Simplified Shear Design of Structural Concrete Members (2005)

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With the issuance of the AASHTO LRFD Bridge Design Specifications in 1994 (1), a new shear design method for reinforced concrete structures was introduced into U.S. bridge design practice. This method, known as the Sectional Design Model, is based on the Modified Compression Field Theory (MCFT) (2). That theory provides a com- plete behavioral model for the response of diagonally cracked concrete to in-plane shear and membrane stresses. In using the Sectional Design Model, the designer eval- uates the axial strain in the member at mid-depth considering the combined actions of axial load, moment, prestressing, and shear, and then uses this strain and the shear design stress level (or cracking spacing) to select values for coefficients β and θ from tables. These values control the concrete and steel contributions to shear resistance. Although this method provided a unified treatment for the design of reinforced and pre- stressed concrete structures and offered some significant performance advantages, the procedure was unfamiliar to design engineers, more complicated than the shear design procedure in the AASHTO Standard Specifications, and often required an iterative solution. The objective of NCHRP Project 12-61 was to develop simplified shear design provisions that would provide an alternative shear design method to that of the LRFD Sectional Design Model. There were many options for the structure of these new simplified provisions because there is considerable disagreement in the research community about the factors that most influence shear capacity. For this reason, the research approach taken on this pro- ject was to begin with a review and evaluation of some of the most prevalent methods for calculating shear capacity, including those of • ACI 318R-02 (3); • AASHTO Standard Specifications for Highway Bridges 16th Edition (4); • AASHTO 1979 provisions (5); • CSA A23.3-94 (Canadian Standards Association: Design of Concrete Structures, 1994) (6); • AASHTO LRFD Bridge Design Specifications 2nd Edition with 2003 Interim Revisions (7); • CSA A23.3-04 (8 ); SUMMARY SIMPLIFIED SHEAR DESIGN OF STRUCTURAL CONCRETE MEMBERS

• Eurocode EC2 (9,10); • German Code (DIN, 2001) (11); • AASHTO Guide Specification for Design and Construction of Segmental Bridges (ASBI) (12); and • The Japanese Code (JSCE Standards, 1986) (13) and the shear design procedure recently developed by Tureyen and Frosch (14). The structure and underlying bases for these methods were examined and their accu- racies assessed using the results of a large experimental database. In addition, a survey was conducted of practitioners in 26 different state DOTs and federal lands bridge design agencies on the use of the LRFD Sectional Design Model and of the AASHTO standard shear design method. These assessments resulted in the following findings subsequently used for devel- oping change proposals and simplified provisions: • The survey of the design practice showed that (1) few organizations had experi- ence in the use of the LRFD shear design specifications. Some were reasonably comfortable with these provisions while others viewed them as a significant hur- dle to be surmounted; (2) All agreed that the LRFD provisions must be automated with software if they are to be used in production design. This limitation naturally leads to loss of comfort with respect to the checking of designs, because the method cannot be readily executed by hand. Most designers also agree that the standard specification method for prestressed design that includes Vci and Vcw must also be automated to be effective in production work, even though that method is executable by hand; (3) One of the most common concerns was that designers were losing their physical “feel” for shear design, owing to the increasing complexity of the design provisions and the resulting automation; and (4) The primary sim- plification that designers were seeking was an elimination of the iterative process required to determine the angle of diagonal compression. • The changes incorporated in the 2004 Canadian Standards Association Code for the Design of Concrete Structures, CSA A23.3-04, greatly simplify the MCFT proce- dure for the design of concrete structures, using an approach that is functionally identical to the LRFD Sectional Design Model. In the CSA A23.3-04, the tables for evaluating β and θ were replaced by the following simple algebraic expressions: where for members with Av < Av,min for members with Av ≥ Av,min, note sxe = 12 inches Furthermore, the CSA procedure for evaluating β and θ in a design was made non- iterative by removing the dependency on the angle θ when calculating the longi- tudinal strain at mid-depth. 1. Traditional U.S. bridge and building design specifications use the diagonal crack- ing strength, Vc, as an estimate of the concrete contribution to shear resistance at the ultimate limit state and the 45-degree parallel chord truss model for calculat- ing the contribution of shear reinforcement to shear capacity. These are empiri- θ = +29 7000
x β = + 4 8 1 1500 . ( )
x β= + + 4 8 1 1500 51 39 . ( )( )
x xes 2

3cal design approaches that are supported by test data. They were found to provide reasonably accurate and conservative estimates of the shear capacity of the mem- bers with shear reinforcement in the experimental database of shear test results. However, these methods were unconservative and poor at predicting the shear capacity of non-prestressed (reinforced) concrete members that did not contain shear reinforcement. 2. Basing the concrete contribution at ultimate on a conservative value of the diago- nal cracking strength enables the designer to check whether or not a member will be cracked in shear under service load levels as well as helps in assessing the con- dition of structures in the field. It was also thought that characterizing the two types of diagonal cracking, web-shear and flexure-shear, as used in ACI 318-02 and the AASHTO Standard specifications, was useful for describing shear behavior. 3. The LRFD Sectional Design Model and the CSA Method produced very similar estimates of the shear capacity of the members in the experimental database of shear test results. From the various design methods considered, the LRFD and CSA methods produced the most accurate estimates of capacity and overall had only about a 10 percent probability of being unconservative. 4. Researchers have not tested the broad range of structures built with design provisions and thus experimental test data alone cannot provide a complete assessment of the suitability of provisions. For example, most members in the experimental database were small, simply-supported, stocky, did not contain shear reinforcement, and were loaded by point loads at small shear span to depth ratios. In addition, nearly all members were designed to be shear critical near an end support and thus test results are particularly ineffective at evaluating the appropriateness of provisions for regions away from supports. 5. Comparing the required strength of shear reinforcement (ρvfy) by different design provisions with each other and with the required amounts determined by the analysis program, Response 2000 (R2K) (15), was a useful way of evaluating the relative conservatism of the different approaches. 6. The AASHTO LRFD Specifications require a larger minimum amount of shear reinforcement than most other codes. This higher requirement was found to be desirable for reliable behavior based on an examination of the experimental data- base of test results. 7. The CSA A23.3-04 (8), AASHTO (1979) (5), AASHTO LRFD (1, 7), Truss Model with Crack Friction (TMwCF) (16), Eurocode 2 (9, 10), JSCE (13), and DIN (11) all enable the designer to use an angle of diagonal compression, θ, flatter than 45 degrees when evaluating the contribution of shear reinforcement to shear capacity. 8. AASHTO LRFD, DIN, and Eurocode 2 allow the engineer to design members to support much larger shear stresses than permitted in other codes of practice. Any shear stress limit is principally intended to guard against diagonal compression failures. In AASHTO LRFD, the shear design stress limit is 0.25f ′c plus the verti- cal component of the prestressing while in ACI 318-02 or AASHTO Standard specifications the limit is approximately . The LRFD stress limit is adequate to prevent web crushing in regions where there is a uniform field of diag- onal compression. However, this limit may be unconservative near supports where there is a significant magnification of the stress as the diagonal compres- sion funnels into the support. Based on these findings, two proposed changes to the LRFD specifications were developed. The first change is the introduction of proposed simplified provisions that 12 ′fc

are a modified version of the AASHTO Standard Specifications for prestressed concrete. These simplified provisions differ from the standard specifications in four principal ways: 1. The expression for calculating the web-shear cracking strength is made more con- servative and applicable for partially prestressed as well as prestressed members; 2. A variable angle truss model is introduced in which the calculated angle of diag- onal cracking is used for evaluating the contribution of the shear reinforcement in web-shear regions. In flexure-shear regions, and all regions where Mu > Mcr, the 45-degree truss model is used; 3. The maximum shear design stress is substantially increased; and 4. Minimum shear reinforcement requirements are made the same as those for the Sectional Design Model. Comparisons with the shear database showed the pro- posed simplified shear provisions to have a six percent probability of being unconservative. The second change is that the LRFD Sectional Design Model be modified to use the relationships of the CSA Method for calculating β, θ, and
x. The primary relationships in the proposed simplified provisions are expressed below in psi units: cot(θ) = 1.0 in flexure-shear regions where Vc is lesser of Vcw and Vci The effect of the proposed changes on bridge design practice, if implemented, depends on which approach is used currently by designers (i.e., the AASHTO Stan- dard or the AASHTO LRFD Sectional Design Method) and on which of the two pro- posed methods is selected for use. Switching from the AASHTO Standard procedure to either of the proposed design methods will allow for the design of members for con- siderably higher levels of shear stress and thereby enable the same size section to be used to span longer distances or support heavier loads. It will also involve an increase in the minimum required amounts of shear reinforcement which will improve safety. Adopting the equations for β, θ, and
x from the CSA Method into the LRFD Sectional Design Model will greatly improve the simplicity of designing by the Sectional Design Model. The CSA method can be used for the design of sections for shear that are subjected to any combination of axial load, moment, and level of prestressing. Adopting the proposed simplified provisions will result in a somewhat more uniformly conservative design procedure for the range of members that will be designed with the LRFD specifications. V V f b d Vc s c v v p+ ≤ ′ +0 25. V A f d s f s v y v pc = = + ′ cot( ) cot( ) . .θ θwhere 1 0 0 095 fc ≤1 8. V f b d V V M M f b dci c v v d i cr c v v= ′ + + ≥ ′0 632 1 9. . max V f f b d Vcw c pc v v p= ′ + +( . . )1 9 0 30 4