Size effect in torsional strength of plain and reinforced concrete

As shown long ago, plain and longitudinally reinforced concrete beams without stirrups exhibit a significant size effect on torsional strength, which was thought to be of a type occurring after long, stable crack growth (called Type II). This paper shows, by experimentally calibrated finite element simulations, that: 1) longitudinally reinforced concrete beams with stirrups also exhibit a significant size effect; and 2) the size effect in beams both with and without stirrups is not of Type II but Type I, characterizing failure at macrocrack initiation. In the practical size range, Type I is deterministic and terminates with a horizontal, rather than inclined, asymptote. The simulations are based on microplane model M7, which was shown to match well all the types of uniaxial, biaxial, and triaxial tests with post-peak softening in tension and compression. The model is calibrated by simulating previous torsional size effect tests of plain concrete beams and of longitudinally reinforced beams without stirrups, as well as the tests of beams with stirrups having different reinforcement ratios and different aspect ratios. The fact that all these tests are fitted closely, in terms of not only the maximum loads but also the crack patterns, lends credence to the predictions of size effect in beams with stirrups.