Theory of structures
Differential equation of beams for axial, flexural and shear deformations. Virtual work theorem.
Stress and Strain
Properties of stress and infinitesimal strain tensors.
Constitutive equations, elastic equilibrium problem and resistance criteria
De Saint Venant problem
Axial force, pure bending, eccentric axial force, torsion, shear.
Elastic stability
Euler’s formula, “omega” method.
Course Content - Part B
Theory of structures
Differential equation of beams for axial, flexural and shear deformations. Virtual work theorem.
Stress and Strain
Properties of stress and infinitesimal strain tensors.
Constitutive equations, elastic equilibrium problem and resistance criteria
De Saint Venant problem
Axial force, pure bending, eccentric axial force, torsion, shear.
Elastic stability
Euler’s formula, “omega” method.
Course Content - Part C
The course provides the tools to face structural problems. At the end of the course the student will be able to: - choose the most suitable physical-mathematical model to predict the mechanical behavior of structures -
analyze statically indeterminate structures under mechanical and thermal actions - verify the strength of structural elements and simple structures - justify their choice, discuss the method and interpret the results of
the analysis - conceive and design simple structures.
L. Gambarotta, L. Nunziante, A. Tralli, Scienza delle costruzioni, McGraw-Hill, Milano, 2003.
M. Capurso, Lezioni di Scienza delle Costruzioni, Pitagora Editrice, Bologna, 1998.
O. Belluzzi, Scienza delle Costruzioni, Vol. I, Zanichelli editore, Bologna, 1996.
L. Gambarotta, L. Nunziante, A. Tralli, Scienza delle costruzioni, McGraw-Hill, Milano, 2003.
M. Capurso, Lezioni di Scienza delle Costruzioni, Pitagora Editrice, Bologna, 1998.
O. Belluzzi, Scienza delle Costruzioni, Vol. I, Zanichelli editore, Bologna, 1996.
Claudia Comi, Leone Corradi Dell'Acqua: Introduzione alla Meccanica Strutturale 3a ediz., McGraw-Hill.
Salvatore Di Pasquale : Scienza delle Costruzioni - Introduzione alla progettazione strutturale, Tamburini ed.
Stephan Timoshenko: Scienza delle Costruzioni, vol. 1, Viglongo.
Odone Belluzzi: Scienza delle Costruzioni, vol. 1, Zanichelli.
Learning Objectives - Part A
The course's goal is to provide the necessary tools for solving simply structural problems . Such a objective is reached by means of the study of fundamental of solid mechanics (stress, strain, stress-strain relationship) and its application to structural problems.
Learning Objectives - Part B
The course's goal is to provide the necessary tools for solving simply structural problems . Such a objective is reached by means of the study of fundamental of solid mechanics (stress, strain, stress-strain relationship) and its application to structural problems.
Learning Objectives - Part C
Structural analysis Methods aimed to structural design.
Prerequisites - Part A
Knowledge of mechanics and mathematics learned in previous courses of “Statica” and “Istituzioni di matematiche”
Prerequisites - Part B
Knowledge of mechanics and mathematics learned in previous courses of “Statica” and “Istituzioni di matematiche”
Prerequisites - Part C
Successful examination at STATICA (Statics)
Teaching Methods - Part C
Lessons, exercises in the classroom
Type of Assessment - Part A
Write and oral exam
Type of Assessment - Part B
Write and oral exam
Type of Assessment - Part C
quiz via moodle, individual oral examination
Course program - Part A
Theory of structures
Differential equation of beams for axial, flexural and shear deformations. Virtual work theorem.
Stress and Strain
Properties of stress and infinitesimal strain tensors.
Constitutive equations, elastic equilibrium problem and resistance criteria
De Saint Venant problem
Axial force, pure bending, eccentric axial force, torsion, shear.
Elastic stability
Euler’s formula, “omega” method.
Course program - Part B
Theory of structures
Differential equation of beams for axial, flexural and shear deformations. Virtual work theorem.
Stress and Strain
Properties of stress and infinitesimal strain tensors.
Constitutive equations, elastic equilibrium problem and resistance criteria
De Saint Venant problem
Axial force, pure bending, eccentric axial force, torsion, shear.
Elastic stability
Euler’s formula, “omega” method.
Course program - Part C
[1]
The goal is the working out of mathematical models of structures and the critical evaluation of results, for their use in the structural design.
[2]
Truss structures, use of software, graphical output, dxf import, limit state of tensile elements.
[3]
Nonlinear trusses: snap through, stable and unstable equilibrium.
[4]
Euler instability of columns.
[5]
Differential equations of beams: eta (deflections), eta', eta", M, T. ; use of a spreadsheet: diagrTM.ods.
Navier: Mx, My, N. Limit state of a bended beam, Wpl.
[6]
Shear: Jourawski theory.
Limit state of beams for shearing stresses.
[7]
Torsion: cylindrical beam, Bredt; membrane and hydrodynamic analogies.
[8]
Principal stresses. Spreadsheet: sigmatau.ods
Eigenvalues and eigenvectors for symmetric nxn matrices.
[9]
Safe state of (pricipal) stress: Tresca , Von Mises.
[10]
Dynamic equations of n-degrees of freedom structures: modal analysis.