Large Displacement Analysis of Fiber-Reinforced RC Members

A new finite element model based on a fiber beam element formulation that considers large displacements is presented. The element is used to model fiber reinforced concrete members. The element uses a displacement based formulation and has the capability to model reinforced concrete members strengthened with carbon fiber sheets under different loading conditions. The element is developed within a two-dimensional Lagrangian corotational beam formulation. Both the element internal and external geometric stiffness matrices are considered. The transformation between the corotational and the global system is made using an enhanced transformation matrix that takes into consideration the current angle of the co-rotating frame with respect to the global coordinate system. When steel fibers are added to the concrete mix, the properties of the concrete are improved such that the tensile strength of the concrete increases and the tension softening stiffness is also modified. The new element can precisely simulate the effect of steel fibers while taking into consideration the second order analysis. Two verification examples commonly used in the literature are first presented to verify the capability of the element to model the non-linear material behavior and the geometric non-linear formulation. The first verification example is the William’s toggle frame and the second is a cantilever beam with a vertical load at the tip. In both examples, the cross section used is steel. It was found that the proposed element results are in good agreement with the analytical solution of the two examples. Later, the new element is employed to model the experiment of a reinforced concrete column hinged at both ends that encounter large displacements, where carbon fiber reinforced polymer (CFRP) sheets are used to strengthen the column. Results show that the element can precisely depict the strengthening effect when the structure is simulated using a second order non-linear analysis.