Size effect in shear failure of RC beams with stirrups: Simulation and formulation

The objectives of the present study are to discover the influences of stirrup ratio and shear-span ratio on the shear failure and size effect of reinforced concrete (RC) beams having different sizes, and to build a theoretical formula for quantitatively describing the size effect on shear failure of RC beams. A three-dimensional meso-scale simulation method for modelling the failure of RC beams is established, and it is utilized to explore the failure behavior of geometrically-similar RC beams. In addition, the influences of shear-span ratio and stirrup ratio on the size effect of shear failure was examined. Finally, a novel size effect law (SEL) for predicting the nominal shear strength of RC beams having different sizes is established and verified. The results indicate that, (1) the shear-span ratio has a great influence on the shear capacity of RC cantilever beams, but has ignorable effect on the size effect; (2) the increase of stirrup ratio increases the shear capacity of RC cantilever beams and weakens the size effect of the shear strength; (3) stirrups cannot increase the shear capacity of RC beams indefinitely, and the increase of shear strength is obvious under the condition of small stirrup ratio; (4) the developed SEL for shear failure of RC beams can well describe the quantitative influence of stirrup ratio and shear-span ratio, and it is consistent with the available test date.