Prediction of shear strength in high-strength concrete beams considering size effect

Recent research has indicated that the current American Concrete Institute (ACI) shear provisions provide nonconservative prediction for large slender beams with a low level of longitudinal reinforcement, but conservative predictions for deep beams. In the present paper, to modify these problems in the ACI shear provisions, the ultimate shear strength equation, considering size effect and arch action, is presented for computing the shear strength in high-strength concrete beams without stirrups. Three basic equations, namely those for the size reduction factor, ρ factor and arch action factor, are derived from the crack band model of fracture mechanics, analysis of previous shear equations for longitudinal reinforcement ratio and concrete strut described as a linear function in deep beams. Constants of basic equations were determined by using statistical analysis of previous shear testing data. To verify the proposed shear strength equation for each variable, about 300 experimental data were used and the proposed equation was compared with ACI 318 code, CEB–FIP model code, Kim and Park's equation, CSA 94 code and Zsutty's equation. While the proposed shear equation is simpler than other shear equations, it gives economical predictions of shear strength and reasonable safety margin.