### Teachings

Select Academic Year:     2017/2018 2018/2019 2019/2020 2020/2021 2021/2022 2022/2023
Professor
ANTONIO MARIA CAZZANI (Tit.)
Period
Second Semester
Teaching style
Convenzionale
Lingua Insegnamento
ITALIANO

Informazioni aggiuntive

Course Curriculum CFU Length(h)
[70/72]  CIVIL ENGINEERING [72/00 - Ord. 2013]  PERCORSO COMUNE 10 100

### Objectives

Theoretical issues and applications to be used for structural design are taught in this class.
Based on knowledge acquired during the first three semesters' classes of Mathematics and Physics, topics peculiar to Solids and Structural Mechanics and Strength of Materials are carefully developed, which will be used in third year's class of Structural Design (Tecnica delle costruzioni).
The aim is that of developing in a sound and rigorous way the basic issues, by making clear the physical meaning of the mechanical models which are introduced and their limits of applicability.
Attending this class, students will become able to develop applications covering all treated issues. In particular, rigid-body systems, statically determinate structures and linear elastic deformable solids will be dealt with.
The fundamental targets of this class are making students able to perform the following tasks:
1. recognizing the bearing elements of a given construction;
2. selecting an appropriate structural scheme;
3. evaluating the stress and strain state in a solid subjected to given forces;
4. assessing the resistance of a structural element;
5. computing displacement components in a given statically determinate or indeterminate structure.
As a long-term aim, the class will also make prospective civil engineers careful about the complexity and importance of structural issues in any construction and about the need of properly setting the structural problems and solving them with appropriate methods.

### Prerequisites

The basic background of high-school and of the first three semesters classes of Mathematics and Physics is assumed as a prerequisite.
In detail, these are the:
A) Physics prerequisites:
A-1 Basic dimensions and units of measures;
A-2 Vectors: fundamental operations and their use in formulating mechanical problems;
A-3 Newton's laws; Equilibrium of the material point and of a system of mechanically interacting material points.
B) Mathematics prerequisites:
B-1 Elementary functions and their graphs;
B-2 Vectors and analytic geometry;
B-3 Matrices, systems of linear algebraic equations, eigenvalues and eigenvectors;
B-4 Derivatives and study of functions by differential calculus;
B-5 Integrals;
B-6 Differential equations.
All these topics are satisfactorily treated in texts B-1/3 shown in bibliograhy.

### Contents

0. Torque and equivalent systems of forces; Equilibrium of a rigid body.
1. Statics of a rigid beam and of systems of rigid beams.
2. Kinematics of a rigid beam and of systems of rigid beams. Rigid plane displacements, kinematic analysis: constrained rigid body and systems of mutually joined beams. The Virtual Work Principle (VWP) for systems of rigid beams.
3. Mass geometry. centroids and first-order moments. Second-order moments. Principal axes of inertia and principal moments of inertia.
4. State of stress. Traction vector on a surface, stress tensor, Cauchy's equations. Stress components on a given plane. Principal stresses and principal directions of stress. Mohr's circle for plane and 3-D stress states. Differential equations of equilibrium.
5. State of strain. Small displacement kinematics for a continuos medium. Rigid body and deformation. Strain components and their physical meaning. Strain components given in any reference system . The VWP for a deformable continuum medium.
6. The elastic constitutive law. Isotropic linear elastic solids and Hooke's law.
7. Resistance criteria for assessing strength of materials.
8. Saint-Venant's elastic problem . Basic cases: axial force, bending; torsion (circular cross sections; general cross sections and approximate solutions for thin-walled beams with open or closed section); Shear force. Derived cases for not centered axial force and two independent bending moments.
9. Elastic beams. Elastically deformed shape of straight beams. Statically indeterminate beams: solution by the elastica method and by VWP.

Note: Topics 0-3 will constitute part A (to which the first written test is relevant); topics 4-10 will constitute part B (to which the second written test is relevant)..

### Teaching Methods

Teaching language is Italian.
Traditional lectures (chalks on blackboard) are interspersed with some exercise sessions, where students are required to solve practical problems, which are similar to those presented in the final tests. In case the necessary financial support will be granted, a tutor will be available to help students improving their skills.
Due to the current epidemiological situation, there is the possibility of live streaming lessons or recordings of the same
available online.
Exercises could be carried out through remote interaction with the available IT supports.

### Verification of learning

The final structure is this: two written tests, each one corresponding to either part A or part B followed by an oral examination.
The written tests consist of practical exercises to be solved and can be taken, in any order, both on the same day or in different exam dates.
When both tests get a positive grade (i.e. a score greater or equal to 18/30) then admission to oral examination, which is related to more theoretical issues, is granted.
Written test are valid only for the year in which they have been taken: as an example, all tests taken from January 2020 through December 2020 will expire at the end of February 2021.
Both written tests are worth 40% of the final grade, (i.e. they sum up to 80%), while 20% is reserved to oral examination.
Students are warmly advised to attend at least 60% of lectures for part A and part B if they want to successfully access finals.
Exam dates are known in large advance and students have to book on-line in due time, at least 48 hour before the exam; students failing to comply with this requirement will not be admitted to the exam room.
Note for Erasmus students: due to the large number of students involved, no special assignments will be available.

### Texts

Bibliography.

A.) Topics taught during class (A1-A3 in Italian; A4-A6 in English):
A-1. M. Capurso, Lezioni di scienza delle costruzioni, Pitagora: Bologna, 1971. (Topics 1,4-10)
A-2. D. Bigoni, et al. , Geometria delle masse, Progetto Leonardo: Bologna, 1995. (Topic 3)
A-3. E. Guagenti et al., Statica – Fondamenti di meccanica strutturale, McGraw-Hill: Milano, 2005. (Topics 0-2)
A-4. F.P. Beer, E.Russell Johnston, Mechanics of Materials, II Ed (in SI Units), McGraw-Hill: New York, etc.,1992
A-5. S.Timoshenko, Strength of Materials - Part I: Elementary Theory and Problems, 2nd Edition, van Nostrand: New York, 1940
A-6. S.Timoshenko, Strength of Materials - Part II: Advanced Theory and Problems, 2nd Edition, van Nostrand: New York, 1941.

B.) Topics necessary as prerequisites (B1-B2 in Italian; B3 in English):
B-1 E. Guagenti et al., Statica – Fondamenti di meccanica strutturale, McGraw-Hill: Milano, 2005.
(Physical prerequisites: Chapters 1-3 and Appendices A and D)
B-2 A. Ratto, A. Cazzani, Matematica per le scuole di Architettura, Liguori:Napoli, 2010. (Mathematical prerequisites matematici: Chapters 1-2, 5-6, 8-12).
B-3 A. Bedford, W.L. Fowler, Engineering Mechanics – Statics, Addison-Wesley: Reading MA etc., 1995. (Physical prerequisites)

C.) For deeper understanding (C1-C5 in Italian; C6-C8 in English)
C-1 L. Gambarotta, L. Nunziante, A. Tralli, Scienza delle costruzioni, McGraw-Hill: Milano, 2003.
C-2 O. Belluzzi, Scienza delle costruzioni, vol. 1, Zanichelli: Bologna, 1941.
C-3 J.E. Gordon, Strutture sotto sforzo, Zanichelli: Bologna, 1991.
C-4 M. Salvadori, Perché gli edifici stanno in piedi, Bompiani: Milano, 1990.
C-5 M. Levy, M. Salvadori, Perché gli edifici cadono, Bompiani: Milano, 1997.
C-6 J.E. Gordon, Structures: or Why Things Don't Fall Down, Da Capo Press: Cambridge, MA, 1981.
C-7 M. Salvadori, Why Buildings Stand Up, Norton & Company: New York, 1990.
C-8 M. Levy, M. Salvadori, Why Buildings Fall Down: How Structures Fail, Norton & Company: New York, 1994.

D.) Collection of exercises (in Italian):
D-1 A. Castiglioni et al., Esercizi di scienza delle costruzioni, Masson: Milano, 1981.