Torsional Failure of Beams
Torsion leads to another type of brittle failure of reinforced concrete beams. The classical test data existing in the literature, which were analyzed by Bazant and §ener (1987), and particularly the data by Humphrey (1957), Hsu (1968), and McMullen and Daniel (1975), reveal that a size effect exists, but cannot indicate which equation should describe it because the data were too scattered, the size range was too narrow, and geometrical similarity was not maintained.
Geometrically similar tests of size range 1:4 were conducted on microconcrete beams with reduced maximum aggregate size by Baz. ant, §ener and Prat (1988). The tests were made both on unreinforced beams and beams reinforced longitudinally. These tests clearly revealed a strong size effect and were shown to agree well with the size effect law. The results were briefly described in Section 1.5, Fig. 1.5.7 (series J1 and J2). From these tests it appears that the size effect in torsion is very strong, and the behavior is quite close to the LF. FM asymptote. However, the scatter of the limited experimental data is quite large, and more extensive tests are needed. The scatter is larger for longitudinally reinforced beams, which
may be attributed to the fact that bond failure must accompany a torsional crack, and bond failure is a phenomenon of high random scatter.
The code formulas for torsion of beams with rectangular cross section are based on the plastic limit analysis solution, which indicates that the nominal shear strength in torsion (Park and Paulay 1975) is vu = Т/(apb2D), ap = [1 — (b/3D)}/2, where T = torque, b — length of the shorter side of the rectangular cross section, D — length of the longer side (depth). Since the small size limit of the size effect law should coincide with the plastic solution, Bazant, §ener and Prat (1988) proposed the correction indicated, in general, by Eq. (10.1.13) and showed that it agrees well with the data. Calculations with the microplane model by Bazant, Ozbolt and Eligehausen (1994) also agree quite well with the experimental points and the size effect correction.
No test data seem to exist on the size effect in torsional failure of reinforced concrete beams with stirrups. However, it may be expected that the stirrup effect would be similar to that discussed for diagonal shear, and that the size effect would disappear beyond a certain critical reinforcement ratio of the stirrups.
Torsion in beams is normally combined with bending, and so the interaction diagram between the maximum torque and the maximum bending moment is of considerable interest for design. Hawkins (1985) examined the test results of Wiss (1971) on diagonal tension cracking combined with torsion and bending. Using an energy based fracture criterion for failure under combined loading, he calculated the interaction diagram and showed it to be circular (when the maximum shear force and the maximum torque are normalized with respect to their values for pure torsion or pure shear). He suggested this was an argument for applicability of fracture mechanics, pointing out that the strength-based criteria yield a straight-line interaction diagram. However, this is not sufficient proof of fracture mechanics applicability because the lower-bound plastic limit analysis also gives a circular interaction diagram (e. g., Hodge 1959).