Aplicação de formulação completa para o dimensionamento de pilares esbeltos em concreto armado

Abstract

The design of reinforced concrete slender columns according to ABNT NBR 6118:2023 must be performed based on a complete nonlinear analysis. This analysis requires a refined discretization, and the element formulation may consider geometric and material nonlinearity, in addition to incremental-iterative methods for solving the nonlinear system. To simplify this process, this work proposes a formulation that uses a single element for the design of reinforced concrete slender columns based on analytical interpolation functions associated with the moment-curvature relationship and the Two Iterative Cycle Method. By employing interpolation functions corresponding to the homogeneous solution of the differential equation of the problem, the exact behavior of the structure is obtained, without the need for discretization. Material nonlinearity is considered using moment-curvature diagrams updating the analytical stiffness matrix, while the Two Iterative Cycle method avoids the need to implement robust nonlinear solution schemes. The proposed element was implemented in VBA Microsoft Excel, and the results demonstrate the efficiency of the formulation to predict the P- and P- effects, and calculate the bending moment along slender columns, using a single element, with accurate results and low computational cost