Statistical Analysis of the Mechanical Properties and Weight of Reinforcing Bars

Abstract

The variability of the mechanical properties and weight of steel reinforcing bars produced in the United States and Canada under ASTM A 615, A 616, and A 706 in 1997 is evaluated and expressions are developed to represent the probability distribution functions for yield and tensile strength. Thirty-four mills were invited to submit data on yield strength, tensile strength, elongation, and percent of nominal weight. Of these, 29 mills submitted data on a heat-by-heat basis, three mills provided average values (no data on a heat-by-heat basis), one mill provided data on “No Grade” bars (these were not used in this analysis), and one mill did not respond to the request for data. A statistical analysis of bar properties is conducted. Trends in the data are evaluated based on grade, bar size, and production mill. Beta functions are developed to represent the probability distribution functions for yield and tensile strength for each bar size, grade, and steel type, as well as for all bars for each grade and steel type. The analyses show that less than 0.1% of the steel heats failed to meet minimum ASTM standards for yield strength, and less than 0.1% of the steel heats failed to meet minimum ASTM standards for tensile strength. Approximately 1.2% of the steel heats failed to meet minimum ASTM standards for elongation, but no heats failed to meet the minimum ASTM standard for weight. The beta distributions for yield strength covering all A 615 Grade 40 and all A 615 Grade 60 bars provide good representations for the distributions for individual bar sizes within each of these grades, with the exception of A 615 No. 14 and No. 18 bars, which exhibit significantly different distribution functions. Both normal and beta distribution functions (for the individual bars and all bars) can be used to represent the distributions of yield strength for A 615 Grade 75, A 616, and A 706 bars. For tensile strength, the distribution for all bar sizes is recommended for A 615 Grade 40 bars. The beta functions developed for the individual bar sizes for A 615 Grade 60 bars provide a good match with the actual tensile strength distributions, with the exception of No. 3 through No. 5 and No. 7 bars. Both normal and beta distribution functions can be used to represent the distributions of tensile strength for A 615 Grade 75, A 616, and A 706 bars for both individual bar sizes and all bars.