Rectangular sheared keys are used to improve the resistance against shear slip of joints between the segments of prestressed box-girder bridges. Buyukozturk and Lee (1992a) showed that this is a very brittle type of failure, exhibiting a strong size effect dose to LEFM. They used LEFiM mixed-mode fracture analysis (Swartz and Taha 1990, 1991) to study the failure of typical shear keys used in bridge construction (Fig. 10.5.7). In contrast to the diagonal shear cracks in beams, which can be counteracted by shear reinforcement (stirrups), a diagonal crack which is initiated at the shear key may also propagate parallel to the joint. Such a path is not crossed by any shear reinforcement (Buyukozturk, Baklioum and Beattie 1990).
The design provisions of the Post-Tensioning Institute (1988) for the segments of prestressed box-girder bridges are at present empirical and follow the strength theory, exhibiting no size effect. They are based on the shear capacities determined by tests of prestressed beams failing by flexure-shear cracks or web-shear cracks. An enhanced formula was proposed by Buyukozturk, Baklioum and Beattie (1990), but this was still free from size effect.
Based on their mixed-mode LEFM analysis, Buyukozturk and Lee calculated design charts corresponding to the failure criterion
ClKj + Kj, = Kjc (10.5.11)
where K;, Kjj = stress intensity factors in Mode I and Mode II, Kic = Mode I fracture toughness of concrete, and Ck — empirical constant (which obviously represents the ratio of Mode II fracture toughness to К[г). The high brittleness of failure is further compounded by the use of high strength concrete in these bridges. Another aggravating factor for brittleness is the presence of large uniaxial compressive stresses normal to the joint, which are beneficial by increasing friction but detrimental increasing the brittleness. Thus, even though this relatively small size of the shear keys would indicate the use of nonlinear fracture mechanics with a transitional size effect (following the size effect law), it appears that LEFM is applicable.