A new method for modelling reinforcement and bond in finite element analysis of reinforced concrete
In conventional finite element analysis of reinforced concrete the steel bars are normally assumed to lie along the concrete element edges and very often the bond gripping the steel to the concrete is assumed to be infinitely stiff. The first assumption makes it difficult to model all steel bars leading to the inclusion of only a few representative bars. Shear reinforcement is usually ignored. Thin concrete cover also creates difficulty by causing long thin finite elements in that region. The second assumption does not reflect the true behaviour of the system. In this research a new method for the modelling of steel in reinforced concrete by finite element analysis has been developed which allows all steel reinforcement to be included in the analysis. The method is based on modelling the steel and concrete separately, the two materials being interconnected by the bond forces between them. Thus, bond stiffness is naturally included in the analysis. Such interconnection of steel and concrete is achieved by an interface bond matrix which is derived from the relative displacements between the steel and the concrete at the steel nodes. A linear bond slip relation is assumed for the bond, and a linear stress strain relation is assumed for the concrete and the steel. The work has extended also to nonlinear bond stress-slip relation. Concrete is represented by 8-noded isoparametric quadrilateral elements, and the steel is represented by two noded bar elements. The bond is represented by springs joining each steel node to all 8-concrete nodes. The solution of the resulting system of equations is achieved in an iterative manner which converges quite rapidly, and which requires less computation than the direct solution needs. Three types of problems are analysed in two dimension to demonstrate the application of this new method. These are beam, cantilever and pullout problems. The first two, being real problems, demonstrate the ability of the method to handle complex steel arrangements, thin concrete covers and anchorage of steel, while the third problem shows the application of load to the steel rather than to the concrete. Concrete and steel deformations and stresses are calculated at their nodes. Bond stresses are given at all steel nodes. In the nonlinear bond analysis, deterioration of bond will be demonstrated in pullout and pushout tests at high loads.