Three-dimensional non-linear finite element analysis of reinforced concrete beams in torsion : reinforced concrete members under torsion and bending are analysed up to failure : a non-linear concrete model for general states of stress including compressive strength degradation due to cracking is described
This thesis describes a non-linear finite element model suitable for the analysis of reinforced concrete, or steel, structures under general three-dimensional states of loading. The 20 noded isoparametric brick element has been used to model the concrete and reinforcing bars are idealised as axial members embedded within the concrete elements. The compressive behaviour of concrete is simulated by an elasto-plastic work hardening model followed by a perfectly plastic plateau which is terminated at the onset the . crushing. In tension, a smeared crack model with fixed orthogonal cracks has been used with the inclusion of models for the retained post-cracking stress and the reduced shear modulus. The non-linear equations of equilibrium have been solved using an incremental-iterative technique operating under load control. The solution algorithms used are the standard and the modified Newton-Raphson methods. Line searches have been implemented to accelerate convergence. The numerical integration has been generally carried out using 15 point Gaussian type rules. Results of a study to investigate the performance of these rules show that the 15 point rules are accurate and computationally efficient compared with the 27(3X3X3) point Gaussian rule. The three- dimensional finite element model has been used to investigate the problem of elasto-plastic torsion of homogeneous members. The accuracy of the finite element solutions obtained for beams of different cross-sections subjected to pure and warping torsion have been assessed by comparing them with the available exact or approximate analytical solutions. Because the present work is devoted towards the analysis of reinforced concrete members which fail in shear or torsional modes, the computer program incorporates three models to account for the degradation in the compressive strength of concrete due to presence of tensile straining of transverse reinforcement. The numerical solutions obtained for reinforced concrete panels under pure shear and beams in torsion and combined torsion and bending reveal that the inclusion of a model for reducing the compressive strength of cracked concrete can significantly improve the correlation of the predicted post-cracking stiffness and the computed ultimate loads with the experimental results. Parametric studies to investigate the effects of some important material and solution parameters have been carried out. It is concluded that in the presence of a compression strength reduction model, the tension-stiffening parameters required for reinforced concrete members under torsion should be similar to those used for members in which bending dominates.