SIZE EFFECT IN SHEAR FAILURE OF LONGITUDINALLY REINFORCED BEAMS.

Abstract

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 (1 plus d/d//a lambda //o)** minus ** one-half , in which d equals beam depths, d//a equals maximum aggregate size, and lambda //o equals constant. For relatively small beams the nominal stress at failure is nearly constant; however, for much deeper beams it considerably declines with increasing size. 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.