average maximum strain 2 minutes before failure being between 5,000 and 6,000 microstrain. • After diagonal cracking, strains in the flexure-shear regions increased more rapidly with increasing load than strains in the web-shear region. • The strains in Girder 6 were low; this member failed in the web-shear region before the development of significant flexure-shear cracking and thus significant flexure-shear stirrup strains. This observation was particularly true for the west end of Girder 6, which had a lower shear capacity than the east end due to the debonding of some strands. • Due to a dramatic change in the loading pattern in a final attempt to fail the west part of Girder 9, the shear force in the flexure-shear region was reduced, and that reduction is responsible for the apparent decrease in strain for that test with increasing load. It is interesting to note that before this change in loading pattern, and at a uniformly distributed loading of 32.8 kips/ft, the maximum measured flexure- shear strain was 1,486 microstrain, and that value was larger than the maximum measured web-shear strain of 1,026 microstrain. 2.6.5 Longitudinal Reinforcement Strains This section reports the measured strains in the longitu- dinal reinforcement. These strains include the longitudinal strains in the confinement cages, the longitudinal strains on some deformed bars that were connected to bearing plates at the east ends of Girders 1 and 2, and the longitudinal strains in the additional web skin reinforcements in the west ends of Girders 3 and 4. The locations of the gages on the confinement reinforcement are shown in Figure 55, and the locations on other bars are reported in the appendices. The changes in strain during the tests can be used to exam- ine the demands placed on the longitudinal reinforcement. When interpreting the results from these measurements, it G7W w m1 m2 m3 m ma <Crk 24.40 11 8 -13 11 2 CS1 31.23 11 27 71 71 36 CS2 33.47 700 171 1600 1,600 824 CS3 40.57 978 440 2,357 2,357 1,258 2<F 44.50 1,211 2,483 2,357 2,483 2,017 <Fail 44.76 1,262 2,484 2,357 2,484 2,034 G7E w m1 m2 m3 m ma <Crk 18.90 0 -3 -19 0 0 CS1 24.40 0 22 -19 22 1 CS2 31.23 0 213 965 965 392 CS3 32.27 0 328 1,085 1,085 471 2<F 32.93 37 1,103 1,349 1,349 830 <Fail 33.47 72 1,217 1,098 1,217 796 G8W w m1 m2 m3 m ma <Crk 18.20 -11 2 21 21 4 CS1 21.50 -12 21 103 103 37 CS2 23.65 -11 36 162 162 62 CS3 26.44 -8 61 522 522 192 2<F 32.36 2 187 662 662 284 <Fail 32.70 8 198 675 675 293 G8E w m1 m2 m3 m ma <Crk 21.50 -9 8 13 13 4 CS1 27.90 12 0 55 55 22 CS2 32.70 179 399 1,590 1,590 723 CS3 38.60 418 257 1,715 1,715 797 2<F 43.30 753 560 4,000 4,000 1,771 <Fail 43.73 763 579 1,888 1,888 1,077 G9W w m1 m2 m3 m4 m ma <Crk 22.12 -14 3 -3 -14 3 -7 CS1 25.80 166 134 765 152 765 304 CS2 30.80 540 170 1,193 882 1,193 696 CS3 32.80 525 210 1,486 1,130 1,486 838 2<F 36.45 266 88 618 654 654 407 <Fail 37.19 0 102 660 717 717 370 G9E w m1 m2 m3 m4 m ma <Crk 17.00 -19 8 16 -36 16 -8 CS1 22.12 125 32 104 -45 125 54 CS2 25.80 153 712 375 857 857 525 CS3 30.80 534 1,032 875 1,400 1,400 960 2<F 32.28 606 1,044 997 1,625 1,625 1,068 <Fail 32.80 613 803 1,020 1,680 1,680 1,029 G10W w m1 m2 m3 m ma <Crk 23.91 0 19 0 19 6 CS1 29.12 91 1,028 212 1,028 444 CS2 33.68 621 1,513 1,277 1,513 1,137 CS3 38.56 939 1,890 1,628 1,890 1,486 2<F 42.51 1,547 2,504 2,143 2,504 2,065 <Fail 42.85 1,567 2,545 2,172 2,545 2,094 G10E w m1 m2 m3 m ma <Crk 15.84 0 76 0 76 25 CS1 20.21 0 373 187 373 187 CS2 23.91 0 822 1,112 1,112 645 CS3 29.12 1,039 1,293 1,252 1,293 1,195 2<F 33.61 5,518 1,741 1,860 5,518 3,040 <Fail 33.93 1,314 1,776 1,908 1,908 1,666 Table 20. (Continued).

95 G1E G1W G5E G5W G7W G1W G5E G1E G5W G7W G3E G3W G6E G6W G3W G6E G3E G6W G7E G8E G8W G8E G7E G8W G2E G2W G10E G10W G2W G10E G2E G10W G4E G4W G9E G9W G4W G9E G4E G9W (a) Overall Maximum Strain of Stirrups in Flexure-Shear Region of Each End G1E G1W G5E G5W G7W G7W G5E G1W G5W G1E G3E G3W G6E G6W G3W G6E G3E G6W G7E G8E G8W G8E G7E G8W G2E G2W G10E G10W G2W G10E G2E G10W G4E G4W G9E G9W G4W G9E G4E G9W (b) Average Maximum Strain of Stirrups in Flexure-Shear Region of Each End 0 5 10 15 20 25 35 45 40 30 -1000 0 1000 2000 3000 4000 5000 Strain (x10-6) Un ifo rm L oa d (ki p/f t) 0 5 10 15 20 25 35 45 40 30 -2000 0 2000 4000 6000 8000 Strain (x10-6) Un ifo rm L oa d (ki p/f t) 0 5 10 15 20 25 35 45 40 30 -2000 0 2000 4000 6000 Strain (x10-6) Un ifo rm L oa d (ki p/f t) 0 5 10 15 20 25 35 45 40 30 -2000 0 2000 4000 6000 Strain (x10-6) Un ifo rm L oa d (ki p/f t) 0 5 10 15 20 25 35 45 40 30 -1000 0 1000 2000 3000 Strain (x10-6) Un ifo rm L oa d (ki p/f t) 0 5 10 15 20 25 35 45 40 30 -1000 0 1000 2000 3000 4000 Strain (x10-6) Un ifo rm L oa d (ki p/f t) 0 5 10 15 20 25 35 45 40 30 -500 0 500 1000 1500 2000 Strain (x10-6) Un ifo rm L oa d (ki p/f t) 0 5 10 15 20 25 35 45 40 30 -500 0 500 1000 1500 2000 Strain (x10-6) Un ifo rm L oa d (ki p/f t) 0 5 10 15 20 25 35 40 30 -1000 0 1000 2000 3000 4000 5000 Strain (x10-6) Un ifo rm L oa d (ki p/f t) 0 5 10 15 20 25 35 40 30 -1000 0 1000 2000 3000 4000 5000 Strain (x10-6) Un ifo rm L oa d (ki p/f t) Figure 86. Maximum stirrup strain in flexure-shear region.

96 is useful to note that the strain in the bottom bulb due to the effects of prestressing typically changed linearly from 0 microstrain at the very end of the member to between –700 and –1,500 microstrain at 30 inches from the end of the member depending on the amounts of prestressing, debonding, and draping of tendons. Figure 87 shows the longitudinal strains as measured by Gages 1, 2, 3, and 4 in the bottom cages for all girders. Those gages were located at longitudinal distances of 10, 20, 30 and 40 inches from the actual end of the girder. Figure 87 shows that strains in Gages 1 and 2 typically increased more rapidly than those in Gages 3 and 4. Most strains in Gage 1 and/or Gage 2 were larger than 1,200 microstrain at maximum load, and some reached very high values due to cracks that extended from the web and into the bottom bulb near the support. Usu- ally Gage 4, located 40 inches from the very end, had strain increases that were small and less than 200 microstrain. Figures 88(a) and 88(b) show the longitudinal strains in the bottom bars (No.8 deformed bars) of G1E and G2E, respec- tively. Gages 1, 2, and 3 were located at 46, 27, and 19 inches from the actual end of the girder, respectively. Figures 88(c) through 88(f) show the longitudinal strains in the skin bars in the west webs of Girders 3 and 4. As discussed in Section 2.3, two No. 3 horizontal bars at 6-inch centers were distributed over the depth of the webs of Girders 3 and 4. Those bars extended to 10 feet from the west ends of the girders. Six gages were attached to the two skin bars at heights of 18 and 30 inches from the bottom of the girders. Those results are labeled as h18 and h30 in Figure 88. Gages 1, 2, and 3 on bar h18 were located at 6, 21, and 45 inches, respectively, from the actual end of the girder, while Gages 1, 2, and 3 on bar h30 were at 21, 45, and 75 inches, respectively, from the actual end. Rapid increases in the longitudinal strains occurred with web- shear cracking. In G3W, the distributed horizontal bars yielded, while in G4W the maximum measured strains were less than yield. The very large longitudinal reinforcement strains that were measured near the support indicate that the tensile force demands specified in the LRFD specifications section S5.8.3.5 are very real and need to be resisted by appropriately detailed longitudinal reinforcement. Some of these strains were in excess of the yield strain well before the design strength of the member was realized. This result suggests that adding addi- tional longitudinal reinforcement would have improved the response of the girders and that to accommodate the absence of such reinforcement some internal redistribution of the shear force resisting mechanisms must have occurred. 2.6.6 Confinement Reinforcement Strains In accordance with LRFD specifications, confinement cages were used to enclose the strands in the bottom bulb of the test girders over a distance of 100 inches from the ends of each girder. The purpose of this reinforcement was to aid in preventing splitting cracks in the end anchorage region and to enhance prestress transfer between the steel and con- crete through bond. This reinforcement consisted of twenty-one No. 3 hoops arranged at a spacing of 5 inches on centers. Six strain gages, numbered 5 through 10 in Figure 55, were used to measure the strains in this reinforcement. Gages 5 through 7 were on the inclined reinforcement near the top of the bottom bulb, while Gages 8 through 10 were located on the reinforcement crossing the bottom of the bottom bulb. Figure 89 shows the strains measured by the gages on the cages. Compressive strains developed in Gages 5, 6, and 7 over the first segment of the loading history. This increase in compressive strain is probably due to the vertical compo- nents of the diagonal compression in the member. The only other possibility would seem to be a decrease in the Poisson’s effect–induced tensile strain, which would have produced a similar decrease in Gages 8, 9 and 10. However, a similar decrease was not seen in these gages. Most gages reached strain values less than 500 microstrain at failure of the girder. Gages 6 and 7 typically developed the largest strains. Those strains reached values as large as 2,000 millistrain and occurred in regions where shear cracking progressed into the bottom bulb. The significant levels of straining meas- ured in the cages indicate that those cages provided signifi- cant confinement for the anchorage of the prestressing strands. 2.6.7 Longitudinal Strain of Web at Mid-Depth (x) In the LRFD Sectional Design Model, the longitudinal strain at mid-depth, ex, is used in conjunction with the design shear stress ratio (v/f c´) to characterize the condition of the web of a member in shear for members with shear reinforce- ment. From these characterizing values of εx and (v/f c´), the contributions of the concrete and reinforcement are deter- mined from the MCFT, as reflected in the values for β and θ in Table 5.8.3.4.2-1 of the LRFD specifications. To monitor the development of longitudinal strain, two LVDTs were attached to the web of each end of each girder. One of these LVDTs was located in the first critical design region, as shown in Figure 53. The center position of this transducer was within a few inches of dvcotθ/2 from the support. The gage length of the LVDT was 48 inches; hence, by dividing the measured change in distance by 48 inches, the average strain over this length can be calculated. The LVDT recorded the deforma- tion due to externally applied load only and therefore did not include the deformation caused by the prestressing force

97 0 5 10 15 20 25 30 -2 00 0 0 2000 4000 6000 Strain (x10-6) Un ifo rm L oa d (ki p/f t) Ga ge 1 Ga ge 2 Ga ge 4 Gage 4 Gage 1 Gage 2 G1E 0 5 10 15 20 25 30 35 -200 0 0 2000 4000 6000 Ga ge 1 Ga ge 2 Ga ge 3 Ga ge 4 Gage 3 Gage 4 Gage 1 Gage 2 G1W 0 5 10 15 20 25 30 35 -1 00 0 0 1000 2000 3000 4000 5000 Ga ge 1 Ga ge 2 Ga ge 3 Ga ge 4 Gage 4 Gage 3 Gage 1 Gage 2 G2E 0 5 10 15 20 25 30 35 40 -200 0 0 2000 4000 6000 8000 Ga ge 1 Ga ge 2 Ga ge 4 Gage 4 Gage 2 Gage 1 G2W 0 5 10 15 20 25 30 35 40 -1 00 0 1 00 20 0 3 00 40 0 5 00 600 G age 1 G age 2 G age 3 G age 4 Gage 2 Gage 3 Gage 1 Gage 4 G3E 0 5 10 15 20 25 30 35 40 0 2 00 40 0 6 00 800 1000 Ga ge 1 Ga ge 2 Ga ge 3 Ga ge 4 Gage 4 Gage 3 Gage 1 Gage 2 G3W 0 5 10 15 20 25 30 35 40 45 -300 -200 -100 0 1 00 20 0 3 00 40 0 5 00 G age 2 G age 4 Gage 4 Gage 2 G4E 0 5 10 15 20 25 30 35 40 45 -1 00 0 1 00 200 300 Ga ge 1 Ga ge 2 Ga ge 3 Ga ge 4 Gage 4 Gage 3 Gage 1 Gage 2 G4W 0 5 10 15 20 25 -5 00 0 5 00 1000 1500 2000 2500 3000 G age 1 G age 2 G age 3 G age 4 Gage 4 Gage 3 Gage 1 Gage 2 G5E 0 5 10 15 20 25 -500 0 5 00 1000 1500 2000 2500 Ga ge 1 Ga ge 2 Ga ge 3 Ga ge 4 Gage 4 Gage 3 Gage 1 Gage 2 G5W 0 5 10 15 20 25 30 35 40 -2 00 0 2 00 40 0 6 00 80 0 1 000 1200 G age 1 G age 2 G age 3 G age 4 Gage 4 Gage 3 Gage 2 Gage 1 G6E 0 5 10 15 20 25 30 -2 00 0 2 00 40 0 6 00 80 0 1 00 0 1 200 Gage 1 Gage 2 Gage 3 Gage 4 Gage 4 Gage 3 Gage 1 Gage 2 G6W Strain (x10-6) Strain (x10-6) Strain (x10-6) Strain (x10-6) Strain (x10-6) Strain (x10-6) Strain (x10-6) Strain (x10-6) Strain (x10-6) Strain (x10-6) Strain (x10-6) Un ifo rm L oa d (ki p/f t) Un ifo rm L oa d (ki p/f t) Un ifo rm L oa d (ki p/f t) Un ifo rm L oa d (ki p/f t) Un ifo rm L oa d (ki p/f t) Un ifo rm L oa d (ki p/f t) Un ifo rm L oa d (ki p/f t) Un ifo rm L oa d (ki p/f t) Un ifo rm L oa d (ki p/f t) Un ifo rm L oa d (ki p/f t) Un ifo rm L oa d (ki p/f t) Figure 87. Longitudinal strains in the confinement cages.

98 prior to testing. To obtain the total strain in the web, the strains prior to testing were computed using the finite element program Vector2, and then those values were added to the measured values. Those total strains were compared with the calculated values for the same location based on the corresponding equations and the overall strain distribution for the section provided by the LRFD expression for εx. The comparison of the measured and calculated values is presented in Figure 90, from which the following observa- tions can be made: • There was reasonably good agreement between the LRFD-cal- culated strain at mid-depth due to the effects of prestressing and the strain calculated from Vector2. This result was to be expected, for the girders behave as linear elastic structures prior to the application of the distributed loading. • The kink in some of the LRFD-calculated relationships for εx is because the LRFD specifications use two different equations to compute the longitudinal strain. One rela- tionship is used when the axial straining is all expected to be compressive, and the other is used when the member is 0 5 10 15 20 25 30 35 -2 00 0 2 00 40 0 6 00 80 0 1 000 1200 G age 1 G age 2 G age 3 G age 4 Gage 4 Gage 3 Gage 1 Gage 2 G7E 0 5 10 15 20 25 30 35 40 45 50 -2 00 0 2 00 40 0 6 00 80 0 1 00 0 1 200 Ga ge 1 Ga ge 2 Ga ge 3 Ga ge 4 Gage 4 Gage 1 Gage 3 Gage 2 G7W 0 5 10 15 20 25 30 35 40 45 -2 00 0 2 00 40 0 6 00 80 0 1 00 0 1 200 G age 1 G age 2 G age 3 G age 4 Gage 4 Gage 3 Gage 1 Gage 2 G8E 0 5 10 15 20 25 30 35 -100 0 1 00 20 0 3 00 40 0 5 00 600 Ga ge 1 Ga ge 3 Ga ge 4 Gage 4 Gage 3 Gage 1 G8W 0 5 10 15 20 25 30 35 -500 0 5 00 10 00 1 500 2000 G age 1 G age 2 G age 3 G age 4 Gage 4 Gage 3 Gage 1 Gage 2 G9E 0 5 10 15 20 25 30 35 40 -200 0 2 00 40 0 6 00 80 0 1 000 Ga ge 1 Ga ge 2 Ga ge 3 Ga ge 4 Gage 4 Gage 3 Gage 1 Gage 2 G9W 0 5 10 15 20 25 30 35 -500 0 5 00 10 00 1 500 2000 G age 1 G age 2 G age 3 G age 4 Gage 4 Gage 3 Gage 1 Gage 2 G10E 0 5 10 15 20 25 30 35 40 45 -500 0 5 00 1000 1500 2000 Ga ge 1 Ga ge 2 Ga ge 3 Ga ge 4 Gage 4 Gage 3 Gage 1 Gage 2 G10W Strain (x10-6) Un ifo rm L oa d (ki p/f t) Strain (x10-6) Strain (x10-6) Strain (x10-6) Strain (x10-6) Strain (x10-6) Strain (x10-6) Strain (x10-6) Un ifo rm L oa d (ki p/f t) Un ifo rm L oa d (ki p/f t) Un ifo rm L oa d (ki p/f t) Un ifo rm L oa d (ki p/f t) Un ifo rm L oa d (ki p/f t) Un ifo rm L oa d (ki p/f t) Un ifo rm L oa d (ki p/f t) Figure 87. (Continued).

99 predicted to be cracked in flexure. The LRFD equation for εx was successful in about 50 percent of the cases in pro- viding a reasonable estimate for the development of longi- tudinal strain at mid-depth. In the worst cases, the calculated values and measured values differed by up to 1 millistrain at the design load level, which translates to a dif- ference in β of up to 0.8 and in θ of up to 10 degrees. • The plane section assumption was adopted in the LRFD equa- tion for calculating the longitudinal strain at mid-depth. However, the experimental results showed that the longitudi- nal strain in the web could be tensile due to web-shear crack- ing, even while the bottom bulb and top flange remain uncracked. This may be a source of the significant differences in predicted and measured levels of longitudinal straining at mid-depth. 2.6.8 Web-Shear Strains LVDTs were installed on the surface of the web to measure the web strains, as shown in Figure 53. In most cases, 12 LVDTs were used, and they were grouped in four rosettes. Each rosette contained two diagonal LVDTs on an inclination of ±45 degrees and one LVDT that measured horizontal deformation. Those rosettes were normally located in the critical shear design regions. There were typically two rosettes at one end, and they were located at 3 feet and 6 feet from the support, respectively. The gage lengths of the LVDTs were all 48 inches. Thus, the strains computed from the LVDTs are average strains over a distance of 48 inches. Note that the measured values from the LVDTs were the deformations due to externally applied load only and therefore did not include the deformations due to the effects of prestressing prior to testing. From the two diagonal LVDTs, the change in shear strain due to the externally applied load can be computed for each rosette. Because the shear strain in the web due to effects of prestressing is very small, the measured shear strain change can be treated as the actual shear strain in the web. Thus, the measured shear strain can be obtained by γ = ε(diagonal 1) – ε(diagonal 2). Figure 91 presents plots of the measured shear strain versus the shear force for each end of each girder. Note that the shear force was computed for the section located at the center point of the rosette. From these plots, the following observations can be made: Strain (x10-6) 0 5 10 15 20 25 30 35 40 -1 00 0 0 1000 2000 3000 4000 h30- 1 h30- 2 h30- 3 h30-1 h30-2 h30-3 (d) Strains in skin bars at G3W (h30) 0 5 10 15 20 25 30 35 40 45 -5 00 0 5 00 1000 1500 h18- 1 h18- 2 h18- 3 h18-1 h18-2 h18-3 (e) Strains in skin bars at G4W (h18) 0 5 10 15 20 25 30 35 40 45 -100 0 1 00 20 0 3 00 400 500 h30- 1 h30- 3 h30-1 h30-3 (f) Strains in skin bars at G4W (h30) 0 5 10 15 20 25 30 -500 0 5 00 1000 1500 Ga ge 1 Ga ge 3 Gage 3 Gage 1 (a) Strains in bottom bar at G1E 0 5 10 15 20 25 30 35 40 0 5 00 1000 1500 Ga ge 1 Ga ge 2 Ga ge 3 Gage 3 Gage 1 Gage 2 (b) Strains in bottom bar at G2E 0 5 10 15 20 25 30 35 40 -200 0 0 2000 4000 6000 8000 h18- 2 h18- 3 h18-2 h18-3 (c) Strains in skin bars at G3W (h18) Un ifo rm L oa d (ki p/f t) Un ifo rm L oa d (ki p/f t) Un ifo rm L oa d (ki p/f t) Un ifo rm L oa d (ki p/f t) Un ifo rm L oa d (ki p/f t) Un ifo rm L oa d (ki p/f t) Strain (x10-6) Strain (x10-6) Strain (x10-6) Strain (x10-6) Strain (x10-6) Figure 88. Longitudinal strains in bottom bars (G1E, G2E) and web skin bars (G3W, G4W).

0 5 10 15 20 25 30 -300 0 300 600 900 1200 1500 Strain (x10-6) Un ifo rm L oa d (ki p/f t) Gage 5 Gage 6 Gage 7 Gage 8 Gage 9 Gage 10 Gage 5 Gage 7 Gage 10 Gage 8 Gage 6 Gage 9 G1E G1W -400 0 400 800 1200 1600 Strain (x10-6) 0 5 10 15 20 25 30 35 Un ifo rm L oa d (ki p/f t) Gage 5 Gage 6 Gage 7 Gage 8 Gage 10 Gage 5 Gage 7 Gage 6 Gage 8 Gage 10 G2E -200 0 200 400 600 800 1000 Strain (x10-6) 0 5 10 15 20 25 30 35 Un ifo rm L oa d (ki p/f t) Gage 6 Gage 7 Gage 8 Gage 9 Gage 10 Gage 9 Gage 7 Gage 10 Gage 6 Gage 8 G2W -500 0 500 1000 1500 2000 2500 Strain (x10-6) 0 5 10 15 20 25 30 35 40 Un ifo rm L oa d (ki p/f t) Gage 5 Gage 6 Gage 7 Gage 8 Gage 9 Gage 10 Gage 5 Gage 7 Gage 10 Gage 6 Gage 8 Gage 9 G3E -500 0 500 1500 1000 Strain (x10-6) 0 5 10 15 20 25 30 35 40 Un ifo rm L oa d (ki p/f t) Gage 6 Gage 7 Gage 8 Gage 9 Gage 10 Gage 7 Gage 10 Gage 6 Gage 8 Gage 9 G3W -500 0 500 1500 1000 Strain (x10-6) 0 5 10 15 20 25 30 35 40 Un ifo rm L oa d (ki p/f t) Gage 5 Gage 6 Gage 8 Gage 9 Gage 10 Gage 8 Gage 5 Gage 10 Gage 6 Gage 9 G4E -200 -100 0 200 150 Strain (x10-6) 0 5 10 15 20 25 30 35 45 40 Un ifo rm L oa d (ki p/f t) Gage 6 Gage 7 Gage 10 Gage 7 Gage 10 Gage 6 0 5 10 15 20 25 30 35 45 40 Un ifo rm L oa d (ki p/f t) Gage 5 Gage 6 Gage 7 Gage 8 Gage 9 Gage 10 Gage 5 Gage 7 Gage 10 Gage 6 Gage 8 Gage 9 -200 -100 0 100 200 300 Strain (x10-6) G4W 0 5 10 15 20 25 Un ifo rm L oa d (ki p/f t) Gage 8 Gage 9 Gage 10 Gage 10 Gage 8 Gage 9 -200 0 200 400 600 Strain (x10-6) G5E G5W 0 5 10 15 20 25 Gage 5 Gage 6 Gage 7 Gage 8 Gage 9 Gage 10 Gage 5 Gage 7 Gage 10 Gage 6 Gage 8 Gage 9 -100 0 100 200 300 400 500 600 Strain (x10-6) Un ifo rm L oa d (ki p/f t) G6E Gage 5 Gage 6 Gage 7 Gage 8 Gage 9 Gage 10 Gage 5 Gage 7 Gage 10 Gage 6 Gage 8 Gage 9 -100 -50 0 50 100 150 200 Strain (x10-6) 0 10 5 15 25 20 30 40 35 Un ifo rm L oa d (ki p/f t) G6W Gage 5 Gage 6 Gage 7 Gage 8 Gage 9 Gage 10 Gage 6 Gage 7 Gage 10 Gage 5 Gage 8 Gage 9 -100 -50 0 50 100 150 200 Strain (x10-6) 0 10 5 20 15 25 30 Un ifo rm L oa d (ki p/f t) Figure 89. Transverse strains in confinement cages.

101 • Prior to cracking, the behavior was essentially linear elastic. After cracking, there was an abrupt change in stiff- ness followed by another region of essentially elastic behav- ior before shear strains began to develop rapidly with large increases in strain for only small increases in shear once shear strains reached 3,000 microstrain and above. • Rosettes in the same girder yielded similar elastic slopes or stiffness prior to cracking. The shear strain at cracking was small, ranging from 200 to 600 microstrain. • Immediately after cracking, there was often a sudden jump in shear strain without any increase in load (a plateau) of the shear strain. The length of the plateau depended on the stirrup reinforcement ratio. Members with low stirrup reinforcement ratios had longer plateaus than members with higher stirrup reinforcement ratios. For example, the longest plateau, 1,200 microstrain, occurred in G5E, where the stirrup reinforcement was only ρvfy = 169 psi. • Within the inelastic portion of the response, the initiation of stirrup yielding had a significant influence on the slope of the curve. Before stirrup yielding, the response was almost linear, as exhibited in G4E, G4W, G9E, and G9W, in which little or no stirrup yielding occurred. When more G10E 0 10 5 15 20 25 35 30 Un ifo rm L oa d (ki p/f t) Gage 5 Gage 6 Gage 7 Gage 8 Gage 9 Gage 10 Gage 5 Gage 7 Gage 10 Gage 6 Gage 8 Gage 9 -200 0 200 400 600 800 1000 Strain (x10-6) G7E Gage 5 Gage 6 Gage 7 Gage 8 Gage 9 Gage 10 Gage 5 Gage 7 Gage 10 Gage 6 Gage 8 Gage 9 -200 -150 -100 -50 50 0 100 150 200 Strain (x10-6) 0 10 5 15 20 25 35 30 Un ifo rm L oa d (ki p/f t) G8W Gage 7 Gage 8 Gage 10 Gage 7 Gage 10 Gage 8 -100 -50 0 50 100 150 200 Strain (x10-6) 0 10 5 15 20 25 35 30 Un ifo rm L oa d (ki p/f t) G9E Gage 5 Gage 6 Gage 9 Gage 5 Gage 6 Gage 9 -400 -300 -200 -100 0 100 200 300 Strain (x10-6) 0 10 5 15 20 25 35 30 Un ifo rm L oa d (ki p/f t) G7W Gage 5 Gage 6 Gage 7 Gage 8 Gage 9 Gage 10 Gage 5 Gage 7 Gage 10 Gage 6 Gage 8 Gage 9 -100 -50 0 100 200 300 400 Strain (x10-6) 0 10 5 20 15 25 35 30 50 45 40 Un ifo rm L oa d (ki p/f t) G8E Gage 5 Gage 7 Gage 8 Gage 5 Gage 7 Gage 8 -200 0 200 400 600 Strain (x10-6) 0 10 5 20 15 25 35 30 50 45 40 Un ifo rm L oa d (ki p/f t) G10W Gage 5 Gage 7 Gage 9 Gage 10 Gage 5 Gage 7 Gage 10 Gage 9 -500 0 500 1000 1500 Strain (x10-6) 0 10 5 20 15 25 35 30 45 40 Un ifo rm L oa d (ki p/f t) G9W Gage 5 Gage 6 Gage 7 Gage 8 Gage 9 Gage 10 Gage 5 Gage 6 Gage 10 Gage 8 Gage 7 Gage 9 -400 -300 -200 -100 0 100 200 300 Strain (x10-6) 0 10 5 15 25 20 30 40 35 Un ifo rm L oa d (ki p/f t) Figure 89. (Continued).

102 0 5 10 15 20 25 30 35 - 400 - 200 0 200 400 600 800 1000 1200 G1 W- WD 2 G1 W- LR FD 0 5 10 15 20 25 30 35 40 -4 00 -2 00 0 2 00 400 600 80 0 1 000 G2 W- WD 2 G2 W- LR FD 0 5 10 15 20 25 30 35 40 - 300 - 200 - 100 0 1 00 200 300 G3 E- ED 5 G3 E- LR FD 0 5 10 15 20 25 30 35 40 -4 00 -2 00 0 2 00 40 0 6 00 800 G3 W- WD 5 G3 W- LR FD 0 5 10 15 20 25 30 35 40 45 -400 -200 0 200 400 600 G4 E- ED 5 G4 E- LR FD 0 5 10 15 20 25 30 35 40 45 -3 00 -2 00 -1 00 0 1 00 200 G4 W- WD 5 G4 W- LR FD 0 5 10 15 20 25 -5 00 0 5 00 1000 1500 G5 E- ED 5 G5 E- LR FD 0 2 4 6 8 10 12 14 16 18 20 -4 00 -2 00 0 2 00 40 0 6 00 80 0 1 000 G5 W- WD 5 G5 W- LR FD Un ifo rm L oa d (ki p/f t) Un ifo rm L oa d (ki p/f t) Un ifo rm L oa d (ki p/f t) Un ifo rm L oa d (ki p/f t) Un ifo rm L oa d (ki p/f t) Un ifo rm L oa d (ki p/f t) Un ifo rm L oa d (ki p/f t) Un ifo rm L oa d (ki p/f t) Longitudinal Strain at Mid-Depth (microstrain) Longitudinal Strain at Mid-Depth (microstrain) Longitudinal Strain at Mid-Depth (microstrain) Longitudinal Strain at Mid-Depth (microstrain) Longitudinal Strain at Mid-Depth (microstrain) Longitudinal Strain at Mid-Depth (microstrain) Longitudinal Strain at Mid-Depth (microstrain) Longitudinal Strain at Mid-Depth (microstrain) Figure 90. Longitudinal strain at web.

103 0 5 10 15 20 25 30 35 40 - 400 - 200 0 200 400 600 G9 E- ED 5 G9 E- LR FD 0 5 10 15 20 25 30 35 40 45 -4 00 -2 00 0 2 00 400 600 G9 W- WD 5 G9 W- LR FD 0 5 10 15 20 25 30 35 - 300 - 200 - 100 0 100 20 0 3 00 400 500 G1 0E -E D5 G1 0E -LRF D 0 5 10 15 20 25 30 35 40 45 -4 00 -2 00 0 2 00 40 0 6 00 800 G1 0W -W D5 G1 0W -LRF D 0 5 10 15 20 25 30 35 40 - 400 -2 00 0 200 400 600 G6 E- ED 5 G6 E- LR FD 0 5 10 15 20 25 30 -4 00 -2 00 0 2 00 400 600 G6 W- WD 5 G6 W- LR FD 0 5 10 15 20 25 30 35 - 400 -3 00 - 200 - 100 0 1 00 200 G7 E- ED 5 G7 E- LR FD 0 5 10 15 20 25 30 35 40 45 -4 00 -2 00 0 2 00 400 600 G7 W- WD 5 G7FS -L RF D Un ifo rm L oa d (ki p/f t) Un ifo rm L oa d (ki p/f t) Un ifo rm L oa d (ki p/f t) Un ifo rm L oa d (ki p/f t) Un ifo rm L oa d (ki p/f t) Un ifo rm L oa d (ki p/f t) Un ifo rm L oa d (ki p/f t) Un ifo rm L oa d (ki p/f t) Longitudinal Strain at Mid-Depth (microstrain) Longitudinal Strain at Mid-Depth (microstrain) Longitudinal Strain at Mid-Depth (microstrain) Longitudinal Strain at Mid-Depth (microstrain) Longitudinal Strain at Mid-Depth (microstrain) Longitudinal Strain at Mid-Depth (microstrain) Longitudinal Strain at Mid-Depth (microstrain) Longitudinal Strain at Mid-Depth (microstrain) Figure 90. (Continued).

104 significant yielding of the stirrups occurred, there was a marked change in shear stiffness. • As is expected, the rosette close to the actual end measured higher shear strains than the rosette farther from the end. The shear strain under the peak or failure load ranged from 4,000 microstrain to 6,000 microstrain for the rosette close to the actual end. Based on the above observations, a simplified tri-linear curve can be used to model the relationship of the sectional shear force versus shear strain, as shown in Figure 92. The idealized response consists of three line segments defined by four points:A,B,C,and D.Line segment AB represents the elastic range of behavior,while the inelastic range is divided into two straight segments defined by BC and CD. C is the characteristic point where the stirrups start to yield.The girder failed or the maximum load was reached at point D. The slopes of these three segments are designated in the figure as Se, St1 and St2, with Se > St1 > St2. Table 21 presents the characteristic points of the tri-lin- ear model for the plots in Figure 91. In the second column 0 100 200 300 400 500 600 700 0 1 000 200 0 3 000 4000 5000 WD 1 and WD 3 WD 4 and WD 6 WD 4 and WD 6 WD 1 and WD 3 WD1 and WD3 G1W 0 100 200 300 400 500 600 700 800 0 100 0 2 000 300 0 4 000 5 000 WD 1 and WD 3 G2W 0 100 200 300 400 500 600 700 800 0 1 000 2000 3000 4000 5 000 ED 1 and ED 3 ED 4 and ED 6 ED 4 and ED 6 ED 1 and ED 3 G3E 0 100 200 300 400 500 600 700 800 900 0 1 000 2000 3 000 4000 5000 6000 WD 1 and WD 3 WD 4 and WD 6 WD 4 and WD 6 WD 1 and WD 3 G3W 0 100 200 300 400 500 600 700 800 900 1000 0 100 0 2 000 3000 4000 ED 1 and ED 3 ED 1 and ED 3 G4E 0 100 200 300 400 500 600 700 800 900 1 000 0 100 0 2 000 3000 4000 WD 1 and WD 3 WD 4 and WD 6 WD 4 and WD 6 WD 1 and WD 3 G4W Sh ea r F or ce (k ips ) Sh ea r F or ce (k ips ) Sh ea r F or ce (k ips ) Sh ea r F or ce (k ips ) Sh ea r F or ce (k ips ) Sh ea r F or ce (k ips ) Shear strain (microstrain) Shear strain (microstrain) Shear strain (microstrain) Shear strain (microstrain) Shear strain (microstrain) Shear strain (microstrain) Figure 91. Web-shear strain versus sectional shear force.

105 of the table, x is the location of the center of the rosette measured from the actual end of the girder. The measured shear force, V, and the measured shear strain, γ, are listed in turn in each of the subsequent columns for each point A, B, C, and D. The elastic stiffness Se and tangent stiff- nesses St1 and St2 are listed in the last three columns of the table. The following subsections discuss findings concerning the elastic behavior and the inelastic behavior in detail. For the elastic stage, the shear stress distribution was computed using elastic theory, and the calculated elastic stiffness was com- pared with the measured values. For the inelastic stages, equa- tions for computing the tangent stiffnesses St1 and St2 are proposed based on analysis of the test data. Elastic Stage By the traditional theory for homogeneous and elastic beams, the shear stress v on any section can be computed using Equation 42: 0 100 200 300 400 500 600 0 2000 4 000 6000 8000 ED 1 and ED 3 ED 1 and ED 3 G5E 0 100 200 300 400 500 0 1 000 2000 3 000 4000 5000 6000 WD 1 and WD 3 WD 4 and WD 6 WD 4 and WD 6 WD 1 and WD 3 G5W 0 100 200 300 400 500 600 700 800 0 1000 2000 3000 4000 5 000 6000 ED 1 and ED 3 ED 1 and ED 3 G6E 0 100 200 300 400 500 600 700 0 1000 2000 3000 4000 5 000 WD 1 and WD 3 WD 4 and WD 6 WD 4 and WD 6 WD 1 and WD 3 G6W 0 100 200 300 400 500 600 700 800 0 1000 200 0 3 000 4 000 5000 ED 1 and ED 3 ED 1 and ED 3 G7E 0 100 200 300 400 500 600 0 2 000 4000 6000 8000 WD 1 and WD 3 WD 4 and WD 6 WD 4 and WD 6 WD 1 and WD 3 G7W Sh ea r F or ce (k ips ) Sh ea r F or ce (k ips ) Sh ea r F or ce (k ips ) Sh ea r F or ce (k ips ) Sh ea r F or ce (k ips ) Sh ea r F or ce (k ips ) Shear strain (microstrain) Shear strain (microstrain) Shear strain (microstrain) Shear strain (microstrain) Shear strain (microstrain) Shear strain (microstrain) Figure 91. (Continued).

106 where: V = shear force on the cross section, I = moment of inertia of the cross section, Q = first moment about the neutral axis of the part of the section lying between the bottom or top edge and the point where the shear stress is being calculated, and b = width of the member where the stress is being calculated. v VQ Ib = (42) Figure 93 shows the typical shear stress distribution calcu- lated by the foregoing equation for the composite section of the test girders. Note that the composite section properties were calculated based on the transformed slab width and the calcu- lated modulus of the precast girder. The shear stress on the web is much higher than that on the top flange and bottom bulb. The maximum stress occurred at the location of the neutral axis. The average stress within the web region (45 inches deep) was also computed, and that stress is indicated in Figure 93. Following the above procedure, the shear stress distribu- tion on the girder section under a shear force of V = 100 kips Figure 91. (Continued). 0 100 200 300 400 500 600 700 0 1000 2000 3000 4000 WD 1 and WD 3 WD 1 and WD 3 G8W 0 100 200 300 400 500 600 700 800 0 1 000 2000 3 000 4000 ED 1 and ED 3 ED 1 and ED 3 ED1 and ED3 G9E 0 100 200 300 400 500 600 700 800 900 0 1000 2000 3000 4000 WD 1 and WD 3 WD 4 and WD 6 WD 4 and WD 6 WD 1 and WD 3 G9W 0 100 200 300 400 500 600 700 800 0 100 0 2 000 300 0 4 000 5000 ED 1 and ED 3 G10E 0 100 200 300 400 500 600 700 800 900 1000 0 1000 200 0 3 00 0 4 000 5000 6000 WD 1 and WD 3 WD 4 and WD 6 WD 4 and WD 6 WD 1 and WD 3 G10W Shear strain (microstrain) Shear strain (microstrain) Shear strain (microstrain) Shear strain (microstrain) Shear strain (microstrain) Sh ea r F or ce (k ip/ ft) Sh ea r F or ce (k ips ) Sh ea r F or ce (k ips ) Sh ea r F or ce (k ips ) Sh ea r F or ce (k ips )

107 was computed for each girder. Table 22 lists the calculated results. The shear force resistance is provided by three parts: Vtop, the shear force in the top flange and deck; Vweb, the shear force in the web; and Vbot, the shear force in the bottom bulb. It is seen that the web provides about 75 percent of the total shear force resistance. The remaining 25 percent is provided by the top flange and deck (17 percent) and by the bottom bulb (8 percent). The ratio between the maximum shear stress τmax and the average stress within the web τavg is 1.070, with values ranging from 1.065 to 1.077. The last column of Table 22 provides the calculated elastic stiffness Se,cal which is computed as where: τavg = average sheer stress over the web region, G = shear modulus of the girder computed from the measured concrete elastic modulus, v = Poisson ratio = 0.2. To evaluate the accuracy of elastic theory in predicting the measured stiffness, Table 23 compares the average value of the measured stiffness for each girder with the value calcu- lated by the foregoing equation. The ratio of the average measured stiffness to the calculated stiffness ranges from 0.80 to 1.18, with a mean value of 0.96 and a COV of 0.12. Note that no comparison was made for G8W because of the two strengthening plates that were placed on the west end of that girder. G E v = +2 1( ) , and S V G e , / cal avg (43)= τ O A B C D Measured Shear Strain γ Cracking Se ct io na l S he ar F or ce V Yielding Failure 1 Se 1 St1 1 St2 Figure 92. Idealized tri-linear curve of shear strain versus shear force. A B C D Stiffness Girder x(in) V(kips) (ms) V (kips) (ms) V (kips) (ms) V (kips) (ms) Se (kips) St1 (kips) St2 (kips) G1WD13 70 23.8 0 362.8 414 522.5 2,569 606.8 4,671 818,841 74,107 40,105 G1WD46 106 20.3 0 318.4 340 462.7 1,770 516.5 3,161 876,765 100,909 38,677 G2WD13 70 23.8 0.0 431.4 478 755.5 3,349.0 781.3 3,777 852,727 112,887 60,280 G3ED13 48 26.0 0 312.0 244 707.0 3,168 785.0 4,201 1,172,295 135,089 75,508 G3ED46 84 22.4 0 277.4 207 677.9 3,175 677.9 3,175 1,231,787 134,939 N/A G3WD13 48 26.0 0 321.2 343 774.7 3,752 854.0 5,184 860,758 133,030 55,377 G3WD46 84 22.4 0 277.4 298 611.6 2,864 737.6 4,824 855,638 130,242 64,286 G4ED13 48 26.0 0 313.7 308 938.3 3,591 N/A N/A 934,221 190,253 N/A G4WD13 48 26.0 0 339.7 343 938.3 3,117 N/A N/A 914,694 215,789 N/A G4WD46 84 22.4 0 293.4 307 810.4 3,061 N/A N/A 882,671 187,727 N/A G5ED13 48 26.0 0 369.6 438 521.4 6,569 N/A N/A 784,566 24,759 N/A G5WD13 48 26.0 0 266.2 402 394.8 3,520 437.8 5,575 597,612 41,244 20,925 G5WD46 84 22.4 0 226.1 278 340.9 3,180 378.1 5,210 732,662 39,559 18,325 G6ED13 48 26.0 0 363.7 483 654.5 3,168 760.3 4,735 699,255 108,305 67,518 G6WD13 48 26.0 0 379.9 466 599.6 2,914 612.7 3,210 759,528 89,747 44,257 G6WD46 84 22.4 0 328.1 431 517.9 2,786 529.2 3,004 709,234 80,594 51,835 G7ED13 48 26.0 0 398.2 502 736.3 4,054 N/A N/A 741,514 95,186 N/A G7WD13 175 13.5 0 273.4 354 463.1 3,912 511.0 5,968 734,261 53,316 23,298 G7WD46 211 9.9 0 268.1 364 376.7 5,580 N/A N/A 709,254 20,821 N/A G8WD13* 48 26.0 0 252.3 363 399.4 1,038 667.1 3,952 623,526 217,926 91,867 G9ED13 48 26.0 0 352.0 422 721.6 3,439 N/A N/A 772,607 122,506 N/A G9WD13 48 26.0 0 475.2 675 840.5 3,119 N/A N/A 665,541 149,468 N/A G9WD46 84 22.4 0 400.7 525 684.3 2,658 N/A N/A 720,533 132,958 N/A G10ED13 48 26.0 0 273.5 359 690.5 3,542 746.5 4,521 689,526 131,008 57,201 G10WD13 48 26.0 0 407.4 556 837.1 3,886 939.7 5,644 686,043 129,039 58,362 G10WD46 84 22.4 0 363.3 490 641.3 2,102 N/A N/A 695,673 172,457 N/A *Aluminum plates were plated at the west end of Girder 8. Table 21. Characteristic points of the tri-linear model for measured web strains.

108 Inelastic Stage After web cracking occurred, the shear behavior exhibited an inelastic response. Shear strains in a cracked web result from three primary components: deformations of the uncracked concrete, opening of the diagonal cracks, and relative slip between crack faces along the crack surface. Compared with the latter two components, the deformation of the uncracked concrete is small. Hence, the total shear strain depends on the crack width and crack slip. Because the crack width and crack slip are strongly influenced by the stirrup reinforcement ratio, the test results were used to develop a relationship for shear stiffness that depended on the stirrup reinforcement ratio. Table 24 lists relative stirrup reinforcement ratios and rela- tive stiffness ratios St1/Se and St2/St1, respectively, for each of the test girders.Values for Se, St1, and St2 were presented in Table 21. Table 24 introduces a nondimensional parameter nρv, where n = (Es/Ec) and ρv =Av/(bs). This parameter takes into account the influences of both the stirrup reinforcement ratio and its stiff- ness. The ratio of St1/Se ranges from 0.07 to 0.25, while the ratio of St2/St1 ranges from 0.38 to 0.64 and averages 0.50. Figure 94 presents the stiffness ratio St1/Se versus the nondi- mensional parameter nρv. It is seen that when nρv is less than around 0.06, there exists a good correlation between St1/Se and nρv. However, for values of nρv greater than 0.06, the St1/Se values tend to be constant at values between 0.18 and 0.25. Regression analysis was used on the results to obtain the following equations: when nρv ≤ 0.065 when nρv > 0.065 Figure 95 shows the stiffness ratio St2/St1 versus the same nondimensional parameter nρv. It can be seen that ratios oscillate around a value of 0.5 and depend little on nρv. For simplicity, the following relationship is suggested: S S t t 2 1 0 5 45= . ( ) S S bt e 1 0 21 44= . ( ) S S n at e v 1 2 45 0 05 44= +. ( ) . ( )ρ Figure 93. Shear stress distribution in girder section. Girder Vtop(kips) Vweb (kips) Vbot (kips) max (ksi) avg (ksi) Se,cal (kips) Girder 1 18.2 73.8 8.0 0.296 0.276 860,807 Girder 2 19.0 73.1 7.8 0.294 0.273 973,675 Girder 3 17.7 74.2 8.1 0.297 0.278 873,554 Girder 4 18.8 73.3 7.9 0.295 0.274 884,561 Girder 5 18.7 73.4 7.9 0.295 0.275 889,735 Girder 6 19.7 72.6 7.7 0.294 0.271 833,250 Girder 7 19.1 73.1 7.8 0.294 0.273 690,471 Girder 8 19.9 72.4 7.7 0.294 0.271 697,005 Girder 9 19.0 73.2 7.8 0.295 0.274 817,476 Girder 10 19.5 72.8 7.7 0.294 0.272 681,468 Measured Stiffness Se,test (kips) Girder ED13 ED46 WD13 WD46 Average Se, cal (kips) cal,e test,e S S Girder 1 N/A N/A 818,841 876,765 847,803 860,807 0.98 Girder 2 N/A N/A 852,727 N/A 852,727 973,675 0.88 Girder 3 1,172,295 1,231,787 860,758 855,638 1,030,120 873,554 1.18 Girder 4 934,221 N/A 914,694 882,671 910,528 884,561 1.03 Girder 5 784,566 N/A 597,612 732,662 704,946 889,735 0.79 Girder 6 699,255 N/A 759,528 709,234 722,672 833,250 0.87 Girder 7 741,514 N/A 734,261 709,254 728,343 690,471 1.05 Girder 8 N/A N/A 623,526 N/A N/A 697,005 N/A Girder 9 772,607 N/A 665,541 720,533 719,560 817,476 0.88 Girder 10 689,526 N/A 686,043 695,673 690,414 681,468 1.01 Average 0.96 COV 0.12 Table 22. Shear force and stress distribution under shear force V = 100 kips Table 23. Measured and calculated shear stiffness. Bottom (10.5 in) Web (45 in) Top (17.5 in) Average Stress Maximum Stress Shear Stress Distribution

109 2.6.9 Time-Dependent Losses As mentioned in Section 2.3, a Whittemore gage was used to measure changes in deformation along the length of the bottom bulb of the girders. Measurements were usually taken before strand release, after strand release, at periodic inter- vals between strand release and testing, and shortly before testing to assess the transfer length, the prestressing loss, and the development of strains prior to testing. Those measure- ments also provided experimental data for the evaluation of the time-dependent prestress losses due to concrete shrink- age and creep, as well as strand relaxation. The detailed meas- urements for each girder are presented in the associated appendices. In Article 5.8.5.4, the LRFD specifications present a refined method for computing time-dependent losses. The refined method, based on the measured material properties and measured elastic shortening, was used to compute the calcu- lated time-dependent losses. Figure 96 compares the calcu- lated total losses with the measured values for each girder. The calculated total prestress loss was computed by adding the measured elastic loss to the calculated time-dependent loss. The comparisons show that, for the data as a whole, the refined estimates of time-dependent losses agree reasonably well with the experimental data. 2.6.10 Transfer Length Elastic shortening due to strand release was obtained from the two sets of Whittemore readings, with one reading taken immediately before strand release and one reading taken immediately after strand release. From the strain profile of the elastic shortening, the transfer length was measured for each end of each girder. Table 25 lists the measured transfer lengths for the two ends for each girder. Transfer lengths range from 18 to 28 inches and average 23 inches. The LRFD specifica- tions suggest that the transfer length is 60 times the strand diameter, or 36 inches for the test girders. The measured transfer length is only about two-thirds of the LRFD value. ACI Code 318-05 specifies a transfer length equal to effective prestress divided by three, in ksi units, times the strand diam- eter. For the typical effective prestress for these girders of 160 ksi, the corresponding transfer length is 53 times the strand diameter, or 32 inches. 2.7 Components of Shear Resistance 2.7.1 Introduction As discussed in Chapter 1, there are substantial differ- ences in how codes of practice evaluate the contributions of transverse reinforcement, Vs, and concrete, Vc, to shear Girde 100r n v St1/Se St2/St1 G1WD13 0.56 0.09 0.54 G1WD46 2.42 0.12 0.38 G2WD13 4.00 0.13 0.53 G3ED13 3.16 0.12 0.56 G3ED46 3.16 0.11 N/A G3WD13 3.16 0.15 0.42 G3WD46 3.16 0.15 0.49 G4ED13 6.45 0.20 N/A G4WD13 6.45 0.24 N/A G4WD46 6.45 0.21 N/A G5ED13 0.66 0.03 N/A G5WD13 0.66 0.07 0.51 G5WD46 0.66 0.05 0.46 G6ED13 3.66 0.15 0.62 G6WD13 3.66 0.12 0.49 G6WD46 3.66 0.11 0.64 G7ED13 3.57 0.13 N/A G7WD13 0.68 0.07 0.44 G7WD46 0.68 0.03 N/A G9ED13 7.76 0.16 N/A G9WD13 12.61 0.22 N/A G9WD46 12.61 0.18 N/A G10ED13 5.33 0.19 0.44 G10WD13 5.33 0.19 0.45 G10WD46 5.33 0.25 N/A Table 24. Ratios between measured stiffness. 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 e t S S 1 nρv = 2.45(nρv) + 0.051S S e t 0.211 S S e t Figure 94. nv versus stiffness ratio St1/Se. 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.00 0.01 0.02 0.03 0.04 0.05 0.06 1 2 t t S S = 0.50 1 2 S S t t nρv Figure 95. nv versus stiffness ratio St2/St1.

110 resistance. For example, the AASHTO Standard Specifica- tions evaluate Vs based on a 45-degree truss model, whereas the LRFD specifications use a variable angle truss model in which the angle of diagonal compression can be as low as 18 degrees. The effect of this difference is that the calculated Vs contribution to shear resistance according to the LRFD spec- ifications can be two to three times larger than that calculated by the AASHTO Standard Specifications for the same mem- ber with the same quantity of shear reinforcement. There are similarly large differences in the magnitude of the calculated concrete contribution to shear resistance with the additional complication of different explanations for the source of this resistance. In the AASHTO Standard Specifications, Vc is taken as the calculated diagonal cracking strength, while in the LRFD specifications, Vc is calculated from the average principal postcracking tensile stress that can be carried in the web of a member and is limited by the shear slip resistance along a crack face. Other codes and shear design methods provide different explanations for the concrete contribution to resistance. Gi rd er 1 0 10 20 30 40 50 0 5 0 100 150 200 25 0 Me as ur em en t LR FD Ca lc ul at io n Gi rd er 2 0 10 20 30 40 50 60 0 5 0 1 00 15 0 2 00 250 300 350 Me as ur em en t LR FD Ca lc ul at io n Gi rd er 3 0 10 20 30 40 50 0 5 0 1 00 15 0 2 00 250 Me as ur em en t LR FD Ca lc ul at io n Gi rd er 4 0 10 20 30 40 50 60 0 1 00 200 30 0 4 00 500 Me as ur em en t LR FD Ca lc ul at io n Gi rd er 5 0 10 20 30 40 0 5 0 100 150 200 Me as ur em en t LR FD Ca lc ul at io n Gi rd er 6 0 10 20 30 40 50 0 5 0 1 00 150 Me as ur em en t LR FD Ca lc ul at io n Lo ss o f P re st re ss (k si) Lo ss o f P re st re ss (k si) Lo ss o f P re st re ss (k si) Lo ss o f P re st re ss (k si) Lo ss o f P re st re ss (k si) Lo ss o f P re st re ss (k si) Concrete Age (day) Concrete Age (day) Concrete Age (day) Concrete Age (day) Concrete Age (day) Concrete Age (day) Figure 96. Comparison between the measured and calculated prestress losses.

111 In this section, the contributions of the transverse rein- forcement and the concrete to the shear resistance are evalu- ated over the loading history of each girder, with Vs evaluated from free-body diagrams and from measured values for stir- rup strains from strain gauge readings. The results are used to investigate influencing factors and the safety of the LRFD specifications. Section 2.7.2 describes the method used to evaluate the components of resistance, and Section 2.7.3 describes the method used to evaluate the components’ contributions over the loading history for all girder ends. Sec- tion 2.7.4 introduces a new term, called the “characteristic angle,” for evaluation of postcracking behavior, and Section 2.7.5 evaluates the LRFD method for calculating the compo- nents of resistance. 2.7.2 Method for Evaluating Vs and Vc Crack-Based Free Body Diagram As reported in Section 2.5, the loading of each girder was paused at several load stages in the testing of each girder to mark cracks and to make other key measurements. The loca- tions of these cracks were recorded by photographs, and then an image analysis method was used to produce a com- plete cracking history for each girder, as described in Appen- dix 11. For every diagonal crack at the ultimate crack pattern, a free body between the end of the girder and this crack was produced. In this evaluation, that free body is termed a “crack-based free body diagram” (CFBD). Figure 97 gives an example of the selection of crack-based free body for the west end of Girder 1. Figure 97(a) shows the crack pattern of the west end of Girder 1 (G1W), and Figure 97(b) shows the dimensions for the CFBD of a selected diagonal Gi rd er 7 0 10 20 30 40 50 0 1 0 2 0 3 0 50 40 50 40 Me as ur em en t LR FD Ca lc ul at io n Gi rd er 8 0 10 20 30 40 50 60 0 5 0 100 15 0 2 00 250 Me as ur em en t LR FD Ca lc ul at io n Gi rd er 9 0 10 20 30 40 0 1 0 2 0 3 0 Me as ur em en t LR FD Ca lc ul at io n Gi rd er 10 0 10 20 30 40 50 0 5 0 1 00 150 200 25 0 3 00 350 Me as ur em en t LR FD Ca lc ul at io n Lo ss o f P re st re ss (k si ) Lo ss o f P re st re ss (k si ) Lo ss o f P re st re ss (k si ) Lo ss o f P re st re ss (k si ) Concrete Age (day) Concrete Age (day) Concrete Age (day) Concrete Age (day) Figure 96. (Continued). Transfer Length (in) Girder West East Girder 1 28 28 Girder 2 23 23 Girder 3 NA 18 Girder 4 23 23 Girder 5 23 25 Girder 6 N/A 23 Girder 7 23 23 Girder 8 23 23 Girder 9 20 23 Girder 10 23 N/A Table 25. Measured trans- fer length.

112 crack. Figure 97(c) shows the vertical forces acting on the free body. These forces consist of the reaction force “R” at the end support, the external distributed load on the top of the girder, the forces in the stirrups, the vertical component of the prestress, and the concrete contribution Vc to shear resistance. The individual components of Vc are not shown, but they are recognized to consist of interface shear transfer, shear in the uncracked compression zone at the top of the member, shear in the typically uncracked bottom bulb, dowel action, and stress transmitted directly across a crack. While there are several potential free body diagrams at the end of each girder, each corresponding to a different diagonal crack, one CFBD was selected for each end to be used for presenting the measured components of resistance. The exceptions were the west end of Girder 7 and the east end of Girder 8, in which two CFBDs were selected. Table 26 presents the geometric and reinforcement details for each of these selected CFBDs. The dimensional parameters used in Table 26 are defined in Figure 97(b). Lb and Lt are longitudinal distances from the center of the support to the very bottom and very top points of the cracks, respectively. Lc is the horizontal projec- tion of the crack; hb and ht are the uncracked concrete depths of the bottom bulb and the top flange, respectively; and hc is the overall depth of the crack. For the test girders, hc ranges from 38.95 to 51.73 inches and averages 46.3 inches, which is very close to the web depth of 47 inches.Also listed in the table are the measured crack angle θ and the numbers and yield strength of the stirrups that cross the selected cracks. The last two columns of Table 26 list the sum of the yield force of those stirrups, Vy, and the effective stirrup strength, ρvfyv, for the stir- rups that crossed the boundary crack of the free body. Two considerations controlled the selection of the critical crack. The first was that it should be in the region of the widest cracks, the largest stirrup strains, and the location where the failure was observed. Second, if there were two or more cracks in this failure region, the crack whose mid- point was closest to the LRFD-specified critical section (0.5dvcotθ from the inside face of the support) was selected, as illustrated in Figure 97. Method for Evaluating Vs and Vc As shown in Figure 97(c), the total shear force V in the inclined section was computed from the reaction force and the external test load. The vertical component of the prestress force Vp was calculated from geometry and neglected the increment in prestress force due to the external load. The con- tribution of the stirrup reinforcement was evaluated from strain gage readings, and then Vc was directly calculated from equilibrium of the vertical forces. Evaluation of Vs The transverse reinforcement was extensively instru- mented, with four gages on 10-inch centers applied over the depth of between 14 and 18 transverse bars. The measured strain gage readings were used to compute the stirrup stresses and their forces. To compute the shear contribution of the stirrups, Vs, the strains at crack locations along every stirrup should be measured. Because this was not practical, an approach was adopted for making the best possible estimate of stirrup strains. This method can effectively use the strain gage readings and deals with both gauged and ungauged stir- rups using different approaches. For gauged stirrups, if crack- ing was located between two consecutive gages, then the strain at the boundary crack was obtained from the gage with the higher reading. If the boundary crack point was located outside any two consecutive gages, then the strain at the boundary crack point was taken as that at the nearest gage. For stirrups without gages, the strain at the boundary crack point was interpolated from the “crack strains” of the two gauged stirrups on either side of the ungauged stirrup or was 0.5dvcotθ1 0.5dvcotθ1 dvcotθ1 dvcotθ2 Critical Section of LRFD Prediction Selected Critical Cracks (a) Selected Crack for Free Body Diagram Analysis θ L t Lb Lc hb hc ht (b) Dimensions of Selected Free Body Diagram Stirrup External Load R Draped Strand V = Vs + Vc + Vp V Vs Vp Vc (c) Shear Resistance in the Crack Section Figure 97. Free body diagram for components of shear resistance.

113 taken from the nearest gauged stirrup if there were only one gauged stirrup available on one side of the boundary crack. By using this method, all stirrups in the free body were assigned a strain considered to be the best possible estimate of the strain along the line of cracking. Once the strains at cracks had been calculated, the rein- forcement stresses were computed using the measured mate- rial properties of the reinforcement. When the measured strain was above the yield strain, then the yield stress was used. This approach is considered appropriate for all of the girder tests except for the east side of Girder 5, in which the welded wire fabric would be expected to exhibit a cold-rolled stress-strain response. Thus, Vs may be underestimated and Vc overestimated for the east end of Girder 5. The contribu- tion of the stirrups Vs was then obtained by summing the forces in all the stirrups crossing the boundary crack. Evaluation of Vc It was impractical to attempt to directly measure the concrete contribution to shear resistance. Therefore, it was computed from equilibrium by subtracting Vs and Vp from the total shear force V acting on the section. 2.7.3 Shear Resistance Components By using the above procedure, the shear components for all selected CFBDs shown in Table 26 were computed. The results are presented in the 22 plots shown in Figure 98, where Vp is considered to be part of Vs for ends with draped strands. The difference between the sectional shear force V and the contribution of the shear reinforcement Vs is the concrete contribution Vc. The calculated yield strength of the stirrups Vy is also shown in these figures and is useful for assessing when in the history of loading, if at all, the maxi- mum potential contribution of the shear reinforcement was realized. The plots of sectional shear force versus shear compo- nents, as shown in Figure 98, can be idealized as four linear segments defined by five points OABCD, as shown in Figure 99. Segment OA is the response before cracking. In this stage, the contribution of the stirrups to resistance is very small and nearly all of the shear force is carried by the uncracked concrete in tension. Cracking occurs at point A. Segment AB is straight and vertical, which means that part of the shear force previously carried by the uncracked con- crete is transferred to the stirrups, with a sharp increment in stirrup force. Segment BC is effectively a serviceability behavioral stage where the stirrup force increases linearly with increase in the external test load. The characteristic angle a for this stage reflects directly the concrete contribu- tion Vc. Yielding of the stirrups occurs at point C. In seg- ment CD, with the stirrups yielding, any further shear force increment must be carried by the concrete. In this idealiza- tion, the possible contribution from strain hardening of the stirrups is ignored. Dimensions for Free Body Diagrams Stirrup Layout Girder Lb (in) Lc (in) Lt (in) hb (in) hc (in) ht (in) (deg) v A yvf (ksi) yV * (kips) yvv f * (psi) G1E 27.67 91.41 119.08 10.62 47.39 14.99 27.2 7-2#4 70.0 196.0 357 G1W 22.48 92.48 114.96 9.20 47.68 16.12 28.2 8-2#4 70.0 224.0 404 G2E 34.99 92.28 127.28 11.58 45.53 15.89 26.4 8-2#5 79.3 393.3 710 G2W 26.70 87.46 114.16 10.47 47.20 15.33 29.8 8-2#5 79.3 393.3 750 G3E 23.59 97.94 121.53 10.55 47.02 15.43 26.0 13-2#4 67.8 352.6 600 G3W 33.43 89.96 123.39 10.89 46.26 15.85 27.3 11-2#4 67.8 298.3 553 G4E 24.26 82.46 106.72 10.66 47.41 14.93 28.4 13-2#5 64.6 520.7 1,052 G4W 17.48 92.35 109.83 9.03 48.74 15.23 28.4 16-2#5 64.6 640.8 1,157 G5E 31.29 125.93 157.22 9.70 49.23 14.07 21.1 6-2#3 82.2 121.7 161 G5W 12.30 120.13 132.43 7.60 51.73 13.67 23.7 6-2#3 76.5 101.0 140 G6E 16.73 79.93 96.66 11.47 46.25 15.28 30.1 7-2#5 64.7 280.8 585 G6W 38.15 73.06 111.21 13.94 41.33 17.73 29.9 6-2#5 64.7 240.7 549 G7E 21.79 94.40 116.19 10.81 45.03 17.17 25.9 12-2#4 69.2 332.2 586 G7W 81.52 103.82 185.34 13.01 45.09 14.90 23.6 8-2#4/1-2#3 69.2/74.5 237.8 382 G7FS 161.04 91.89 252.93 10.64 46.31 16.06 25.9 4-2#3 74.5 65.6 119 G8E 24.22 80.79 105.01 11.30 46.74 14.96 30.1 10-2#4 69.2 276.8 571 G8EB 49.48 99.79 149.26 10.54 47.62 14.83 25.1 12-2#4 69.2 332.2 555 G8WP 21.84 80.16 101.99 10.96 47.65 14.39 30.0 10-2#4 69.2 276.8 576 G9E 19.34 85.16 104.50 13.22 43.42 16.36 27.8 14-2#5 65.4 567.7 1,111 G9W 28.51 55.73 84.24 15.12 38.95 18.93 35.7 14-2#5 65.4 567.7 1,698 G10E 10.84 73.94 84.78 7.46 42.54 23.01 30.8 8-2#5 65.4 324.4 731 G10W 9.91 90.64 100.54 6.76 49.42 16.82 29.2 10-2#5 65.4 405.5 746 * vyvy AfV , )Lb/(Vf cwyyvv , and 6wb inches. Table 26. Dimensions and transverse reinforcement in selected free body diagrams.

114 G1E5 ( f 'c = 12.1 ksi, ρv fyv = 357 psi) G1W5 ( f 'c = 12.1 ksi, ρv fyv = 404 psi) G2E5 ( f 'c = 12.6 ksi, ρv fyv = 710 psi) G2W5 ( f 'c = 12.6 ksi, ρv fyv = 750 psi) G3E7 ( f 'c = 15.9 ksi, ρv fyv = 600 psi) G3W9 ( f 'c = 15.9 ksi, ρv fyv = 553 psi) 0 100 200 300 400 500 600 0 100 200 300 400 500 600 V s V V c V y = 298. 3k ip s Sh ea r C om po ne nt s (ki ps ) Shear V (kips) 0 100 200 300 400 500 600 0 100 200 300 400 500 600 V s V V c V y = 352. 6ki ps Sh ea r C om po ne nt s (ki ps ) Shear V (kips) 0 100 200 300 400 500 0 100 200 300 400 500 V c V s V V y = 393. 3ki ps Sh ea r C om po ne nt s (ki ps ) Shear V (kips) 0 100 200 300 400 500 600 700 0 100 200 300 400 500 600 700 V s +V p V V c V y +V p =4 27. 7ki ps Sh ea r C om po ne nt s (ki ps ) Shear V (kips) 0 100 200 300 400 500 0 100 200 300 400 500 V s +V p V V c V y +V p = 264 .9 ki ps Sh ea r C om po ne nt s (ki ps ) Shear V (kips) 0 100 200 300 400 0 100 200 300 400 V s V V c V y = 196. 0ki ps Sh ea r C om po ne nt s (ki ps ) Shear V (kips) Figure 98. Components of resistance over loading history.

115 G4E7 ( f 'c = 16.3 ksi, ρv fyv = 1052 psi) G4W8 ( f 'c = 16.3 ksi, ρv fyv = 1157 psi) G5E8 ( f 'c = 17.8 ksi, ρv fyv = 161 psi) G5W4 ( f 'c = 17.8 ksi, ρv fyv = 140 psi) G6E4 ( f 'c = 12.7 ksi, ρv fyv = 585 psi) G6W6 ( f 'c = 12.7 ksi, ρv fyv = 549 psi) 0 100 200 300 400 500 600 700 0 100 200 300 400 500 600 700 V s V V c V y = 520. 7ki ps Sh ea r C om po ne nt s (ki ps ) Shear V (kips) 0 100 200 300 400 500 600 700 0 100 200 300 400 500 600 700 V s V V c V y = 640. 8k ip s Sh ea r C om po ne nt s (ki ps ) Shear V (kips) 0 50 100 150 200 250 300 0 5 0 1 00 15 0 2 00 250 300 V s V V c V y =1 01. 0ki ps Sh ea r C om po ne nt s (ki ps ) Shear V (kips) 0 50 100 150 200 250 300 0 5 0 1 00 150 20 0 2 50 300 V s V V c V y = 121. 7ki ps Sh ea r C om po ne nt s (ki ps ) Shear V (kips) 0 100 200 300 400 500 600 0 100 200 300 400 500 600 V s V V c V y = 280. 8ki ps Sh ea r C om po ne nt s (ki ps ) Shear V (kips) 0 100 200 300 400 500 0 100 200 300 400 500 V s V V c V y = 240. 7ki ps Sh ea r C om po ne nt s (ki ps ) Shear V (kips) Figure 98. (Continued).

116 G7E7 ( f 'c = 12.5 ksi, ρv fyv = 586 psi) G7W13 ( f 'c = 12.5 ksi, ρv fyv = 382 psi) G7W20 ( f 'c = 12.5 ksi, ρv fyv = 119 psi) G8E5 ( f 'c = 13.3 ksi, ρv fyv = 571 psi) G8E8 ( f 'c = 13.3 ksi, ρv fyv = 555 psi) G8W4P ( f 'c = 13.3 ksi, ρv fyv = 576 psi) 0 100 200 300 400 500 600 0 100 200 300 400 500 6 00 V s V V c V y = 332. 2ki ps Sh ea r C om po ne nt s (ki ps ) Shear V (kips) 0 100 200 300 400 500 0 100 200 300 400 500 V s V V c V y = 237. 8ki ps Sh ea r C om po ne nt s (ki ps ) Shear V (kips) 0 100 200 300 400 500 600 700 0 100 200 300 400 500 600 700 V s V V c V y =2 76. 8ki ps Sh ea r C om po ne nt s (ki ps ) Shear V (kips) 0 50 100 150 200 0 50 100 150 200 V s V V c V y = 65. 6ki ps Sh ea r C om po ne nt s (ki ps ) Shear V (kips) 0 100 200 300 400 500 600 0 100 200 300 400 500 600 V s V V c V y = 332. 2ki ps Sh ea r C om po ne nt s (ki ps ) Shear V (kips) 0 100 200 300 400 500 0 100 200 300 400 500 V s V V c V y =2 76. 8k ip s Sh ea r C om po ne nt s (ki ps ) Shear V (kips) Figure 98. (Continued).

117 Each plot in Figure 98 was used to derive characteristic val- ues for the points OABCD and angle a. The resultant values are listed in Table 27 for each CFBD. From these tables and plots, the following observations are made. • With first diagonal cracking, the stirrups in both G1E (ρvfyv = 357 psi) and G1W (ρvfyv = 404 psi) quickly yielded and the contribution of the concrete decreased to a very small frac- tion of what the concrete had provided before cracking. After the stirrups yielded, the member supported an addi- tional 60 to 80 percent of the stirrup yield load. All that contribution was provided by the contribution of the concrete. • After first diagonal cracking, the stirrups strains in G2E (ρvfyv = 710 psi) and G2W (ρvfyv = 750 psi) increased rapidly with increasing load but at a rate less than that for Girder 1. G2E failed when the stirrups yielded,while G2W failed shortly after G9E6 ( f 'c = 9.6 ksi, ρv fyv = 1111 psi) G9W8 ( f 'c = 9.6 ksi, ρv fyv = 1698 psi) G10E6 ( f 'c = 10.6 ksi, ρv fyv = 731 psi) G10W4 ( f 'c = 10.6 ksi, ρv fyv = 746 psi) 0 100 200 300 400 500 600 0 100 200 300 400 500 600 V s V V c V y = 567.7kips Sh ea r C om po ne nt s (ki ps ) Shear V (kips) 0 100 200 300 400 500 600 700 0 100 200 300 400 500 600 700 V s +V p V V c V y +V p =608.5kips Sh ea r C om po ne nt s (ki ps ) Shear V (kips) 0 100 200 300 400 500 600 700 800 0 100 200 300 400 500 600 700 800 V s +V p V V c V y +V p =447.7kips Sh ea r C om po ne nt s (ki ps ) Shear V (kips) 0 100 200 300 400 500 600 700 0 100 200 300 400 500 600 700 V s V V c V y =324.4kips Sh ea r C om po ne nt s (ki ps ) Shear V (kips) O A B C D Vc Vs V a Before Cracking Cracking After Cracking (Serviceability) Yielding (Ultimate) Sh ea r C om po ne nt s Figure 98. (Continued). Figure 99. Idealized components of shear resistance.

118 the stirrups yielded. After shear cracking, the concrete contri- bution decreased with increasing load but then increased again with increasing load after the stirrups yielded. • The results for G3E (ρvfyv = 600 psi) illustrate that there are some inaccuracies in the calculation method, as the calcu- lated contribution of the stirrups in G3E to the shear capacity exceeds the total shear V. This probably occurred because some ungauged stirrups that may not have yielded were assigned yield strains and therefore higher strengths than their real values because the adjacent gauged stirrups had yielded. Both G3E and G3W (ρvfyv = 553 psi) supported considerable additional load after stir- rup yielding and with all this additional load being sup- ported by the concrete. • Girder 4 was very heavily reinforced in shear (in G4E, ρvfyv = 1,052 psi; in G4W, ρvfyv = 1,157 psi).While the member failed in flexure before failing in shear, it is still very useful to exam- ine the contributions of the stirrups and the concrete up to the failure load, particularly because of how different the pattern of those contributions is from that measured in the tests on the first three girders. After diagonal cracking, there was only a gradual increase in stirrup strain with increasing load. In G4E, the concrete contribution remained relatively constant with increasing load. In G4W, there was a some- what more rapid increase in stirrup strain with increasing load before Vc began to remain relatively constant. • Girder 5 contained the minimum required amount of shear reinforcement. The plots for G5E (ρvfyv = 161 psi) and G5W (ρvfyv = 140 psi) illustrate that the stirrups yielded very shortly after diagonal cracking occurred. There was considerable increase in the calculated concrete contribu- tion to shear resistance after the stirrups yielded. This was especially evident in G5W. • In both G6E (ρvfyv = 585 psi) and G6W (ρvfyv = 549 psi), there was only a modest increase in the straining in the stir- rups following initial shear cracking. These stirrup strains increased roughly in proportion to the increase in loading, and both ends of the girder failed soon after the stirrups first yielded. • In both G7E (ρvfyv = 586 psi) and G7W (ρvfyv = 382 psi), after initial shear cracking, there were only modest increases in strain in the stirrups with increases in load. The strain in the stirrups increased gradually with increasing load, while the concrete contribution remained relatively constant. The girder failed when the stirrups reached yield. An additional free body diagram was prepared for Girder 7 at a location farther from the support than the location for the first diagram and in a transition region between web-shear and flexure-shear behavior, G7W20 (ρvfyv = 119 psi). The stirrups in this region came close to yielding, but did not yield, and the member did not fail in this region. This plot is shown because the member was designed to fail in shear in Region 2 but did not due to the stronger than anticipated contribution of the concrete to shear resistance. Note that the contribution of the concrete to shear resistance for that region is the largest for any of the regions studied and for all of the girders. Table 27. Characteristic shear force points for selected free bodies. A B C D Characteristics Free Body Diagram V p (kips ) V (kips ) V s (kips ) V c (kips ) V (kips ) V s (kips ) V c (kips ) V (kips ) V s (kips ) V c (kips ) V (kips ) V s (kips ) V c (kips ) T ype Stirrup G1E5 0.0 242.5 8.6 233.9 242.5 196.0 46.5 242.5 196.0 46.5 392.4 196.0 196.4 90 o I Yield G1W5 40.9 307.5 0.0 266.6 307.5 224.0 42.6 307.5 224.0 42.6 464.0 224.0 199.1 90 o I Yield G2E5 0.0 293.3 8.5 284.8 293.3 101.4 191.9 486.3 393.3 93.0 486.3 393.3 93.0 57 o II Yield G2W5 34.4 357.0 13.6 309.0 357.0 110.2 212.4 529.0 393.3 101.3 600.0 393.3 172.3 59 o II Yield G3E7 0.0 269.5 15.0 254.5 269.5 203.5 66.0 391.0 352.6 38.4 530.6 352.6 178.0 51 o II Yield G3W9 0.0 235.9 7.0 228.9 235.9 80.0 155.9 350.4 298.3 52.1 571.3 298.3 273.0 62 o II Yield G4E7 0.0 248.6 5.0 243.6 248.6 35.3 213.3 688.4 382.4 306.0 688.4 382.4 306.0 38 o IV No G4W8 0.0 371.4 5.0 366.4 371.4 236.0 135.4 676.0 544.6 131.4 676.0 544.6 131.4 45 o III No G5E8 0.0 200.0 1.0 199.0 200.0 121.7 78.3 200.0 121.7 78.3 282.0 121.7 160.3 90 o I Yield G5W4 0.0 183.0 5.0 178.0 183.0 101.0 82.0 200.0 101.0 99.0 277.9 101.0 176.9 90 o I Yield G6E4 0.0 280.0 5.0 275.0 280.0 65.0 215.0 566.6 280.8 285.8 566.6 280.8 285.8 37 o II Yield G6W6 0.0 282.0 5.0 277.0 282.0 54.0 228.0 435.2 240.7 194.5 435.2 240.7 194.5 51 o II Yield G7E7 0.0 274.0 5.0 269.0 274.0 50.0 224.0 512.7 332.2 180.5 512.7 332.2 180.5 50 o II Yield G7W 0.0 231.4 0.0 231.4 231.4 27.0 204.4 427.6 237.8 189.8 427.6 237.8 189.8 47 o II Yield G7W20 0.0 125.0 0.0 125.0 125.0 20.0 105.0 167.8 51.5 116.3 167.8 51.5 116.3 37 o II No G8E5 0.0 261.4 5.0 256.4 261.4 15.0 246.4 563.9 276.8 287.1 661.2 276.8 384.4 40 o II Yield G8E8 0.0 222.0 5.0 217.0 222.0 40.0 182.0 510.8 332.2 178.6 510.8 332.2 178.6 45 o III Yield G8W4P 0.0 210.5 0.0 210.5 210.5 0.0 210.5 487.3 276.8 210.5 487.3 276.8 210.5 45 o III Yield G9E6 0.0 257.8 12.0 245.8 257.8 12.0 245.8 534.4 384.7 149.7 534.4 384.7 149.7 53 o IV No G9W8 40.8 392.0 9.2 342.0 392.0 79.2 272.0 623.6 195.0 387.8 623.6 195.0 387.8 27 o II No G10E6 0.0 220.0 0.0 220.0 220.0 31.0 189.0 608.5 324.4 284.1 608.5 324.4 284.1 57 o IV Yield G10W4 42.2 285.0 0.0 246.4 285.0 0.0 246.4 620.0 405.5 172.3 709.2 405.5 261.5 50 o IV Yield

119 • The plots for G8E (ρvfyv = 571 psi) and G8E8 (ρvfyv = 555 psi) show that G8E failed shortly after the stirrups yielded. Two different sections are also shown for G8E. On the west end of Girder 8, two aluminum plates were placed back to back along the expected shear critical plane to minimize interface shear transfer over the height of the web. The plot of G8W4P (ρvfyv = 576 psi) illustrates that there was a much more gradual increase in stirrup strain with increas- ing load than for the other tests. That gradual increase is likely due to the shear plane of weakness, and conse- quently the concrete contribution remained relatively constant from when the stirrups first began to carry load up until the time of stirrup yielding. Then, once the stir- rups yielded, the member failed. Because of the plane of weakness, the concrete contribution must have been due principally to shear transfer through the top and bottom flanges. • Both G9E (ρvfyv = 1,111 psi) and G9W (ρvfyv = 1,698 psi) were designed to contain particularly heavy amounts of shear reinforcement. G9E failed by concrete crushing along the main diagonal when the maximum strain in an indi- vidual stirrup was 80 percent of the yield strain. G9W contained a particularly heavy amount of shear reinforce- ment. Yet there was still a very significant contribution of Vc to the total shear resistance. • Upon first cracking in G10E (ρvfyv = 731 psi) and G10W (ρvfyv = 746 psi), the stirrups strains increased gradually in response to additional loading and the contribution of the concrete remained relatively constant or increased slightly with increasing load. 2.7.4 Characteristic angle  and its classification This section introduces the concept of a parameter, desig- nated as the characteristic angle, , that is used in describ- ing the concrete contribution Vc to the capacity between the load for diagonal cracking and the load for yield of the shear reinforcement. With this parameter, the patterns of the dif- ferent contributions to the shear component can then be classified into four types, with an angle value as shown in Figure 100: • Type I: α = 90 degrees, stirrup yielded immediately after cracking. • Type II: 45 degrees < α < 90 degrees, stirrup contribution increases and concrete contribution decreases with increasing applied load. • Type III: α = 45 degrees, concrete contribution constant between cracking and stirrup yielding. Figure 100. Shear component resistance patterns. O A B,C D Vc Vs V Sh ea r C om po ne nt s Type I O A B C D V α<45° Sh ea r C om po ne nt s Type IV O A B C D V α=45° Sh ea r C om po ne nt s Type III O A B C D Vc Vs Vc Vs Vc Vs V α>45° Sh ea r C om po ne nt s Type II α=90°

120 • Type IV: 0 degrees < α < 45 degrees, both stirrup contri- bution and concrete contribution increase with increasing applied load in the service load stage. The characteristic angle α depends on crack length and crack width as well as the tensile strength of the concrete. If the boundary crack grew during the service load stage, the concrete contribution usually decreased and the characteristic angle α was larger than 45 degrees. The crack width affects the interface shear transfer, and that transfer contributes directly to the con- crete shear component. If the crack width was larger than a crit- ical value, then interlock was negligible and the result was a high characteristic angle α. In most cases, the crack length did not change significantly after cracking occurred, and therefore, the crack width, or the interface shear transfer component, was the most important factor influencing the characteristic angle. The amount and strength of the shear reinforcement control the crack width and effectiveness of the interface shear transfer component. Plotted in Figure 101 are the relationships (a) between the characteristic angle α and the stirrup strength ρvfyv and (b) between the characteristic angle α and the ratio , with the latter relationship capturing the influence of concrete strength. Both plots show that the characteristic angle decreased from 90 degrees to 28 degrees as ρvfyv or increased. The characteristic angle for the stirrup reinforcement ratio ranged from 35 to 60 degrees. ρv yv cf f/ ´ ρv yv cf f/ ´ Figure 101. Influence of shear reinforcement on characteristic angle . (a) ρv fy versus characteristic angle α 0 10 20 30 40 50 60 70 80 90 0 500 1000 1500 2000 ρvfy (psi) α (deg) ρvfy (psi) 0 10 20 30 40 50 60 70 80 90 α (deg) 0 5 10 15 20 (b) ρv fy/√f 'c versus characteristic angle α

121 2.7.5 Comparison with LRFD Prediction Table 28 summarizes the shear forces at the inclined section of selected CFBDs for the ultimate load resisted by each girder. The sectional forces M and V were calculated from the value of the uniform load supported by the beam at failure. The contributions of the shear reinforcement Vs and the concrete Vc were computed using the procedure described in Section 2.7.2. The stirrup strength was calculated as ρvfs = Vs /(bwLc), where bw equals 6 inches and Lc is the value given in Table 26. Comparisons between the θ, Vc, and Vs values determined from the free bodies selected from the test girders and the val- ues of the same quantities calculated from LRFD predictions are given in Table 29. The ratio of the measured crack angle θtest to the angle θLRFD predicted by the LRFD procedure ranges from 0.93 to 1.27, and the mean of the ratio θtest/θLRFD is 1.09, with a COV of 0.09. In the derivation of the LRFD method, it is possible that the angle of diagonal compression is derived as flatter than the actual crack angle due to the effects of interface shear transfer. The LRFD section design model for shear was derived from the MCFT. The MCFT assumes that the concrete contribu- tion to shear strength is limited by the resistance to shear slip along cracks. The ratio of the measured concrete contribution Vc,test to the LRFD prediction Vc,LRFD is also shown in Table 29. Test LRFD Prediction Girder test (deg) test,cV (kips) sv f (psi) LRFD (deg) LRFD,cV (kips) yvv f (psi) LRFD test LRFD,c test,c V V G1E 27.2 196.4 357 23.2 121.0 389 1.17 1.62 G1W 28.2 199.1 404 24.9 118.9 389 1.13 1.67 G2E 26.4 93.0 710 25.5 109.0 745 1.04 0.85 G2W 29.8 172.3 749 27.8 106.3 745 1.07 1.62 G3E 26.0 178.0 600 23.7 132.1 565 1.10 1.35 G3W 27.3 273.0 553 23.7 132.1 565 1.15 2.07 G4E* 28.4 306.0 773 28.5 118.0 1,113 1.00 - G4W* 28.4 131.4 983 28.5 118.0 1,113 1.00 - G5E 21.1 160.3 161 21.8 189.0 169 0.97 0.85 G5W 23.7 176.9 140 21.8 189.0 140 1.09 0.94 G6E 30.1 285.8 586 23.7 118.1 557 1.27 2.42 G6W 29.9 194.5 549 25.9 113.5 557 1.15 1.71 G7E 25.9 180.5 587 24.2 113.5 577 1.07 1.59 G7W 23.6 189.8 382 23.7 117.2 577 1.00 1.62 G7FS* 25.9 116.3 93 23.9 135.4 119 1.08 - G8E 30.1 384.4 571 23.7 120.9 577 1.27 3.18 G8EB 25.1 178.7 555 23.7 120.9 577 1.06 1.48 G8WP 30.0 210.5 576 23.7 120.9 577 1.27 1.74 G9E 27.8 149.7 753 30.0 83.6 1,040 0.93 1.79 G9W* 35.7 387.8 583 - - 1,690 - - G10E 30.8 284.1 731 28.8 93.2 751 1.07 3.05 G10W 29.2 261.5 746 27.6 91.2 751 1.06 2.87 Average 1.09 1.80 COV 0.09 0.38 *No shear failure occurred. Table 28. Shear components at ultimate load for selected free body diagrams. Table 29. Comparison between test results and LRFD predictions. Free Body Diagram Load (kips/ft) M (k-ft ) V (kips ) V s (kips ) V c (kips ) V p (kips ) s v f (psi) G1E 26.03 5,058.2 392.4 196.0 196.4 0.0 357 G1W 30.09 5,689.7 464.0 224.0 199.1 40.9 404 G2E 33.79 6,907.0 486.3 393.3 93.0 0.0 710 G2W 38.74 7,286.5 600.0 393.3 172.3 34.4 749 G3E 35.68 7,042.4 530.6 352.6 178.0 0.0 600 G3W 38.82 7,751.8 571.3 298.3 273.0 0.0 553 G4E 42.74 7,619.5 688.4 382.4 306.0 0.0 773 G4W 42.74 7,796.4 676.0 544.6 131.4 0.0 983 G5E 23.70 5,621.9 282.0 121.7 160.3 0.0 161 G5W 19.90 4,189.0 277.9 101.0 176.9 0.0 140 G6E 38.32 5,634.8 566.6 280.8 285.8 0.0 586 G6W 27.66 5,096.0 435.2 240.7 194.5 0.0 549 G7E 33.47 6,382.2 512.7 332.2 180.5 0.0 587 G7W 44.76 9,235.4 427.7 237.8 189.8 0.0 382 G7FS 44.76 10,934.3 167.8 51.5 116.3 0.0 93 G8E 43.73 5,785.9 661.2 276.8 384.4 0.0 571 G8EB 43.73 7,965.7 510.8 332.2 178.7 0.0 555 G8WP 32.70 5,175.2 487.3 276.8 210.5 0.0 576 G9E 32.80 5,749.4 534.4 384.7 149.7 0.0 753 G9W 37.19 5,497.5 623.6 195.0 387.8 40.9 583 G10E 33.93 4,993.2 608.5 324.4 284.1 0.0 731 G10W 42.85 7,252.8 709.2 405.5 261.5 42.2 746 No failure occurred for G4E and G4W. ). Lb/(Vf cwssv b w = 6 inches. L c was given in Table 26.

122 The ratios ranged from 0.85 to 3.18, with almost all values being greater than 1.0. The mean of the ratios is 1.80, and the COV is 0.38. The high mean suggests that either the LRFD method underestimates the interface shear transfer resistance or that the top and bottom flanges contribute significantly to shear resistance. Such contributions are not included in the MCFT. It is also useful to examine the concrete contribution to shear resistance at ultimate capacity as a function of the strength of the shear reinforcement. The results of that corre- lation are shown in Figure 102. There is an increase in the concrete contribution with increasing amounts of shear rein- forcement. The points for G4E, G4W, and G9W are lower than they would be if it had been possible to continue the loading of these members until shear failure occurred. 2.7.6 Significance of This Evaluation Selected crack-based free body diagrams and measured stirrup strains were used to assess what portion of the applied shear load was carried by the transverse reinforcement and then, by subtraction, what remaining component was carried by the concrete. The results indicate that the amount of stir- rup reinforcement had a significant effect on the concrete contribution, and this suggests that the level of resistance pro- vided by interface shear transfer is influenced by the amount of shear reinforcement provided. This result is consistent with what would be suggested by the MCFT in that crack opening stiffness would affect slip resistance. In the LRFD method, the effect of transverse reinforcement on opening stiffness is ne- glected in an effort to provide a hand-based design procedure. The assumptions made in this derivation are shown by test results to be conservative. A complicating factor in the assess- ment of Vc is understanding what portion of this resistance is provided by the uncracked compression zone at the top of the member and what portion is provided by the bottom bulb. This subject deserves further research. 2.8 Shear Friction Tests 2.8.1 Introduction The LRFD Sectional Design Model is derived from the MCFT, in which the concrete contribution to shear resistance is limited by interface shear transfer resistance. The underly- ing MCFT relationship for evaluating interface shear slip resistance is a function of crack width, crack roughness, con- crete strength, and the resistance to crack opening provided by the longitudinal reinforcement (30). One of the motiva- tions for NCHRP Project 12-56 was that shear cracks in HSC specimens could be much smoother than in a normal strength concrete structure, and this increased smoothness could lead to much less interface shear transfer resistance than assumed in the derivation in the LRFD Sectional Design Model. The results from the tests on the HSC girders provided the data necessary to evaluate the safety of the LRFD Sectional Design Model, but they did not provide data that can be directly used to evaluate the appropriateness of the extension of the MCFT relationship for shear slip resistance to HSC structures. To this end, 18 shear transfer test specimens were cast in conjunction with the large concrete bridge girders for this project. These shear transfer specimens were cast using the same concrete materials as those used to cast the first six girders, and they contained the same quantity of reinforce- ment as used in the webs of the first six girders. The remain- ing sections describe the details of the shear transfer test specimens, the test setup, the instrumentation, and the test results. 0 100 200 300 400 500 0 500 1000 1500 2000 Yielded Non-Yielded Vc (kips) ρvfy (psi) Figure 102. Influence of shear reinforcement on concrete contribution.

123 2.8.2 Design of Test Specimens The experimental variables considered during the con- struction of the 18 test specimens included: • Concrete strength: The original intent of the study was to look at specimens cast with 10, 14, and 18 ksi concrete. • Reinforcement spacing: The shear reinforcement across the cracks was spaced at intervals varying from 6 to 12 inches. Normal deformed bars were used for all the tests, and those bars were No. 3, No. 4, or No. 5 bars, depending on the specimen. • Angle of reinforcing bars: The shear reinforcement was oriented at either 25 degrees or 35 degrees from the plane of the face of cracking. This orientation was intended to accommodate the fact that diagonal cracking in the test girders was likely to occur at between 25 degrees and 35 degrees to the longitudinal axis of the girder. Table 30 and Figure 103 present the dimensional and reinforcement details for all 18 test specimens. The designator of each specimen was selected so that it could serve as an iden- tifier that described all relevant details of the specimen. The first two characters indicate the girder with which the specimen was cast (for example, “g1” indicates a specimen that was cast with Girder 1). The next two characters, “sh” and “sl,” indicate whether the specimen represented a region of the girder subjected to higher shear stress (closest shear design section to support) or lower shear stress (farther shear design section from support), respectively. The next numeral indicates the number of reinforcing bars in the location of that shear stress level. Note there are two locations in each specimen, such that the number 2 indicates there are a total of 4 bars in that partic- ular specimen. The bar size is indicated by the next entry in the code with 3, 4, or 5 corresponding to the customary U.S. bar size designation. The final entry is the angle of the orientation of the reinforcing bars relative to normal from the shear plane, either 25 degrees or 35 degrees. Additional specimen informa- tion is included in Table 30, including the yield strength of the reinforcing bars, the spacing of the shear reinforcement (s), and the length of the shear plane (L). Figure 103 shows pertinent dimensional information that corresponds to values in Table 30 for each specimen. The thickness for the shear plane for each specimen was 6.5 inches. 2.8.3 Instrumentation and Testing Details The first step in testing a specimen was to attach Whitte- more targets to the surfaces of the specimen in order to measure initial crack widths. A total of eight targets were attached to both sides of the specimen in a rectangular con- figuration that was 12 inches high and 10 inches wide. The rec- tangle was oriented such that its center corresponded with the mid-length of the shear plane. This configuration of targets allowed for two measurements of initial crack width on each side of the specimen. Initial crack widths are referenced by their location (top or bottom) and by which side of the speci- men they were taken on (Krypton side or LVDT side, as described later). The next step in the testing procedure was to specimen L (in) Label A s (in) (°) fy (ksi) g1sh_2_4_25 26.5 2- #4 (0.4 in2) 12 25 70.0 g1sl_1_4_25 26.5 1- #4 (0.4 in2) 12 25 70.0 g1sh_2_4_35 29.25 2- #4 (0.4 in2) 12 35 70.0 g1sl_1_4_35 29.25 1- #4 (0.4 in2) 12 35 70.0 g2sh_2_5_25 24.25 2- #5 (0.62 in2) 11 25 79.3 g2sl_1_5_25 18.75 1- #5 (0.62 in2) 8.5 79.3 g2sh_2_5_35 26.875 2- #5 (0.62 in2) 11 35 79.3 g2sl_1_5_35 20.75 1- #5 (0.62 in2) 8.5 79.3 g3sh_2_4_25 17.625 2- #4 (0.4 in2) 8 67.8 g3sl_2_4_25 26.5 2- #4 (0.4 in2) 12 25 67.8 g3sh_2_4_35 19.5 2- #4 (0.4 in2) 8 67.8 g3sl_2_4_35 29.25 2- #4 (0.4 in2) 12 35 67.8 g4sh_2_5_25 13.45 2- #5 (0.62 in2) 6 64.6 g4sl_2_5_35 14.625 2- #5 (0.62 in2) 6 25 35 25 35 25 35 64.6 g5sh_1_3_25 22.125 1- #3 (0.11 in2) 10 25 76.5 g5sh_1_3_35 24.375 1- #3 (0.11 in2) 10 35 76.5 g6sh_2_5_25 26.5 2- #5 (0.62 in2) 12 25 64.7 g6sh_2_5_35 29.25 2- #5 (0.62 in2) 12 35 64.7 Table 30. Test specimen details.

124 precrack the test specimen. To accomplish this, each specimen was placed in the testing frame in a horizontal orientation with 1-inch diameter round bars placed into the triangular grooves that had been cast into the faces of the specimen. Figure 104 shows a photograph of one specimen positioned in the testing machine for precracking. Forcing the round bars into the tri- angular grooves generated a splitting force sufficient to initi- ate cracking. Load was applied to a specimen in a controlled manner in an effort to minimize the width of the initial cracks. After precracking, the initial crack width was measured using a Whittemore gage at all four locations. Next, three LVDTs were installed on one face of the test specimen, two for measuring crack opening at distances of 7.5 inches above and below mid-height (6 inches above and below mid-height for the G4 specimens) and one for meas- uring slip at mid-height. The specimen was then placed in the testing frame in a vertically oriented manner with rollers on the bottom surface and a swivel on the top. Krypton targets were then affixed to the other side of the test specimen to also measure displacements during the test. Twelve targets were affixed to each specimen, with six on each side of the shear plane arranged in a grid at a spacing of 7.5 inches for all of the specimens except the G4 specimens. In G4 specimens, the vertical spacing was reduced to 6 inches. Figure 105 presents a photograph of a specimen positioned in the testing machine for a shear friction test. The specimens were loaded in a 600-kip servo-controlled hydraulic testing machine that was operated in displacement control. The loading procedure was as follows. Specimens were preloaded with 1 kip of force before any data acquisition equipment was activated. Displacement was increased at a rate of 0.02 inch (0.5 millimeter) per minute until the total Figure 103. Test specimen geometry. Figure 104. Precracking set-up. Figure 105. Shear friction test set-up. 12" teflon L 8" 10" 10" 20" 8" L + 16 " 4" 2 - #4 Label A 2 - #3 2 - #2 8" C L 8" s s/ co s θ s/ co s θ 2 s/ co s θ 2 θ°

125 load on the specimen reached 10 kips. Then, from that point on, the loading rate was decreased to 0.008 inch (0.2 mil- limeter) per minute. Finally, the loading rate was increased to 0.016 inch (0.4 millimeter) per minute after the applied load reached 5 percent less than the peak load obtained during the test. Specimens were loaded until the slip along the crack reached 0.4 inch (10 millimeters) or until a reinforcing bar ruptured. The data for the tests was acquired using two PC-based data acquisition systems that each recorded data at a sam- pling rate of 2 Hz. The first data acquisition system ran a program written using National Instruments’s LabVIEW and was responsible for acquiring data for the load and posi- tion of the testing machine and the data for crack width and slip from the three LVDTs. The second data acquisition sys- tem was responsible for collecting the data for the 12 Kryp- ton targets. This data consisted of the three-dimensional position of each target located on the specimen to an accu- racy of ±0.001 inch (0.02 millimeter). The testing of an indi- vidual specimen typically took about 1 hour to complete. 2.8.4 Summary of Experimental Results Of the 18 specimens, 16 were tested successfully and failed in shear at the desired location. Two specimens (g2sh_2_5_35 and g4sl_2_5_35) did not reach the peak shear loads because other parts of the specimen first failed in flexure. Upon deter- mining that flexure might be a problem in more heavily rein- forced specimens, additional external flexural reinforcement was added to subsequent specimens to ensure that the desired shear failure could be achieved. The two specimens from Girder 6 were enhanced with external reinforcement, and peak shear loads were obtained, but flexural problems were encountered before the specimens reached 0.4 inch (10 mil- limeters) of shear slip. Figure 106 shows shear stress versus crack opening, shear stress versus crack slip, and crack open- ing versus crack slip results for each of the 18 test specimens. The crack opening plots are offset by the initial crack width for each specimen. Care was taken during precracking to ensure that initial crack widths were kept to a minimum. However, in many of the lightly reinforced specimens it was difficult to control the initial crack width. The scales for crack slip and crack opening are constant in all the figures so that relative comparisons can be made between these figures. The scale for shear stress varies because there is a wide range of values for maximum shear stress for the specimens. Maintaining the constant scales makes it evident that Specimens g2sh_2_5_35 and g4sl_2_5_35 did not reach peak loads and that the two Girder 6 specimens were unable to be taken to the same level of crack opening and crack slip as the other specimens. Table 31 shows the primary test results from each of the 18 specimens. Values reported include the initial crack width at all four measuring points, as well as the maximum applied load and the corresponding maximum shear stress. Again, it should be noted that the applied load values reported for the g2sh_2_5_35 and g4sl_2_5_35 specimens are not maxi- mums, as denoted by the asterisk in Table 31. 2.8.5 Interpretation of Experimental Results In an effort to make meaningful comparisons with code predictions for the shear strength of the test specimens, it was necessary to make some assumptions. The specimens that were tested had reinforcing bars that crossed the shear plane at an angle. As a result, the effective clamping force provided by the reinforcing steel was adjusted to compensate for the angle of the bars. Similarly, the angled bars would also have a component of their resistance that would act along the shear plane. To compensate for this, it was assumed that the bars yielded when peak load was reached, and then the com- ponent of the resistance of the bar along the shear plane was determined based on this assumption and subtracted from the total applied load, thereby allowing for a net shear stress to be calculated. Table 32 presents a more detailed analysis of the experimental results, including the foregoing assump- tions mentioned and comparisons with LRFD code predic- tions. An explanation of the contents of Table 32 is now presented. The effective clamping stress (ρvfy**), as adjusted for the angle of the reinforcing bars, is shown in Column 3 of Table 32. This value was calculated by multiplying the value for clamping stress (ρvfy) in Column 2 by the cosine of the angle in Column 4. Similarly, the net shear stress (Column 6) was calculated by multiplying the clamping stress (ρvfy) from Column 2 by the sine of the angle from Column 4 and sub- tracting it from the maximum shear stress shown in Column 5. The effective clamping stress was used for predicting the strength of the test specimens using the LRFD specifications and was compared with the experimental values for net shear stress. The predicted strength of the test specimens was deter- mined using Section 5.8.4, “Interface Shear Transfer—Shear Friction,” from the LRFD specifications. According to the LRFD specifications, the nominal shear resistance of the interface plane,Vn, shall be taken as: where: Avf = area of shear reinforcement crossing the shear plane and Pc = permanent net compressive force normal to the shear plane. V cA A f Pn cv vf y c= + +[ ] −μ ( . . . )5 8 4 1 1

126 Crack Opening [mm] 0 200 400 600 800 Sh ea r St re ss [p si ] Top Bottom Top Bottom 0 200 400 600 800 Sh ea r St re ss [p si ] Crack Slip [mm] 0 0 1 2 3 4 5 6 Crack Slip [mm] 0 1 2 3 4 5 6 0 200 400 600 800 Sh ea r St re ss [p si ] Crack Slip [mm] 0 1 2 3 4 5 6 0 0.5 1 1.5 2 2.5 Crack Opening [mm] 0 200 400 600 800 Sh ea r St re ss [p si ] 0 0.5 1 1.5 2 2.5 0.5 1 1.5 2 2.5 3 3.5 Cr ac k O pe n in g [m m ] Crack Slip [mm] 0 0 1 2 3 4 5 6 0.5 1 1.5 2 2.5 3 3.5 Cr ac k O pe n in g [m m ] Top Bottom Top Bottom (a) G1SH_2_4_25 (b) G1SH_2_4_35 Figure 106. Experimental results.

127 0 0.5 1 1.5 2 2.5 Crack Opening [mm] 0 0.5 1 1.5 2 2.5 Crack Opening [mm] 0 100 200 300 400 Sh ea r St re ss [p si ] 0 100 200 300 400 Sh ea r St re ss [p si ] Top Bottom 0 100 200 300 400 500 Sh ea r St re ss [p si] 0 100 200 300 400 500 Sh ea r St re ss [p si] Top Bottom Crack Slip [mm] 0 1 2 3 4 5 6 Crack Slip [mm] 0 1 2 3 4 5 6 Crack Slip [mm] 0 1 2 3 4 5 6 0 0.5 1 1.5 2 2.5 3 3.5 Cr ac k O pe ni ng [m m] Crack Slip [mm] 0 1 2 3 4 5 6 0 0.5 1 1.5 2 2.5 3 3.5 Cr ac k O pe n in g [m m] Top Bottom Top Bottom (c) G1SL_1_4_25 (d) G1SL_1_4_35 Figure 106. (Continued).

128 0 250 500 750 1000 Sh ea r St re ss [p si] Top Bottom Top Bottom Top Bottom Top Bottom (e) G2SH_2_5_25 (f) G2SH_2_5_35 0 0.5 1 1.5 2 2.5 Crack Opening [mm] 0 250 500 750 1000 Sh ea r St re ss [p si] 0 200 400 600 800 Sh ea r St re ss [p si] 0 200 400 600 800 Sh ea r St re ss [p si] 0 0.5 1 1.5 2 2.5 Crack Opening [mm] Crack Slip [mm] 0 1 2 3 4 5 6 Crack Slip [mm] 0 1 2 3 4 5 6 Crack Slip [mm] 0 1 2 3 4 5 6 0 0.5 1 1.5 2 2.5 3 3.5 Cr ac k O pe ni ng [m m] Crack Slip [mm] 0 1 2 3 4 5 6 0 0.5 1 1.5 2 2.5 3 3.5 Cr ac k O pe ni ng [m m ] Figure 106. (Continued).

129 0 200 400 600 800 Sh ea r St re ss [p si] 0 200 400 600 800 Sh ea r St re ss [p si] Top Bottom 0 100 200 300 400 500 600 700 Sh ea r St re ss [p si] 0 100 200 300 400 500 600 700 Sh ea r St re ss [p si] Top Bottom Top Bottom Top Bottom (g) G2SL_1_5_25 (h) G2SL_1_5_35 0 0.5 1 1.5 2 2.5 Crack Opening [mm] 0 0.5 1 1.5 2 2.5 Crack Opening [mm] Crack Slip [mm] 0 1 2 3 4 5 6 Crack Slip [mm] 0 1 2 3 4 5 6 Crack Slip [mm] 0 1 2 3 4 5 6 Crack Slip [mm] 0 1 2 3 4 5 6 0 0.5 1 1.5 2 2.5 3 3.5 Cr ac k O pe ni ng [m m] 0 0.5 1 1.5 2 2.5 3 3.5 Cr ac k O pe ni ng [m m] Figure 106. (Continued).

130 Top Bottom Top Bottom Top Bottom Top Bottom (i) G3SH_2_4_25 (j) G3SH_2_4_35 0 250 500 750 1000 Sh ea r St re ss [p si] 0 0.5 1 1.5 2 2.5 Crack Opening [mm] 0 250 500 750 1000 Sh ea r St re ss [p si] 0 0.5 1 1.5 2 2.5 Crack Opening [mm] 0 250 500 750 1000 Sh ea r St re ss [p si] Crack Slip [mm] 0 1 2 3 4 5 6 0 250 500 750 1000 Sh ea r St re ss [p si] Crack Slip [mm] 0 1 2 3 4 5 6 Crack Slip [mm] 0 1 2 3 4 5 6 0 0.5 1 1.5 2 2.5 3 3.5 Cr ac k O pe ni ng [m m] Crack Slip [mm] 0 1 2 3 4 5 6 0 0.5 1 1.5 2 2.5 3 3.5 Cr ac k O pe ni ng [m m] Figure 106. (Continued).

131 Top Bottom Top Bottom Top Bottom Top Bottom (k) G3SL_2_4_25 (l) G3SL_2_4_35 0 200 400 600 800 Sh ea r St re ss [p si] 0 0.5 1 1.5 2 2.5 Crack Opening [mm] 0 200 400 600 800 Sh ea r St re ss [p si] 0 0.5 1 1.5 2 2.5 Crack Opening [mm] 0 200 400 600 800 Sh ea r St re ss [p si] Crack Slip [mm] 0 1 2 3 4 5 6 0 200 400 600 800 Sh ea r St re ss [p si] Crack Slip [mm] 0 1 2 3 4 5 6 Crack Slip [mm] 0 1 2 3 4 5 6 0 0.5 1 1.5 2 2.5 3 3.5 Cr ac k O pe ni ng [m m] Crack Slip [mm] 0 1 2 3 4 5 6 0 0.5 1 1.5 2 2.5 3 3.5 Cr ac k O pe ni ng [m m] Figure 106. (Continued).

132 0 250 500 750 1000 1250 1500 Sh ea r St re ss [p si ] 0 250 500 750 1000 1250 1500 Sh ea r St re ss [p si ] Top Bottom Top Bottom Top Bottom Top Bottom (m) G4SH_2_5_25 (n) G4SL_2_5_35 0 0.5 1 1.5 2 2.5 Crack Opening [mm] 0 250 500 750 1000 1250 1500 Sh ea r St re ss [p si] 0 0.5 1 1.5 2 2.5 Crack Opening [mm] Crack Slip [mm] 0 1 2 3 4 5 6 0 250 500 750 1000 1250 1500 Sh ea r St re ss [p si ] Crack Slip [mm] 0 1 2 3 4 5 6 Crack Slip [mm] 0 1 2 3 4 5 6 0 0.5 1 1.5 2 2.5 3 3.5 Cr ac k O pe n in g [m m] Crack Slip [mm] 0 1 2 3 4 5 6 0 0.5 1 1.5 2 2.5 3 3.5 Cr ac k O pe ni ng [m m] Figure 106. (Continued).

133 0 100 200 300 400 Sh ea r St re ss [p si] 0 100 200 300 400 Sh ea r St re ss [p si ] Top Bottom 0 50 100 150 200 250 300 Sh ea r S tre ss [p si] 0 50 100 150 200 250 300 Sh ea r S tre ss [p si ] Top Bottom Top Bottom Top Bottom (o) G5SH_1_3_25 (p) G5SH_1_3_35 0 0.5 1 1.5 2 2.5 Crack Opening [mm] 0 0.5 1 1.5 2 2.5 Crack Opening [mm] Crack Slip [mm] 0 1 2 3 4 5 6 Crack Slip [mm] 0 1 2 3 4 5 6 Crack Slip [mm] 0 1 2 3 4 5 6 0 0.5 1 1.5 2 2.5 3 3.5 Cr ac k O pe ni ng [m m] Crack Slip [mm] 0 1 2 3 4 5 6 0 0.5 1 1.5 2 2.5 3 3.5 Cr ac k O pe ni ng [m m] Figure 106. (Continued).

134 0 250 500 750 1000 Sh ea r St re ss [p si] 0 250 500 750 1000 Sh ea r St re ss [p si] Top Bottom 0 250 500 750 1000 Sh ea r St re ss [p si ] 0 250 500 750 1000 Sh ea r St re ss [p si] Top Bottom Top Bottom Top Bottom (q) G6SH_2_5_25 (r) G6SH_2_5_35 0 0.5 1 1.5 2 2.5 Crack Opening [mm] 0 0.5 1 1.5 2 2.5 Crack Opening [mm] Crack Slip [mm] 0 1 2 3 4 5 6 Crack Slip [mm] 0 1 2 3 4 5 6 Crack Slip [mm] 0 1 2 3 4 5 6 0 0.5 1 1.5 2 2.5 3 3.5 Cr ac k O pe ni ng [m m] Crack Slip [mm] 0 1 2 3 4 5 6 0 0.5 1 1.5 2 2.5 3 3.5 Cr ac k O pe ni ng [m m ] Figure 106. (Continued).

135 specimen designation vfy (psi) vfy** (psi) angle ( ° ) max shear stress (psi) net shear stress (psi) LRFD vn (psi) LRFD+ vn (psi) vci MCFT w=.3 mm (psi) vci MCFT w=.75 mm (psi) vtest / vn vtest / vn + vtest / vci w=.3 mm vtest / vci w=.75 mm g1sh_2_4_25 325 295 25 749 611 355 517 330 175 1.72 1.18 1.85 3.50 g1sl_1_4_25 163 147 25 359 291 223 385 330 175 1.31 0.76 0.88 1.66 g1sh_2_4_35 295 241 35 705 536 307 469 330 175 1.74 1.14 1.63 3.07 g1sl_1_4_35 147 121 35 451 366 199 361 330 175 1.84 1.02 1.11 2.10 g2sh_2_5_25 624 565 25 1078 814 599 761 338 179 1.36 1.07 2.41 4.54 g2sl_1_5_25 403 366 25 744 573 419 581 338 179 1.37 0.99 1.69 3.20 g2sh_2_5_35* 563 461 35 880 557 505 667 338 179 1.10 0.83 1.65 3.11 g2sl_1_5_35 365 299 35 678 469 359 521 338 179 1.31 0.90 1.39 2.62 g3sh_2_4_25 473 429 25 1001 801 476 638 366 194 1.68 1.26 2.19 4.13 g3sl_2_4_25 315 285 25 766 632 347 509 366 194 1.82 1.24 1.73 3.26 g3sh_2_4_35 428 351 35 958 713 405 567 366 194 1.76 1.26 1.95 3.68 g3sl_2_4_35 285 234 35 738 574 300 462 366 194 1.91 1.24 1.57 2.96 g4sh_2_5_25 916 830 25 1672 1285 720 999 366 194 1.78 1.29 3.51 6.62 g4sl_2_5_35* 843 690 35 1587 1104 711 873 366 194 1.55 1.26 3.01 5.69 g5sh_1_3_25 117 106 25 311 261 185 347 376 199 1.41 0.75 0.69 1.31 g5sh_1_3_35 106 87 35 288 227 168 330 376 199 1.35 0.69 0.60 1.14 g6sh_2_5_25 466 422 25 1120 923 470 632 330 175 1.96 1.46 2.79 5.28 g6sh_2_5_35 422 346 35 946 704 401 563 330 175 1.76 1.25 2.13 4.03 * Specimen did not reach ultimate load ** clamping force adjusted for angle of bars + Proposed LRFD equation Table 31. Test results. Table 32. Comparison of test results with predictions. top botto m t op botto m g1sh_2_4_25 0.48 0.19 0.43 0.15 172. 3 0 .8 0.46 70.0 13.46 128. 9 49 g1sl_1_4_25 0.30 0.16 0.28 0.13 172. 3 0 .4 0.23 70. 0 1 3.46 61.9 359 g1sh_2_4_35 0.12 0.13 0.13 0.12 190. 1 0 .8 0.42 70.0 13.46 134. 0 05 g1sl_1_4_35 0.26 0.36 0.10 0.22 190. 1 0 .4 0.21 70. 0 1 3.46 85.7 451 g2sh_2_5_25 0.00 0.03 0.06 0.05 157. 6 1 .2 4 0 .79 79.3 14.17 169.9 1078 g2sl_1_5_25 0.03 0.04 0.24 0.25 121. 9 0 .6 2 0 .51 79. 3 1 4.17 90. 6 44 g2s h_2_5_35* 0.14 0.19 0.04 0.09 174. 7 1 .2 4 0 .71 79. 3 1 4.17 153.7 880 g2sl_1_5_35 0.26 0.12 0.47 0.32 134. 9 0 .6 2 0 .46 79. 3 1 4.17 91. 4 7 7 7 6 78 g3sh_2_4_25 0.17 0.27 0.08 0.17 114. 6 0 .8 0.70 67.8 16.6 114.7 1001 g3sl_2_4_25 0.12 0.10 0.10 0.32 172. 3 0 .8 0.46 67.8 16.6 131.9 766 g3sh_2_4_35 0.06 0.24 0.20 0.39 126. 8 0 .8 0.63 67.8 16.6 121.5 958 g3sl_2_4_35 1.20 0.70 0.71 0.24 190. 1 0 .8 0.42 67.8 16.6 140.2 738 g4sh_2_5_25 0.14 0.23 0.02 0.09 87.4 1.24 1.42 64.6 16.6 146.2 1672 g4sl_2_5_35* 0.15 0.11 0.15 0.11 95.1 1.24 1.30 64. 6 1 6.6 150.9 1587 g5sh_1_3_2 5 0 .6 9 0 .1 4 0 .9 3 0 .4 1 1 43. 8 0 .2 2 0 .15 76. 5 1 7.51 44.7 311 g5sh_1_3_3 5 0 .9 6 1 .2 9 0 .5 3 0 .6 5 1 58. 4 0 .2 2 0 .14 76. 5 1 7.51 45.7 288 g6sh_2_5_2 5 0 .2 4 0 .1 8 0 .2 2 0 .1 3 1 72. 3 1 .2 4 0 .72 64.7 13.5 192.8 112 0 g6sh_2_5_3 5 0 .1 1 0 .1 2 0 .2 5 0 .2 8 1 90. 1 1 .2 4 0 .65 64.7 13.5 179.9 946 * Specimen did not reach ultimate load f'c (ksi ) M ax Load (kips) Ma x shea r st ress (psi ) A cv (i n 2 ) A sv (i n 2 ) r v (% ) f y (ksi ) lvdt side krypton side initial crack widths (mm) specimen de si gnation

136 The nominal shear resistance, Vn, used in the design shall not be greater than the lesser of: or Equation 5.8.4.1-1 was adjusted in the following manner to allow for comparison with the experimental data: where:  = strength reduction factor and vn = nominal shear stress over the shear plane. Values for c and μ were obtained from Section 5.8.4.2, “Cohesion and Friction,” with c taken as 100 psi and μ taken as 1.0. Because all of the specimens were precracked prior to testing in shear and the surfaces were not intentionally rough- ened to an amplitude of 0.25 inch or more, the correct appli- cation of the LRFD specifications would require that c be taken as 75 psi and μ as 0.60. However, as explained later, the former values gave reasonable agreement with the test data, and so it was not necessary to use the more conservative val- ues for concrete not intentionally roughened. Equation 46 was used in all cases except one, where φvn exceeded 720 psi, which is the upper limit permitted by Equa- tion 5.8.4.1-3. Column 7 in Table 32 presents the predicted value of shear stress (φvn) based on Section 5.8.4 of the LRFD specifications, as described above. An additional prediction was made based on a recent pro- posed code change to the LRFD specifications in WAI 57. Under the proposed change, the value of c corresponding to that used to calculate the values of Column 7 in Table 32 would be increased to 280 psi, and μ would remain at 1. An upper limit of 1,800 psi for vn would also be provided, similar to Equation 5.8.4.1-3 from the existing code. Due to the lower levels of shear reinforcement present in the test specimens, this upper limit was never invoked. Column 8 presents the predictions of shear stress (φvn) based on this method, which is denoted as LRFD+ in Table 32. One final comparison was made with vci predictions from the MCFT (3). According to the MCFT, the shear stress that can be carried across a crack (vci) is a function of crack width (w) and aggregate size (a) and is given by the following equation (29). Evaluations of the shear stress according to the MCFT were made using crack widths of 0.0118 inch (0.3 millimeter) and 0.0295 inch (0.75 millimeter). The resultant vci values are v f w a ci c = + + 2 16 0 31 24 0 63 . ´ . . (in inches and psi) ( )47 φ φ ρμv c fn v y= +( )[ ] ( )** 46 V An cv≤ −0 8 5 8 4 1 3. ( . . . ) V f An c cv≤ −0 2 5 8 4 1 2. ´ ( . . . ) displayed in Columns 9 and 10 of Table 32. Columns 11 through 14 present the ratios of the experimental values for shear stress divided by the various predicted values. Figure 107 shows a plot of the net shear stress normalized by the square root of the concrete strength versus crack open- ing (crack width) for the test specimens. The experimental net shear stress curves were determined by estimating the strain in the reinforcing steel based on displacement data from the Krypton machine. This allowed for the contribution of the steel to resisting slip along the crack to be removed from the total load applied to the specimen. Comparisons are made to the vci curves that are also normalized by the square root of concrete strength for aggregate sizes of 0 inch and 1/2 inch. The results illustrate that the interface shear transfer resistance that can be provided by the concrete is larger than that calculated using the vci expression in the MCFT for crack widths up to 0.04 inch (1 millimeter) in all cases tested and for crack widths up to 0.08 inch (2 millimeters) in most cases. Figure 108 presents a plot of the interface shear resistance versus the clamping stress. The experimental results are pre- sented in comparison with the existing expression of the LRFD specifications as well as the proposal from the T10 Work Action Item (WAI 57). These results illustrate that the current provisions are conservative and that the WAI proposal is also conservative when clamping stresses exceed 0.4 ksi and c and μ values are chosen as described below. 2.9 Deformation Patterns in End Regions 2.9.1 Introduction The LRFD specifications permit the use of the LRFD Sec- tional Design Model for the shear design of regions between the support and the first critical section from the support. For that design, the shear force to be used is that at the first criti- cal section.As discussed in Chapter 1 and demonstrated by the test data from earlier in this chapter, this approach may not be appropriate because the Sectional Design Model was derived based on the assumptions that plane sections remain plane and that there is a uniform field of diagonal compression over the depth of a member. However, in the behavior of end regions, there is a very complex flow of forces due to disconti- nuities introduced by the vertical reaction force, the anchor- age of the prestressing strands, and the stress-free surface at the actual end of a simply supported member. Of particular concern is that the funneling of the diagonal compression field from above a support into the support must lead to a magni- fication in the principal compressive stress in the web above a support, and this could lead to premature crushing of the con- crete as well as large horizontal shear stresses between the lower bulb and web of the girder near the support.

137 Many assumptions that are involved in the LRFD Sectional Design Model can be assessed and validated by examining the detailed deformation patterns in the end regions of girders. The deformation pattern in these regions was recorded by the Krypton Dynamic Measurement Machine (DMM) and con- crete surface strain gages. Section 2.9.2 describes the method- ology that was used to acquire and analyze this detailed data from the Krypton system. This information is used to exam- ine the behavior of the west end of Girder 10, the results and interpretation of which are presented in Sections 2.9.3 and 2.9.4. Section 2.9.5 presents an analysis of selected concrete surface strain gage results. The remainder of Section 2.9 summarizes the primary rel- evant observations from the tests on the behavior of end regions. It does not provide a complete analysis of all test data. Such detailed analysis is considered beyond the scope of this project and will be reported subsequently in the technical literature. 2.9.2 Instrumentation Layout and Methodology Detailed displacement measurements were taken for the end regions of girders using the Krypton DMM system. The Kryp- ton DMM system is capable of measuring the three-dimen- sional position of infrared LED targets to an accuracy of ±0.0008 inch (0.02 millimeter). This level of accuracy allows strain measurements to be discerned from displacement 0 1 2 3 4 Crack Opening [mm] 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 v c / S qr t(f 'c) [k si / Sq rt( ks i)] vci, a = 0.5" vci, a = 0.5" G4, ρvf y = 916 psi, f 'c= 16.6 ksi, θ = 25° G6, ρvf y = 466 psi, f 'c= 13.5 ksi, θ = 25° G3, ρvf y = 428 psi, f 'c= 16.6 ksi, θ = 35° G3, ρvf y = 473 psi, f 'c= 16.6 ksi, θ = 25° G2, ρvf y = 624 psi, f 'c= 14.2 ksi, θ = 25° G2, ρvf y = 365 psi, f 'c= 14.2 ksi, θ = 35° G1, ρvf y = 325 psi, f 'c= 13.5 ksi, θ = 25° G3, ρvf y = 315 psi, f 'c= 16.6 ksi, θ = 25° G1, ρvf y = 294 psi, f 'c= 13.5 ksi, θ = 35° G1, ρvf y = 163 psi, f 'c= 13.5 ksi, θ = 25° G1, ρvf y = 147 psi, f 'c= 13.5 ksi, θ = 35° G5, ρvf y = 117 psi, f 'c= 17.5 ksi, θ = 25° G5, ρvf y = 106 psi, f 'c= 17.5 ksi, θ = 35° G4, ρvf y = 843 psi, f 'c= 16.6 ksi, θ = 35° G6, ρvf y = 422 psi, f 'c= 13.5 ksi, θ = 35° Figure 107. Comparison of test results with Vci predictions.

138 measurements provided that there is a sufficient gage length between the LED targets. The circles in Figure 109 represent the typical layout of Krypton targets in the end region of a girder. The typical lay- out consisted of 99 targets arranged in 9 rows and 11 columns. The rows were spaced at 5-inch intervals covering the central 40 inches of the 45-inch clear height of the web. The columns were spaced at 10-inch intervals over a 100-inch length of the web that started 5 inches behind the center line of the support and extended 95 inches towards mid-span. The decision was made to space the targets at 5 inches vertically and 10 inches horizontally because greater deformations and variability in the distribution of measurements were expected in the vertical direction. Displacement measurements were acquired at a rate of 1 per second for each LED throughout the duration of a typical test, and the displacement data were correlated with the applied load data. The number of targets placed on a girder affords a myriad of analysis possibilities. At the most basic level, displace- ment measurements for every target can be evaluated. Fur- ther analysis of the displacements with some additional postprocessing can provide the linear strain between any 0 200 400 600 800 1000 1200 1400 0 100 200 300 400 500 600 700 800 900 1000 Clamping Stress ρvfy* (psi) Fa ct or ed In te rfa ce S he ar R es is ta nc e, φνφν n (p si) Test Specimens Existing LRFD Specification Proposed Figure 108. Comparison of test results with LRFD predictions. Figure 109. Layout of Krypton targets for selected vertical strain measurements. a b c d X Y 13 " 10" 5" 73 " 35" 7" 12"

139 two targets located on the girder. This result is especially useful for evaluating distributions of vertical, horizontal, and diagonal strains. Strains between individual targets can also be combined to calculate the magnitude and direction of principal strains. Combining detailed strain distributions with crack patterns, data obtained from concrete surface gages, and strain gages embedded on shear reinforcement can provide significant insight into the behavior of end regions. It should be noted that the data presented in this section does not take into account strains that are a result of the release of the prestressing strands or strains caused by the construction of the cast-in-place deck. The Krypton targets were applied to the girder immediately prior to test- ing. The Krypton data can be used in conjunction with analysis results to estimate strain as a result of both initial prestressing and the applied uniformly distributed labora- tory loading. 2.9.3 Experimental Results The experimental results included in this report are pre- sented first, with a figure highlighting which Krypton targets were used to derive the results, followed by plots of the results obtained from these targets. Results derived from the analysis of selected vertical, horizontal, shear, and diagonal strains are presented in this section. All strains calculated using dis- placement information from the Krypton system were deter- mined using the following method. First, the distance between the two targets of interest was calculated at each entry in the data file. Next, an average value was calculated from the first 20 entries of the calculated distance. This value represented the original distance between targets and was used as a baseline to determine the change in the distance between the targets of interest. Finally, the strain was calcu- lated by dividing the change in distance by the original dis- tance. A moving average algorithm was then implemented to smooth the data. All strain results that are reported in this sec- tion are referenced to the location of the targets used to cal- culate the strain value. The coordinate axis located at the left side of Figure 109 was used to describe the coordinate system used for the locations of the strain measurements. The coor- dinate value used to describe the location of a particular strain corresponds to the mid-point between the two targets that were used to calculate that strain value. Figures that include references to the applied load are based on the six load levels of 1.2 kips/ft, 10 kips/ft, 20 kips/ft, 30 kips/ft, 40 kips/ft, and 42.8 kips/ft. The level of 1.2 kips/ft corresponds to the dead load of the girder and the testing equipment, while the applied load of 42.8 kips/ft is the load acting on Girder 10 immediately before its west end failed. Figure 109 shows a typical end region of a girder with the location of the Krypton targets marked. The four groups of targets that are outlined in vertical rectangles were used to evaluate vertical strain distributions along those lines over the height of the web. Each line of nine targets allows for the cal- culation of eight strains with a gage length of 5 inches each. Figure 110 displays the plots that correspond to the locations labeled (a) through (d) on Figure 109. The vertical axis of each plot in Figure 110 represents the height up the web cor- responding to the location of the strain measurement. The horizontal axis is the value of measured strain in microstrain. Each line on the plot represents the strain distribution at a particular applied load, as indicated by the legend. As expected, a large variation of the strain throughout the depth of the web was observed. High values of strain correspond to the location of larger cracks in the web of the girder. Figure 111(a) shows the distribution of average strain along the length of the end region for each column of targets. The aver- age strain was calculated by using the displacements from the top and bottom targets in each column. The horizontal axis represents the location along the length of the girder refer- enced to the centerline of the support, and the vertical axis represents the measured value of the average strain in microstrain. Each line on the plot shows the strain distribu- tion that corresponds to the applied load indicated in the legend. Figure 111(b) displays the applied load versus the average strain for each of the four columns of targets (a) through (d) indicated in Figure 109. Figure 112 displays a typical girder end region, with the locations of the Krypton targets marked. The targets out- lined in horizontal rectangles were used to measure hori- zontal strain distributions at the bottom and the mid-height of the web. Each line consists of 11 targets, and that config- uration allows for 10 individual strain measurements to be calculated, each with a gage length of 10 inches. Figures 113(a) and (b) present the horizontal strain distributions corresponding to the labels (a) and (b) in Figure 112. In the Figure 113 plots, the vertical axes represent the measured horizontal strain values in microstrain, while the horizontal axes represent the horizontal position along the length of the girder where the strain measurements were taken in inches. Each line in the plots represents the horizontal strain distribution corresponding to an applied load, as indicated in the plot legend. Figure 114 displays the average horizon- tal strain values for the horizontal lines labeled (a) and (b) in Figure 112. The vertical axis represents the applied load, and the horizontal axis represents the measured average horizontal strain. As expected, the average horizontal strain at the bottom of the web exceeds the average horizontal strain at mid-height. Figure 115 displays the typical layout of Krypton targets on the end region of a girder. The targets that are outlined in large diagonal rectangles labeled (a) and (b) are used to calculate average shear strain values based on a 40-inch by 40-inch square section of the web. The targets that are outlined in small diagonal rectangles labeled (c) and (d) were used to calculate

140 (a) Distribution at x = 35" 10 15 20 25 30 35 40 45 50 -1000 0 1000 2000 3000 4000 5000 Vertical Strain (με) Ve rt ic al P os iti on (in ) 1.2 kips / ft 10 kips / ft 20 kips / ft 30 kips / ft 40 kips / ft 42.8 kips / ft (b) Distribution at x = 55" Vertical Strain (με) 10 15 20 25 30 35 40 45 50 -1000 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 Ve rt ic al P os iti on (in ) 1.2 kips / ft 10 kips / ft 20 kips / ft 30 kips / ft 40 kips / ft 42.8 kips / ft (c) Distribution at x = 75" Vertical Strain (με) 10 15 20 25 30 35 40 45 50 -1000 0 1000 2000 3000 4000 5000 6000 7000 Ve rt ic al P os iti on (in ) 1.2 kips / ft 10 kips / ft 20 kips / ft 30 kips / ft 40 kips / ft 42.8 kips / ft (d) Distribution at x = 95" Vertical Strain (με) -1000 0 1000 2000 3000 4000 5000 6000 Ve rt ic al P os iti on (in ) 10 15 20 25 30 35 40 45 50 1.2 kips / ft 10 kips / ft 20 kips / ft 30 kips / ft 40 kips / ft 42.8 kips / ft Figure 110. Vertical strain distributions in Girder 10. Figure 111. Average vertical strain in Girder 10. 0 5 10 15 20 25 30 35 40 45 -10 490 990 14 90 1990 2490 2990 349 0 Average Vertical Strain (με) A pp lie d Lo ad (K ips / f t) x = 35" x = 55" x = 75" x = 95" -500 0 50 0 10 00 15 00 20 00 25 00 30 00 35 00 -1 0 10 30 50 70 90 Horizontal Position (in) A ve ra ge V er tic al S tra in (μ εμε ) 1.2 kips / ft 10 kips / ft 20 kips / ft 30 kips / ft 40 kips / ft 42.8 kips / ft (a) Average Vertical Strain Distribution (b) Applied Load versus Average Vertical Strain

141 -1000 0 1000 2000 3000 4000 5000 0 10 20 30 40 50 60 70 80 90 Horizontal Position (in) H or iz on ta l S tra in (μ εμε ) 1.2 kips 10 kips 20 kips 30 kips 40 kips 42.8 kips -3000 -2000 -1000 0 1000 2000 3000 4000 0 10 20 30 40 50 60 70 80 90 Horizontal Position (in) H or iz on ta l S tra in (μ εμε ) 1.2 kips 10 kips 20 kips 30 kips 40 kips 42.8 kips (b) Distribution at y = 33”(a) Distribution at y = 13” 0 5 10 15 20 25 30 35 40 45 0 200 400 600 800 1000 1200 Average Horizontal Strain (με) A pp lie d Lo ad (k ips /ft ) middle row y = 33" bottom row y = 13" Figure 112. Layout of Krypton targets for selected horizontal strain measurements. Figure 113. Horizontal strain distributions in Girder 10. Figure 114. Applied load versus average horizontal strain in Girder 10. a b X Y 10" 73 " 7" 12" 13 "

142 average shear strains based on a 20-inch by 20-inch square section of the web that is aligned with the midheight of the web. Fig- ure 116 displays the average shear strain values corresponding to the different measurement configurations (a) through (d). The vertical axis represents the applied load, while horizontal axis represents the measured average shear strain. Figure 117 highlights which targets in the typical layout were used to measure diagonal compressive strains. The left diagonal rectangle, labeled (a), which is oriented at a 45- degree angle, includes five targets and allows for the meas- urement of four compressive strain values. The right diagonal rectangle, labeled (b), which is oriented at a 26.5-degree angle, includes nine targets and allows for the measurement of eight compressive strain values. Figures 118(a) and 118(b) show the compressive strain distributions corresponding to the lines labeled (a) and (b) in Figure 117. The horizontal axes represent the horizontal distances along the length of the girder where the strain measurement was taken. The vertical axes represent the value of the diagonal compressive strain in microstrain. Each line on the plot represents the distribution of diagonal compressive strain for an applied load value, as indicated in the legend. Figure 119 shows the average diago- nal compressive strain along lines (a) and (b) from Figure 117. The vertical axis represents the applied load, while the horizontal axis represents the value of the average diagonal compressive strain. Figure 120 shows which targets in the typical layout were used to measure the distribution of diagonal tensile strain. The diagonal rectangles that are labeled (a) and (b) each include five targets that were used to measure four diagonal 0 5 10 15 20 25 30 35 40 45 0 1000 2000 3000 4000 5000 6000 Average Shear Strain (με) A pp lie d Lo ad (k ips /ft ) a c b d Figure 115. Layout of Krypton targets for selected shear strain measurements. Figure 116. Applied load versus average shear strain in Girder 10. a b X Y 10" 73 " 7" 12" 13 " c d

143 Figure 117. Layout of Krypton targets for selected diagonal strain measurements. -1600 -1400 -1200 -1000 -800 -600 -400 -200 0 10 15 20 25 30 35 40 Horizontal Position (in) D ia go na l S tra in (μ εμε ) 1.2 kips/ft 10 kips/ft 20 kips/ft 30 kips/ft 40 kips/ft 42.8 kips/ft -1700 -1500 -1300 -1100 -900 -700 -500 -300 -100 100 10 20 30 40 50 60 70 80 Horizontal Position (in) D ia go na l S tra in (μ εμε ) 1.2 kips/ft 10 kips/ft 20 kips/ft 30 kips/ft 40 kips/ft 42.8 kips/ft (a) Distribution at 45 degrees (b) Distribution at 26.5 degrees 0 5 10 15 20 25 30 35 40 45 -1200-1000-800-600-400-2000 Average Diagonal Strain (με) A pp lie d Lo ad (k ips /ft ) 45 degree 26.5 degree Figure 118. Diagonal compressive strain distributions in Girder 10. Figure 119. Applied load versus average diagonal compressive strain in Girder 10. a b X Y 10" 73 " 7" 12" 13 "

144 strain values and are oriented along a 45-degree angle. Figures 121(a) and 121(b) show the diagonal tensile strain distribu- tions that correspond to the labels (a) and (b) in Figure 120. Again, the horizontal axes represent the horizontal position of the strain measurement along the length of the girder. The vertical axes represent the value of the diagonal tensile strain. Each line on the plot displays the distribution of the diagonal tensile strain corresponding to a value of the applied load, as indicated in the legend. Figure 122 shows the average diago- nal tensile strain along the lines (a) and (b). Again, the verti- cal axis represents the applied load, while the horizontal axis represents the average value of the diagonal tensile strain. 2.9.4 Interpretation of Results Further inspection of the experimental results presented in Figure 110 provides insight into the distribution of vertical strains through the height of the girder web and along the length of the girder. Figure 110 shows a positive correlation between the vertical position and horizontal position of the maximum vertical strains in the girder web. This indicates that a plane of weakness forms at an angle along a group of shear cracks, as is expected. This observation correlates well with other test observations. In Figure 111(a), it is observed that the average vertical strain just before failure is at a maxi- mum value for the measurements taken at a distance of 75 and 85 inches from the support and decreases for the meas- urement taken 95 inches from the support. It is also of inter- est to note that the average vertical strain at a distance of 15 inches from the support is essentially zero throughout the entire loading sequence. This result confirms the rationality of the design assumption that the shear reinforcement used at the first critical section is sufficient for the region from the support to this section. Figure 120. Layout of Krypton targets for selected diagonal strain measurements. -500 500 1500 2500 3500 4500 5500 20 25 30 35 40 45 50 Horizontal Position (in) D ia go na l S tra in (μ εμε ) 1.2 kips/ft 10 kips/ft 20 kips/ft 30 kips/ft 40 kips/ft 42.8 kips/ft 0 1000 2000 3000 4000 5000 6000 7000 60 65 70 75 80 85 90 Horizontal Position (in) D ia go na l S tra in (μ εμε ) 1.2 kips/ft 10 kips/ft 20 kips/ft 30 kips/ft 40 kips/ft 42.8 kips/ft (a) Distribution for line a (b) Distribution for line b Figure 121. Diagonal tensile strain distributions in Girder 10. a b X Y 10" 73 " 7" 12" 13 "

145 An inspection of the horizontal strain distributions pre- sented in Figure 113(a) indicates that a significant increase in the horizontal strain at a horizontal distance of 20 inches from the support precedes the failure of the girder. This evidence supports the observation that a loss of prestress and excessive demand on the longitudinal reinforcement is exhibited prior to the failure of a typical girder. The horizontal strain distri- butions in Figure 113(b) show less of a trend because of the spacing of shear cracks crossing the line along which meas- urements were taken. However, Figure 114 shows that the average strain associated with Figure 113(b) is in tension and increases with the applied load. Figure 116 compares the shear strain values obtained from the large measurement field with the values from the small measurement field. The figure indicates that the shear strains measured from the small measurement field are consistently greater than those obtained from the large measurement field but that overall they are reasonably close. This result indicates that the top and bottom edges of the web are restrained by the top flange and bottom bulb, respectively, of the girder, and, because of its depth, the mid- dle of the web is able to experience greater shear strains than the boundaries. Comparisons of the diagonal compressive strains shown in Figures 118 and 119 indicate that the average compressive strain along the 45-degree line is greater than the average compressive strain along the 26.5-degree line. This would lead one to believe that the greatest average compressive strain would occur at an angle between 26.5 degrees and 45 degrees. However, the distribution of straining along the 26.5- degree line had higher peak compressive strain values than the distribution along the 45-degree line. Again, these strains do not consider pretest strains. The distribution of diagonal tensile strain in Figure 121(a) illustrates that there is very little diagonal tensile strain in the top of the web near the support. This is consistent with other experimental test findings, such as the minimal cracking in this region because forces are flowing into the support via a direct strut. Figure 122 shows that the average tensile strain corresponding to the (b) distribution is greater than that cor- responding to the (a) distribution. This result could be artifi- cially influenced by the low values included in the (a) distribution closer to the support. Averaging the 3 largest val- ues from the (a) distribution provides an average strain value close to the average strain value of the (b) distribution just before failure. 2.9.5 Concrete Surface Strain Gage Measurements This section presents the data collected by selected concrete surface strain gages. It illustrates the measured concentration of compressive straining that occurred due to the funneling of the diagonal compression forces into the support, as well as the factors that influenced the measured magnification in straining. Figure 123 presents the positions of selected strain gages on Girder 10 and the measured change in strain in these gages due to the imposed loading. At the onset of diagonal crack- ing, the rate of compressive straining in gages close to the sup- port increased more rapidly than in gages further from the support. The east end of Girder 10 anchored 34 straight strands, of which eight were debonded, while the west end of Girder 10 anchored 34 strands, of which 10 were draped and splayed over the depth at the end of the girder. As shown, the average magnification of the straining in the west end region 0 5 10 15 20 25 30 35 40 45 0 500 1000 1500 2000 2500 3000 3500 4000 4500 Average Diagonal Strain (με) A pp lie d Lo ad (K ips /ft ) a b Figure 122. Applied load versus average diagonal tensile strain in Girder 10.

146 0 5 10 15 20 25 30 35 Lo ad (k ips /f t) 0 5 10 15 20 25 30 35 Lo ad (k ips /f t) 0 0 -0.25 -0.5 -0.75 Strain [10^-3] -1 -1.25 -1.50 -0.5 Strain [10^-3] -1 -2 e9 e7 e3 -1.5 0 -0.5 Strain [10^-3] (a) 10 East (b) 10 West -1 -2-1.5 10 20 40 30 Lo ad (k ips /f t) e8 e5 e1 w4 w2 Figure 123. Measured concrete surface strains in Girder 10.

147 0 5 10 15 20 25 30 35 Lo ad (k ips / f t) 0 5 10 15 20 25 30 35 Lo ad (k ips / f t) 0 0 -0.25 -0.5 -0.75 Strain [10^-3] -1 -1.250 -0.5 Strain [10^-3] -1 -2 e9 e8 e3 -1.5 -3-2.5 0 -0.5 Strain [10^-3] (c) 9 East (d) 9 West -1 -2-1.5 10 20 40 30 Lo ad (k ips / f t) e7 e2 w5 w1 0 0 -0.25 -0.5 -0.75 Strain [10^-3] -1 -1.25 10 20 40 30 Lo ad (k ips / f t) w6 w2 Figure 124. Measured concrete surface strains in Girder 9.

148 is smaller than in the east end due to the effectiveness of the draping and splaying of the strands at providing a larger region for anchoring of the diagonal compressive force. Figure 124 presents the position of selected strain gages in Girder 9 and the measured change in strain in these gages due to the imposed loading. The east end of Girder 9 anchored 34 straight strands, while the west end of Girder 9 anchored 34 strands, of which 10 were draped and splayed as was done in Girder 10. The observations are very similar in Girder 9 as in Girder 10, but the extent of the beneficial effect of draping and splaying strands is more pronounced. This result suggests that there is a detrimental effect for the anchoring of the di- agonal compressive force when some of the tendons are debonded. Because prestressing alone can introduce significant com- pressive stresses at the base of the web, the likely pretest strains should be taken into consideration when reviewing the results of concrete surface strain gauges, particularly the results of gages near the base of webs and on the bottom bulb. These pretest strain levels are predicted from the finite ele- ment analyses reported in Section 2.10. 2.10 Prediction of Behavior of Girders Using Finite Element Analyses 2.10.1 Overview This section presents the behavior of the girders as pre- dicted using nonlinear finite element analyses. The analyses were conducted using the program Vector2, which fully imple- ments the MCFT. This section summarizes the Vector2 pro- gram (2.10.2), the development of the geometric model of the girders (2.10.3), the characteristics of the selected material models (2.10.4), material properties (2.10.5), and the overall load-deformation response predictions (2.10.6) for all girders. It then provides selected results of the analyses, including strain distributions prior to loading (2.10.7), cracking strengths and crack patterns (2.10.8), modes of failures (2.10.9), shear deformations (2.10.10), shear slip (2.10.11), and strain and deformation patterns (2.10.12). Many of these predictions are then compared with the results of the experi- mental testing program that were documented in Sections 2.4 through 2.9. These comparisons are used to assess the effec- tiveness of Vector2 at predicting overall strength, load- deformation response, mode-of-failure, and distribution of straining. If Vector2 is deemed to be successful, then the result is extremely significant, for it implies that this program can be reliably used for predicting the response of somewhat similar members that were not tested in this research program. This will be particularly important if design cases are identified for which there are concerns about the appropriateness of using the LRFD Sectional Design Model. 2.10.2 The Vector2 Program Vector2 is a nonlinear finite element program for the analy- sis of two-dimensional reinforced concrete structures. The theoretical bases of Vector2 are the MCFT (2) and the Dis- turbed Stress Field Model (DSFM) (31). The program was principally developed by Professor Frank Vecchio and his stu- dents over the last 20 years and was previously known as Trix. The MCFT and DSFM are analytical models for the response of a two-dimensional membrane structure sub- jected to in-plane normal and shear stresses. The models account for the average or smeared stress-strain relation- ships in cracked concrete, as well as perform an equilibrium check of conditions at crack locations. The DSFM differs from the MCFT in that it takes into consideration the defor- mation associated with slip along the crack faces. As a result, unlike the MCFT, the DSFM does not assume that the angle of principal stress corresponds to the angle of principal strain. Vector2 computes the response of structures by using constitutive relationships, including compression softening, tension stiffening, tension softening, and tension splitting (28). For each constitutive relationship, Vector2 provides several choices, as have been developed by prominent researchers. Therefore, Vector2 has the capacity to predict the response of a wide range of two-dimensional concrete structures. One of the main objectives of the girder tests was to study the shear behavior of the web. Because the primary behavior of the web is similar to that of a two-dimensional panel, and because the main objective of Vector2 is to analyze such ele- ments, Vector2 is an appropriate tool for analyzing the behavior of these girders.Vector2 provides for the use of con- stant strain triangular elements, four-node quadrilateral ele- ments for smeared reinforced concrete elements, and two-node linear truss elements for discrete reinforcement modeling. Because, in general, the finite element analysis for structural concrete requires relatively dense meshing, using a low-order element is appropriate. Vector2 solves the non- linear problems using a secant stiffness algorithm, which is usually adopted for monotonic loading, and the path-inde- pendent nonlinear elasticity due to its robustness and sim- plicity. This approach provides good convergence stability for postpeak behavior. 2.10.3 Modeling of Girders Because Vector2 is a two-dimensional continuum analysis program, the variations in width of the bulb-tee had to be taken into account by using elements of different thicknesses. This results in some simplification of the cross section, as shown in Figure 125. The area and moment of inertia are only marginally different in the model than in the real member.

149 Only one-half of the length of girders was modeled at any one time in order to decrease solution time. The typical analy- sis model is shown in Figure 126. Because the transverse rein- forcement was well distributed, it was modeled as smeared reinforcement. The prestressing strands were modeled as dis- crete truss bars to facilitate the application of prestrains and to account for transfer lengths. Longitudinal reinforcement in the web was also modeled as discrete truss bars, because it is unreasonable to assume that such reinforcement is distrib- uted over the web evenly. The bold lines in Figure 126 indi- cate the locations of the discrete reinforcement. The load was assumed to be uniformly distributed over the 44-foot loaded length, as was used in the physical experiments. In Vector2, point loads along the nodes in the upper flange were applied to simulate the uniformly dis- tributed load. In the tests, there were some uneven load cases, such as in the east side of Girder 6 and the west side of Girder 9. In these cases, small shear forces exist at mid- span of the girders due to the nonsymmetric load pattern. This force was accounted for in the analyses by applying upward nodal forces at the right side boundary of the model. The load distributions used in the analyses are shown in Figure 127. The prestress is applied in the form of prestrain. Prestrain is calculated based on the experimentally measured effective pre- stress prior to loading. The prestrain is applied to the prestress 0.125 80@0.100 = 8.000 0.050 0.125 0.100 15 0 1 00 10 0 1.067 0.100 0. 25 0 0.152 11 @ 0. 10 0 = 1. 10 0 0.65 0 0.050 0.100 0.50 0 0.66 0 0.150 1. 85 0 1. 20 0 1. 85 0 Figure 125. Comparison of cross sections used in experiments and analysis (in millimeters). Figure 126. Typical analysis model (in millimeters). 0. 25 4 0. 08 9 0. 05 1 0. 05 1 0. 11 4 0. 15 2 1. 14 3 1. 85 4 0.660 0.406 1.067 0.152 0.051 1.067 0. 10 0 1. 85 0 0. 15 0 0.660 0. 05 0 0. 10 0 0. 25 0 1. 20 0 0.500 0.152 0.650 A = 680.6 × 103 mm2 I = 288,206.5 × 103 mm4 A = 688.4 × 103 mm2 I = 290,479.0 × 103 mm4 (a) experiment (b) model

150 tendons,and thus the strain offset between the concrete element and the strands effectively models the effect of prestressing. The transfer length of the prestressing tendon was considered to be 50db from the actual end of the girder. Within the transfer length, the prestrain was applied in the manner of stepwise increments. In the experiments, steel bearing plates were used to avoid stress concentration above the supports. However, in Vector2, only reinforced concrete material can be used for membrane elements, and thus it was not possible to model steel bearing plates directly. If such support conditions are modeled in terms of a one-point roller boundary condition, spurious stress concentrations can result. Therefore, fictitious bearing plate elements were made up of relatively strong reinforced concrete. This fictitious plate prevented the local stress con- centration and distributed the stress to the girder in a man- ner similar to the steel plate. One of the most important model parameter selections in Vector2 is that of estimating the crack spacing because the crack width is taken as the principal tensile strain mul- tiplied by the crack spacing. The crack width controls the ability of the shear stress to be transferred across the crack. In these analyses, average crack spacing was computed according to CEB-FIP model code 1990 (32). The calcula- tion example of average crack width used in the analysis is shown in Table 33, in which sm refers to the mean crack spacing. Average crack spacing is defined for the x-axis and y-axis. 2.10.4 Material Models As mentioned previously, Vector2 provides a selection of constitutive relationships that can be used in the analyses for the compression prepeak response, the compression postpeak response, compression softening, the tension stress-strain relationship, and tension softening. To obtain the most reli- able results from the analyses, the most appropriate material model should be selected. The models selected for use in this analysis are described in the following sections. Compression Prepeak Response The compression prepeak response model is used for the computation of the principal compressive stress before the strain reaches the strain corresponding to the peak compres- sive stress. The selected relationship is for the uniaxial response, but may be subsequently modified according to the selected compression-softening relationship. Because HSC was used in the girders, and because the strength of the con- crete has a large effect on the compressive response, the selected material model should account for that characteris- tic. For this purpose, the Popovics model for HSC (33) was Figure 127. Loading pattern in modeling. (a) Most girders (b) G6E (c) G8E Model Length = 26 ft 22 ft 3 ft midspan W Model Length = 26 ft 22 ft 3 ft midspan W V Model Length = 26 ft 16 ft 9 ft midspan W V Model Length = 26 ft 22 ft 3 ft midspan W V 0.626W 10 ft 4 ft 12 ft (d) G9W

151 selected because it adequately shows the large linear range of response that occurs before peak stress for HSC. Compression Postpeak Response The compression postpeak response model accounts for ductile behavior and strength enhancement due to confine- ment of the concrete by transverse stresses. Because the webs of the girders are unconfined in the out-of-plane direction, ductile behavior does not occur in that direction. Conse- quently, the postpeak part of the Popovics model for HSC (33), which has a steep descending branch, is used. The typi- cal relationship is shown in the Figure 128(a) and is expressed by Equation 48: f f n n ci ci p p ci p nk ci = ⎛ ⎝⎜ ⎞ ⎠⎟ − + ⎛ ⎝⎜ ⎞ ⎠⎟ ε ε ε ε ε 1 for < 0 48( ) where fci = principal compressive stress; εci = principal compressive strain; εp = strain corresponding to the peak compressive stress, fp; fp = peak concrete compressive stress; e1, e2 = parameters in compression-softening model; βd = compression-softening reduction factor; εc1 = average concrete axial strain in the principal tensile direction; εc2 = average concrete axial strain in the principal com- pressive direction; ε0 = strain corresponding to the peak compressive stress, f c´; f ac1 = average concrete tensile stress determined by tension-stiffening effect; εcr = concrete cracking strain; Section number Axis db 15db clear cover maximum spacing s k1 k2 As Acef rho_ef sm (mm) x 19.1 287 41 254 254 0.4 0.25 2840 266750 0.011 313 y 15.9 239 475 102 102 0.4 0.25 2388 102030 0.023 1038 x 28.7 431 36 193 193 0.4 0.25 3876 106700 0.036 191 y 15.9 239 475 102 102 0.4 0.25 2388 102030 0.023 1038 x 0 0 0 0 0 0.4 0.25 0 0 0.000 0 y 15.9 239 266 102 102 0.4 0.25 2388 102030 0.023 621 x 0 0 0 0 0 0.4 0.25 0 0 0.000 0 y 15.9 239 17 102 102 0.4 0.25 2388 45600 0.052 85 x 15.2 228 43 51 51 0.8 0.25 840 50000 0.017 278 y 15.9 239 199 102 102 0.4 0.25 2672 102030 0.026 479 x 15.2 228 43 51 51 0.8 0.25 3640 99000 0.037 179 y 15.9 239 279 102 102 0.4 0.25 2672 102030 0.026 639 x 19.1 287 41 254 254 0.4 0.25 2840 266750 0.011 313 y 12.7 191 475 152 152 0.4 0.25 5676 1080770 0.005 1222 x 28.7 431 36 193 193 0.4 0.25 3876 102030 0.038 187 y 12.7 191 475 152 152 0.4 0.25 5676 1080770 0.005 1222 x 0 0 0 0 0 0.4 0.25 0 0 0.000 0 y 12.7 191 266 152 152 0.4 0.25 5676 1080770 0.005 805 8 9 7 5 6 1 2 3 4 Table 33. Calculation example of average crack spacing. 0 20 40 60 80 100 120 140 160 0.000 0.002 0.004 0.006 0.008 fp=40MPa fp=60MPa fp=80Mpa fp=100MPa fp=120MPa fp=140MPa 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 5 10 15 20 0 0.5 1 1.5 2 2.5 3 3.5 4 0 0.0002 0.0004 0.0006 0.0008 0.001 εc (a) Compressive Response (b) Compression Softening (c) Tension Stiffening cf c cf crf εc1 εc2 βd Figure 128. Constitutive relationships.

152 n = k = Compression Softening Compression softening is the softening and weakening of the compressive response due to transverse tensile straining. In the original MCFT formulation, the softening was only a func- tion of transverse strain, but more recent shear tests on HSC elements (34) found that the use of a compression-softening relationship that includes a concrete strength factor provided for better results. Therefore, two modified models—a strength and strain-softened model, and a strength-only softening model—were proposed, and it was concluded that a strength and strain-softened model gave more accurate predictions for HSC elements. Hence, in this study, the strength and strain- softened model, which is also known as the Vecchio 1992-A (e1/e2) model, is used. The relationship is shown in Figure 128(b). The relationship is given by Equation 49: Tension Stiffening After concrete cracks, the concrete is still effectively bonded to the reinforcement between cracks and can carry significant tensile stresses. This action is referred to as the “tension-stiffening effect” and is accounted for by using an average tensile stress in the concrete even when the principal tensile strain is greater than the cracking strain. The tension- stiffening effect is largest for members in which there is a sig- nificant amount of deformed bar reinforcement. For these analyses, the research team selected the tension-stiffening relationship proposed by Bentz (35), which is a modification of the tension-stiffening model of Collins and Mitchell (36). Additional information on this model is available in Bentz’s “Sectional Analysis of Reinforced Concrete Members” (35). The typical curve is shown in the Figure 128(c). The rela- tionship is given by Equation 50: βd s d d C C C r r = + × ≤ = −( ) 1 1 1 0 0 35 0 28 0 8 if > 0.28 . . . 0 1 2 400 49 1 if > 0.28 if she r r C c c s ⎧⎨⎩ = − ≤ = ε ε ( ) er slip not considered if sheer slip co0 55. nsidered{ = ′ = f fp d c p d β ε β ε0 1 0 0 0 67 17 1 0 0 . . . for for ε ε ε ε p ci p ci p p f f < < + ≥ < < in MPa( ) ⎧ ⎨⎪ ⎩⎪ ⎫ ⎬⎪ ⎭⎪ 0 80 17 . ;+ ( )f fp p in MPa and where the parameter m accounts for bond and depends on the ratio of the area of the concrete to the bonded surface area of the reinforcement. Slip Distortion The essential difference between the DSFM and the MCFT is that the DSFM removes the shear stress limit at the crack surface of the MCFT and replaces it with a slip distortion rela- tionship. Several models have been proposed to address the slip-shear stress relationship at a crack. The relationship devel- oped by Walraven (37) depends on the shear stress at a crack surface only, whereas the Hybrid III relationship computes the slip distortion as the maximum of the Walraven estimate and a constant orientation lag. If this option is activated, Vector2 employs the DSFM, while if no slip distortion is selected, then the MCFT is used. In this study, the MCFT was selected and a specific element slip distortion relationship was not used because the shear equation of the LRFD specifications is based on the MCFT, and that the comparison is meaningful. There- fore, 1.0 was used for Cs in the compression-softening model. The selected main material models are summarized in Table 34. The default values of the programs were used for any other required material models. 2.10.5 Material Properties of the Girders While the material models were presented in the previous section, the detailed material properties used in those material models are given in this section. Because the vari- ables for the selected material models were limited to the peak stress f c´ and its corresponding associated strain, εc, those val- ues were obtained from the uniaxial cylinder test results com- pleted as part of the girder test program. The values for those quantities are given in Table 35. 2.10.6 Prediction of Capacity and Mid-Span Deflection Vector2 was not only able to provide a detailed prediction of the behavior of the test girders, but also able to simply pre- dict the overall capacity of each test girder. Table 36 com- f f m c a cr c cr c1 1 11 3 6 0 50= + × < < . ( ) ε ε εfor Material Model Category Selected Model Compression Prepeak Response Compression Postpeak Response Compression Softening Tension Stiffening Element Slip Distortion Popovics (High Strength) Popovics (High Strength) Vecchio 1992-A ( 1 2e e ) Bentz 1999 Not considered Table 34. Selected material models.

153 pares the measured capacities of the girders with the strengths predicted using various methods, including Vec- tor2, R2K, the LRFD specifications, and the AASHTO Stan- dard Specifications. As explained in Section 2.10.3, some girders were not subjected to uniformly distributed loads over the standard 44-foot length. This fact was taken into consideration in the derivation of the calculated values shown in Table 36. The mean value and the coefficient of variation of wtest/wVector2 excludes the result for Girder 4 because that girder failed in flexure due to premature debonding of an external plate. In general, Vector2 was able to predict the capacity of the test girders to within 10 percent. Although Vector2 typically overestimated the capacity, the coefficient of variation of the strength ratio with Vector2 was only 0.08. That value is remarkably good for predictions of the behavior of complex structural concrete members. This success suggests that Vec- tor2 can be used to predict the capacity of members when it is not possible to test experimentally; thus, Vector 2 can address other important design considerations. Despite the generally excellent strength predictions by Vec- tor2, the predicted behavior of the west side of Girder 8 was poor. In this experiment, two back-to-back aluminum plates were inserted in the web of the girder to create a shear plane of weakness and to minimize aggregate interlock effects. In order to model this experimental setup in the analysis cor- rectly, a contact-type element that would resist normal com- pressive forces and not resist tension and shear forces should have been used. However, this type of element was not pro- vided in Vector2, and thus the elements on each side of the plate were simply separated in the numerical model. As a result, the analysis tool showed difficulties such as overlap in early load stages or excessive separation of elements at later load stages. This result is far from the experimental observa- tions and was undoubtedly the cause of considerable error in the strength prediction. In addition to predicting girder strength, Vector2 was used to calculate the overall load-deformation response of the girders. While shear distortion contributes little to mid-span displacement, the mid-span deflection can be a good indica- tor of the usefulness of an analysis tool for evaluating global stiffness. Figure 129 presents a comparison of predicted and measured load versus mid-span displacement relationships Table 36. Comparison of prediction of ultimate strength (kip/ft). Girder Test Vector2 R2K LRFD STD w tes t / w Vector2 w tes t / w R2K w test / w LRFD w test / w ST D East 26.03 26.73 23.14 24.47 19.46 0.97 1.12 1.06 1.34 G1 West 30.09 30.16 23.71 24.72 20.29 1.00 1.27 1.22 1.48 East 33.79 37.70 36.90 35.08 25.59 0.90 0.92 0.96 1.32 G2 West 38.73 37.70 37.57 33.60 26.15 1.03 1.03 1.15 1.48 East 35.68 35.64 29.68 31.98 25.73 1.00 1.20 1.12 1.39 G3 West 38.82 38.38 29.68 31.98 25.73 1.01 1.31 1.21 1.51 East 42.65 a 50.72 43.28 43.43 33.20 0.84 0.99 0.98 1.28 G4 West 42.65 a 50.72 43.28 43.43 33.20 0.84 0.99 0.98 1.28 East 23.70 21.25 21.86 19.31 16.31 1.12 1.08 1.23 1.45 G5 West 19.91 23.30 21.70 17.80 15.75 0.85 0.92 1.12 1.26 East 38.32 40.44 34.29 34.88 25.76 0.95 1.12 1.10 1.49 G6 West 27.85 30.16 29.95 27.67 20.91 0.92 0.93 1.01 1.33 East 33.47 34.96 28.41 30.69 24.82 0.96 1.18 1.09 1.35 G7 West 33.47 34.96 28.41 30.69 24.82 0.96 1.18 1.09 1.35 East 43.72 42.49 36.35 39.74 34.26 1.03 1.20 1.10 1.28 G8 West 32.70 41.81 31.46 34.85 25.92 0.78 1.04 0.94 1.26 East 32.80 37.70 37.83 36.63 25.33 0.87 0.87 0.90 1.29 G9 West 37.19 41.81 50.74 43.46 25.61 0.89 0.73 0.86 1.45 East 33.93 36.33 31.56 29.09 24.40 0.93 1.08 1.17 1.39 G1 0 West 42.85 39.07 34.85 31.89 26.63 1.10 1.23 1.34 1.61 Mean b 0.96 1.08 1.09 1.39 Standard Deviation 0.08 0.16 0.12 0.10 COV 0.09 0.14 0.11 0.07 a Maximum applied load, not an ultimate load. b Except for G4. Table 35. Properties of concrete. Girder Girder Slab Girder number f’c (ksi) c(µ ) f’c (ksi) G1 12.1 3000 4.5 G2 12.6 2600 8.6 G3 15.9 3300 3.6 G4 16.3 3400 6.3 G5 17.8 2700 6.1 G6 12.7 2800 9.2 G7 12.5 3200 4.5 G8 13.3 3200 7.0 G9 9.6 2400 6.0 G10 10.6 2600 5.4

154 West East 0 5 10 15 20 25 30 35 0 2 41 3 5 0 1 20.5 1.5 2.5 Un ifo rm L oa d (ki p/f t) Experiment Vt2 0 5 10 15 20 25 30 Experiment Vt2 (a) G1 0 5 10 15 20 25 30 35 40 45 0 2 4 6 8 10 Experiment Vt2 0 5 10 15 20 25 30 35 40 45 0 2 4 6 8 10 Midspan Deflection (in) Experiment Vt2 (b) G2 0 5 10 15 20 25 30 35 40 45 0 2 4 6 8 Experiment Vt2 0 5 10 15 20 25 30 35 40 0 1 2 3 4 5 Experiment Vt2 (c) G3 Un ifo rm L oa d (ki p/f t) Un ifo rm L oa d (ki p/f t) Un ifo rm L oa d (ki p/f t) Un ifo rm L oa d (ki p/f t) Un ifo rm L oa d (ki p/f t) Midspan Deflection (in)Midspan Deflection (in) Midspan Deflection (in) Midspan Deflection (in) Midspan Deflection (in) Figure 129. Load-deflection at mid-span. for all of the test girders. As shown in the figure, the experi- mental result and the prediction are reasonably close in most cases, both in the elastic region and in the inelastic region. Even though the quality of prediction is excellent, Vector2 predicts that the girder is more ductile than the measured result in about half the cases. 2.10.7 Predicted Strain Distribution Prior to Loading The experimental results reported in Sections 2.4 through 2.9 presented the change in strains and deformations in the test girders due to the application of the uniformly distributed load.

155 Experiment Vt2 Experiment Vt2 Experiment Vt2 Experiment Vt2 Experiment Vt2 Experiment Vt2 West East 0 5 10 15 20 25 30 35 0 2 41 3 5 Un ifo rm L oa d (ki p/f t) 0 10 20 30 40 50 60 (d) G4 (e) G5 (f) G6 Un ifo rm L oa d (ki p/f t) Midspan Deflection (in) 0 2 41 3 65 Midspan Deflection (in) 0 2 41 3 0 10 20 30 40 50 60 Un ifo rm L oa d (ki p/f t) Midspan Deflection (in) 0 1 20.5 1.5 32.5 Midspan Deflection (in) 0 1 20.5 1.5 32.5 Midspan Deflection (in) 0 1 20.5 1.5 Midspan Deflection (in) 0 5 10 15 20 25 30 35 40 45 Un ifo rm L oa d (ki p/f t) 0 5 10 15 20 25 30 Un ifo rm L oa d (ki p/f t) 0 5 10 15 20 25 Un ifo rm L oa d (ki p/f t) Since these changes do not account for the strains due to the effects of prestressing, Vector2 was used to predict the effects of the prestressing strains that occurred prior to loading. The effect of the prestressing force can be documented in diagrams that describe the state of strain, including the prin- cipal compressive strain, ε2, and vertical strain, εy. Selected analyses were conducted on numerical models of the girders without the top slab in order to obtain these pretest states of strain. In this section, four representative girders were selected to estimate the level of initial strains, two for the upper and lower bounds of the initial strains and two for evaluation of the effects of inclined prestressing tendons. Figure 129. (Continued).

156 Experiment Vt2 Experiment Vt2 Experiment Vt2 Experiment Vt2 West East (g) G7 (h) G8 0 5 10 15 20 25 30 35 40 Un ifo rm L oa d (ki p/f t) 0 1 20.5 1.5 32.5 Midspan Deflection (in) 0 5 10 15 20 25 30 45 35 50 40 Un ifo rm L oa d (ki p/f t) 0 5 10 15 20 25 30 45 35 50 40 Un ifo rm L oa d (ki p/f t) 0 1 20.5 1.5 32.5 Midspan Deflection (in) 0 5 10 15 20 25 30 45 35 40 Un ifo rm L oa d (ki p/f t) 0 1 20.5 1.5 32.5 3.5 Midspan Deflection (in) 0 1 20.5 1.5 32.5 3.5 Midspan Deflection (in) Figure 129. (Continued). The elastic strains due to prestressing were calculated first because it was reasonable to assume that all materials were in an elastic state. Note that the principal compressive strain is directly proportional to the prestressing force and its direc- tion is close to horizontal. It is also useful to note that vertical strains develop through the Poisson’s effect and, thus, are directly proportional to the principal compressive strain. The resulting initial strains due to prestressing are presented in Table 37. The strain levels were calculated for the girder with- out a slab and were evaluated at the bottom of the web at mid- span. To evaluate the upper and lower bounds of initial strains, two girders were selected and the distribution of strains due to prestressing were evaluated. As indicated in Table 37, the results from Girder 5 were selected as a lower bound, and those from Girder 7 were selected as an upper bound. To evaluate the effects of the inclined prestressing tendons on the initial strain, the west halves of Girder 2 and Girder 10 were selected for examination. Because the west half of Girder 9 was very similar to the west half of Girder 10, it was to be expected that the strain distribution for those two girders would also be very similar. For the west parts of Girders 2, 5, 7, and 10, the vertical strains are shown on the left and the principal compressive strains are shown on the right in Figure 130.The results are for girders with- out the slab and with consideration of self-weight.All strains are in millistrain. The lines of the lower part of the vertical strain results for the girders indicate the presence of truss element rep- resenting the prestressing tendons. They do not indicate the strain levels in the concrete or reinforcement. For Girders 5 and 7, the results presented in Figure 130 suggest that the vertical strains are influenced by cracking in the end region of the girder, since outside of that region there is very little vertical strain. By contrast, results for Girders 2 and 10 indicate that the initial cracking of the end region is reduced and small vertical strains develop in the remaining parts of the girder.As is the case for the vertical strains, the elastic state of strain dominates in most of the region for the principal compressive strain diagrams. Moreover, in the end region, very little compressive strain develops. There- fore, initial vertical strains in the web can be ignored, and initial

157 principal compressive strains can be calculated assuming that strains remain in the elastic range of behavior. 2.10.8 Cracking Patterns One of the most desirable features for a finite element analysis program for structural concrete members is the ability to accurately predict cracks and their locations, directions, and average widths because the stiffness, shear transfer efficiency, and global behavior of concrete members are strongly affected by cracking. Thus, a program should not be considered effec- tive if it cannot accurately predict the state of cracking, even if its ability to predict strength is reasonably accurate. Figure 131 shows the crack patterns of the final load steps for several girders and, thereby showing the ability of program Vec- tor2 to predict cracking properly. The final loading steps were Experiment Vt2 Experiment Vt2 Experiment Vt2 Experiment Vt2 West East (i) G9 (j) G10 0 5 10 15 20 25 30 35 40 Un ifo rm L oa d (ki p/f t) 0 1 20.5 1.5 32.5 Midspan Deflection (in) 0 5 10 15 20 25 30 45 35 50 40 Un ifo rm L oa d (ki p/f t) 0 1 20.5 1.5 32.5 Midspan Deflection (in) 0 5 10 15 20 25 30 45 35 40 Un ifo rm L oa d (ki p/f t) 0 1 2 43 5 Midspan Deflection (in) 0 5 10 15 20 25 30 45 35 40 Un ifo rm L oa d (ki p/f t) 0 1 20.5 1.5 32.5 3.5 Midspan Deflection (in) Figure 129. (Continued). Girder # of Strand Effective Strain ( ) Prestress Force (k) Eccen. (in) Moment (k.in) Elastic Modulus (ksi) x ( ) y ( )(= * x) G1 34 6,318 1,329 24.355 32,356 6,270 581 0.105 G2 40 6,262 1,549 23.720 36,744 6,398 656 0.118 G3 44 6,141 1,671 24.320 40,641 7,187 637 0.115 G4 40 5,970 1,477 23.720 35,031 7,277 550 0.099 G5 24 6,525 968 29.120 28,203 7,605 383 0.069 G6 44 6,588 1,793 24.302 43,567 6,424 765 0.138 G7 44 6,735 1,833 24.302 44,539 6,373 788 0.142 G8 44 6,407 1,743 24.302 42,370 6,574 727 0.131 G9 36 6,667 1,484 23.009 34,154 5,585 709 0.128 G10 36 6,823 1,519 23.009 34,953 5,869 691 0.124 Table 37. Strains due to prestress.

158 chosen for comparisons with the program predictions because, at such stages, the final crack patterns are fully estab- lished and obvious. In Figure 131, the thickness of a given line represents the crack width; a thin line is for a crack predicted to have a width less than 0.04 inch (1.0 millimeter), the line of midwidth is for a crack 0.04 to 0.08 inch (1.0 to 2.0 mil- limeters), and the thick line is for a crack wider than 0.08 inch (2.0 millimeters). More detailed diagrams for the experimen- tally measured development of cracking are reported in the appendices. There is good agreement between measured and predicted results in Figure 131. Figure 132 shows detailed comparisons between the meas- ured and predicted crack patterns for the east half of Girder 3, thereby showing the ability of Vector2 to predict crack devel- opment. The comparison shows that Vector2 successfully predicts crack locations, directions, and widths for each step in the loading history of the girder. As discussed previously, the first web-shear cracks occurred at a load of 19.2 kip/ft in the analysis, a value that is reasonably close to the experimentally observed first cracking load of 16.2 kip/ft. By Load Stage 3, both the experimental results and the analysis showed well-devel- oped web-shear cracks and a similar extent of flexural crack- ing. By Load Stage 4, the flexural cracking in the girder had developed a little more in the analyses than in the experiment, and flexure-shear cracking was occurring in both the experi- ment and the analysis. By Load Stage 5, the extent of the exper- Figure 130. Strain distribution prior to loading. (a) G2 West (b) G5 West (c) G7 West (d) G10 West εy ε2

159 imentally measured web-shear cracking and flexure-shear cracking, as well as the crack widths, were well predicted by the program, with the fan-shape of the web-shear cracks being very similar from the measurements and from the analyses. 2.10.9 Mode of Failure To further evaluate the utility of using Vector2 for conduct- ing analytical studies on the shear performance of HSC girders, this section compares the modes of failure predicted by this program with those measured in the experiments.As is the case with experimental test data, the predicted behavior from the analyses had to be carefully examined in order to correctly assess the predicted mode of failure. To this end, Figure 133 shows the vital signs calculated by Vector2 for the final load step of repre- sentative girders for each failure mode. The vital signs include the ratio of the maximum current compressive stress to the possible peak stress for the concrete (shown in the left side of Figure 133) and the ratio of the current steel strain to the yield strain for the reinforcement (shown in the right side of Figure 133). These two ratios help to explain the cause of failure and can be used for selecting the predicted mode of failure. Figure 131. Crack patterns at final step. (a) G1 (b) G2 (c) G3 (d) G4 (e) G5 West East

160 Figure 133(a) shows the two ratios for the west half of Girder 1. The compressive stress ratio is shown on the left side, and the reinforcement strain ratio is shown on the right side. From the left graph, it is evident that the com- pressive stress above the support reached its peak value, while from the right graph it can be seen that the strains in most of the stirrups have already exceeded their yield strain. Therefore, it can be concluded that the predicted mode of failure is local crushing above the support following exten- sive yielding of the shear reinforcement. For comparison, Figure 133(b) shows the example of the predicted diagonal tension failure of the west end of Girder G5. In the right graph, the yielding of the stirrup is concentrated over a very narrow band. Moreover, it can be seen that the strain ratio within the band is extremely high. In the left graph, many elements in the band have lost their stiffness due to the large crack width and show very low compressive stresses. Lastly, Figure 133(c) shows the predicted failure mode of local crushing prior to stirrup yielding for the east end of Girder 9. In the left graph, the elements above the support have reached their possible peak stress over a relatively wide area. The right graph indicates that the reinforcing steel above the Figure 131. (Continued). (f) G6 (g) G7 (h) G8 (i) G9 (j) G10 West East

161 (a) Load Stage 1 (Load = 14.9 kip/ft, wcr- experiment: 0mm, Vector2: 0.01mm) (b) Load Stage 2 (Load = 16.2 kip/ft, wcr- experiment: 0.2mm, Vector2: 0.01mm) (c) Load Stage 3 (Load = 26.1 kip/ft, wcr- experiment: 0.35mm, Vector2: 0.40mm) (d) Load Stage 4 (Load = 28.2 kip/ft, wcr- experiment: 0.5mm, Vector2: 0.48mm) (e) Load Stage 5 (Load = 32.4 kip/ft, wcr- experiment: 0.55mm, Vector2: 0.85mm) (f) Load Stage 6 (Load = 35.7 kip/ft, wcr- experiment: 0.75~1.5mm, Vector2:1.0~2.0mm) Figure 132. Crack development of east part of Girder 3.

162 support has reached its yield strain but that the region is very small and the strain level is relatively small. It is evident that the cause of failure is therefore not yielding of the trans- verse reinforcement. The above examples illustrate that the cause of failure can be identified relatively clearly from the analyses. On the basis of these vital signs, the mode of failure for each girder was predicted, and the results are summarized in Table 38. These predicted modes of failure are reasonably close to those determined from the measured and observed experi- mental responses. While Girder 4 did not fail in shear, the predicted mode of failure from the analyses is presented for reference. 2.10.10 Shear Deformations A comparison is now made of the predicted and measured shear strains of the girders immediately inside of the support. The region of the girder whose response was measured by the set of LVDTs closest to the support is used for this compari- son. LVDTs WD1 and WD3 were used for calculating the measured shear strains in the west end of the girders, while LVDTs ED1 and ED3 were used for calculating those in the east end. Comparisons of measured and predicted results are shown in Figure 134 for both ends of all the test girders. While Vector2 frequently overestimated the length of the region of elastic response, it did reasonably well at predicting the stiff- ness of the region of inelastic response. 2.10.11 Shear Slip at Crack Surface One of the main components of the concrete contribution to shear resistance is assumed to be interface shear transfer across diagonal cracks. For this mechanism, the direction of Current Compressive Stress/Possible Peak Stress Current Stirrup Strain/Yield Strain (a) Stirrup yielding followed by local crushing (G1 west) (b) Diagonal tension (G5 west) (c) Local crushing almost without stirrup yielding (G9 east) Figure 133. Vital signs of girders. Mode of Failure Girder Stirrups yielding followed by local crushing G1,G2,G3,G4,G6,G7,G8,G10 Diagonal tension (Local stirrup yielding) G5 Local crushing before stirrup yielding G9 Table 38. Comparison of mode of failure.

163 West East 0 5 10 15 20 25 30 35 0 1000 2000 3000 4000 5000 Shear Strain (με) 0 1000 2000 3000 4000 5000 Shear Strain (με) 0 1000 2000 3000 4000 5000 Shear Strain (με) 0 1000 2000 3000 4000 60005000 Shear Strain (με) Shear Strain (με) Shear Strain (με) Lo ad (k /ft ) Vt2 Experiment 0 5 10 15 20 25 30 0 200 400 600 800 1000 1200 1400 Lo ad (k /ft ) Vt2 Experiment (a) G1 0 5 10 15 20 25 30 35 40 45 Lo ad (k /ft ) 0 5 10 15 20 25 30 35 40 45 Lo ad (k /ft ) 0 5 10 15 20 25 30 35 40 Lo ad (k /ft ) 0 5 10 15 20 25 30 35 40 45 Lo ad (k /ft ) Vt2 Experiment 0 500 1000 1500 2000 2500 3000 3500 4000 Vt2 Experiment (b) G2 Vt2 Experiment Vt2 Experiment (c) G3 Figure 134. Shear deformations of web.

164 Vt2 Experiment Vt2 Experiment (e) G5 Vt2 Experiment Vt2 Experiment (f) G6 0 10 20 30 40 50 60 Lo ad (k /ft ) 0 10 20 30 40 50 60 Lo ad (k /ft ) 0 5 10 15 20 25 30 Lo ad (k /ft ) 0 5 10 15 20 25 35 30 Lo ad (k /ft ) 0 5 10 15 20 25 Lo ad (k /ft ) Vt2 Experiment Vt2 Experiment (d) G4 Shear Strain (με) 0 1000500 20001500 2500 3000 3500 4000 0 1000 2000 3000 4000 5000 Shear Strain (με) 0 2000 4000 6000 8000 10000 12000 Shear Strain (με) 0 2000 4000 6000 8000 10000 12000 Shear Strain (με) 0 1000 2000 3000 4000 5000 Shear Strain (με) 0 1000 2000 3000 4000 60005000 Shear Strain (με) 0 5 10 15 20 25 30 35 40 45 Lo ad (k /ft ) West East Figure 134. (Continued).

165 Vt2 Experiment Vt2 Experiment Vt2 Experiment Vt2 Experiment Vt2 Experiment Vt2 Experiment West East (g) G7 (h) G8 (i) G9 0 1000 2000500 1500 350030002500 Shear Strain (με) 0 5 10 15 20 25 30 45 35 50 40 Lo ad (k /ft ) 0 1000 2000500 1500 350030002500 Shear Strain (με) 0 5 10 15 20 25 30 45 35 50 40 Lo ad (k /ft ) 0 1000 2000500 1500 35003000 40002500 Shear Strain (με) 0 5 10 15 20 25 30 45 35 40 Lo ad (k /ft ) 0 2000 40001000 3000 8000700060005000 Shear Strain (με) 0 5 10 15 20 25 30 45 35 50 40 Lo ad (k /ft ) 0 5 10 15 20 25 30 45 35 50 40 Lo ad (k /ft ) 0 2000 40001000 3000 5000 Shear Strain (με) 0 2000 40001000 3000 5000 Shear Strain (με) 0 5 10 15 20 25 30 35 40 Lo ad (k /ft ) Figure 134. (Continued).

166 shear friction is assumed to be coincident with the external shear force. However, the experimental observations showed that shear slip frequently occurred in the direction reverse to that which is customarily assumed. It is useful to use Vector2 to more closely examine the cause of this experimental obser- vation and to assess its implications. Because shear slip at cracks is not considered when the MCFT is used, shear stresses along cracks are shown instead in this comparison. The shear stresses at crack surfaces were evaluated along a 30-degree line drawn from the inside face of the support for the east end of Girder 3. The resultant predicted stresses are given in Figure 135. For the load step, w = 30.15 kip/ft and the shear stresses along the crack are positive, while for the final load step, w = 35.64 kip/ft and most of the stresses are negative. The results of the analyses indicate that the lower part of the crack moved upward due to the anchorage of the significant prestressing force in the earlier load step. However, as the loading was increased, the Vt2 Experiment Vt2 Experiment West East ( j) G10 0 2000 40001000 3000 700060005000 Shear Strain (με) 0 5 10 15 20 25 30 45 35 40 Lo ad (k /ft ) 0 2000 40001000 3000 5000 Shear Strain (με) 0 5 10 15 20 25 30 35 40 Lo ad (k /ft ) Figure 134. (Continued). 0 10 20 30 40 50 60 70 80 -0.300 -0.250 -0.200 -0.150 -0.100 -0.050 0.000 0.050 0.100 0.150 0.200 Shear Stress (ksi) Y- Co or di na te (in ) 30.15 k/ft 35.64 k/ft 30° + Figure 135. Shear stress at crack.

167 shear force induced by the external force overcame the pre- stressing force and the direction of shear slip was reversed. Because Vector2 uses nonlinear elasticity theory, such accu- mulated plastic deformation is not addressed properly, which means that the reversed stress direction does not always indicate that the direction of shear slip deformation is reversed also. However, the prediction from the analyti- cal model indicates that the direction of shear slip has begun to reverse. Note that shear stress is in the traditional direction in the upper part of the web. 2.10.12 Strain Patterns Vector2 can also be used to predict the distribution of straining. The selected components are horizontal strain εx, vertical strain εy, principal compressive strain ε2, and shear strain γ for the east half of Girder 3 at the final load step, as shown in Figure 136. Figure 136(a) shows that the largest hor- izontal strain increases are mainly due to the applied bending moment and are located around mid-span. By contrast, as shown in Figure 136(b), the largest vertical strains develop in the midheight of the web near the end region and are due to diagonal tensions. This result is consistent with the data pre- sented in Section 2.9. Figure 136(c) shows that a compressive strut above the support has developed, and the strain in some parts of the strut have exceeded the peak strain. Thus, there has been softening due to lateral cracking. Figure 136(d) shows, as expected, that large shear strains develop near the end region due to the web-shear cracking. 2.10.13 Summary A nonlinear finite element program, Vector2, was used to predict the behavior of the test girders. This program uses the MCFT for modeling shear behavior and can be consid- ered to provide a complete MCFT prediction of the load- deformation response of the test girders. For these analyses, a modified Popovics expression was used for modeling the compressive stress-strain response for high-strength con- crete. Vector2 was shown to be very effective at predicting the strength, strain patterns, modes of behavior, and overall load-deformation responses of the test girders. Conse- quently, Vector2 could be used to study the shear behavior of HSC girders with properties other than those of the girders tested in this program and could be useful for subsequent parametric investigations. Vector2 was also used to predict the distribution of the elastic strains due to prestressing. Such values are useful for evaluating the total strain in the test girders in combination with the strains due to loading, as presented in previous sections of Chapter 2. (a) εx (b) εy (c) ε2 (d) γ Figure 136. Strain at final load step.