Can Stirrups Suppress Size Effect on Shear Strength of RC Beams?

This paper demonstrates the size effect on the shear strength of reinforced concrete (RC) beams with stirrups and does so in two separate and independent ways: (1) by fracture mechanics, based on finite-element analysis calibrated by a large beam test; and (2) by purely statistical analysis in which a newly assembled database of 234 tests is filtered to eliminate spurious size effects caused by nonuniformity of secondary influencing parameters. Both ways show that stirrups, whether minimum or heavier, cannot suppress the size effect completely, although they can mitigate it significantly for beam depth $d<1\mathrm{m}$ (39.4 in.). The effect of stirrups is to push the size effect curve in logarithmic scale into sizes larger by about one order of magnitude. For beam depths $d<0.5\mathrm{m}$ , 1, 2, and 6 m (19.7, 39.4, 78.7, and 236.2 in.), the percentages of beams whose shear strength is below the code limit are calculated as 3.5, 6.5, 15.7, and 55.1%, respectively. The corresponding failure probabilities are ${10}^{-6}$ , ${10}^{-5}$ , ${10}^{-4}$ , and ${10}^{-3}$ , whereas ${10}^{-6}$ is the generally accepted standard for a tolerable maximum in risk analysis. It follows that, for beams with stirrups having depth $>1\mathrm{m}$ (39.4 in.), the size effect cannot be neglected.