Minimizing Statistical Bias to Identify Size Effect from Beam Shear Database

A broad database can be used to statistically calibrate a design formula capturing the size effect on shear strength of reinforced concrete beams without stirrups. This database, however, can have a bias of two types: 1) most data points are crowded in the small size range; and 2) the means of the subsidiary influencing parameters, such as the steel ratio and shear-span ratio are very different within different intervals of beam size or beam depth. The database must be properly filtered to minimize the second type of bias. To this end, the size range is first subdivided into intervals of constant size ratio. Then, in each size interval, a computer program progressively restricts the range of influencing parameters both from above and from below, until the mean of the influencing parameter values remaining in that interval attains about the same value in all the size intervals. The centroids of the filtered shear strength data within the individual size interval are found to exhibit a rather systematic trend. Giving equal weight to each interval centroid overcomes the first bias. The centroids can be closely matched by bivariate least-square regression using Bazant’s size effect law. This purely statistical inference of minimized bias also supports the previous fracture-mechanics-based conclusion that, for large sizes, the bi-logarithmic size effect plot must terminate with the asymptotic slope of –1/2. Similar filtering of the database gives further evidence for the previous empirical observation that the shear strength of beams is approximately proportional to the 3/8-power of the longitudinal reinforcement ratio. The proposed statistical procedure can be used to improve the calibration of formulas in concrete design codes.