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

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185 4.1 Introduction This chapter summarizes all major observations and con- clusions from this project. The summary is not limited to an examination of the LRFD specifications, but covers all aspects of the design and behavior of the tests conducted and reviewed in this project. 4.2 Conclusions Four primary issues for normal-weight concretes with f c´ values up to 18 ksi were addressed by this research: (1) the validity of the angle for diagonal compression θ used in the LRFD tables; (2) the validity of the concrete contribution as controlled by the parameter β; (3) minimum shear rein- forcement requirements; and (4) maximum shear strength limits. The principal conclusions reached on those issues were as follows: • Issues (1) and (2): The LRFD tabular values for θ and β are safe to use for the design of members with f c´ up to 18 ksi. Similarly, the alternative shear design provisions that are incorporated for the first time in the fourth edition of the LRFD specifications are also applicable for the design of members with f c´ up to 18 ksi. • Issue (3): The minimum shear reinforcement requirements were valid for f c´ up to 18 ksi. • Issue (4): The maximum shear stress limit needs to be restricted to 0.18f c´ + vp unless the end region of the mem- ber is designed by strut-and-tie procedures or the end of the member is built integrally into its support. The research also found that use of the staggered shear design concept of the LRFD commentary should be discontinued. The foregoing principal conclusions are part of the more detailed conclusions that are presented below in Sections 4.2.1 through 4.2.11. These detailed conclusions are derived from the detailed observations and findings that were presented in Chapter 2. They are organized by subject headings that corre- spond to the associated topic heading in Chapter 2.Additional information on any of these conclusions can be obtained by referring back to the referenced section of Chapter 2. 4.2.1 Evaluation of LRFD Sectional Design Model by Shear Database (Section 2.2) This project began with an analysis of existing test data from a shear database that contained shear test results from 1,874 tests on reinforced and prestressed concrete members. The ratio of measured to LRFD-calculated shear strength, herein referred to as the “shear strength ratio,” was compared for these tests results and then used to examine the influence of several design variables on the shear strength ratio. From this review, the following primary observations and conclu- sions were made: 1. Concrete Compressive Strength: Through an examina- tion of the influence of concrete compressive strength on the shear strength ratio (Vtest/VLRFD), it was concluded that the LRFD Sectional Design Model was just as accurate and conservative for members cast with HSC as it was for members cast with normal-strength concrete. This con- clusion is considered to be equally valid for reinforced and prestressed concrete members, with and without shear reinforcement, and either precast or cast-in-place concrete members. 2. Maximum Shear Stress Limit: There was limited test data from which to evaluate the shear strength ratio for mem- bers containing very high levels of shear reinforcement. Nevertheless, the available data suggested that the higher shear design strength permitted in the LRFD specifica- tions is reasonable. 3. Minimum Shear Reinforcement: The test data suggested that the minimum shear reinforcement requirements in C H A P T E R 4 Conclusions

186 the LRFD specifications are appropriate for ensuring that the calculated nominal shear capacity of the member is achieved. 4. Size Effect in Shear: The Sectional Design Model contains a factor to account for the size effect in shear for members without shear reinforcement and in which the values for β and θ are a function of the spacing of the layers of crack control reinforcement. This approach was found from the existing test data to be effective at accounting for the size effect in shear. 5. Longitudinal Reinforcement Ratio: The shear strength ratio (Vtest/VLRFD) increases with increasing levels of longi- tudinal reinforcement. For members with very light amounts of longitudinal reinforcement, the LRFD provi- sions were somewhat unconservative. 6. Field Structures Versus Laboratory Structures: The types of members tested in laboratories do not well represent the types of structures built in the field. As a consequence, an evaluation of code shear design provisions purely through a comparison with prior experimental test data is insuffi- cient. The farther a design case is from the types of mem- bers tested in laboratories, the greater is the uncertainty that the accuracy of code provisions can be empirically determined from test data. Some of the primary differ- ences between field and laboratory structures are summa- rized below: i. Members in the field are typically slender (L/d > 10) and support distributed loads, while members tested in laboratories are typically stocky and support one or two point loads. ii. Members in the field are often large and continuous and contain flanges, while members tested in labora- tories are typically small, simply supported, and rectangular. iii. Members in the field typically contain shear reinforce- ment, while the majority of members tested in labora- tories do not contain shear reinforcement. iv. Members in the field are designed to fail in flexure, while members in laboratories are over-reinforced in flexure, often to extreme limits, in the regions of potential shear failure. v. Members in the field need to be designed for shear over their entire length, while members in laboratories are typically designed to fail in shear near supports. vi. For examining the validity of extending the LRFD Sectional Design Model to HSC, tests on large pre- stressed concrete members designed for low to very high levels of shear reinforcement are required. This conclusion, which resulted from the review of the large experimental shear database, was the impetus for the specific testing program conducted in this project. 4.2.2 Evaluation of LRFD Sectional Design Model by Girder Tests (Section 2.4.1) The following conclusions are made from Section 2.4.1: 1. The LRFD Sectional Design Model provided relatively accurate estimates for the shear capacities of the 63-inch deep bulb-tee girders that were tested in this research program and that had concrete strengths that ranged from 10- through 18-ksi concrete. This conclusion was valid regardless of whether straight, draped, or debonded strands were used in the girders. 2. A slight exception to the foregoing observation was that the LRFD specifications become slightly unconservative for members designed to resist shear stresses exceeding approximately v = 0.18f c´. This unconservatism was due to the funneling into the support of the diagonal compressive stresses above the support. That funneling led to local diagonal crushing and very high horizontal shear stresses at the interface between the bottom bulb and the base of the web. 3. Design of the end regions of a beam—including considera- tion of the consequences of using draped strands, debonded strands, and added deformed bar longitudinal reinforce- ment—had a significant effect on the overall shear strength of the girders.The use of draped strands,particularly strands that were distributed over the depth of the web of the girder in its end region, significantly improved the shear capacity and performance under service load levels of the end region. 4.2.3 Evaluation of Other Codes and Methods from Girder Tests (Section 2.4.2) The measured strengths of the test girders were also com- pared with capacities calculated by the AASHTO Standard Specifications, the program R2K, CSA A23.3-04, and the AASHTO simplified proposed specifications. The last of these are contained in the fourth edition of the LRFD specifications (2007) in Article 5.8.3.4.3, “Simplified Procedure for Pre- stressed and Nonprestressed Sections.” From those compar- isons, the following observations are drawn: 1. All four methods predicted the capacity of the test girders to an acceptable level of accuracy. 2. The strength ratios from the LRFD and CSA methods pro- duced very similar results, as was expected because both methods were derived from the MCFT and use the longi- tudinal strain at mid-depth to characterize the condition of the member in shear. 3. The AASHTO Standard Specifications method was the most conservative and had the lowest COV. The ratio of

187 the measured to code calculated nominal shear strengths ranged from 1.12 to 1.50. 4. The program R2K had the lowest average strength ratio. 5. The proposed simplified provisions provided a safe esti- mate of the capacity of all test girders that failed in shear. It was particularly conservative at predicting the capacity of Girder 5, which contained minimum shear reinforcement only. These provisions were intentionally more conserva- tive for lightly reinforced members to guard against serviceability and fatigue problems. For the above calculations, because the girders were sub- jected to uniformly distributed loads, the shear forces varied along the length of the span and each successive shear design region was designed for the shear force acting at the section in the middle of that region. If, instead, the staggered shear design concept of the LRFD commentary had been employed over the entire length of the member so that the member was designed for the lowest shear force in each successive shear design region, then it was observed that the shear capacities calculated by the LRFD, R2K, CSA, and simplified proposed provisions were somewhat unconservative. 4.2.4 Modes of Failure (Section 2.4.4) The capacities of the members were limited by yielding of shear reinforcement, localized diagonal compressive failure of the concrete, concrete horizontal shear resistance between the bottom bulb and the base of the web, shear slip resistance along cracks, bond strength of the reinforcement, the diago- nal compressive strength across a region of distributed crushing, or some combination of the above. The most brit- tle modes of failure were observed in the members designed to resist the higher shear stresses, and in those modes the fail- ure was precipitated by a sudden localized diagonal com- pressive failure or a horizontal shear-compression failure between the bottom bulb and the web. In those cases, there was an explosive compressive failure of the web and a large relative shear displacement between the bottom bulb and the web. More ductile shear failures were observed in members that contained light amounts of shear reinforcement and in which failures occurred away from the end region. The dis- cussion of modes of failure is presented in Section 2.4.4 and in Appendix 11. 4.2.5 Cracking (Section 2.5) Section 2.5 presented the measured cracking loads, crack angles, spacing of cracks, and crack widths. Measured values were compared with the shear cracking loads calculated using the AASHTO Standard Specifications, with crack angles calculated using Mohr’s circle of stress and the angles of diagonal compression calculated using the LRFD specifi- cations, and with the spacing of cracks predicted using the CEB-FIP model. Some of the key observations from those comparisons were as follows: 1. Typically web-shear cracks occurred very suddenly, along straight lines, and with a significantly loud “pop.” 2. The first web-shear crack usually occurred within a lon- gitudinal distance equal to the overall height of the mem- ber from the center of the support. The closer the crack was to the end of the member, the steeper was the crack angle as the effect of the longitudinal prestressing decreased as the end of the member was approached. 3. The angle of web-shear diagonal cracking in the first shear design region (a flexural region in the terms of Arti- cle 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 to 32 degrees, with an average angle of 27.8 degrees. 4. The angle of web-shear diagonal cracking was accurately predicted using Mohr’s circle of stress. 5. The angle of web-shear diagonal cracking in the first shear design region was typically a little steeper than the angle of diagonal compression calculated from Table 5.8.3.4.2-1 of the LRFD Sectional Design Model. Conse- quently, the LRFD method may overestimate the contri- bution of the shear reinforcement in this region unless there are significant shear stresses acting on the faces of the cracks. 6. The angle of potentially critical flexure-shear cracks can be upward of 60 degrees, which suggests that the contri- bution of the shear reinforcement by most codes of prac- tice is likely to be overestimated in flexure-shear regions. 7. The spacing of shear cracks in the web was on average about half the values predicted using the CEB-FIP expression for crack spacing. 8. The AASHTO Standard Specifications provided a rea- sonably accurate and somewhat conservative estimate of the web-shear cracking load,Vcw, even when the full value of fpc was used in the calculations. 9. First web-shear cracking was observed to occur at between 33 and 87 percent of the LRFD shear design stress. Values for first cracking can be a much lower per- centage of the shear design stress than would have been possible with the use of Standard Specifications because the LRFD specifications permit members to be designed for shear stresses up to 0.25f c´. 10. The AASHTO Standard Specifications marginally over- estimated the flexure-shear cracking loads Vci. 11. The flexural cracking loads were reasonably well pre- dicted by Mcr when the tensile cracking stress was taken as (in psi units).7 5. ´f c

188 12. Upon initiation of web-shear cracking, the first measured web-shear crack width ranged from 0.012 inch (0.3 mil- limeter) to 0.02 inch (0.5 millimeter). The initial crack widths were larger for members with less shear rein- forcement. 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. 4.2.6 Reinforcement Strains (Section 2.6) The strains in the transverse and deformed bar longitudi- nal reinforcement of the test girders were extensively meas- ured. While it is recognized that the magnitudes of measured reinforcement strains highly depend on the location of a gage relative to the nearest crack, the measured strains are still use- ful for evaluating the demands on the test girders. For the measured strains, the following observations and conclusions were drawn: 1. Prior to first shear cracking, the strains in the stirrups were small and less than 30 microstrain, which corre- sponds to a stress of less than 1 ksi. 2. Immediately after occurrence of web-shear cracking, strains in some gages jumped to very close to the yield strain. With the development of additional web-shear cracks, similarly large jumps in stirrup strains were observed. 3. There was a dramatic variation in strain in some stir- rups, with a gage near a crack measuring strains greater than the yield strain, while gages farther from the same crack measured less than 100 microstrain (<5 percent of yield). However, prior to failure, yielding progressed until it extended over the height of the stirrups in the field of web-shear cracking. 4. For members with the least amount of shear reinforce- ment, ρvfy, the increase in stirrup strains at the onset of web-shear cracking and the strains prior to failure were the largest, and in some cases were greater than 10,000 microstrain. By contrast, the members with the largest amount of shear reinforcement failed when the maxi- mum stirrup strains were only slightly beyond yield or somewhat less than yield. 5. 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 maxi- mum web-shear stirrup strains in the ends of the same girders where the strands were straight. 6. As with the development of web-shear cracking, there was a rapid increase in stirrup strain following the for- mation of flexure-shear cracking, with strain values that approached the yield strain being measured immedi- ately 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 gages showing strains close to the yield strain, with an increase in loading of around 10 to 15 percent. 7. Within the flexure-shear region, the farther a stirrup was from mid-span, the larger was the shear, the flatter was the flexure-shear crack, and the larger was the magnitude of the stirrup strains. 8. Even when strains in the stirrups in the flexure-shear region were well above failure, there were no signs of impending failure. 9. In general, the strains in the stirrups 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. 10. The very large longitudinal reinforcement strains that were measured near the support, as reported in Section 2.6, indicate that the tensile force demands specified by LRFD S5.8.3.5 are very real and need to be resisted by appropriately detailed longitudinal reinforcement. 11. The significant levels of straining measured in the con- finement cages indicate that those cages provided signif- icant confinement for the anchorage of the prestressing strands. 4.2.7 Mechanisms of Shear Resistance (Section 2.7) 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 indicated that the amount of stirrup reinforcement had a significant effect on the concrete contribution, and this suggests that the level of resistance provided by interface shear transfer is influenced by the amount of shear reinforcement provided. This finding is consistent with what would be suggested by the MCFT in that crack opening stiffness affects slip resistance. In the LRFD method, the effect of the transverse reinforcement on crack opening stiffness is neglected in an effort to provide a hand- based design procedure. The assumptions made in this deri- vation are shown by the test results to be conservative. A complicating factor in the assessment of Vc is understanding what portion of this resistance is provided by the uncracked

189 compression zone at the top of the member and by the bottom bulb. 4.2.8 Interface Shear Transfer (Section 2.8) Eighteen interface shear transfer experiments on HSC specimens were conducted to evaluate the safety of the expression for interface shear transfer resistance that is used in the MCFT. The results illustrated 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 millime- ters) in most cases tested. The results also indicated that the current provisions of the LRFD specifications for interface shear transfer in S5.8.4 are conservative. 4.2.9 Behavior of End Regions (Section 2.9) The distributions of strains and deformations in the end regions were measured using the Krypton Coordinate Mea- surement Machine and concrete surface strain gages, as described in Section 2.9. The initial examination of this test data resulted in the following observations and conclusions: 1. The vertical straining increases from the support to a maximum at a distance approximately equal to the depth of the member from the support. This result con- firms 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 first critical section. 2. An inspection of the horizontal strain distributions at the base of the girder indicated that a significant increase in the horizontal strain at a horizontal distance of 20 inches from the support preceded 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 typi- cal girder. 3. The distribution of the diagonal tensile strains illustrated that there was very little diagonal tensile strain in the top of the web near the support. This result is consistent with other experimental test data, such as the observation that there is little cracking in this region because forces are flowing directly into the support via strut action. 4. The results from the concrete surface strain gage read- ings indicate that there can be a twofold increase in the compressive strain from the top to the bottom of the strut that runs to the support. This observation is con- sistent with the observed pattern of cracking that also illustrated a funneling of the compression to the sup- port. The effect of using draped strands was to decrease the magnification of the compressive strains. 4.2.10 Capabilities of Finite Elements Methods (Section 2.10) The program Vector2, which is a two-dimensional con- tinuum analysis tool that fully implements the MCFT, was used to predict the overall strength, load-deformation response, mode of failure, and distribution of strains in each of the test girders. A comparison with the test data was made to both assess the accuracy of the MCFT and evaluate whether Vector2 can be used to reliably predict the response of somewhat similar members that were not tested in this research program. Vector2 was able to predict the capacity of the test girders to within 10 percent. Although Vector2 typically somewhat overestimated the capacity, the COV of the shear strength ratio with Vector2 was only 0.08. Vector2 was also able to well predict the overall load-deformation response, but generally underestimated the stiffness of these girders. There was gen- erally good agreement between the predicted and measured cracking loads, locations, and angles. Vector2 also proved to be effective at predicting the test girders’ observed mode of failure. Vector2 frequently overestimated the length of the region of elastic shear stress versus shear strain response, but did reasonably well at predicting the stiffness of the inelastic portion of this response. Vector 2 was able to predict the reverse direction of shear slip that was observed at the base of the web near the support. It was generally effective at predict- ing distributions of horizontal, vertical, and principal strains. The relatively good agreement between the behavior of the test girders and the predictions of Vector2 indicate that the MCFT is an effective model for capturing the complexity of the behavior of these test girders and that Vector2 can be used for providing reliable analytical predictions for the behavior of similar types of structures. This finding may be particularly useful if there is concern about the applicability of the LRFD Sectional Design Model for the many design situations in which there is little experimental test data. 4.2.11 Miscellaneous Conclusions The following miscellaneous conclusions were made: 1. Shear cracking has little effect on the overall load- deformation response of the test girders (Section 2.4.5). 2. The LRFD expression for longitudinal strain at mid-depth provides a rough estimate only of the actual straining at

190 the mid-depth of the first critical shear design section (Section 2.6.7). 3. The shear stress versus shear strain response can be characterized as a tri-linear relationship consisting of one line to represent the stiffness prior to cracking, another line to represent the stiffness between shear cracking and yielding of the shear reinforcement, and a third line to represent the stiffness between yielding of the shear rein- forcement and when the ultimate capacity is reached. Post cracking stiffness values can be predicted based on the modular stiffness ratio of the concrete and the reinforce- ment and the percentage of shear reinforcement used in the girder. 4.3 Background Statement to Suggested Research There is an underlying and simple model for calculating axial and flexural capacities such that test strengths can usu- ally be predicted to within 10 to 20 percent regardless of the size of the member or material strengths. By contrast, there is considerable debate about (a) how best to design members for shear, (b) what maximum and minimum shear stress design limits are appropriate, and (c) what factors influence shear capacity. This debate is further complicated by the com- plex flow of forces in end regions. The only aspect of shear behavior upon which there is international agreement is the use of the parallel chord truss model for evaluating the contribution of transverse reinforcement to shear capacity. However, there is no inter- national agreement on the appropriate angle for diagonal compression in this truss, the appropriate way to calculate the shear depth of the truss, and the appropriate way to characterize the contributions of concrete to shear resist- ance in a flexural member. The developments of the Com- pression Field Theory and the subsequent MCFT have been among the most significant advances in modeling shear behavior in the last 100 years. However, these approaches can be fully implemented only in two-dimensional contin- uum analysis tools, and, even then, there are uncertainties as to how best to predict crack spacing and crack width and how to evaluate interface shear transfer resistance. Further- more, the methods fail to account for shear slip along cracks, as is now done in the Disturbed Stress Field Model; therefore, their application to structures without well- distributed reinforcement in two directions is debatable. For the purposes of structural design, the challenge has been how to use the MCFT for the design of typical struc- tures such as the flexural members examined in this study. In flexural members, there can be both a linear and a non- linear variation in strain over the depth of the member, and there are significant top and bottom flanges that restrain the deformations of the web. These effects are combined with the effects of a concentrated prestressing force. The LRFD Sectional Design Model was carefully derived from the MCFT, but the assumptions necessary to develop the hand-based sectional design procedure, and its potentially wide range of applications, limit the general applicability of the method. The shear provisions for the bridge and building codes of practice in the United States differ from those in other nations. The differences include ways in which the contribu- tion of the transverse reinforcement is evaluated by different methods, as well as the calculated concrete contributions to capacity and to the maximum shear design stress limits. Researchers also differ on the mechanics of shear resistance. These differences in codes and among researchers, especially the very large differences in codes, are a cause for considerable concern. Because the test data upon which provisions are val- idated does not well represent the types of structures built in the field, the true capacity of members in the field is unfortu- nately relatively uncertain. The life safety issues raised by this uncertainty suggest that systematic efforts should be under- taken to determine how best to design members for shear. Those efforts should continue until researchers agree on a method for calculating the nominal shear strength that can provide predictions within 20 percent of the measured shear strengths, as validated by comprehensive, weighted, and extensive test data. Current research practices, in which sev- eral hundred uncoordinated shear tests on structural concrete members are conducted each year, most of which are on members not representative of those used in practice, will not necessarily answer the life safety questions raised by the shear design issue. 4.4 Suggested Research and Changes to the Code Development Practice Based on the review of experimental research and familiar- ity with how changes to code provisions are made, the follow- ing suggestions are made for new directions in experimental research on shear strength and the development of code shear provisions: 1. It is estimated that there have been between 6,000 and 10,000 shear tests on beams, but few of these results are ever used by researchers in the design of a research pro- gram or by members of code committees in the extension of shear provisions. Thus, there is the need for a national and/or international database of test results that is fully maintained and available to the research, design, and reg- ulatory communities. The creation of this database will require the development of, and agreement upon, standards

191 for test data acceptance. Such standards must define the checks necessary against anchorage failures and flexural failures, as well as those needed to ensure that proper boundary conditions were provided. 2. This experimental database needs to be compared with the types of members built in the field and the results used to set a national agenda for the types of experiments that are required. It is anticipated that 90 percent of the tests currently conducted each year are redundant, adding little to the collective understanding of shear behavior. As pre- viously stated, most shear tests in laboratories are on small members (<18 inches overall depth) that have rec- tangular cross sections, are stocky, are loaded at one or two points, are simply supported, are over-reinforced in flexure, and are designed to fail within one or two effec- tive depths from the end of the member. By contrast, most members in the field are large, support distributed loads at the time of maximum shear loading, and are designed for shear over their entire length. Furthermore, many of these members have flanges, are slender, and are continu- ous over supports. 3. New standards are required for material testing to be done in conjunction with large-scale shear tests. This testing needs to include the measurement of the compressive response, tensile strength, and fracture characteristics of the concrete, and the full stress-strain relationships of all reinforcing materials. 4. A new standard is needed for ensuring appropriate sup- port conditions in test set-ups. This need is illustrated by the difficulties apparent in the test girders in the funneling of the compressive forces into the end supports. Standards need also to be established for the measurements of load, displacements, and strains. 5. It would also be useful to establish a program that enabled the testing to failure of more realistically sized and loaded members that are not well represented in the experimen- tal database of laboratory test results. This would lead to a better assessment of the conservatism and safety concerns with present codes. It is expected that these tests would be on structures being removed from the field, members that are rejected for use in the field, or unused inventory from producers.