The elastic limit and ultimate strength of reinforcing steel are often stated to be a function of bar size owing to differences in the rates of cooling when rolled. The following data were obtained by random sampling of the delivered reinforcing steel for a particular job.
The steel was classed as "intermediate grade," and the allowable design working stress was 20,000 psi. Bar number equals the diameter in eights of an inch.
(a) Make a regression analysis of the elastic limit data on bar size. The elastic limit may vary linearly with bar diameter or with bar area. Make a preliminary plot to determine which is the best measure for use in a regression analysis. Test the assumption that the elastic limit is a function of bar size.
(b) Repeat (a) for ultimate strength.
(c) Are elastic limit and ultimate strength correlated?