Kinematics-Based Modelling of Deep Transfer Girders in Reinforced Concrete Frame Structures

Reinforced concrete deep beams often carry heavy loads as transfer girders in high-rise buildings, pile caps in bridges or other important structural members. Due to their small slenderness, they exhibit shear failure with disturbed deformation patterns differently from slender beams. Many experiments have revealed the complexity of the shear mechanisms of deep beams, and a number of formulations and models have been proposed attempting to explain their behaviour. However, up to the present, the accurate prediction of the shear response of deep beams remains a challenge. Considering the importance of such kind of structural element, this thesis is dedicated to make a further investigation on the shear mechanisms and provide a useful tool to predict the entire shear response of deep beams. More than seventy models for deep beams are firstly summarized and classified into different categories according to their main characteristics. Detailed evaluation is made on ten models among them, with the help of a database of 574 deep beam tests. It is found that a semi-empirical strut-and-tie model (STM) and a two-parameter kinematic theory (2PKT) for deep beams produce the least scattered predictions in terms of shear strength experimental-to-predicted ratio Vexp/Vpred. Further studies are conducted to explore the effect of various important parameters, e.g. shear-to-span-depth ratio (a/d), size effect, and other. While the 2PKT produces uniform Vexp/Vpred across the entire range of experimental data and captures well the effects of all studied parameters, the semi-empirical STM exhibits certain bias with respect to the beam slenderness and does not account for the important size effect in shear. In order to evaluate the serviceability, safety and resilience of deep beams, the thesis continues with the development of a 1D macroelement based on a three-parameter kinematic theory (3PKT) which is an extension of the 2PKT method to continuous deep beams. This macroelement aims at capturing the entire response of deep beams including both the pre- and post-peak regimes. One macroelement represents a deep shear span by using only two nodes with two degrees of freedom per node. Both simply-supported and continuous deep beams are modelled with the proposed 1D macroelement. It is shown that the macroelement captures well the force redistribution between shear spans in continuous members, and in this way predicts their enhanced ductility as compared to simply supported deep beams. It is also shown that the model captures the opening of the critical shear cracks under increased loading. The crack predictions can be compared with field measurements to accurately evaluate the safety of the structure, and in this way to avoid potential costly strengthening measures. As a result of the compatibility between the proposed 1D macroelement and classical 1D slender beam elements, a mixed-type modelling framework is proposed to overcome the high cost of analysis on large frame structures including deep transfer girders modelled with 2D high-fidelity finite element procedures. The framework is implemented in an existing nonlinear analysis procedure and is used to model eighteen deep beam tests and a twenty-story frame. It is shown that the proposed framework provides similarly accurate predictions to 2D high-fidelity procedures but requires a fraction of the time for modelling and analysis. Furthermore, the macroelement improves the post-peak predictions, and therefore the proposed framework is suitable for evaluating the resilience of structures under extreme loading. Although the full shear response of solid deep beams can be well captured with the proposed macroelements, it is still an open issue to understand the behaviour of deep beams with web openings. In practice, web openings are inevitably installed in deep transfer girders to allow for windows, doors and different conduits. They may disrupt the flow of forces from the loads to the supports and significantly reduce the shear strength of deep members. To address this issue, a new model for deep beams with rectangular openings is proposed based on the 2PKT method for solid beams. It is established based on an analysis of the shear behaviour and failure modes of test specimens using nonlinear finite element and strut-and-tie models. In the new model, two sub deep beams form above and below the web opening. Each sub shear span is modelled with two kinematic parameters as in solid shear spans, and the deformation pattern of the entire shear span can be described by these four degrees of freedoms (DOFs). The model is validated with 27 tests from the literature showing adequate shear strength predictions. It is shown that shear strength of deep beams with web openings is more affected by the depth of the opening than by its horizontal dimension. Also, the transition from deep to slender beam behaviour in members with openings occurs at smaller aspect ratios than in solid members. These experimental observations are well captured by the 2PKT approach