ANALYTICAL STUDIES ON BEHAVIOR OF REINFORCED CONCRETE MEMBERS SUBJECTED TO COMBINED LOADINGS

The present study on analysing the behaviour of RC members while subjected to combined loading and cyclic loading is presented in three parts (A, B and C). In part-A of the thesis, an improved softened membrane model for analysing the Reinforced Concrete (RC) columns while subjected to combined loading of shear and Torsion is proposed and discussed. RC columns are subjected to combined loadings of axial, shear, bending and torsion especially in the cases of skewed and curved bridges with unequal spans and column heights. The complex stress state created due to the combined loading triggers the pre anticipated failure of members. The behaviour of rectangular RC members subjected to combined loadings has been studied analytically in this study. Earlier, Greene (2006) proposed an analytical model based on membrane element formulation. The model is used for predicting the response of a reinforced concrete members subjected to combined loads that includes Torsion, Axial, Shear and Bending moments. The model consists of a set of equations, derived from the equilibrium and compatibility conditions at element level and section level. The solution of the set of equations is nothing but the analytical response of the member. (Hsu and Zhu, 2002) developed Softened Membrane model (SMM) by including the Poisson’s ratio effect. The consideration of bidirectional stresses using Poisson ratio helps in predicting the post peak behaviour accurately. In this research work, a solution algorithm based on SMM is proposed for analysing the Reinforced Concrete(RC) sections subjected to combined torsion and shear loadings. The rectangular cross sections are modelled as an assembly of four cracked shear panels (Greene 2009). The applied external loadings are distributed among these four shear panels. The set of non-linear equations satisfying the equilibrium and compatibility conditions were solved using Gradient Descent method, an optimisation technique. The proposed solution algorithm has been validated with experimental data obtained from literature and conclusions made. In Part-B of the thesis, softened membrane model has been applied for proposing an improved model which can be applied for analysing the RC members subjected to Cyclic torsional loading. RC bridge columns are very often subjected to torsional moment in addition to flexure and shear during seismic vibration. Ignoring torsion in the design can trigger unexpected shear failure of the columns. Performance based seismic design is an emerging design philosophy which calls for accurate prediction of the hysteresis behaviour of structural elements to ensure safe and economical design under earthquake loading. However, very few investigations in the past focused on the development of analytical models to accurately predict the response of RC members under cyclic torsion. Previously developed hysteresis models are not readily applicable for torsional loading owing to significant pinching and stiffness degradation associated with torsion. The present study aims at filling this knowledge gap by proposing an improved polygonal hysteresis model which can accurately predict the hysteretic behaviour of RC circular and square columns under torsion. The primary curve is obtained from mechanics based softened truss model for torsion. The proposed model is validated with experimental data of two circular and square columns. Close correlation is observed between the predicted and measured torque-twist behaviour and dissipated energy. In Part-C of the thesis, Modified Compression Field Theory(MCFT) has been studied. MCFT is another type of space truss model used for modelling the cracked concrete section under combined loading. MCFT similar to SMM, developed at the University of Toronto. Cracked concrete is treated as a material with its own stress-strain characteristics. Equilibrium, compatibility and stress-strain relationships are formulated in terms of average stresses and average smeared strains. In the current study, the model developed by Vecchio and Collins for predicting the Shear flexure interaction has been presented and discussed. The model was based on Modified compression field Theory (MCFT). The model has been validated with the available experimental data from the literature for a detailed understanding of the flexure shear interaction of concrete sections