A design shear resistance formula for Y-type perfobond rib shear connectors is proposed with the various reduction factors, which can be selected depending on the target safety level. The nominal shear resistance formula is improved based on the systematic sensitivity analysis as well as the regression fit test based on 84 push-out test results, including 15 additional push-out tests to extend the application ranges and reduce the estimation errors, compared to the formula proposed in previous studies. Some design variables are additionally included in the proposed design formula: the yield strengths of rebar and rib plate. The basic design variables in the proposed design formula are (1) number of ribs and transverse rebars, (2) concrete compressive strength, (3) rebar diameter and yield strength, and (4) rib thickness, width, height, and yield strength. The application ranges of the basic design variables are recommended for the proposed design formula. The various shear resistance reduction factors are proposed based on the probabilistic ultimate shear resistance model of Y-type perfobond rib shear connectors. The proposed procedure may be recommended to develop the design formula for shear connectors with various shapes.

Crack control for slabs and beams in current design practices in Korea are based on the Frosch’s model, which is adapted in ACI 318. It is more difficult to have consistent quality control in underground construction sites, such as the RC box culverts used for electric power distribution built below the ground level. There are more discrepancies between the as-built dimensions and the design dimensions provided in drawings in these structures. Due to this variability in construction error, the crack widths measured in such structures have higher potential to have more differences than the calculated values. Although crack control is a serviceability concern, if the owner chooses to have a target crack width that needs better control, crack width estimations can be improved by considering such construction variability. The probability-based crack width model suggested in this study will allow minimizing the discrepancies between the measured and calculated crack widths and provide reliable estimations of crack widths. Typical size of slabs and beams ranging between 300 mm (12 in.) to 500 mm (20 in.) used in underground RC box culverts in Korea were tested under the four-point bending test program. The thicker specimens had smaller bar spacings which created more cracks with smaller crack widths. However, with smaller crack widths generated in these specimens, there were more errors between the measurements and calculated values. From site investigations in Korea, the thickness of slabs in underground box culverts varied the most among all parameters. As a result, the bottom concrete covers had the highest variability. Bottom concrete covers and bar spacings are the two most important parameters in concrete crack control. A probability-based crack width estimation model for flexural members was developed in this study to consider this construction variability. Monte Carlo simulations were performed to evaluate the probabilistic characteristics of the design surface crack widths with a target width of either 0.3 mm (12 mils) or 0.5 mm (20 mils). The probabilistic models of design variables included in the crack width estimation model were generated based on field-collected information from construction sites in Korea. Because the surface crack widths in RC flexural members are sensitive to the construction errors of concrete cover depths, and since there are differences between the assumed and actual stress distribution closer to the reinforcing bars, the probability of having surface cracks of 0.3 mm width (12 mils) is found to be quite high, such as 89% at the positive moment region (mid-span, bottom surface) of the top slab in RC box culverts and 45% for the negative moment region (support area, top surface) of the top slab with current design practice. In order to ensure crack widths to be smaller than the design target width, probability-based crack width factors are recommended in this study to improve estimations depending on the selected target reliability levels.