Fracturing Truss Model: Size Effect in Shear Failure of Reinforced Concrete

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Abstract
The classical truss model (or strut-and-tie model) for shear failure of reinforced concrete beams is modified to describe fracture phenomena during failure. The failure is assumed to be caused by propagation of a compression fracture across the concrete strut during the portion of the loading history in which the maximum load is reached. The compression fracture may consist of a band of splitting cracks that later interconnect to form a shear crack or a shear fracture band inclined to the strut. The width of the fracture band is assumed to occupy only a portion of the strut length and to represent a fixed material property independent of the beam depth. The energy release from the truss is calculated using two alternative approximate methods: (1) using the potential energy change deduced from the concept of stress relief zones; and (2) using the complementary energy change due to stress redistribution caused by propagation of the fracture band across the compressed concrete strut. Both approaches show that a size effect on the nominal strength of shear failure must exist and that it should approximately follow the size effect law proposed by Bažant in 1984. The physical mechanism of the size effect is also explained in a clear and simple intuitive manner. Finally, it is shown that the applied nominal shear stress that causes large initial diagonal cracks to form also exhibits a size effect.