Overview
Numerical simulation is the act of estimating structural behaviour in a computer analysis based on the principles of equilibrium, compatibility and stressstrain relationships. For some materials, such as steel prior to yield or concrete prior to cracking, the relationships are relatively simple to apply and there is little international disagreement about how the analysis should be done. Even with such cases, however, the boundary conditions are crucial to model appropriately. For nonlinear material behaviour, such as concrete after cracking, steel after yield, and timber in general, more advanced constitutive models are needed. Tools implementing these models are available either as general purpose software tools (e.g. SFrame, ABAQUS, ANSYS, etc) or as special purpose tools that specifically aim to directly model complex structural components. These analysis tools excel at models that range from the material level, through the subsystem level, up to full structural levels.
At the University of Toronto we have developed a collection of different analysis tools, particularly suited for reinforced and prestressed concrete structures. Some of these are described below.
At the University of Toronto we have developed a collection of different analysis tools, particularly suited for reinforced and prestressed concrete structures. Some of these are described below.
VecTor Programs 
Professor Frank Vecchio and his team have developed the general finite element toolset known as the VecTor suite. These tools allow for analysis of concrete plates, shells, frames and solids accounting for the key behaviours of creep, shrinkage, cracking, slip on cracks, yielding, strain hardening and compression softening. Each program in the suite is a different finite element program which can be downloaded directly from the VecTor website (www.civ.utoronto.ca/vector) Each of these is described briefly below.
VecTor2: Two dimensional analysis of membrane structures. This is the most widely used VecTor program and allows analysis of general twodimensional reinforced or prestressed concrete structures. The figure shows a series of real reinforced and prestressed concrete structures that have been analysed with VecTor2 for safety and exploratory analyses. The elements assume plane stress and the constitutive relationships of the Modified Compression Field Theory (MCFT) as well as the more advanced Disturbed Stress Field Model (DSFM). Most experiments on twodimensional concrete lab specimens in Toronto (for example beams and walls) are modelled by VecTor2 as part of student theses with the analyses being done by the students themselves. Over the years a great deal of confidence in the results of this program has be obtained by experienced users. VecTor3 is a threedimensional brickbased finite element analysis program as an extension of the above. This type of analysis is needed for more complex structures such as large foundations. VecTor4 is a general purpose finite element analysis program that uses shell elements for slabs, walls, etc, which are not two dimensional. It has been used for analyses of thick slabs and nuclear containment structures for example. VecTor5 is a frame analysis program which has been used for structural/thermal analyses and general frame analysis accounting for cracking etc. VecTor6 is an axisymmetric version of VecTor2 for analysis of round columns, cylinders etc. All programs are available from the same website listed above for VecTor2. 
Response2000 
Professor Evan Bentz has developed his program Response (originally titled Response2000) for the nonlinear sectional analysis of reinforced and prestressed concrete structures. The program assumes that plane sections remain plane, that there is zero clamping in the transverse direction for the member, and that the equations of the MCFT can accurately explain the behaviour of cracked reinforced concrete. The program is freely available online (http://www.ecf.utoronto.ca/~bentz/r2k.htm) and has been downloaded by 64,000 engineers and researchers in 155 countries as of March 2016. In the summer of 2016 a new version will be released allowing more general analyses to be performed and an improved interface. The analysis shows the results of a 4 metre thick slab strip test, 20 metres long, performed at the University of Toronto along with predictions by Response. As can be seen, reasonably good results can be obtained even for cases that are well outside the norm, and it should be noted that the predictions were made prior to the test being performed. For comparision, the ACI shear provisions predict that the failure load should have been about 2.9 times higher than that observed in the test. While a tool like VecTor2 can provide a more precise prediction than Response, the speed with which the Response analysis runs for this nonlinear problem can be very helpful. In addition, the interface has been written so that it is easy to run even for nonexperts.
In addition to Response2000, Bentz has also written Membrane2000 (www.ecf.utoronto.ca/~bentz/m2k.htm) which is a detailed look at a single element of a shell as well as Triax2000 (www.ecf.utoronto.ca/~bentz/t2k.htm), which considers a single triaxial element. Each program has been written to highlight the interpretation of the results to help the user understand “why” and not just “what”. 
AugustusII 
As an extension of the Response and Membrane Programs, Professor Bentz has written an analysis tool called AugustusII. This tool shown in the image with a progressive collapse calculation of a building in the Toronto area, combines the strengths of VecTor2 for modelling of walls along with the speed of Response for the beam and column elements in this analysis. The constitutive models are based on Response2000 and Membrane2000, see above, and the analysis is based on general finite element principles.
