Shear strength prediction for reinforced concrete beams without stirrups

Traditionally, shear design of concrete beams without stirrups has relied on empirical equations derived from laboratory experiment data. However, such methods lack a sound theoretical basis for shear failure of reinforced concrete (RC) structures due to the complexity of the failure mechanism. In the 1980s, a relatively rational model based on the modified compression field theory (MCFT) was developed at the University of Toronto and subsequently accepted worldwide; it forms the basis of shear provisions in Canadian standards and American specifications for the design of concrete structures. This paper describes further research based on the MCFT. An expression for the average shear stress across a crack was derived and a simplified equation of shear strength considering the size effect in shear was developed. The obtained equations were verified with extensive sets of experimental data from different sources (598 beams in total). It was found that the variation coefficients of the ratio of shear strength calculated using the derived average shear stress across a crack based on the MCFT and the simplified expressions to the test data was small; the mean was about 0·8. It is thus considered that the simplified expressions are suitable for shear analysis and design of RC beams without stirrups.