Beams in Shear - Unified Theory of Concrete Structures - page 363

Beam B4 showing 45 ◦ failure crack in flexural-shear failure zone Figure 8.13

shear strength, then the concept of decompression will show that the ultimate shear strength is
only slightly affected by the prestress force. This concept of prestressed beam behavior after
decompression was substantiated by Lyngberg (1976). Lyngberg's test program consisted of
nine beams, in which the major variable was the intensity of prestress. The cross-section, web
reinforcement, ultimate moment, and shear span were held constant. The test results showed
convincingly that the influence of prestress force on the shear strength can be neglected. As
such, the prestress force need not be taken as a variable in an equation for shear strength.

Failure crack angle
Figure 8.13 shows the failure crack angle of beam B4 that failed in flexural-shear. In this case,
the AASHTO shear provisions would assume a crack angle much smaller than 45 ◦ according
to the principal compressive direction of concrete in the prestressed webs. Such a crack with
small angle is shown in Figure 8.13 by the major crack that passed through grid 4 at the
bottom edge of the web. However, this crack with small angle did not develop to form a failure
surface at ultimate load. In fact, Figure 8.13 shows that another major crack with angle of
approximately 45 ◦ developed and passed through grid 8 at the bottom edge of the web. This
approximately 45 ◦ crack was observed to cause failure.
The assumption of 45 ◦ failure crack can also be supported by a study of energy dissipations
in the failure zone. According to Laskar (2009), a crack with inclination close to 45 ◦ would
result in minimum shear energy dissipation.