Beams in Shear - Unified Theory of Concrete Structures - page 369

Figure 8.17 Variation of ultimate strength with concrete strength

Equation (8.21) was introduced into the first edition of the AASHTO LRFD Specifications
(1994), based on the truss model concept first introduced by the Canadian Standard (1977) and
the CEB-FIP Model Code (1978). No change was made in the second edition of AASHTO
(1998), up to the current fourth edition of AA SH TO (2007).

The fact that V n , max is proportional to f c in the ACI Code, Equation (8.20), and is
proportional to f c in the ASSHTO Specifications, Equation (8.21), testifies to the confusion
surrounding the formulas for V n , max . These two equations are plotted in Figure 8.17.
In Figure 8.17, the ACI and AASHTO formulas are checked by the prestressed beams
of Bennett and Balasooriya (1971), Rangan (1991), and Ma et al . (2000), which are over-
reinforced in shear. It can be seen that the ACI formula is way too conservative. The AASHTO
formula is more reasonable when compared with the test data. However, the AASHTO formula
is expected to be unsafe for beams with concrete strength higher than 60 MPa (8700 psi),

8.3.4.2 UH Maximum Shear Strength
According to Sections 2.3.3.1 and 6.1.7.2, the maximu m shear strength V n , max can be expressed

as a function of the concrete compression strength f c

and the web area b w d :

C 1 f c b w d

V n , max = (8.22)

where C 1 is a constant to be determined by the shear tests of prestressed I-beams.
Before deciding on the constant C 1 for the maximum shear strength, we must first calibrate
the balanced condition defined as:

C b f c b w d V n , b = (8.23)