A new approach to finite element modeling of crack in RC beams

In this paper a new approach was proposed for modeling of the crack in opening mode I of reinforced concrete Euler-Bernoulli beams. The characteristics properties of the crack are simulated by making use of a rotational spring. Beam elements are divided into two categories which include elements with and without crack. In the elements without the crack, the standard governing relationships of the beam are established with considering the moment of inertia of the reinforced cross section. In the elements with the crack, a change in the cross-section of the reinforced concrete due to the crack and a discontinuity in the crack point resembled by modification of the standard governing relationships.In this case, the simulation of the crack is done by dividing the element to two sub-elements in each side of the rotational spring. The stiffness matrices of the two sub-elements and the improved stiffness matrix of the whole element are derived by satisfying the continuity equation at the crack point. The effects of the depth and position of the crack and the location and the cross-section area of reinforcing bars on the static behavior of the reinforced concrete beam were investigated. The results were compared with those obtained from analyses performed by commercial software (Abaqus) which proved the excellent accuracy of the proposed model.