Evaluation of Moment-Curvature Relationship for Reinforced Concrete Beam Element

Abstract

The relationship between Moment and Curvature of Reinforced Concrete sections is an important parameter for Nonlinear Analysis of RC framed structure. This helps in determining strength, stifeness, ductility, and energy dissipation capacity of the RC sections. The moment-curvature relationship would enable us to observe the strength reduction beyond the yield point and degradation of the exural rigidity. Theory of beam exure states that curvature is the second derivate of displacement. Moment-Curvature (M-;) relation is then very important as it helps to calculation of displacement due to the forces acting in to the inelastic elements. Analytical as well as experimental study is carried out for RC beam section. A well-established models of stress-strain for concrete and steel material are used. Mod- els showing relationship of stress-strain for both confine as well as unconfined concrete are studied. Six deferent stress-strain models are selected. Among those IS 456 Model, Hongnestad Model, Kent and Park Model, IRC Model are pertaining to unconfined concrete and Cusson Model and Mendar Model are pertaining to confined concrete. For steel material King Model is used. A MATLAB based program is developed to derive Moment-Curvature relationship for RC beam elements using above mentioned models for concrete and steel material analytically. An experimental program is design to evaluate Moment-Curvature relationship for RC beam elements. Both singly and doubly reinforced sections are design with under and over reinforcement for each section. Three sample specimens of dimension 120mm 150mm 1700mm are prepared for each case leading to total twelve numbers of test specimens. Loads and strain are measured to derive Moment-Curvature for each test specimens. It is found that well established models of stress-strain for material to derive Moment- Curvature relationship closely match with the Moment-Curvature relation- ship experimentally. It is noticed that model suggested by IRC 112 shows good agrement with experimentally obtain Moment-Curvature relationship.