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 in simple structures
-justify their choice/design, discuss the analysis method and interpret the results.
Modal analysis of n dof is included.
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
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. Theory of structures: Differential equation of beams for axial, flexural and shear deformations. Virtual work theorem. Static and kinematic approach; Elastic stability: Euler's formula, "omega" method.
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.
The use of one of the following textbooks is suggested:
- Luciano Nunziante, Luigi Gambarotta, Antonio Tralli, “Scienza delle costruzioni”, McGraw-Hill, Milano, 2011.
- Odone Belluzzi, “Scienza delle Costruzioni”, Vol. I e II, Zanichelli editore, Bologna, 1996.
- Erasmo Viola, “Lezioni di scienza delle costruzioni” Pitagora
In order to practice, the following exercise book is suggested:
- Erasmo Viola, “Esercitazioni di scienza delle costruzioni”. Vol. 2 Pitagora
Learning Objectives - Part A
Structural analysis methods aimed to structural design.
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
The course is an introduction to structural design methods and problems.
By the end of the course the student will be able to:
- Understand the basic principles of material strength and deformation
- Apply the knowledge of strength of materials on engineering applications and design problems
- Analyze low degree statically indeterminate beam structures
- Define the model of a beam structure, justify the choice, discuss the method and interpret the results of the analysis
- Conceive simple structures and systems.
Prerequisites - Part A
Successful examination at STATICA (Statics)
Prerequisites - Part B
Knowledge of mechanics and mathematics learned in previous courses of “Statica” and “Istituzioni di matematiche”
Prerequisites - Part C
The course is designed for students who have a good knowledge of algebra, linear algebra, geometry, trigonometry, elementary physics and mechanics, generally provided by the previous courses of “Mathematical Analysis and Geometry” and “Statics”; this knowledge is essential.
Teaching Methods - Part A
Lessons, exercises in the classroom
Teaching Methods - Part C
Frontal in-door lessons according the time-table, alternating theoretical lessons and exercises. The attendance to lessons is not compulsory. The achievements of the objectives is evaluated via final exam.
In order to achieve the expected objectives, students are strongly recommended to: attend regularly and participate actively in the lessons; study individually during the semester; meet the teacher for further clarifications when necessary, both during office hours and during/after the lessons; attend the in-class tests.
Further information - Part A
Students will be obliged to enroll via moodle (e-l.unifi.it) according to the procedures given by the teacher during the first lesson (see the course calendar 2017-18).
Further information - Part C
Every topic listed under “Content” is important; for this reason the grading in different areas cannot be summed. The evaluation is based on the acquiring of the following abilities that are reported in increasing order, from the minimum to the maximum grade:
- correctly use the acquired methods for the analysis;
- use the acquired methods in a critical way, opportunely interpret structural problems, making the best choice both for the analysis and for the design of a structure;
- justify properly and effectively the choices made and the methods employed.
Type of Assessment - Part A
quiz via moodle, individual oral examination
Type of Assessment - Part B
Write and oral exam
Type of Assessment - Part C
The exam consists of a written test and, after passing that, a following oral examination.
In-class tests will be given during the lesson period.
Course program - Part A
[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]
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.
[5]
Euler instability of columns.
[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.
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.