A Mixed Analytical Approach based on Semi-Timoshenko Planar Fiber Frame Element and Modified Compression Field Theory in RC Structures

An accurate assessment of the behavior of structures by an analytical method should be able to estimate the initial stiffness of the structure, the maximum capacity and the local and global ductility. In this research, in order to simulate the nonlinear behavior of reinforced concrete structures under monotonic loading, a new fiber beam-column element has been developed with a displacement control method using linearized arc-length approach. The formulation of the implemented element is based on the combination of Bernoulli and Timoshenko's theory along with the axial, flexural, and shear interaction effects of each element. The cross-sectional area of each element in Gaussian points is equivalent to a set of discrete fibers with uniaxial constitutive behavior in the process of nonlinear solution. Also, in order to consider the elemental shear deformation, the four-way smeared cracked approach and the modified compression field theory (MCFT) have been considered in nonlinear shear analysis by using the direct-displacement control algorithm in the main sub-program. The reference configuration of numerical formulation is considered according to the configuration of the previous step and the initial configuration, simultaneously. The analytic approach of the algorithm has the ability to change the updated Lagrangian formulation to the total Lagrangian in accordance with the problem-solving convergence. The developed fiber element has been validated by numerous experimental experiments and the evaluation of the proposed analytical method has been tested. The proposed method leads to an appropriate solution and an acceptable convergence process with high processing speed for problems with mixed combinational mechanisms.