Fracturing Truss Model for Shear Failure of Beams
The truss model of Ritter (1899) and Morsch (1903), also called the strut-and-tie model, has been widely used in successively refined versions to analyze the failure of beams in diagonal shear (Nielsen and Braestrup 1975; Thtirlimann 1976; Collins 1978; Collins and Mitchell 1980; Marti 1980, 1985; Schlaich, Schafer and Jannewein 1987; Hsu 1988, 1993; Collins, Mitchell ct al. 1996). A fracture model retaining the basic hypotheses of the truss model has recently been proposed. It explains the size effect observed in this type of structures based on the concepts previously analyzed in Section 9.5, particularly the generation and growth of a band of axial splitting cracks parallel to the compressive principal stress (Bazant 1996b), or alternatively a shear compression crack propagating across the strut. In this section we present the
Figure 10.3.1 (a) Compression strut in a beam without stirrups and crushing zone propagating across the compression strut during failure, (b) stress relief zones caused by crushing band propagating across compression strut in beams of different sizes.
basic hypotheses underlying the inode] and two alternative theoretical analyses, one based on the stress relief zone and strain energy release, and the other based on the stress redistribution and complementary energy. The section closes by discussing the size effect on the cracking load, which is sometimes claimed to be free from siz. c effect.