Numerical analysis of reinforced concrete asymmetric cross-section beams under oblique bending

Abstract

The problem of symmetric cross-section beams under oblique bending is well known to professional designers and academy. In fact, symmetric elements make up most of the cross-sections defined in design. The case of the asymmetric cross-sections is, however, little discussed in literature, but is a particular problem, especially in bridge girder design, joined in loco. The asymmetry generates oblique bending when the load is out of the principal inertia planes. Thus, this article presents a comparison of results between a numerical solution of the elastic curve differential equations, and a Finite Element Model (FEM), for a 10m span reinforced concrete beam, with gutter-shaped asymmetric cross-section, whose only load is its own weight. The required geometric properties were determined by the Green Theorem. From theoretical study, the elastic curve differential equations were obtained, in the vertical and horizontal directions. The angular displacement conditions at the beginning of the span were obtained by the Virtual Work Method. After integration using the Runge-Kutta Method, the maximum displacements in the vertical and horizontal directions, in the middle span, are 0.904cm and 0.611cm, respectively (1.091cm resultant displacement). The Finite Element Model was performed in ANSYS 9.0. The resultant displacement of the numerical model was 1.16cm. Concurrently, the axial stresses were studied in the middle span. The stress results for both approaches (Runge-Kutta and FEM) differed by no more than 8.72%. These results guarantee reliability to the Runge-Kutta integration, from a design view point, to the proposed problem analysis in Serviceability Limit State.