Further study of stress-strain deformation of some structural reinforcement steel rods with different diameters from a mini mill in Nigeria using theoretical and regression analysis

Abstract

Further study of stress-strain deformation of some structural reinforcement steel rods with different diameters from a mini mill in Nigeria using theoretical and regression analysis has been undertaken. The work utilized result test of mechanical testing carried out on different sizes of reinforcement steel bars for concrete reinforcement ranging from 10 mm to 28mm in diameter. The deformation pattern of the work was highlighted using stress-strain graph and subjected to theoretical analysis, where the result showed that it is a ductile material with all the deformation regions associated with a ductile material. It equally has an elongation % of 9.36 at the point of failure during the test. Values of % elongation, ultimate tensile strength generated with different sizes of reinforcement steel bar were subjected to different regression models to establish their relationship, and to also find out which model best fit the relationship between the diameter variation of the steel rod and the % elongation, and the diameter variation of the steel rod and the ultimate tensile strength. The result showed that the relationship was linear, and linear regression model was better than hyperbolic curve model, and exponential function model. Therefore linear regression model was used to develop prediction model equations to estimate the values of % elongation and ultimate tensile strength. These models were evaluated using coefficient of determination r2, standard error of regression, confidence limits, standard errors of the intercept (a) and the gradient (b), confidence interval for intercept and gradient, and finally significance test was carried out on the intercept and the gradient. The standard error of regression for model equation Y1 was very small; 0.37, and that of model equation Y2 was 60.18. The coefficient of determination r2 was 21% for model equation Y1 and 1.49% for model equation Y2. The results also show that the general confidence interval has a narrower range than the individual confidence interval. The rank correlation coefficient has indicated that the association of the diameter variation of the steel rod was in perfect negative to the % elongation at failure and ultimate tensile strength. In conclusion this work has further thrown light to the stress-strain deformation of different diameters of structural reinforcement steel rods.