Simplified Shear Design of Structural Concrete Members (2005)

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CHAPTER 2 FINDINGS In accordance with the research approach, a review and evaluation was conducted of existing models and approaches for shear design. This study revealed that there are dramati- cally different methods and bases for shear design provi- sions. In Section 2.2, a comparison of relationships used in codes and suggested by researchers is made. This led to the identification of positive attributes of different shear design methodologies. Section 2.3 presents an evaluation of the accuracy of prominent shear design provisions. Section 2.4 presents the results of a survey conducted to evaluate the experience of practitioners in using the LRFD Sectional Design Model and the AASHTO shear design provisions. Using the findings from Sections 2.1 through 2.4, criteria were developed for the simplified provisions. See Section 2.5. This led to the development of the proposed changes to the LRFD Sectional Design Model and the Proposed Simpli- fied Provisions presented in Chapter 3. Chapter 2 summarizes the findings. More comprehensive results are presented in the following appendixes: • Appendix A: Models for Shear Behavior • Appendix B: Shear Design Provisions • Appendix C: Shear Database • Appendix D: Evaluation of Shear Design Provisions • Appendix E: Field Performance Data and Practitioner Experience • Appendix F: Recommended Revisions to Shear Provi- sions of AASHTO LRFD Concrete Provisions • Appendix G: Evaluation of the Proposed Simplified Provisions with Selected Shear Database • Appendix H: Examination of Proposals Using Design Database • Appendix I: Utilization of NCHRP Process 12-50 • Appendix J: Examples of Shear Design These appendixes are available in NCHRP Web-Only Document 78. 2.1 DIFFERENCES IN UNDERLYING BASES OF CODE PROVISIONS As discussed in Chapter 1, the 100-year-old parallel chord truss model is the predominant model for describing the flow of shear forces in a reinforced or prestressed concrete beam. 20 There is also general agreement in the research community that the concrete contribution to shear resistance results prin- cipally from a combination of interface shear transfer across cracks in the body of the beam and shear in the compression zone. However, because of the many different ways used to calculate the angle of diagonal compression and the many factors influencing interface shear transfer and shear transfer in the compression zone, the existing forms of shear design provisions differ greatly. For example, in determining the angle of diagonal com- pression it is traditional U.S. design practice to assume a 45-degree angle because this approach has been considered to always lead to conservative designs. By contrast, in Euro- pean practice the angle of diagonal compression is taken as low as 18 degrees while in the LRFD Sectional Design Model this angle is determined by considering the calculated longitudinal strain at mid-depth of the member. These different approaches for determining the contribution of the shear reinforcement then lead to different approaches in calculating the concrete contribution to shear resistance because Vc = Vtest − Vs. Before presenting and discussing the different shear design relationships in codes of practice, it is useful to fur- ther classify shear design approaches by the information on which they are based: empirical test data, an equilibrium model for the condition of a beam in its ultimate limit state, a comprehensive behavioral model for shear resistance, or some combination of the above. Relying on each of these three types of information has its advantages and limitations as discussed below. 2.1.1 Type 1: Empirical Relationships Designed to Fit Test Data Empirical provisions are those based primarily on experi- mental test data. Because of the complexity of how shear is carried in structural concrete and the lack of a universally accepted model for shear behavior, this approach has many clear advantages. No consensus is needed from any commit- tee and no selected model for behavior will bias the resulting provisions from accounting for the complexity of shear behavior. The primary problem with this empirical approach is the deficiencies in the experimental test data that are available

and therefore used in developing the resulting empirical approaches. As will be discussed in Section 2.3, there are large deficiencies in what has been tested experimentally; most experiments have been on small, rectangular, simply supported members that are over-designed in flexure, loaded by one or two point loads, and supported on bearings posi- tioned underneath the member. In addition, most tests have been on members that do not contain shear reinforcement. By contrast, most members in practice are continuous and large, have top flanges, contain shear reinforcement, are acted on by distributed loads, and are built integrally into supports at their ends. Because what has been tested does not represent what is designed with provisions, there is no reason to believe that empirically derived provisions will provide a reasonable and conservative design procedure for members that fall outside the range of the experimental database used in developing the empirical provisions. This fact was illustrated in Section 1.2.4 where new types of tests illustrated that the effect of depth, concrete strength, and axial effects were not reasonably accounted for in traditional U.S. design practice. A further complication is that only a limited selection of experimental test data has previously been available to code committees in developing or validating empirical design approaches. The database effort being led by Professors Reineck and Kuchma is attempting to overcome this problem by assembling most of the published test results. A remain- ing challenge is in selecting which test results to use in eval- uating provisions because even within the narrower range of what has been tested there is a bias toward members of par- ticular types. Furthermore, not all tests are equally reliable and those classified as shear tests may actually have included beams failing in flexure, because of anchorage failures, or tests deficient in their setups or members deficient in their detailing. Therefore, to use this database effectively for developing shear provisions, a means of selecting and weighting test data still needs to be developed. An example of provisions that are effectively empirical is the AASHTO standard provisions for reinforced concrete mem- bers. These provisions are empirical because the angle of diag- onal compression is assumed to be 45 degrees and because the concrete contribution is taken as the diagonal cracking strength which is not physically related to the concrete contribution at the ultimate limit state. It is only through validation with exper- imental test data that these provisions can be justified as effec- tive. The AASHTO standard provisions are not based on a fully consistent mechanistic model of shear behavior 2.1.2 Type 2: Relationships Based on Specific Condition of Member in Its Ultimate Limit State Design provisions may also be based on the condition of a member in its ultimate limit state. In this approach, there is one equilibrium diagram showing all of the forces that act on a given section. This is a very powerful approach because it 21 enables the designer to consider the differing contributions of the various mechanisms of resistance to shear capacity and the factors that can influence these mechanisms of resistance. There are two principal shortcomings with this approach. First, in developing this equilibrium diagram, many assump- tions are made that cannot be fully substantiated. For exam- ple, it is typical that these approaches focus on only one of the multiple mechanisms of resistance (e.g., shear in compression zone, interface shear transfer, dowel action, arch action, and direct transmission of tensile stress across cracks) that exist. Second, these approaches then assume that mechanism is the dominant mechanism for all loading and material conditions. No single equilibrium diagram can capture accurately the crit- ical condition for all types of members at any point along the design span and for any combination of loading. A further complication is that the experimentally measured concrete contribution to shear resistance used to calibrate this type of model also requires an assumption for the angle of diag- onal compression to be used in calculating the concrete contri- bution to shear resistance. Thus, the concrete contribution to shear strength Vc cannot be clearly established by this approach. Although the angle of cracking may seem to be a clear indicator of the direction of diagonal compression, many researchers contend that substantial shear stress is transferred across these shear cracks with the effect that the true angle of diagonal compression is typically smaller than the angle of diagonal cracking. In NCHRP Project 12-56, shear tests on large bulb-tee girders were conducted from which the angle of diagonal compression was often somewhat larger than the angle of diagonal cracking near the end regions of members because of the introduction of the large anchorage force from the strands. A further complication is in counting how many stirrups cross the line of diagonal compression. Some researchers argue that cracks often do not cross stirrups and are likely to run from the top of one stirrup to the base of another. Thus, these researchers propose that the number of stirrups that should be considered to cross the plane of equi- librium in these models should be taken as dvcotθ/s − 1. To describe more accurately how shear is carried, some of these provisions provide two different relationships for Vc, one for members with shear reinforcement and one for mem- bers without shear reinforcement. The truss model with crack friction is an example of a model based on an equilibrium diagram of a member in its ultimate limit state. Additional information on this method is available in Appendix A, which is included in NCHRP Web- Only Document 78. 2.1.3 Type 3: Relationships Derived from Comprehensive Behavioral Model The strength of this approach is that it is based on a com- prehensive behavioral model of the beam. This approach has the potential to capture the true complexity of shear behav- ior in which the angle of diagonal compression is calculated

based on the calculated stiffness characteristics of the mem- ber, in which all mechanisms of resistance can contribute to carrying shear, and in which failure by breakdown of one or more mechanism of resistance can be considered. There are three principal shortcomings of this approach. First, there are the shortcomings of the behavioral model itself. Second, the development of a hand-based design pro- cedure from a comprehensive behavioral model requires many simplifications and can result in significantly reduced reliability of the model. Third, to fully understand the provisions requires an understanding of the underlying com- prehensive behavioral model and that may be beyond the interests of most design engineers. The LRFD Sectional Design Model is an example of shear provisions that have been implemented in codes of practice derived from a comprehensive model for behavior. This design procedure was described in Section 1.1. The potential shortcomings of the MCFT and the effect of assumptions made in deriving the LRFD Sectional Design Model on the effectiveness of these provisions are described below. The MCFT is a smeared crack model for predicting the complete response of diagonally cracked concrete to in- plane shear and membrane stresses as shown in Figure 6. Because the effect of cracking is smeared, it does not attempt to model the development of individual discrete cracks. If the behavior of a member is dominated by the development of a single discrete crack, then an approach based on fracture mechanics (50) may be more appropriate. It is also a rotating angle crack model that assumes that the direction of cracking will rotate as the orthotropic stiffness characteristics of the element change over the loading history of the element. Research results suggest that this will only occur after very significant changes in relative stiffness characteristics; little to no crack rotation was observed in the girders tested as part of NCHRP Project 12-56. The evaluation of the angle of diagonal compression in the MCFT was made possible by the assumption that the angle of diagonal compressive stress coincided with the angle of diagonal compressive strain. This has also been experimentally observed to be an approxima- tion and the Disturbed Stress Field Model by Vecchio in 2000 (39) was developed to account for the difference in 22 these angles by considering slip deformations along crack interfaces. Furthermore, the MCFT was derived from experiments on elements or panels in which there was a uniform distribution of stress across the width of the test specimens. By contrast, the LRFD Sectional Design Model is permitted by the LRFD specifications to be used for the design of end regions of members for which there is a very non-uniform distribution of stress and in the design of members that can have upper and lower flanges that are very stiff relative to the web and restrain the deformations of the web. These effects can lead to (1) unconservative results because of the additional stresses created by funneling the diagonal compressive stresses into the supports or (2) conservative results because of the restraint of the web deformations by the flanges. Determining internal stresses in an element corresponding to a particular state of stress (vxy, fx, fy) by the MCFT is a mul- tistep and highly iterative process. By contrast, the comple- tion of a shear design by the LRFD Sectional Design Model is a comparatively simple hand-based procedure. Developing this hand-based procedure from the MCFT required several assumptions. Predicting the full effect of these assumptions is beyond the scope of this project but a few simple observa- tions follow: 1. In a multilayer sectional analysis, such as conducted using Response 2000, the longitudinal strain varies over the depth of the member. When the MCFT is then used to calculate the shear stress at each level, the distribu- tion of shear stress over the depth of the member varies. By contrast, in the LRFD Sectional Design Model the shear stress is assumed to be constant over the depth of the member and only the calculated longitudinal strain at mid-depth, εx, is used in calculating its value. If this shear stress at mid-depth is similar to the average stress over the depth of the member, as would be predicted by a multilayer analysis, then the effect of this assumption is minimal. See Figure 18. If that is not the case, the effect can be significant. 2. In the derivation of the LRFD Sectional Design Model, the stress-strain relationship in concrete is dv dv εv 2 Figure 18. Shear stress distribution.

assumed to be parabolic with a strain at the peak stress of −0.002. This assumption is not consistent with the stress-strain behavior of high-strength concrete where the strain at peak stress can exceed −0.003 for an 18,000 psi concrete. 3. In the derivation of the LRFD Sectional Design Model for members with shear reinforcement, the average crack spacing was assumed to be 12 inches. This value was used in calculating the crack width (crack spacing × principal tensile strain
1) from which the resistance to crack slip was determined. This affected some of the values of β and θ in Table 1. Given that a conserva- tive (larger than typical) value for crack spacing was assumed, this approach was considered to lead to a con- servative estimate of shear capacity. 2.2 COMPARISON OF SHEAR DESIGN METHODS The approach used in this research was to derive the simplified design provisions after a thorough review and evaluation of current code provisions and other relationships proposed by researchers. The following shear design proce- dures were selected as the most useful for providing poten- tial direction for the simplified provisions to be developed in this project: • ACI 318-02; • AASHTO Standard Specifications 16th Edition; • AASHTO 1979 provisions; • CSA A23.3-94 (Canadian Standards Association: Design of Concrete Structures, 1994); • AASHTO LRFD Bridge Design Specifications 2nd Edition; • CSA A23.3-04; • Eurocode EC2, Part 1(1991), Eurocode EC2 (2003); • German Code (DIN, 2001); • AASHTO Guide Specification for Segmental Bridges (ASBI); • The Japanese Code (JSCE Standards, 1986); and • The shear design approach recently developed by Tureyen and Frosch. These shear design procedures are summarized in Appen- dix B, which is included in NCHRP Web-Only Document 78. In this section, a comparison is made of how Vc, Vs, Vn,max, and Av,min are evaluated. See Table 3. To compare these provi- sions, relationships have been modified when possible in order to use LRFD nomenclature and psi units. Based on the comparison of design formulas presented in Table 3, and from consideration of the underlying bases for these expressions, the following observations were made. (A focus on the attributes of each design approach was consid- ered important for the selection and development of the pro- posed simplified provisions.) 23 1. The changes incorporated in the 2004 Canadian Stan- dards Association Code for the Design of Concrete Structures, CSA A23.3-04, greatly simplify the proce- dure for the design of concrete structures using an approach functionally identical to the LRFD Sectional Design Model. In the CSA A23.3-04, the following sig- nificant changes were made: (a) The tables for calculat- ing β and θ were replaced by simple formulas that are easy to remember. See Equations 12 and 13. where for members with Av < Av,min (Eq. 12a) for members with Av ≥ Av,min, note sxe = 12 inches (Eq. 12b) (Eq. 13) (b) A further simplification is that the iterative means of calculating β and θ is eliminated by assuming that the angle θ is equal to 30 degrees in the evaluation of
x. Thus, Equation 1-6 is simplified to Equation 14. (Eq. 14) However, the procedure for analyzing the shear capac- ity remained iterative given that the longitudinal strain is a function of the shear design force. The combina- tion of these two changes greatly simplifies the design procedure to the extent that the use of the Sectional Design Model in CSA A23.3-04 is at least as simple, if not simpler to use, than the AASHTO standard method. The reality of this observation is apparent in the design examples of Appendix J (included in NCHRP Web- Only Document 78). 2. In ACI 318-02, AASHTO standard and ASBI, the cal- culated value for Vc is an estimate of the diagonal crack- ing load. This approach was considered useful for both assessing the condition of a member in the field and for checking whether or not the member was expected to be cracked in shear under service loads. It was also thought that independent consideration of the two types of diag- onal cracking, web-shear and flexure-shear, as used in ACI 318-02 and the AASHTO Standard Specifications, was useful for characterizing shear behavior and for visualizing the effectiveness of the shear reinforcement. 3. The AASHTO LRFD specifications require a larger minimum amount of shear reinforcement than most other codes. This requirement was examined using the results of the experimental database of test results.

x t u v u u p ps po s s p ps M d N V V A f E A E A = = + + − − +2 0 5 2 / . ( ) θ= +29 7000
x β = + 4 8 1 1500 . ( )
x β = + + 4 8 1 1500 51 39 . ( )( )
x xes

24 TABLE 3 Comparison of different design approaches (units: psi, in, lbs)

25 4. The CSA A23.3-04, AASHTO (1979), AASHTO LRFD, Truss Model with Crack Friction, Eurocode 2, JSCE, and DIN all enable the designer to use an angle of diagonal compression flatter than 45 degrees when evaluating the contribution of shear reinforcement to shear capacity. 5. AASHTO LRFD, DIN, and Eurocode 2 allow the engi- neer to design a member to support a much larger shear stress than permitted in other codes of practice. This shear stress limit is intended principally to guard against diagonal compression failures. In the AASHTO LRFD, the shear design force limit is 0.25f ′c plus the vertical component of the prestress, while in ACI 318- 02 the limit is approximately plus the vertical component of the prestress when the web-shear crack- 12 ′fc TABLE 3 (Continued)

ing shear Vcw governs. (Example, when f ′c = 10,000 psi, the LRFD stress limit is 2,500 psi while the AASHTO Standard Specifications limit is 1,000-1,400 psi). Although the authors have concluded that the LRFD stress level is sufficient to prevent web crushing in regions where there is a uniform field of diagonal com- pression, they are concerned that this limit may be unconservative near supports where there is a signifi- cant magnification of the stress as the diagonal com- pression funnels into the support. 6. The approach by Tureyen and Frosch is not sufficiently mature for the complete design of reinforced through prestressed concrete members of all shapes and load- ings. In addition, this approach is a significant depar- ture from how most of the research community views the transfer of shear, even in web-shear regions. Since the publication of this method, members of the research community have responded with experimental evi- dence that suggests that for beams with shear rein- forcement most of the shear carried by the concrete could not be transmitted in the uncracked compression zone suggested by Tureyen and Frosch. 2.3 EVALUATION OF SHEAR DESIGN METHODS USING TEST DATABASE To evaluate the accuracy of different national codes of prac- tice, a large experimental database was used to evaluate the shear strength ratio (Vtest /Vcode) for six different Codes for 1,359 selected beam tests results. Following a brief description of the experimental database, the results of this evaluation are summarized. More detailed information on the database and an evaluation of Codes is presented in Appendixes C and D, which are part of NCHRP Web-Only Document 78. The 1,359-member database consists of 878 reinforced concrete (RC) and 481 prestressed concrete (PC) members. 26 These members were selected from the larger shear database so that members in which significant arch action or flexural failures were suspected were removed from the database. Most of the RC members had rectangular cross sections and were simply supported using bearings positioned underneath the member. Of these, 718 did not contain shear reinforce- ment and 160 did. The PC members consisted of rectangular, T-shaped, and I-shaped sections and most of the members were simply supported, again on bearings positioned under- neath the member. Of these, 321 did not contain shear reinforcement and 160 did. About 80 percent of both the members in the RC and PC components of the database had depths less than 20 inches. Table 4 presents an examination of the Shear Strength Ratios (Vtest /Vcode) and Coefficients of Variation (COV) for ACI 318-02, AASHTO LRFD Bridge Design Specifications (2001), CSA A23.3-04, JSCE Code (1986), Eurocode EC2 2003, and the German Code (DIN, 2001). The code calcu- lated strengths are nominal capacities and therefore all resis- tance and strength reduction factors are set to 1.0. As a result, the calculated strengths by ACI 318-02 would be equivalent to the calculated strengths by the AASHTO Standard Speci- fications (16th edition). In this table, the mean and COV are presented for seven segments of the database, all members, all RC members, all RC members without shear reinforce- ment, all RC members with shear reinforcement, all PC members, all PC members without shear reinforcement, and all PC members with shear reinforcement. From Table 4, the following observations can be made: • The AASHTO LRFD and CSA approaches were best able to predict the capacity of the members in this data- base. The mean of the strength ratios for both of these approaches was very consistent across the different cat- egories of selected members and of a value (1.19−1.46) that would be expected to result in conservative designs TABLE 4 Code assessment for RC and PC members

that made reasonably efficient use of shear reinforce- ment. The small COV was particularly impressive for PC members with shear reinforcement. • The close correlation between the means and COV for the AASHTO LRFD and CSA methods indicates that these two methods would yield similar designs in terms of the amount of required shear reinforcement. As a result, it is concluded that the equations for calculating β, θ, and
x in CSA A23.3-04 are reasonable replacements for the tables and the old equation for
x of AASHTO LRFD that could result in an iterative design approach. • Although the overall COV for the ACI (AASHTO Stan- dard Specifications) approach is about 40 percent greater than the least overall COV, this results princi- pally from the poor performance of these design provi- sions in predicting the capacity of RC members that do not contain shear reinforcement. Both the mean and COV of the ACI (AASHTO Standard Specifications) method for RC and PC members with shear reinforce- ment were quite good. Regarding the prediction of RC members without shear reinforcement, given the mea- sured shear capacity of many of the members, the ACI (AASHTO Standard Specifications) approaches would frequently have required designs with minimum shear reinforcement because of the rule that Av,min is required when Vu ≥ φ Vc / 2. • The JSCE code was somewhat better than the ACI (AASHTO Standard Specifications) approach at calcu- lating the shear strength of RC members, but very con- servative at calculating the shear strength of prestressed concrete members. This conservatism results from a limitation in the Japanese code of only doubling Vc due to the effect of prestressing and because a 45-degree 27 parallel chord truss model is used in calculating the con- tribution of the shear reinforcement. • Both the EC2 and DIN Codes were considerably less successful in predicting the capacity of members in the shear database. There was a surprisingly large variation in the means across the different categories of members. This large database of shear test results is also useful for examining minimum required amounts of shear reinforce- ment in codes of practice. In Figure 19, the shear strength ratio (Vtest /VAASHTO-STD) is examined for reinforced concrete beams that contain reasonably light amounts of shear rein- forcement. The results illustrate that traditional amounts of minimum shear reinforcement, ρv fy = 40-60 psi, were insuf- ficient to ensure that code provisions were conservative. This illustrates why the larger amounts of minimum shear rein- forcement required by AASHTO LRFD Sectional Design Model are appropriate. This database is also useful for evaluating the maximum shear stress design limit. The LRFD Sectional Design Model enables the design of members for up to 2.5 times the maxi- mum shear design stress permitted in the AASHTO Standard Specifications. Figure 20 reveals that the AASHTO Standard Specifications are unduly conservative. However, the authors are concerned that the LRFD limit of 0.25 f ′c may be too high. As observed in NCHRP Project 12-56, in the end regions of prestressed concrete bulb-tee girders, the funneling of the diagonal compressive stresses into the support results in stresses that are significantly higher than those assumed in the LRFD Sectional Design Model which was developed for regions of members in which the diagonal compression field is parallel. However, most available test results are for beams simply supported on bearings positioned underneath the 0.00 0.50 1.00 1.50 2.00 2.50 3.00 0 5000 10000 15000 40-60 psi 60-80 psi 80-100 psi 100-120 psi 120-140 psi > 140 psi ACI test V V )(′ psif c Value yv fρ Figure 19. Strength ratio versus concrete compressive strength for RC members.

member. In many situations in practice, the ends of beams are built integrally at their ends into piers, columns, or diaphragms. The results of the beam tests conducted for NCHRP Project 12-56 demonstrate that higher maximum shear stresses can be achieved for that situation than for beams simply supported on bearings positioned underneath the member. 2.4 RESULTS OF SURVEY OF PRACTICE A survey of the design practices of 26 different state DOTs and federal lands bridge design agencies was conducted. This survey included both a written questionnaire and either a telephone briefing on the response to the questionnaire or a written response. Of the 26 agencies polled, 21 responded; these are listed alphabetically at the end of this section. The specific questions and the responses are included in Appen- dix E, which is part of NCHRP Web-Only Document 78. The questionnaire was to determine the status of conversion to LRFD, identify specific problems and practices with respect to concrete element shear design, ascertain preferences for shear design methodologies, and provide a vehicle for orga- nizations to express their opinion of the current LRFD shear design methodology. Some recurring themes and trends emerged. First, many of the organizations have not yet converted the bulk of their practice to LRFD, although most have undertaken serious in- house evaluation of the likely effects of conversion. In most cases, the in-house evaluators were interviewed and were the primary respondents to the Questionnaire. Only 7 of 21 had converted to LRFD for most of their bridges, even though a deadline for conversion has been set nationally. Conse- 28 quently, many organizations are actively beginning the conversion process, and thus are on, or just beginning, the learning curve with the LRFD Sectional Design Model (Section 5.8.3.3 of the LRFD specification). This is relevant because two camps of designers seem to exist: those that have become reasonably comfortable with the production of LRFD shear designs and those who view it as a significant hurdle yet to be surmounted. Although some users have become famil- iar with the mechanics of the method, almost universally designers report that the method is not easily executed by hand and that one often loses sight of the relative mechanics of what is happening in the structure. All agree that the LRFD shear design provisions must be automated with software to be used in production design. This fact naturally leads to loss of comfort with respect to checking designs, because the method cannot be readily executed by hand. Most designers also agree that the Standard Specification method for pre- stressed design (Section 9.20) that includes Vci and Vcw must also be automated to be effective in production work, even though that method is executable by hand. Thus, with the existing AASHTO LRFD provisions one of the most preva- lent comments was that designers are losing their physical “feel” for shear design because of the increasing complexity of the design provisions and the resulting automation. Most agencies using the LRFD shear provisions make no modifications or simplifications to the process before adop- tion into their design procedures, although many respondents indicated that they would if the simplifications were reason- able. The primary simplification that is being used by a few organizations is the elimination of the iterative process required to determine the crack angle, θ. Almost all respondents indicated that there had been some difficulty in applying the MCFT provisions and that often 0 10 20 30 40 50 0 500 1000 1500 2000 2500 Stirrup Strength, ρ v fy (psi ) Limit on Vn for RC members in AASHTO STD Limit on Vn for PC members in AASHTO STD (fpc/sqrt(f'c)=10, f'c=10000 psi) (f'c=10000 psi) V u test f 'c Figure 20. Test data and maximum shear stress limit.

difficulties also arose when applying the provisions to bent cap beams, columns, and footings. Difficulties in applying the strut-and-tie method were also commonly reported, par- ticularly for indeterminate beams. Furthermore, the potential for more than one shear design solution was perceived as a problem by about one-third of the respondents, although this was not seen as a significant problem by most. When asked whether the LRFD shear provisions produce significantly different designs than the Standard Specifica- tion method, the responses were mixed. Many were not sure yet, but about one-third indicated that more shear steel is often required, although the amounts of the increase were quite variable, with the high response being about 40 to 50 per- cent increases for bridges with large skews. This particular respondent also indicated that the demand side had as much to do with the increase as the resistance side, because the LRFD load combinations often produce larger design forces. Several respondents indicated that the revisions to the β and θ values incorporated into the second edition of LRFD helped bring the steel contents into parity with the Standard Specifications method. Regarding the use of the simpler 1979 AASHTO shear design procedure allowed by the Standard Specifications in a footnote to Section 9.20, about one-third indicated that they still used this method. Furthermore, they report that no prob- lems have apparently arisen from the continued use of the 1979 method. Nearly all the respondents indicated that a relative simple design method would be highly desirable, even if it was used for checking only. In fact, a simple checking method is one of the most requested items. Also, many designers recognize the advantages of the LRFD provisions for a more accurate evaluation of shear resistance. The LRFD shear provisions thus can often offset the increases on the demand side that are common with LRFD, though this tends toward less conserv- ative designs for shear. Most designers seem to prefer a palette of design approaches. If simple methods provide sim- ilar designs to more complex methods, the need to switch to the complex method is not felt warranted. Some would even prefer to include some of the older, tried and proven shear design methods as alternates. This would ease the ‘transition trauma’ associated with the LRFD learning curve. The most common types of concrete bridges appear to be prestressed concrete girder bridges, including those designed as simple spans for both dead and live loads and those made continuous for live load. Only a few respondents indicated a routine use of box girders and segmental construction. Most did not know of any cases where the LRFD shear design had eliminated a bridge type from consideration for a given proj- ect. However, one case of deeper girders being required when high skews were present was cited. For PC girder bridges, standard designs have been common in the past and are still desirable. However, standard designs have been difficult, if not impossible to achieve, with the LRFD shear procedures. 29 Most of the LRFD users thought that the engineering time for shear design is not significantly increased over that for the Standard Specifications, provided that shear design is auto- mated using spreadsheets, MathCAD, or other software. How- ever, if designs are attempted by hand, the design time is often significantly increased over that required by the Standard Spec- ifications. This is often a source of discontent when the effort is increased, but the results change very little. The discontent is reinforced by the fact that shear steel is not typically a signifi- cant cost relative to the entire bridge cost and by the fact that many designers prefer to be conservative for shear design. For the relatively common case of girders made continu- ous for live load, it is widely thought that the current LRFD provisions do not adequately explain the application of the method to this case. Problems seem to be particularly com- mon in the negative moment region. The problem of appro- priate use of simultaneously acting internal forces in the resistance equations is, however, not new to LRFD, although confusion seems to be worse with the LRFD shear design procedure. This confusion stems from the fact that cases arise in practice that are more complex than those envisaged dur- ing the development of the specifications, thereby producing confusion among designers. This problem is at least in part related to definitions, where common cases are not always clearly explained. Definition problems are compounded when confusion also arises over appropriate signs to be used for internal forces. The common themes in terms of the most important design issues can be synthesized into the following: (1) There should be a simple, logical method for performing shear design or alternately, checks of designs; (2) The method should provide a feel for the mechanics and should help designers develop a comfort level with the results; (3) The simplified method need not supplant the MCFT theory, but need only supplement the method and provide a logical alter- nate; and (4) The method does not need to be highly accu- rate, provided it is conservative. Regarding field problems that may be related to shear design, most indicated that few, if any, problems have occurred with the more modern design procedures. Several designers outlined problems that have arisen in older bridges whose design predates the current procedures in the Standard Specifications. However, one respondent did indicate that potential problems in segmental construction have arisen when using the LRFD methods because of the lack of a prin- cipal tension check for the webs. With respect to fabrication of precast elements, many designers indicated that conges- tion at the ends of beams is quite common, although this stems more from the confinement steel requirements than from shear steel requirements. Finally, the issue of bridge rating using LRFR (the LRFD rating approach) versus the current LFR rating is a source of ongoing concern, although most have not had any experience with the LRFR method yet. Whether this is a potential problem depends primarily on how the method is phased in and whether

it is mandated for older bridges. This is viewed as more of a pol- icy issue to ensure consistency, than a technical issue. The following states responded to the questionnaire: Alaska, Arkansas, California, Delaware, FHWA CFLHD, Florida, Georgia, Illinois, Kansas, Kentucky, Missis- sippi, Missouri, Montana, Nevada, New Hampshire, New Jersey, Oregon, Pennsylvania, Tennessee, Texas, and Washington. 2.5 CRITERIA FOR PROPOSED SIMPLIFIED PROVISIONS Based on the experiences of practicing engineers, the review of shear design methods in codes of practice, the analysis of experimental test data, and a comparison of the required amounts of shear reinforcement for sections in a design database (presented in Section 2.9), the following set of criteria were developed for the simplified provisions: The simplified provisions should • Be directly usable, without iteration, for the design of a member; • Be directly usable, without iteration, for evaluating the capacity of a member; • Be useful in conducting field evaluations by providing the engineer with an estimate of the loads at which shear cracking is expected to occur in the member; • Have a basis that can be readily understood and explained by one engineer to another while still being based on a mechanistic model for strength; • Allow for rapid and reliable hand-based designs and checks of existing designs; 30 • Not be a pure simplification of the existing LRFD specifications because a significant shortcoming of the current LRFD shear design provisions was considered to be the difficulty of fully understanding the MCFT and how the LRFD provisions were derived from this theory. • Avoid the necessity of calculating the angle θ. If a sim- ple relationship is to be suggested for calculating θ, then there needs to be a default value that can be used if the engineer does not wish to make this calculation; • Not enable the effects of all actions (axial load, moment, shear, and prestressing) to be simultaneously considered as this is already done in the current LRFD Sectional Design Model (S5.8.3); • Provide safe and accurate estimates of shear capacity of the members in the selected experimental test database without significant trends in the strength ratios (Vtest /Vcode) with design parameters (d, f ′c, ρv fy, ρl, etc). • Result in reasonable shear reinforcement amounts (ρv fy) being required for the sections in the design database where “reasonableness” is assessed from a comparison of the required amounts of shear reinforcement by analysis methods in comparison with the requirements of other codes of practice and analysis methods. Where the required shear reinforcement amount (ρv fy) by the simplified specifications differs substantially from what is required by the existing AASHTO Standard Specifica- tions, the LRFD specifications, and analytical methods, then the reasons for the required amount of shear reinforcement should be well justified and the required amount of shear reinforcement should be conservative.