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assumed to be parabolic with a strain at the peak stress 1. The changes incorporated in the 2004 Canadian Stan-
of -0.002. This assumption is not consistent with the dards Association Code for the Design of Concrete
stress-strain behavior of high-strength concrete where Structures, CSA A23.3-04, greatly simplify the proce-
the strain at peak stress can exceed -0.003 for an dure for the design of concrete structures using an
18,000 psi concrete. approach functionally identical to the LRFD Sectional
3. In the derivation of the LRFD Sectional Design Model Design Model. In the CSA A23.3-04, the following sig-
for members with shear reinforcement, the average nificant changes were made: (a) The tables for calculat-
crack spacing was assumed to be 12 inches. This value ing and were replaced by simple formulas that are
was used in calculating the crack width (crack spacing × easy to remember. See Equations 12 and 13.
principal tensile strain 1) from which the resistance to
crack slip was determined. This affected some of 4.8 51
the values of and in Table 1. Given that a conserva- = where for members with
(1 + 1500 x )(39 + sxe )
tive (larger than typical) value for crack spacing was
assumed, this approach was considered to lead to a con- Av < Av,min (Eq. 12a)
servative estimate of shear capacity. 4.8
= for members with Av Av,min, note sxe
(1 + 1500 x )
2.2 COMPARISON OF SHEAR = 12 inches (Eq. 12b)
DESIGN METHODS
The approach used in this research was to derive the = 29 + 7000 x (Eq. 13)
simplified design provisions after a thorough review and
evaluation of current code provisions and other relationships (b) A further simplification is that the iterative means
proposed by researchers. The following shear design proce- of calculating and is eliminated by assuming that
dures were selected as the most useful for providing poten- the angle is equal to 30 degrees in the evaluation of
tial direction for the simplified provisions to be developed in x. Thus, Equation 1-6 is simplified to Equation 14.
this project:
M / d + 0.5 N u + Vu - Vp - Aps f po
· ACI 318-02; x = t = u v
2 2( Es As + E p Aps ) (Eq. 14)
· AASHTO Standard Specifications 16th Edition;
· AASHTO 1979 provisions;
· CSA A23.3-94 (Canadian Standards Association: Design However, the procedure for analyzing the shear capac-
of Concrete Structures, 1994); ity remained iterative given that the longitudinal strain
· AASHTO LRFD Bridge Design Specifications 2nd is a function of the shear design force. The combina-
Edition; tion of these two changes greatly simplifies the design
· CSA A23.3-04; procedure to the extent that the use of the Sectional
· Eurocode EC2, Part 1(1991), Eurocode EC2 (2003); Design Model in CSA A23.3-04 is at least as simple, if
· German Code (DIN, 2001); not simpler to use, than the AASHTO standard method.
· AASHTO Guide Specification for Segmental Bridges The reality of this observation is apparent in the design
(ASBI); examples of Appendix J (included in NCHRP Web-
· The Japanese Code (JSCE Standards, 1986); and Only Document 78).
· The shear design approach recently developed by 2. In ACI 318-02, AASHTO standard and ASBI, the cal-
Tureyen and Frosch. culated value for Vc is an estimate of the diagonal crack-
ing load. This approach was considered useful for both
These shear design procedures are summarized in Appen- assessing the condition of a member in the field and for
dix B, which is included in NCHRP Web-Only Document 78. checking whether or not the member was expected to be
In this section, a comparison is made of how Vc, Vs, Vn,max, and cracked in shear under service loads. It was also thought
Av,min are evaluated. See Table 3. To compare these provi- that independent consideration of the two types of diag-
sions, relationships have been modified when possible in onal cracking, web-shear and flexure-shear, as used in
order to use LRFD nomenclature and psi units. ACI 318-02 and the AASHTO Standard Specifications,
Based on the comparison of design formulas presented in was useful for characterizing shear behavior and for
Table 3, and from consideration of the underlying bases for visualizing the effectiveness of the shear reinforcement.
these expressions, the following observations were made. (A 3. The AASHTO LRFD specifications require a larger
focus on the attributes of each design approach was consid- minimum amount of shear reinforcement than most
ered important for the selection and development of the pro- other codes. This requirement was examined using the
posed simplified provisions.) results of the experimental database of test results.

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

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