The paper examines whether the size effect law for failures due to distributed cracking. recently derived from fracture mechanics arguments. is applicable to torsional failure of unreinforced or longitudinally reinforced concrete beams of rectangular cross section without stirrups. The test data available in the literature are used for thi:o; purpose. They confirm that a size effect is present and does not disagree with the size effect law. However, the data range is so narrow and their scatter so large that the precise form of the size effect cannot be identified. A simple. theoretically based formula to take the size effect into account is suggested.
INTRODUCTtONAlthough, whenever possible, it is desirable to design concrete structures to fail in a ductile manner, brittle failures cannot be avoided in some well-known situations. While in ductile failures the load remains constant at increasing deformation after the ultimate state is reached, in brittle failures the load decreases after the ultimate state. The phenomenon of load decrease after the peak has a profound effect on the behavior and safety margins of the structure, and its most significant manifestation is perhaps the size effect. Whereas for plastic behavior (assumed in limit analysis) geometrically similar structures of different sizes fail at the same nominal stress level. for brittle behavior, the larger Ihe structure, the smaller is the nominal stress at failure. This property is a consequence of the fact that if the load decreases after the peak, the failure cannot be simultaneous but occurs through propagation of a failure zone across the structure, one part having already failed when another part reaches its peak capacity. In a larger structure, this propagating, nonsimultaneous nature of failure is more marked. In energy terms, the previously failed regions of the structure cause elastic energy to be released into the currently failing regions and thus help to drive the failure. In a larger structure, the energy release available for further propagating the failure is greater, and hence the size effect.In previous studies (5,12,9-11), the size effect has been analyzed for the diagonal shear failure of concrete beams with longitudinal reinforcement, and both without and with stirrups; for diagonal shear failure of prestressed concrete beams; for punching shear failure; and for beam and ring failures of unreinforced pipes. Another important type of brittle failure is the torsional failure, and for theoretical reasons as well as by analogy with
FIG. 1. Size Effect Lawthe results of previous studies, the existence of the size effect should be expected. The purpose of the present study is to examine this question, drawing on the valuable experimental evidence already documented in the literature (18,20,23). Although there are many other valuable test data on torsion failures (1,2,15,17,21,22,24,25,(28)(29)(30)(31)(32)(33)(34), they cannot be used in this study because they give no information on the size effect.
SIZE EFFECT LAWThe size...