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Nonlinear analysis of reinforced concrete frame structures

Çiftçi, Güçlü Koray
Reinforced concrete frames display nonlinear behavior both due to its composite nature and the material properties of concrete itself. The yielding of the reinforcement, the non-uniform distribution of aggregates and the development of cracks under loading are the main reasons of nonlinearity. The stiffness of a frame element depends on the combination of the modulus of elasticity and the geometric properties of its section - area and the moment of inertia. In practice, the elastic modulus is assumed to be constant throughout the element and the sectional properties are assumed to remain constant under loading. In this study, it is assumed that the material elasticity depends on the reinforcement ratio and its distribution over the section. Also, the cracks developing in the frame element reduces the sectional properties. In case of linear analysis, the material and sectional parameters are assumed to be constant. In practice, the modulus of elasticity E is a predefined value based on previous experiments and the moment of inertia I is assumed to be constant throughout the analysis. However, in this study, E and I are assumed to be combined. In other words, they cannot be separated from each other throughout the analysis. These two parameters are handled as a single parameter as EI . This parameter is controlled by the reinforcement ratio and its configuration, sectional properties and deformation of the member. Two types of analysis, namely a sectional and a finite element analyses, are used in this study. From the sectional analysis, the parameter EI is calculated based on the sectional geometry, material properties and the axial load applied on the section. The parameter EI is then used in the finite element analysis to calculate the sectional forces and the nodal displacements. For the nonlinear analysis, the Newton-Raphson iterative approach is followed until convergence is obtained.