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SIMPLIFIED SHEAR DESIGN
OF STRUCTURAL CONCRETE MEMBERS
SUMMARY 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 and 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 );

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· 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 and were replaced by the following simple algebraic expressions:
4.8 51
= where for members with Av < Av,min
(1 + 1500 x )(39 + sxe )
4.8 for members with Av Av,min, note sxe = 12 inches
=
(1 + 1500 x )
= 29 + 7000 x
Furthermore, the CSA procedure for evaluating and in a design was made non-
iterative by removing the dependency on the angle 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-

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cal 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 (vfy) 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, ,
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 12 fc . 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

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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 , , and x.
The primary relationships in the proposed simplified provisions are expressed below
in psi units:
Vcw = (1.9 fc + 0.30 f pc ) bv dv + Vp
Vi Mcr
Vci = 0.632 fcbv d v + Vd + 1.9 fcbv d v
M max
Av f y d v cot() f pc
Vs = where cot() = 1.0 + 0.095 1.8
s fc
cot() = 1.0 in flexure-shear regions
Vc + Vs 0.25 fc bv dv + Vp 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 , , 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.