The Analysis of the Discrete Cracking Model of Reinforced Concrete Tensile Members

Adequate modelling of reinforced concrete (RC) cracking, particularly post-cracking behaviour (tension stiffening), as one of the major sources of nonlinearity, is the most important and difficult task for deformation analysis. Deformationbehaviour of the cracked RC members is a complex process, including a wide range of effects such as differentstrength and deformation properties of steel and concrete, concrete cracking, tension-softening and tension-stiffening,bond slip between reinforcement and concrete etc. Even under low load, behaviour can be non-linear, which presents a challenge for calculating the deformations of RC members.When stress in concrete first reaches tensile strength at the weakest section,cracking occurs. After the formation of the first primary crack up to the final one, concrete contribution steadily decreases. At the final cracking point, the stable crack pattern has been reached. Increase in load will result in a further decrease of concrete contribution due to bond-slip causing cover-controlled cracks to develop between the primary cracks and a gradual breaking down of the bond. This process can be imagined as the formation of internal secondary cracks along the deformed bar due to bond stress transfer to sound concrete in between primary cracks. Total stresses in the cracked tensile reinforcement consisted of genuine stresses corresponding to the average strain of steel and additional stresses due to tension-stiffening. The internal forces that represent the latter stresses are called the residual and can be used for assessing the average bond behavior of RC members. This paper investigates tension-stiffening effect in RC members. The discrete cracking model of RC member is described in the paper. The discussed approach is based on bond-slip relationship that models the bond-action between concrete and reinforcement. This approach is realistically capable of modelling cracking and determining crack widths and deformations. However, the accuracy of calculation results depends on the assumed bond stress-slip relationship. A number of recent investigations aimed at developing and modifying such models were performed intending that discrete cracking modelling technique could become a powerful tool for the analysis of reinforced concrete members. The present study is dedicated to deformation analysis of reinforced members that are subjected to pure tension and is based on the results of the experimental program reported in literature. The average deformations of such members were calculated applying the discrete cracking method using different bond stress-slip relationships and compared with test results reported in literature. It was concluded that relationship recommended by CEB-FIP MC90 was unacceptable for the analysis performed.