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PROCEEDINGS OF THE ELEVENTH INTERNATIONAL CONFERENCE ON CIVIL, STRUCTURAL AND ENVIRONMENTAL ENGINEERING COMPUTING
Edited by: B.H.V. Topping
Advanced Approach in Numerical Modeling of Reinforced Concrete Frames Loaded by Seismic Actions
Civil Engineering Department, Faculty of Technical Sciences, University of Novi Sad, Republic of Serbia
D. Kovacevic, "Advanced Approach in Numerical Modeling of Reinforced Concrete Frames Loaded by Seismic Actions", in B.H.V. Topping, (Editor), "Proceedings of the Eleventh International Conference on Civil, Structural and Environmental Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 160, 2007. doi:10.4203/ccp.86.160
Keywords: finite element method, numerical modeling, nonlinear analysis, seismic actions, reinforced concrete frames.
This paper is a review of one possibility for numerical modeling of in-plane reinforced concrete frames loaded by seismic actions. The objective of this research is the formulation of one model that is sophisticated enough and suitable for engineering practice, while being a reasonably convenient numerical model.
Physical discretization and mathematical approximation is based on the finite element method (FEM) concept. Finite element (FE) stiffness and geometric matrices are defined by the Lagrange updated formulation. The mass matrix is adopted as a lumped mass matrix neglecting the rotational inertia. The damping matrix is assumed as proportional to the initial stiffness matrix of the FE system.
The Beam FE cross-section is divided into a certain number of finite thickness concrete and steel layers, and the behavior, under the cyclic loading, is modeled by corresponding uniaxial constitutive rules.
The "smeared cracks approach" and "tension stiffening approach" is accepted in zones where the concrete tension strength is reached.
A linear strain distribution is adopted along the height of the cross-section, because of the negligible shear influence in the total deformation field for a typical beam. In this way, the well-known "shear locking" effect (overestimating the participation of shear deformation in the total deformation energy) is avoided. In contrast to shear in the strict sense, axial and shear stresses interaction influence, as a cause of the appearance of inclined cracks must be included in the model.
The inclusion the frame joint deterioration, as well as, interaction of shear and flexural forces (inclined crack effects), in this model, is additionally given.
Straight, plane, two-joint beam FE approximates for a RC element (beam, column) are used. Two displacements and one rotation per joint are the degrees of freedom (DOF). Third degree L'Hermite polynomials and linear functions are adopted as the interpolation functions for transversal and longitudinal displacement fields.
For numerical integration of the dynamic equilibrium, the Newmark integration procedure (with a 5ms increment) is applied as well as a modified Newton-Raphson iterative procedure for balancing the residual loads.
As an illustration of the previous propositions, the results for the four numerical tests are presented: one linear and three nonlinear analysess of one simple reinforced concrete frame loaded by three seismic actions.
The results attained indicate that the proposed numerical concept is one "good compromise" solution. A compromise is made between the accuracy, as an essential parameter, and, on the other hand, simplicity, as an everyday design practice task. The objective of the research presented was to find a middle way in the nonlinear analysis of the structures described.
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