Amirkabir University of Technology Amirkabir Journal of Civil Engineering 2588-297X 51 4 2019 10 23 A Mixed Analytical Approach based on Semi-Timoshenko Planar Fiber Frame Element and Modified Compression Field Theory in RC Structures A Mixed Analytical Approach based on Semi-Timoshenko Planar Fiber Frame Element and Modified Compression Field Theory in RC Structures 733 748 2904 10.22060/ceej.2018.14017.5536 FA Behrooz Yousefi Civil Engineering Department, Ferdowsi University of Mashhad, Mashhad, Iran 0000-0002-4792-5890 Mohammadreza Esfahani Department of Civil Engineering, Ferdowsi Unversity of Mashhad Mohammad Reza Tavakolizadeh Civil Engineering Department, Ferdowsi University of Mashhad, Mashhad, Iran 0000-0002-0932-4605 Journal Article 2018 01 28 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 was developed with a displacement control method using linearized arc-length approach. The formulation of the implemented element was 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 was 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) was considered in nonlinear shear analysis using the direct-displacement control algorithm in the main sub-program. The reference configuration of numerical formulation was considered according to the configuration of the previous step and the initial configuration, simultaneously. The analytic approach of the algorithm had the ability to change the updated Lagrangian formulation to the total Lagrangian in accordance with the problem-solving convergence. The developed fiber element was validated by numerous experimental experiments and the evaluation of the proposed analytical method was tested. The proposed method led to an appropriate solution and an acceptable convergence process with high processing speed for problems with mixed combinational mechanisms. 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 was developed with a displacement control method using linearized arc-length approach. The formulation of the implemented element was 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 was 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) was considered in nonlinear shear analysis using the direct-displacement control algorithm in the main sub-program. The reference configuration of numerical formulation was considered according to the configuration of the previous step and the initial configuration, simultaneously. The analytic approach of the algorithm had the ability to change the updated Lagrangian formulation to the total Lagrangian in accordance with the problem-solving convergence. The developed fiber element was validated by numerous experimental experiments and the evaluation of the proposed analytical method was tested. The proposed method led to an appropriate solution and an acceptable convergence process with high processing speed for problems with mixed combinational mechanisms. https://ceej.aut.ac.ir/article_2904_b8b9c74ac526fffbeb2d39ab038d1cd7.pdf