Size Effect in Shear Failure of Longitudinally Reinforced Beams
Zdenek P. Bazant and Jin-Keun Kim
Appears on pages(s):
beams (supports); building codes; cracking (fracturing); dimensional analysis; failure; reinforced concrete; shear properties; statistical analysis;structural analysis.
Consequences of recent fracture mechanics studies of concrete for analyzing diagonal shear failure of longitudinally reinforced beams or one-way slabs without shear reinforcement were studied. The cracking produced by shear was assumed to propagate with a dispersed zone of microcracks at the fracture front. Dimensional analysis of the energy release rate then shows that the nominal shear stress at failure should not be a constant but should vary as (I + d/d, A,) in which d = beam depths, d, = maximum aggregate size, and A, = constant. For relatively small beams, representing the great majority of those tested in the laboratories, the nominal stress at failure is nearly constant; however, for much deeper beams it considerably declines with increasing size. This trend is confirmed by previous experimental results. In addition to the size effect, a rational formula for the effect of steel ratio and shear span is derived. Comparisons with existing test data involving nearly 300 tests indicate that, compared to the formulas in the current building codes, the coefficient of variation of deviations from the formula is reduced to less than one-half.