There are many researchers who derived tension stiffening models to evaluate the average tensile stress of concrete. Most of them have focused on tensile behaviour before yielding of reinforcement. After the yielding of reinforcement at the crack surface, the average tensile stress of concrete is reduced because the reinforcement stress is limited to its yield strength (line B-C in Figure). Without this equilibrium check, the capacity of concrete members or structures could be not correct because of an overestimation of concrete tensile stress. With this limitation, after the average strain of reinforcement reaches the yield strain, the average tensile stress of concrete becomes zero. Hence, once the average stresses of reinforcement have reached yield, the contribution of concrete on tensile behaviour is ignored, so the tensile behaviour of reinforced concrete members after yielding of reinforcement becomes the same as that of bare steel bars. Consequently, the equilibrium check on the crack surface makes the ultimate strength and strain identical to those of the bare steel bar (line C-D in Figure). However, tensile stress of concrete still exists even after yielding of reinforcement because of bond behaviour between concrete and steel reinforcement. The contribution of concrete tensile stress after yielding of reinforcement makes the strain at the ultimate condition less than that of the bare steel bar (line C-E in Figure). Therefore, the tensile stress of concrete after the yielding of reinforcement should be considered for a more reasonable and precise prediction of structural behaviour of concrete members and structures.

The main objective of this research is on the development of a tension stiffening model which is applicable to the prediction of the post-yield behaviour of RC members. The model to be developed will be implemented on VecTor2.

Fibres have been used in concrete structures to compensate for the weak point of concrete; its brittle tensile behaviour. One of the most important effects of the application of fibres in concrete structures is that non-brittle behaviour after concrete cracking can be achieved. When evaluating the stress-crack opening displacement response due to fibres, the direct tension specimens tested are generally of a small size. Therefore, the effect of the restriction of fibre orientation should be considered in order to apply test results from small specimens to the analysis of real structures with fibre reinforced concrete. Moreover, some of fibres crossing crack surfaces are engaged in tension while the others are not engaged, so the effectiveness of fibres should be also considered.

The objective of this research is on the derivation of a tensile behaviour model for fibre reinforced concrete which takes account of the member size effect, the effectiveness of the fibres, the fibres' random orientation, and so on, all at once. The model to be derived will be expanded into the derivation of a tension stiffening model for fibre reinforced concrete with ordinary deformed steel reinforcing bars. The model to be derived will be implemented in the VecTor analysis programs.

Further development of the software program VecTor4, a nonlinear finite element analysis program for reinforced concrete shells and plates, focused on improving the analysis of structures under static and cyclic loading conditions is currently underway.  The ability to consider dynamic loading conditions such as base accelerations, impact loads, and blast loads will be introduced to the program.  Additionally, an experimental program consisting of both reinforced concrete (RC) and steel-fibre reinforced concrete (SFRC) slab specimens subject to impact loading conditions will be performed.  The focus of the experimental program is to i) assess what effect SFRC has on the dynamic behaviour of the slabs under impact conditions, ii) further refine constitutive relationships used to model SFRC in the VecTor software programs, and iii) to provide data for the corroboration of the VecTor4 analytical results.

As the mechanical properties of reinforced concrete change significantly at elevated temperatures, and as most of the international building codes are getting more concerned with performance-based design having fire-performance criteria, investigating the behaviour of reinforced concrete structures under elevated temperatures and fire is the major area of Fady ElMohandes’ research.  Thermal analysis is being incorporated in VecTor3 software, the part of the VecTor analysis software responsible for the analysis of three-dimensional reinforced concrete solid elements. In addition, dynamic analysis capabilities including blast and impact loading are also being included in the software. For the sake of the corroboration of VecTor3, an intensive experimental program is planned, where various types of elements will be tested with different types of concrete, levels of sustained loading, confinement levels and temperature loading profiles.

The current suite of VecTor analysis programs were developed such that each program is capable of modeling one particular type of structure only. However, there are many applications in which different types of structural components act together. A master program is being developed to account for the interactions between substructures and enable the analysis of mixed-type structures using the VecTor computational methodologies and material model formulations. The concept is to compute displacements at master points which are shared between two or more substructures; based on the computed displacement at each of these principal points, analyses would be performed for each substructure using appropriate VecTor program. This allows the use of parallel processing which results in faster and more efficient analysis.

In addition, work is being done to make the VecTor programs compatible with hybrid simulation tests. Hybrid simulation testing requires the use of a continuous feedback system between the physical model and the numerical model, often in real-time. Enabling the use of the VecTor programs as the numerical model will result in more accurate simulations of the complex nonlinear behaviour of concrete structural elements and, thus, more accurate hybrid simulations.

The area of blast and impact loads is becoming increasingly important and the need exists to have a tool that can assess both the local and global damage a structure will sustain under blast and impact loads. Dynamic analysis capabilities are available in VecTor2 for both impact and impulse loads. However, these have been tested thus far only for high-mass low-velocity impact problems. The focus of Heather’s research is to verify and improve the ability of VecTor to model blast and impulse loads. The modeling of concrete material loss associated with extreme blast and impact loads will also be introduced into VecTor through element erosion.

A series of experiments have been developed to further study the behaviour of FRC in order to develop more robust and accurate constitutive models for the material. Tests on in-plane panel specimens (890x890x70mm) will be performed using the Panel Element Tester. Experimental variables will include the volume percentage of fibres in the mix, length of the fibres, fibre aspect ratio, fibre type (end-hooked steel versus ribbed polypropylene fibres) and loading protocol (monotonic shear, reversed cyclic shear, combined axial tension/compression and shear). From this proposed research, improved constitutive models for representing the behaviour of FRC structures under reversed cyclic loading will be developed and implemented into the VecTor suite of nonlinear finite element analysis programs. The ultimate goal is to contribute to the database, extend the knowledge in this field and improve the ability to accurately analyse and design FRC structures.

Finite element analysis (FEA) programs facilitate the analysis of complex structures which may not be readily designed by traditional means, generating vast arrays of data in approximately predicting the behaviour of a given under a desired loading scenario. Contemporary FEA programs, such as the VecTor software suite, utilize post-processor programs to allow for the multitude of numerical information to be comprehensively displayed graphically for ease of data synthesis, interpretation and verification of results. The proposed Janus post-processor program will be used to augment the existing VecTor structural analysis programs, providing the user with the capability to display both two-dimensional and three-dimensional global structural response characteristics such as: crack patterns, stress contours, deflections, and load patterns. The Janus post-processor will not only allow for the user to comprehensively recall and manipulate structural analysis results on a global scale, but will also have the capacity to display pertinent information for individual specified elements of interest as well.