A parametric shear constitutive law for reinforced concrete deep beams based on multiple linear regression model

摘要

In the present paper, the fiber theory has been employed to model the reinforced concrete (RC) deep beams (DBs) considering the reinforcing steel bar-concrete interaction. To simulate numerically the behavior of materials, the uniaxial materials' constitutive laws have been employed for reinforcements and concrete and the bond stress-slip between the reinforcing steel bars and surrounding concrete are taken into account. Because of the high sensitivity of DBs to shear deformations, the Timoshenko beam theory has been applied. The shear stress-strain (S-SS) relationship has been defined by the modified compression field theory (MCFT) model. By modeling about 300 RC panels and employing a produced numerical database, a study has been carried out to show the sensitivity of the MCFT model. This is performed based on the multiple linear regression (MLR) models. The results of this research also illustrate how different parameters such as characteristic compressive strength of concrete, yield strength of reinforcements and the percentages of reinforcements in different directions get involved in the shear behavior of RC panels without applying complex theories. Based on the results obtained from the analysis of the MCFT S-SS model, a relatively simplified numerical S-SS model has been proposed. Application of the proposed S-SS model in modeling and analyzing the considered samples indicates that there is a good agreement between the simulated and the experimental test results. The comparison between the proposed S-SS model and the MCFT model indicates that in addition to the advantage of better accuracy, the main advantage of the proposed method is simplicity in application.