Seismic Analysis of Nonlinear Reinforced Concrete Frame Structures

Resumo

Seismic structural analysis attracts significant interest in Brazil, even though much of the country exhibits low seismicity. Some regions in northwestern Brazil, such as most of the state of Acre and the southwest of the state of Amazonas, present ground motion accelerations that require dynamic analysis for earthquake loading. The construction of some special structures, such as nuclear power plants, requires the consideration of their seismic responses, regardless of their location. The internal forces provided by the Response Spectrum Method, in the frequency domain, are not always suitable for the design of reinforced concrete structures. The behavior of concrete is different under compression and tension. The sum of the modal absolute values through SRSS (Square Root of the Sum of Squares) and CQC (Complete Quadratic Combinations) approaches provides maximum absolute internal forces. However, negative or positive values indicate compression and tension, and reinforcement design is greatly influenced by whether stresses are compressive or tensile. The purpose of this research is to present a methodology for the seismic dynamic analysis of nonlinear framed structures, in the time domain, in which the equilibrium is rigorously examined at the end of each time step. The constitutive models adopted for the cyclic behavior of concrete and steel are discussed. A Timoshenko beam element suitable for this nonlinear analysis is presented. A time integration algorithm, based on Newmark's implicit method, is developed using the element's implicit stiffness matrix that considers the nonlinear behavior of the material. Equivalent nodal forces are calculated from accelerograms of known earthquakes. The adoption of the classic Rayleigh damping model is discussed. The numerical implementation is detailed. Examples are presented and conclusions are drawn.