Size effect on punching strength of reinforced concrete slabs with and without shear reinforcement

A design equation for punching shear strength vc is developed based on a refined statistical analysis of the ACI 445 database with 440 tests supplemented by finite element (FE) analysis using microplane model M7. Database filtering leads to data subsets in which the averages of secondary variables, such as steel ratio and shape parameters, in subsequent intervals of size d (or slab depth) are almost constant. The resulting trend of the interval means of vc reveals that the slope of log vc versus log d through the practical size range is milder, but not much milder, than -1/2, and that the trend fits the energetic size effect factor endorsed by ACI Committee 446. The design equation with size effect is verified and calibrated by least-square multivariate regression of the database, with weights compensating for the crowding or scarcity of data in parts of the range. The size effect factor is also verified by FE fitting of available broader-range data series.