Theory of Structures is a course whose aim is to provide fundamental knowledge concerning the mono- and bi-dimensional models that find their typical applications in Civil Engineering, so as to allow their consciuos use in common engineering practice. This course is part of the master's degree program in "Civil Engineering for Protection from Natural Risks", whose objective is to train civil engineers with high professional qualifications for the protection from hydrogeological and from seismic risks. Within the framework of this course, the course aims to provide an in-depth knowledge of 1) mono- and bi-dimensional structural models; 2) of some numerical techniques for structural computation. At the end of the course students will be able to: 1) know how to choose the correct model to evaluate the response of a real structure; 2) use the chose model to evaluate the response of the structure, both analytically and numerically.
scheda docente
materiale didattico
Instability of elastic equilibrium: Discrete mechanical systems. Beams with distributed elasticity.
Timoshenko beam model: Formulation of the model, Shear correction factor, Analytical solution, Total Potential Energy, Approximated variational solutions.
Slab model: Plane strain and plane stress conditions, Governing equations, Total Potential Energy, Approximated variational solutions.
Kirchhoff-Love plate model: Formulation of the model, Total Potential Energy, Approximated variational solutions: Mindlin-Reissner plate model: Formulation of the model, Total Potential Energy, Approximated variational solutions.
Introduction to the finite element method.
Finite element method (1D problems): Truss, E-B beam, Shear deformation beam, Locking.
Finite element method (2D problems): Triangular elements for slab, Isoparametric elements for slab, Four-noded elements for slab.
E. Sacco "Appunti del corso di Meccanica delle Strutture".
Reddy: An introduction to the finite element method, McGraw-Hill, 1994.
Zienkiewicz & Taylor: The finite element method, Vol. 1,2,3, Butterworth-Heinemann, 2000.
Crisfield: Non-linear finite element analysis of solids and structures, John Wiley & Sons, 1991.
Programma
Variational formulation of the elasto-static problem: Concepts of Continuum Mechanics, Total Potential Energy, Euler-Bernoulli beam model. Analytical solution, Total Potential Energy, Approximated variational solutions.Instability of elastic equilibrium: Discrete mechanical systems. Beams with distributed elasticity.
Timoshenko beam model: Formulation of the model, Shear correction factor, Analytical solution, Total Potential Energy, Approximated variational solutions.
Slab model: Plane strain and plane stress conditions, Governing equations, Total Potential Energy, Approximated variational solutions.
Kirchhoff-Love plate model: Formulation of the model, Total Potential Energy, Approximated variational solutions: Mindlin-Reissner plate model: Formulation of the model, Total Potential Energy, Approximated variational solutions.
Introduction to the finite element method.
Finite element method (1D problems): Truss, E-B beam, Shear deformation beam, Locking.
Finite element method (2D problems): Triangular elements for slab, Isoparametric elements for slab, Four-noded elements for slab.
Testi Adottati
Capurso M.,Lezioni di Scienza delle Costruzioni,Pitagora Editrice, 1984.E. Sacco "Appunti del corso di Meccanica delle Strutture".
Reddy: An introduction to the finite element method, McGraw-Hill, 1994.
Zienkiewicz & Taylor: The finite element method, Vol. 1,2,3, Butterworth-Heinemann, 2000.
Crisfield: Non-linear finite element analysis of solids and structures, John Wiley & Sons, 1991.
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