## Background

Professor Frank Vecchio, a Bahen/Tanenbaum Professor in Civil Engineering specializes in structural modelling. Collectively, with Professors Evan Bentz and Michael Collins, they are addressing the problem of how engineers can use new approaches in design to better assess and repair structures before catastrophe strikes. Hypotheses on the mechanisms of building collapse are validated using the U of T-designed Shell Element Tester located in the Civil Engineering Structural Testing Facility. This is the only facility of its kind in Canada capable of testing full-scale shell elements subjected to all eight possible force components. Combined with the U of T-designed structural analysis software, “Response”, these researchers can predict the behaviour of structures in extreme circumstances. The “Response” software has helped revolutionize building codes across Canada, the United States and Europe. The advances in testing scope and precision that these collaborators have made will help to make building assessment and maintenance faster and more efficient, enabling engineers to more accurately predict which structures are safe following seismic events, thereby saving lives and reducing costs.

## Presentations & Projects

Steel-concrete (SC) composite elements consist of a thick concrete core section sandwiched between thin steel faceplates. The element core typically contains no conventional reinforcement, but utilizes shear studs and cross-tie bars to join the core to the faceplates, and to serve as transverse shear reinforcement. In the past, there had been considerable interest in the use of SC systems for the construction of nuclear power plant structures due to the significant cost savings which could be attained as a result of employing modular SC systems. Today, the increasing need for design of seismic and impact resistant structures has led to renewed interest in the development of SC composites.

Steel-Concrete (SC) Composite Element

(adapted from Usami et al., 1995)Further development of the software program VecTor4, a nonlinear finite element analysis program for reinforced concrete shell structures, focused on incorporating SC analysis capabilities is currently underway. The resulting analysis procedure will be used to perform a preliminary assessment regarding the behaviour of SC composite shell elements under seismic loading conditions, a research area not previously investigated. The capability of SC elements to achieve desirable ductility levels, specifically under three-dimensional shear critical loading conditions, will be investigated.

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.

Shear wall-frame interactionIn 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.

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Current methods used for analysis of reinforced concrete (RC) structures under impact loading are mainly based on single degree of freedom (SDOF) methods or complex hydrocodes. Most SDOF methods tend to simplify the behavior of the structure, and cannot deliver results in required detail. While, hydrocodes overcome the problems caused by simplification of the behavior, they require a large number of material inputs and modelling of the structure in high detail. The goal of this research is to develop a simplified analytical tool to analyze reinforced concrete slabs under impulsive loading particularly soft and hard missile impacts.

Hard missile impact analysis in VecTor3 (Quarter of the slab is modeled due to symmetry)

The VecTor programs, developed at the University of Toronto, are nonlinear finite element analysis programs for RC structures. These programs are capable of the analysis of shear critical structures accurately using less degrees of freedom than typically required by a hydrocode. This study focusses on improvement of VecTor programs to increase their capability and performance to handle missile impact analyses, where localized severe shear failure is observed.

The susceptibility of constituent materials of a wind turbine foundation (especially reinforcing steel) to fracture under cyclic loading is high, when induced dynamic stresses as a result of wind or waves in the foundation are not properly mitigated in design.

Over the years, the norm in wind turbine foundation design against fatigue considers the material provision to be adequate when the design life cycle is lower than the number of cycles leading to failure at a given stress level. This approach is acceptable for reinforced concrete elements in flexure, as long as bond fatigue does not govern. Hence, the S-N curves and damage models developed for concrete and steel reinforcing bars are sufficient in predicting fatigue failure of beams governed by flexure. However, the behaviour of stirrups under shear fatigue is by far more complex and requires a thorough approach. As such, available S-N curves and damage models may not give appropriate predictions if salient mechanisms in shear fatigue are not taken into consideration.Generally, increased volume of materials are provided to reduce the materials stresses until the corresponding number of cycles to failure increases beyond the design service life cycles. However, some obvious flaws in increasing the amount of stirrups exist. These include: congestion of reinforcement, excess construction time, and poor foundation concreting. In addition, under shear fatigue, the influence of embedded stirrups on the diagonal crack initiation is insignificant. Previous research has shown that fatigue damage accumulation of stirrups begin after diagonal crack. Thereafter, fracture of the stirrups or longitudinal reinforcing bars at intersections with diagonal crack may occur and result in the collapse of the structure. Based on these, an appropriate means of extending the number of cycles at which these cracks occur is deemed crucial.Research on steel fibre has shown its effectiveness in flexure and tension under monotonic loading, impact loading and fatigue resistance in flexure. As such, it is paramount that its influence on shear fatigue diagonal crack is investigated. Further, developments of models which adequately predict reinforced concrete elements responses under constant and variable fatigue load are invaluable. The extension of such models to include the influence of steel fibre is also vital.Currently, the behaviour of steel fibre in enhancing shear fatigue resistance of beams is being investigated in order to improve the analysis and design of wind turbine foundations. Tests on plain and steel fibre reinforced concrete specimens are to be conducted under tensile and compressive fatigue loads in order to develop materials damage models. The models to be developed are also to be corroborated with the behaviour of two large scale wind turbine foundations to be tested under fatigue loading.

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UHPFRC is a new generation material typically containing short steel microfibers with volume ratios of up to 5%. Its outstanding material characteristics include self-consolidating workability, high compressive strengths, high tensile strengths, a strain-hardening post-cracking response, and excellent crack control properties. The high tensile strengths makes it possible, in some cases, to significantly reduce or eliminate conventional reinforcement, reducing congestion and allowing for thinner and more economical sections. These attributes make it advantageous in high-performance applications such as offshore platforms and nuclear power plant buildings, bridge decks, and blast and impact resistant structures. HySFRC contains high strength steel micro- and macro- fibres in effective ratios so as its behavior to be superior compared to the use of a single type of fibre, with no other modifications in the matrix mix. This characteristic is attributed to the synergistic effect of the fibre cocktails.

HySFRC under monotonic shear loading after failure

For both materials the research is driven towards the behavior in shear under monotonic and cyclic loading. Our ability in effectively designing the structures above rides on the development of appropriate constitutive models for the characterization of the novel cracked composite. To more clearly isolate and study the shear behaviour, a series of panel specimens will be tested using the Panel Element Tester facility. The models to be developed will be implemented to facilitate use in the VecTor 2 Finite Element analysis program.

Increasing fiscal limitations to maintenance budgets in recent decades mean that Canadian infrastructure now faces an urgent need to reliably predict the safety of deteriorating structures. The analysis of a deteriorating structure can be a challenging task for a structural engineer. Deterioration effects may not be immediately apparent, they are difficult to accurately quantify, and the engineer is forced to make a large number of assumptions. When faced with such uncertainty, it is practical to employ stochastic analysis techniques to predict the probability of failure.

As part of the IC-IMPACTS initiative, existing statistical distributions will be implemented into VecTor2 to randomize the program inputs and allow the user to conduct Monte Carlo simulations. Behaviour models for corroded reinforced concrete, the effect of corrosion-induced cracking, deterioration of bond strength, and variation in the area of steel will be researched and implemented into VecTor2 providing the ability to analyze corroded reinforced concrete. The ability to quantify the reliability of deteriorating infrastructure will provide engineers with the tools to assess the safety of such infrastructure and potentially predict and prevent events like the collapse of the reinforced concrete factory structure in Bangladesh in April 2013, or the Laval bridge collapse in September 2006. These tools will ultimate contribute to increased public safety in Canada and India.

Chemical deterioration of concrete in the form of alkali-aggregate reaction (AAR) is a slow-evolving but progressive process leading to expansion and cracking of concrete. An extensive amount of research has been made since it’s discovery in 1940 due to an increased manifestation of the reaction in major structures such as bridges, dams and nuclear power plants.

Crack pattern for AAR-affected shear wall

However, it still represents an important durability issue that causes significant economic damage worldwide. Numerical simulation of AAR effects on concrete plays an important role in determining the behavior of AAR-affected structures. As such, constitutive models for AAR-affected concrete were implemented within the architecture of VecTor2. The AAR expansion was treated as a non-recoverable offset strain using a computational procedure previously developed for elastic and plastic offset strains. Two distinct mechanisms were taken into consideration to fully capture the effects of AAR on concrete: material expansion and the accompanying changes in mechanical properties. Verification studies are being performed at two levels: material-level (cylinders, prisms, and cubes) and structural-level (beams, shear walls) by modelling AAR-affected specimens reported in the literature. The analytically determined responses currently show good agreement with the experimental results. The current accuracy will be improved once conclusions are drawn from the material-level investigation and the structural testing, parts of the study that is currently underway.

## Publications

- ElMohandes, F., and Vecchio, F.J., 2014. “Coupled Thermal and Structural Analysis of RC Members Towards Subjected to Fire”,
__ACI Structural J.__, (submitted March 2014) - Trommels, H., and Vecchio, F.J., 2014. “Towards Macro-Modeling Approaches for Analysis of High-Velocity Impact on Concrete Structures”,
__Engineering Structures.__, (submitted July 2013). - Susetyo, J., Gauvreau, P., and Vecchio, F.J., 2014. “Fibre Reinforcement for Control of Shrinkage Cracks: Experimental Program, ASCE
__J. Materials in Civil Engineering__, (submitted July 2013). - Hrynyk, T. and Vecchio, F.J., 2015. “Modeling of Steel-Concrete Composite Elements Under In-Plane and Out-Of-Plane Loads”,
__ASCE J. Structural Engineering.__, (submitted October 2015). - Lee, S.-C., Cho, J.-Y., and Vecchio, F.J., 2015. “Analysis of Steel Fiber Reinforced Concrete in Simplified Diverse Embedment Model for Steel Fiber Reinforced Concrete Elements Subjected to Shear”,
__ACI Structural J.__, (accepted September 2015) - Sadeghian, V., Kwon, O.-S.,and Vecchio, F.J., 2015. “A Framework For Multi-Scale Analysis of Reinforced Concrete Structures”,
__ASCE J. Structural Engineering,__(submitted April 2015) - Carnovale, D., Lee, S.C., and Vecchio, F.J., 2015. “Towards Improved Modeling of Macro-Synthetic Fiber Reinforced Concrete”,
__Concrete and Computers__, (submitted February 2015) - Hrynyk, T. and Vecchio, F.J., 2015. “Capturing Out-Of-Plane Shear Failures in the Analysis of Reinforced Concrete Shells”,
__ASCE J. Structural Engineering.__, (accepted February 2015). - Luo, J.W., and Vecchio, F.J., 2015. “Behavior of Steel Fiber Reinforced Concrete Under Reversed Cyclic Shear”,
__ACI Structural J.__, (accepted May 2015) - ElMohandes, F., and Vecchio, F.J., 2015. “Advanced Modeling of RC Members Subjected to Fire”, ACI Structural J., (accepted December 2014)
- Sadeghian, V., and Vecchio, F.J., 2015. “A Graphical Interface for Stand-Alone and Mixed-Type Modelling of Reinforced Concrete Structures”,
__Computers and Concrete__, Vol. 16, No. 2, pp. 287-309. - Hrynyk, T. and Vecchio, F.J., 2014. “Behavior of Steel Fibre Reinforced Concrete Slabs Under Impact Load”,
__ACI Structural J.__, Vol. 111, No. 5, pp.1213-1224. - Carnovale, D., and Vecchio, F.J., 2014. “Effect of Fiber Material and Loading History on Shear Behavior of Fiber Reinforced Concrete”, ACI Structural J., Vol. 111, No. 5, pp.1235- 1244.
- Facconi, L., Plizzari, G., and Vecchio, F.J., 2014. “Disturbed Stress Field Model for Unreinforced Masonry”,
__ASCE J. Structural Engineering__, Vol. 140, No. 4, 04013085, 11 pp. - Deluce, J.R., Lee, S.-C., and Vecchio, F.J., 2014. “Crack Model for Steel Fiber Reinforced Concrete Members Containing Conventional Reinforcement”,
__ACI Structural J.__, Vol. 111, No. 1, pp.93-102. - Tiberti, G., Minelli, F., Plizzari, G., and Vecchio, F.J., 2014. “Influence of Concrete Strength on Crack Development in SFRC Members”,
__Cement and Concrete Composites__, Vol. 45, pp. 176-185. - Lee, S.-C., Cho, J.-Y., and Vecchio, F.J., 2013. “Simplified Diverse Embedment Model for Steel Fiber Reinforced Concrete Elements in Tension”,
__ACI Materials J.__, Vol. 110, No. 4, July-August 2013, pp. 403-412. - Lee, S.-C., Cho, J.-Y., and Vecchio, F.J., 2013. “Tension Stiffening Model for Steel Fiber Reinforced Concrete Containing Conventional Reinforcement”,
__ACI Structural J.__, Vol. 110, No. 4, pp. 639-648. - Deluce, J.R., and Vecchio, F.J., 2013. “Cracking Behavior of Steel Fiber Reinforced Concrete Members Containing Conventional Reinforcement”,
__ACI Structural J.__, Vol. 110, No. 3, pp. 481-490. - Susetyo, J., Gauvreau, P., and Vecchio, F.J., 2013. “Steel Fibre Reinforced Panels in Shear: Analysis and Modeling”,
__ACI Structural J.__, Vol. 110, No. 2, pp. 285-295. - Abdulridha, A., Palermo, D., Foo, S., and Vecchio, F., 2013. “Behavior and Modeling of Superelastic Shape Memory Alloy Reinforced Concrete Beams”, Engineering Structures, Vol. 49, No.4, 893-904.
- Guner, S., and Vecchio, F.J., 2012. “Simplified Method for Nonlinear Dynamic Analysis of Shear-Critical Frames”, ACI Structural J., Vol. 109, No. 5, pp. 727-737.
- Lee, S.-C., Cho, J.-Y., and Vecchio, F.J., 2011. “Diverse Embedment Model for Steel Fibre Reinforced Concrete in Tension: Model Verification”, ACI Materials J., Vol. 108, No.5, pp. 526-535.
- Lee, S.-C., Cho, J.-Y., and Vecchio, F.J., 2011. “Diverse Embedment Model for Steel Fibre Reinforced Concrete in Tension: Model Development”, ACI Materials J., Vol. 108, No.5, pp. 516-525.
- Vecchio, F.J., and McQuade, I., 2011. “Towards Improved Modeling of Steel-Concrete Composite Wall Elements”, J. Nuclear Engineering and Design, Vol. 241, No.8, pp. 2629- 2642.
- Guner, S. and Vecchio, F.J., 2011. “Assessment of Shear-Critical RC Frame Elements Under Cyclic Loading”, ASCE J. of Structural Engrg, Vol. 137, No. 8, 834-843.
- Susetyo, J., Gauvreau, P., and Vecchio, F.J., 2011. “Effectiveness of Steel Fiber as Minimum Shear Reinforcement”, ACI Structural J., Vol. 108, No. 4, pp. 488-496.
- Sagbas, G., Vecchio, F.J., and Christopoulos, C., 2011. “Computational Modeling of the Seismic Performance of Beam-Column Subassemblies”, Journal of Earthquake Engineering, Vol. 15, No. 4, pp. 640-663.
- Lee, S.-C., Cho, J.-Y., and Vecchio, F.J., 2011. “A Model for Post-Yield Tension Stiffening and Rebar Fracture in Concrete Members”, Engineering Structures, Vol. 33, No. 5, pp. 1723-1733.
- Mostafaei, H., Vecchio, F.J., Gauvreau, P., and Semelawy, M., 2011. “Punching Shear Behavior of Externally Prestressed Concrete Slabs”, ASCE J. of Structural Engrg., Vol. 137, No., pp. 100-108
- Guner, S., and Vecchio, F.J., 2010 “Pushover Analysis of Shear-Critical Frames: Verification and Application”, ACI Structural J., Vol. 107, No.1, pp. 72-81.
- Guner, S., and Vecchio, F.J., 2010. “Pushover Analysis of Shear-Critical Frames: Formulation”, ACI Structural J., Vol. 107, No.1, pp. 63-71.
- Saatci, S., and Vecchio, F.J., 2009. “Nonlinear Finite Element Modeling of RC Structures Under Impact Loads”, ACI Structural J., Vol. 106, No. 5, pp. 717-725.
- Mostafaei, H., Vecchio, F.J., and Kabeyasawa, T., 2009. “Deformation Capacity of Reinforced Concrete Columns”, ACI Structural J., Vol. 106, No. 2, pp. 187-195.
- Saatci, S., and Vecchio, F.J., 2009. “Effects of Shear Mechanisms on the Impact Behaviour of RC Beams”, ACI Structural J., Vol.106, No.1, pp. 78-86.
- Mostafaei, H., and Vecchio, F.J., 2008. “Uniaxial Shear-Flexure Model for Reinforced Concrete Elements”, ASCE J. of Structural Engrg., Vol. 134, No. 9, pp. 1538-1547.
- Mostafaei, H., Vecchio, F.J., and Kabeyasawa, T., 2008. “Nonlinear Displacement-Based Response Prediction of Reinforced Concrete Columns”, Engineering Structures, Vol. 30, No. 9, pp. 2436-2447.
- Kim, S.-W., and Vecchio, F.J., 2008. “Modeling of Shear-Critical Reinforced Concrete Structures Repaired with Fiber-Reinforced Polymer Composites”, ASCE J. of Structural Engrg., Vol. 134, No. 8, pp. 1288-1299.
- Duong, K.V., Sheikh, S.A., and Vecchio, F.J., 2007. “Seismic Behaviour of a Shear-Critical Reinforced Concrete Frame: Experimental Investigation”, ACI Structural J. , Vol. 104, No.3, pp. 304-313.
- Palermo, D., and Vecchio, F.J., 2007. “Simulation of Cyclically Loaded Concrete Structures Based on the Finite Element Method, ASCE J. of Structural Engrg., Vol.133, No.5, pp. 728-738
- Zhou, C.E., and Vecchio, F.J., 2006. “Closed-Form Stiffness Matrix for the Four-Node Quadrilateral Element with a Fully-Populated Material Stiffness”, ASCE J. of Engrg. Mechanics, Vol.132, No.12, pp.1392-1395.
- Bentz, E.C., Vecchio, F.J., and Collins, M.P., 2006. “The Simplified MCFT for Calculating the Shear Strength of Reinforced Concrete Elements”, ACI Structural J. Vol.103, No.4, pp. 614-624.
- Vecchio, F.J. 2006. “On the Post-Peak Ductility of Shear-Critical Beams”, ACI Special Publication SP-237 CD Finite Element Analysis of Reinforced Concrete Structures, Paper SP-237-8, pp. 1-20.
- Montoya, E., Vecchio, F.J., and Sheikh, S.A., 2006. “Compression Field Modelling of Confined Concrete: Constitutive Models”, ASCE J. of Materials in Civil Engrg, Vol. 18, No. 4, pp. 1-8.
- Minelli, F., and Vecchio, F.J., 2006. “Compression Field Modelling of Fibre Reinforced Concrete: Preliminary Numerical Study”, ACI Structural J. , Vol. 103, No.2, pp. 244-252.
- Vecchio, F.J., Gauvreau, P., and Liu, K., 2006. “Modelling of Unbonded Post-Tensioned Concrete Beams Critical in Shear”, ACI Struct. J., Vol. 103, No. 1, pp.57-64.
- Zhou, C.E., and Vecchio, F.J., 2005. “Nonlinear Finite Element Analysis of Reinforced Concrete Structures Subjected to Transient Thermal Loads”, Computers and Concrete, Vol. 2, No. 6, pp. 455- 480.
- Montoya, E., Vecchio, F.J., and Sheikh, S.A., 2004. “Numerical Evaluation of the Behaviour of Steel- and FRP-Confined Concrete Using Compression Field Modelling”, J. Engrg. Structures, Vol. 26, No. 11, pp. 1535-1545.
- Vecchio, F.J. and Lai, D., 2004. “Crack Shear-Slip in Reinforced Concrete Elements”, J. Advanced Concrete Technology, Vol. 2, No. 3, pp. 289-300.
- Palermo, D., and Vecchio, F.J., 2004. “Compression Field Modelling of Reinforced Concrete Subjected to Reversed Loading: Verification”, ACI Structural Journal, Vol. 101, No. 2, pp. 155-164.
- Vecchio, F.J., and Shim, W., 2004. “Experimental and Analytical Re-examination of Classic Concrete Beam Tests”, ASCE J. of Struct. Engrg., Vol. 130, No. 3, pp. 460-469.
- Vecchio, F.J., Bentz, E.C., and Collins, M.P., 2004. “Tools for Forensic Analysis of Concrete Structures, Computers and Concrete, Vol. 1, No. 1, pp. 1-14.
- Palermo, D., and Vecchio, F.J., 2003. “Compression Field Modelling of Reinforced Concrete Subjected to Reversed Loading: Formulation”, ACI Structural Journal, Vol. 100, No. 5, pp. 616-625.
- Sato, Y., and Vecchio, F.J., 2003. “Tension Stiffening and Crack Formation in RC Members with FRP Sheets”, ASCE J. of Struct. Engrg., Vol. 129, No. 6, 717-724.
- Wong, R.S.Y., and Vecchio, F.J., 2003. “Towards Modeling of Reinforced Concrete Members with Externally-Bonded FRP Composites”, ACI Structural Journal, Vol. 100, No. 1, pp. 47-55.
- Vecchio, F.J., 2002. “Contribution of NLFEA to the Evaluation of Two Structural Concrete Failures”, ASCE J. of Performance of Constructed Facilities, Vol. 16, No. 3, pp. 110-115.
- Vecchio, F.J., Haro de la Peña, O.A., Bucci, F., and Palermo, D., 2002. “Behaviour of Repaired Cyclically-Loaded Shear Walls”, ACI Structural Journal, Vol. 99, No. 3, pp. 327-334.
- Vecchio, F.J., and Palermo, D., 2002. “Nonlinear Finite Element Analysis of Reinforced Concrete: Look Both Ways Before Crossing”, ACI Special Publication, No. SP-205, Finite Element Analysis of Reinforced Concrete Structures, pp. 1-14.
- Palermo, D., and Vecchio, F.J., 2002. “Behaviour of 3-D Reinforced Concrete Shear Walls”, ACI Structural Journal, Vol. 99, No. 1, pp. 81-89.
- Vecchio, F.J., 2001. “Nonlinear Finite Element Analysis of Reinforced Concrete: At the Crossroads?”, Structural Concrete: J. of fib, Vol. 2, No. 4, pp. 201-212.
- Palermo, D., and Vecchio, F.J., 2001. “Behaviour of Cyclically Loaded Shear Walls”, ASCE Special Publication, Modelling of Inelastic Behaviour of RC Structures under Seismic Loads.
- Montoya, E., Vecchio, F.J., and Sheikh, S.A., 2001. “Compression Field Modelling of Confined Concrete”, Structural Engrg and Mechanics, Vol. 12, No. 3, pp. 231-248.
- Yamamoto, T., and Vecchio, F.J., 2001. “Analysis of Reinforced Concrete Shells for Transverse Shear and Torsion”, ACI Struct. J., Vol. 98, No. 2, pp. 191-200.
- Vecchio, F.J., Lai, D., Shim, W., and Ng, J., 2001. “Disturbed Stress Field Model for Reinforced Concrete: Validation”, ASCE J. Struct. Engrg., Vol. 127, No. 4, pp. 350-358.
- Vecchio, F.J., 2001. ADisturbed Stress Field Model for Reinforced Concrete: Implementation@, ASCE J. Struct. Engrg., Vol. 127, No. 1, pp. 12-20.
- Vecchio, F.J., 2000. ADisturbed Stress Field Model for Reinforced Concrete: Formulation@, ASCE J. Struct. Engrg., Vol. 126, No. 9, pp. 1070-1077.
- Collins, M.P., Vecchio, F.J., Selby, R.G., and Gupta, P.R., 2000. AFailure of an Offshore Platform@, Canadian Consulting Engineer, March/April, pp. 43-48.
- Vecchio, F.J., 2000. AAnalysis of Shear-Critical Reinforced Concrete Beams@, ACI Structural Journal, Vol. 97, No. 1, pp. 102-110.
- Vecchio, F.J., and Tata, M., 1999. AApproximate Analyses of Reinforced Concrete Slabs@, Struct. Engrg. and Mechanics, Vol. 8, No. 1, pp. 1-18.
- Vecchio, F.J., and Bucci, F., 1999. AAnalysis of Repaired Reinforced Concrete Structures@, ASCE J. of Structural Engineering, Vol. 125, No. 6, pp. 644-652.
- Vecchio, F.J., 1999. ATowards Cyclic Load Modelling of Reinforced Concrete@, ACI Struct. J., Vol. 96, No. 2, pp. 193-202.
- Vecchio, F.J., 1998, ALessons from the Analysis of a 3-D Concrete Shear Wall@, Struct. Engrg. and Mechanics, Vol. 6, No. 4, pp. 439-456.
- Selby, R.G., and Vecchio, F.J., 1997. AA Constitutive Model for Analysis of Reinforced Concrete Solids@, Canadian Journal of Civil Engineering, Vol. 24, No. 3, pp. 460-470.
- Collins, M.P., Vecchio, F.J. and Selby, R.G., 1997. AThe Failure of an Offshore Platform@, Concrete International, Vol. 19, No. 8, pp. 28-35.
- Selby, R.G., Vecchio, F.J. and Collins, M.P., 1996. AAnalysis of Reinforced Concrete Members Subject to Shear and Axial Compression@, ACI Structural Journal, Vol. 93, No. 3, pp. 306-315.
- Collins, M.P., Mitchell, D., Adebar, P.E. and Vecchio, F.J., 1996. AA General Shear Design Method@, ACI Structural Journal, Vol. 93, No. 1, pp. 36-45.
- Vecchio, F.J., and De Roo, A., 1995. ASmeared Crack Modelling of Concrete Tension Splitting@, ASCE J. of Engrg. Mechanics, Vol. 121, No. 6, pp. 702-708.
- Vecchio, F.J., Collins, M.P., and J. Aspiotis, 1994. AHigh Strength Concrete Elements in Shear@ ACI Structural Journal, Vol. 91, No. 4, pp. 423-433.
- Polak, M.A., and Vecchio, F.J., 1994. AReinforced Concrete Shell Elements Subjected to Bending and Membrane Loads@, ACI Structural Journal, Vol. 91, No. 3, pp. 261-268.
- Vecchio, F.J., and Collins, M.P., 1993. ACompression Response of Cracked Reinforced Concrete@, ASCE Journal of Structural Engineering, Vol. 119, No. 12, pp. 3590-3610.
- Polak, M.A., and Vecchio, F.J., 1993. ANonlinear Analysis of Reinforced Concrete Shells@, ASCE Journal of Structural Engineering, Vol. 119, No. 12, pp. 3439-3462.
- Vecchio, F.J., Agostino, N., and Angelakos, B., 1993. AReinforced Concrete Slabs Subjected to Thermal Loads@, Canadian Journal of Civil Engineering, Vol. 20, No. 5, pp. 741-753.
- Vecchio, F.J., 1992. AFinite Element Modelling of Concrete Expansion and Confinement@, ASCE Journal of Structural Engineering, Vol. 118, No. 9, pp. 46-56.
- Vecchio, F.J., and Emara, M.B., 1992. AShear Deformations in Reinforced Concrete Frames@, ACI Structural Journal, Vol. 89, No. 1, pp. 46-56.
- Vecchio, F.J., and Selby, R.G., 1991. ATowards Compression Field Analysis of Reinforced Concrete Solids@, ASCE Journal of Structural Engineering, Vol. 117, No. 6, pp. 1740-1758.
- Vecchio, F.J., and Nieto, M., 1991. AShear-Friction Tests on Reinforced Concrete Panels@, ACI Structural Journal, Vol. 88, No. 3, pp. 371-379.
- Vecchio, F.J., and Tang, K., 1990. AMembrane Action in Reinforced Concrete Slabs@, Canadian Journal of Civil Engineering, Vol. 17, No. 5, pp. 686-697.
- Vecchio, F.J., and Balopoulou, S. 1990. AOn the Nonlinear Behaviour of Reinforced Concrete Frames@, Canadian Journal of Civil Engineering, Vol. 17, No. 5, pp. 698-704.
- Vecchio, F.J., and Chan, C.C.L., 1990. AReinforced Concrete Membrane Elements with Perforations@, ASCE Journal of Structural Engineering, Vol. 116, No.9, pp. 2344-2360.
- Vecchio, F.J., and Sato, J.A., 1990. AThermal Gradient Effects in Reinforced Concrete Frame Structures@, ACI Structural Journal, Vol. 87, No. 3., pp. 262-275.
- Vecchio, F.J., and Collins, M.P., 1990. AInvestigating the Collapse of a Warehouse@, Concrete International: Design and Construction, Vol. 12, No. 3, pp. 72-78.
- Vecchio, F.J., 1990. AReinforced Concrete Membrane Element Formulations@, ASCE Journal of Structural Engineering, Vol. 116, No. 3, pp. 730-750.
- Sato, J.A., Vecchio, F.J., and Andre, H.M., 1989. AScale Model Testing of Reinforced Concrete under Impact Loading Conditions@, Canadian Journal of Civil Engineering, Vol. 16, No. 4, pp. 459-466.
- Vecchio, F.J., 1989. ANonlinear Finite Element Analysis of Reinforced Concrete Membranes@, ACI Structural Journal, Vol. 86, No.1, pp. 26-35.
- Vecchio, F.J., and Sato, J.A., 1988. ADrop, Fire and Thermal Testing of a Concrete Nuclear Fuel Container@, ACI Structural Journal, Vol. 85, No. 4, pp. 374-383.
- Vecchio, F.J., and Collins, M.P., 1988. APredicting the Response of Reinforced Concrete Beams Subjected to Shear using The Modified Compression Field Theory@, ACI Structural Journal, Vol. 85, No. 3, pp. 258-268.
- Vecchio, F.J., 1987. ANonlinear Analysis of RC Frames Subjected to Thermal and Mechanical Loads@, ACI Structural Journal, Vol. 84, No. 6, pp. 492-501.
- Vecchio, F.J., and Collins, M.P., 1986. AThe Modified Compression Field Theory for Reinforced Concrete Elements Subjected to Shear@, Journal of the American Concrete Institute, Vol. 83, No. 2, pp. 219-231.
- Collins, M.P., Vecchio, F.J., and Mehlhorn, G., 1985. AAn International Competition to Predict the Response of Reinforced Concrete Panels@, Canadian Journal of Civil Engrg., Vol. 12, No. 3, pp. 624-644.

- Hrynyk, T.D., and Vecchio, F.J., 2015. “The Influence of Lateral Expansions on the Response of Steel-Concrete Composite Structures”, 23
^{rd}International Conference on Structural Mechanics in Reactor Technology (SMiRT), Manchester, U.K., August 10-14, 2015. - Jurcut, A.C., Vecchio, F.J., Sheikh, S.A., Panesar, D.K., and Obrovic, N., 2015. “Alkali Aggregate Reaction in Nuclear Concrete Structures: Part 4: Modelling and Analysis”, 23
^{rd}International Conference on Structural Mechanics in Reactor Technology (SMiRT), Manchester, U.K., August 10-14, 2015. - Sadeghian, V., Kwon, O.S., and Vecchio, F.J., 2015. “An Integrated Framework for Analysis of Mixed-Type Reinforced Concrete Structures”, COMPDYN 2015, Crete, Greece, May 25-27, 2015.
- Chasioti, S., and Vecchio, F.J., 2015. “Hybrid Steel Fibre Reinforced Concrete Panels in Shear: Experimental Investigation”. HPFRCC7 – High Performance Fiber Reinforced Cement Composites, Stuttgart, June 1-3, 2015.
- Lulec, A., and Vecchio, F.J., 2015. “Development of Simplified Analytical Tools for Impact and Impulsive Loading Analysis of Reinforced Concrete Slabs”. PROTECT 2015 Conference, East Lansing, MI, June 28-30, 2015.
- Hrynyk, T.D., and Vecchio, F.J., 2015. “Modeling of Reinforced Concrete Slabs under High-Mass Low-Velocity Impact”. PROTECT 2015 Conference, East Lansing, MI, June 28-30, 2015.
- Johnson, D.T.C., Sheikh, S.A. and Vecchio, F.J., 2014. “Finite Element Analysis of GFRP Internally Reinforced Concrete Beams” Seventh International Conference on FRP Composites in Civil Engineering, Vancouver, August 20-22, 2014.
- Hrynyk, T.D., and Vecchio, F.J., 2014. “Capturing Out-Of-Plane Shear Failures in the Analysis of Reinforced Concrete Shell Structures”. American Concrete Institute (ACI) Conference, Reno, Nevada, March 23-27, 2014.
- Luo, J.W., and Vecchio, F.J., 2014. “Behavior of Steel Fiber Reinforced Concrete under Reversed Cyclic Loads”, American Concrete Institute (ACI) Conference, Reno, Nevada, March 23-27, 2014.
- Akkaya, Y., Guner, S., and Vecchio, F.J., 2013. “Modeling Inelastic Buckling Behavior of Reinforcing Bars”, American Concrete Institute (ACI) Conference, Phoenix, Oct 20-24, 2013.
- Trommels, H., and Vecchio, F.J., 2013. “Towards Simplified Methods of Analysis of Impact on Concrete Structures”, 22
^{nd}International Conference on Structural Mechanics in Reactor Technology (SMiRT), August 2013, San Francisco. - Sadeghian, V., and Vecchio, F.J., 2013. “FormWorks-Plus: Improved Pre-Processor for VecTor Analysis Software”, 3
^{rd}Specialty Conference on Material Engineering & Applied Mechanics, Canadian Society of Civil Engineering (CSCE), May 2013, Montreal. - Tiberti, G., Minelli, F., Plizzari, G.A., and Vecchio, F.J., 2013. “The Effect of Concrete Strength on Cracking of SFRC Members”, 8
^{th}International Conference on Fracture Mechanics of Concrete and Concrete Structures (FraMCoS-8), March 2013, Toledo, Spain, pp. 1237-1248. - Lee, S.C., Cho, J.Y., and Vecchio, F.J., 2013. “Constitutive Model for Steel Fibre Reinforced Concrete in Tension”, 8
^{th}International Conference on Fracture Mechanics of Concrete and Concrete Structures (FRaMCoS-8), March 2013, Toledo, Spain, pp. 243-252. - Lee, S.C., Vecchio, F.J., and Cho, J.Y., 2012. “Constitutive Models for Steel Fibre Reinforced Concrete Members”, IABSE Conference, September 2012, Seoul, South Korea.
- Hrynyk, T. and Vecchio, F.J.,2012. "Behaviour and Modelling of Reinforced Concrete Shells Subjected to Extreme Loads", Technion-University of Toronto Joint Workshop: Response and Protection of Infrastructure to Extreme Loadings, Haifa, Israel, July 4-6, 2012.
- Hrynyk, T. and Vecchio, F.J., 2012. “Modeling of Steel-Concrete Composite Wall Elements Subject to In-Plane and Out-of-Plane Loads”, ACI Conference, March 2012, Dallas
- Lee, S.C., Vecchio, F.J., and Cho, J.Y., 2011. “Tension Stiffening Behavior of Steel Fiber Reinforced Concrete with Conventional Rebar”, ACI Conference, October 2011, Cincinnati.
- Lee, S.C., Min, D.H., Cho, J.Y., and Vecchio, F.J., 2011. “Model for Steel Fibre Reinforced Concrete in Tension Considering Random Distributions of Fibres”, 9
^{th}Symposium on High Performance Concrete: Design, Verification & Utilization, Rotorua New Zealand, August 9-11, 2011. - Deluce, J., Lee, S.C., and Vecchio, F.J., 2011. “Crack Formation in FRC Structural Elements Containing Conventional Reinforcement”, HPFRCC6 High Performance Fiber Reinforced Cement Composite, Ann Arbor, Michigan, June 19-22, 2011, pp.261-268
- Guner, S. and Vecchio, F.J. (2011), “Nonlinear Analysis of Shear-Critical Reinforced Concrete Frames under Impact, Blast and Seismic Loads,” Canadian Society for Civil Engineers, 2nd International Engineering Mechanics and Materials Specialty Conference, June 14-17, Ottawa, Canada.
- Guner, S.., and Vecchio, F.J., 2010. “Performance Assessment of Shear-Critical Frame Elements Under Dynamic Loading”, ACI Conference, October 2010, Pittsburgh
- Saatci, S., and Vecchio, F.J., 2010. “Behavior and Modeling of Shear-Critical RC Beams Under Impact Loading”, ACI Special Publication “Behavior of Concrete Structure Subjected to Blast and Impact”, October 2010, Pittsburgh, pp. ??
- Susetyo, J., and Vecchio, F.J., 2010. “Effectiveness of Steel Fibre as Minimum Shear Reinforcement: Panel Tests”, Workshop on Shear, October 2010, Salo, Italy, pp. 227-242.
- Susetyo, J., Gauvreau, P., and Vecchio, F.J., 2010. “Effectiveness of Steel Fiber as a Crack Controller: Assessment Using Shear Panel Tests”. Seventh International Conference on Fracture Mechanics of Concrete and Concrete Structures, May 2010, Jeju, South Korea.
- Mostafaei, H., Vecchio, F.J., and Bénichou, N., 2009. “Seismic Resistance of Fire-Damaged Concrete Columns”. ATC-ASCE Conference on Improving the Seismic Performance of Existing Buildings and Other Structures, December 2009, San Francisco, pp. 1396-1407.
- Mostafaei, H., Vecchio, F.J., and Kabeyasawa, T., 2009. “A Simplified Axial-Shear-Flexure Interaction Approach for Load and Displacement Capacity of Reinforced Concrete Columns”. ATC-ASCE Conference on Improving the Seismic Performance of Existing Buildings and Other Structures, December 2009, San Francisco, pp.753-764.
- Vecchio, F.J., 2009. “Climate Change in Computer Modelling of Concrete Structures”. Concrete 2009 – 24
^{th}Biennial Conference of the Australian Concrete Institute, September 2009, Sydney, Australia. - Vecchio, F.J. and Guner., S., 2009. “Performance Assessment of Shear-Critical Reinforced Concrete Frames”. Concrete 2009 – 24
^{th}Biennial Conference of the Australian Concrete Institute, September 2009, Sydney, Australia. - Guner, S., and Vecchio, F.J., 2007. “Nonlinear Analysis of Reinforced Concrete Frames Under Push-Over and Cyclic Loads”, American Concrete Institute, October, 2007, Puerto Rico, U.S.A.
- Duong, K.V., Sheikh, S.A., and Vecchio, F.J., 2007. “Seismic Upgrade of a Shear-Critical Frame with CFRP”, Proc. 8
^{th}Int. Symposium on FRP Reinforcement for Concrete Structures, July 16-18, 2007, Patras, Greece. - Minelli, F., Plizzari, G.A., and Vecchio, F.J., 2007. “Influence of Steel Fibres on Full-Scale RC Beams under Shear Loading”, Proc. 6
^{th}Int. Conf. on Fracture Mechanics of Concrete and Concrete Structures, June 17-22, 2007, Catania, Italy. - Saatci, S., and Vecchio, F.J., 2005. “Finite Element Analysis of Shear-Critical Reinforced Concrete Beams Under Impact Loading”, Proceedings of the 6th Asia-Pacific Conference on Shock & Impact Loads on Structures, December 7-9, 2005, Perth, W. Australia, pp.499-506
- Minelli, F., PLizzari, G.A. and Vecchio, F.J., 2005. "Influence of SFRC on Shear-Critical Beams: Towards a Consistent Design"; Proceedings of the International Conference ConMat '05, Vancouver, Canada, 22-24 August 2005 (Edited by N. Banthia, T. Uomoto, A. Benturt and S.P. Shah, Published by The University of British Columbia), abstract on p. 84, full length paper available on accompanied CD, pp.12.
- Vecchio, F.J., 2003 “Experimental and Analytical Re-Examination of Classic Shear-Critical Beams and Their Relevance to Collapse Load Analysis”, Int’l Workshop on Finite Element Analysis of Reinforced Concrete”, Maui, Hawaii, November 2003.
- Wong, R., and Vecchio, F.J., 2001. “Accounting for Debonding in the Analysis of FRP-Repaired Structures”, CICE 2001, International Conference on FRP Composites in Civil Engineering, Hong Kong, December 2001, Vol. 1, pp. 625-632.
- Vecchio, F.J., 2001. “Application of NLFEA for Investigation of Failed Concrete Structures”, 9th International Expertcentrum Conference, Failures of Concrete Structures, Bratislava, September 2001.
- Palermo, D., and Vecchio, F.J., 1999. ABehaviour and Analysis of Cyclically Loaded Shear Walls@,
__Proc. U.S.-Japan Joint Seminar on Post-Peak Behaviour of Reinforced Concrete__, Tokyo, October 1999, 15 pp. - Vecchio, F.J., 1999. ABehaviour and Analysis of Beams in Shear@,
__Proc. fib Symposium__, Prague, October 1999, 10 pp. - Sheikh, S.A., Vecchio, F.J., DeRose, D., and Bucci, F., 1998, ABehaviour and Analysis of FRP-Repaired Elements@
__Proc. High Performance High Strength Concrete__, Perth, August 1998, pp. 669-683. - Vecchio, F.J., Polak, M.A., and Selby, R.G., 1996. ANonlinear Analysis of Reinforced Concrete; The University of Toronto Experience@,
__Proc. Third Asian-Pacific Conference on Computational Mechanics__, Seoul, Korea. - Vecchio, F.J., and Puri, P., 1991. AFinite Element Analysis of Reinforced Concrete Shear Walls@,
__Proc., Eleventh International Conference on Structural Mechanics in Reactor Technology__, Tokyo, August 1991, Vol. H, Paper H14/1, pp. 401-406. - Vecchio, F.J., 1991. AAnalyses Based on the Modified Compression Field Theory@,
__Proc. Colloquium on Structural Concrete__, IABSE, Stuttgart, April 1991, pp. 321-326. - Collins, M.P., Mitchell, D., Vecchio, F.J., and Adebar, P. 1991. AA Consistent Shear Design Model@,
__Proc. Colloquium on Structural Concrete__, IABSE, Stuttgart, April 1991, pp. 457-462. - Sato, J.A., and Vecchio, F.J., 1989. AMonitoring of a Containment Structure During Pressure Tests@,
__Proc. Tenth International Conference on Structural Mechanics in Reactor Technology__, Anaheim, California, USA, August 1989, Vol. H, pp. 191-196. - Vecchio, F.J., Sato, J.A., and Bhat, P.D., 1987. AThermal Creep in Reinforced Concrete Structures@,
__Proc., 9th International Conference on Structural Mechanics in Reactor Technology__, Lausanne, Switzerland, August 1987, Vol. H, pp. 209-214. - Bhat, P.D., and Vecchio, F.J., 1986. AEffect of High Temperature and Cracking on Creep/ Relaxation of Concrete Structures@,
__Fourth RILEM International Symposium on Creep and Shrinkage of Concrete, Proc.__, Northwestern University, August 1986, pp. 715-722. - Vecchio, F.J., 1985. AModelling the Response of Reinforcing Concrete Structures to Thermal Loads@,
__Proc., 8th International Conference on Structural Mechanics in Reactor Technology__, Brussels, Belgium, August 1985, Vol. H, pp. 331-336. - Vecchio, F.J., 1985. ATEMPEST: A Computer Code for Nonlinear Structural Analysis of R/C Plane Frames@,
__Proc., American Concrete Institute (ACI) Microcomputer Workshop__, Denver, USA, March 1985, ACI Publication COM-2(85), pp. 1-48. - Sturrup, V.R., Vecchio, F.J., and Caratin, H., 1984. APulse Velocity as a Measure of Concrete Compressive Strength@, American Concrete Institute (ACI) Publication SP-82,
__In Situ/ Nondestructive Testing of Concrete__, 1984, pp. 201-227. - Bhat, P.D., and Vecchio, F., ADesign of Reinforced Concrete Containment Structures for Thermal Gradient Effects@,
__Proc., 7th International Conference on Structural Mechanics in Reactor Technology__, Chicago, USA, August 1983, Vol. J, pp. 171-178. - Vecchio, F.J., and Collins, M.P., AStress-Strain Characteristics of Reinforced Concrete in Pure Shear@,
__Proc., Colloquium on Advanced Mechanics of Reinforced Concrete__, International Association for Bridge and Structural Engineering (IABSE), Delft, June 1981, pp. 233-247.

## Teaching

Course Code | Title & Description | Session | Day(s) | Start Time | End | Section |
---|---|---|---|---|---|---|

CIV1163H GradList | Mechanics of Reinforced Concrete Theories of elasticity and plasticity, as applied to reinforced concrete, are examined. Topics include: mechanical properties of concrete and reinforcement; constitutive relations; failure criteria; linear-elastic models; nonlinear-elastic models; elastic-plastic models; limit analysis theorems; and an introduction to fracture mechanics of concrete. Compression field and smeared crack models are discussed, as are methods of their implementation and application in nonlinear finite element analyses. Prerequisites: CIV313H1, CIV510H1. | NOT OFFERED 2021-2022 | LEC0101 |

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