AIMS AND CONTENT

AIMS AND LEARNING OUTCOMES

The aim of the Course is to provide the fundamentals of Solid Mechanics, with particular attention to the Saint Venant problem, which is very useful in structural applications.

The main learning outcomes of the Course are:

• Acquisition of the theoretical bases concerning the analysis of strain and stress in the Cauchy solid

• Acquisition of the theoretical bases on the constitutive modeling of materials and on the failure criteria

• Acquisition of the theoretical basis of the Saint Venant formulation

• Ability to determine the principal stresses and strains in a point of the solid and the relative directions

• Ability to determine the stress state in beams in space

• Ability to determine the strass state in beams deriving from normal stress and bending moment, shear (Jourawsky formulation) and twisting moment (Bredt formulation)

• Ability to identify the most stressed points of a section and carry out a strength verification

TEACHING METHODS

The course is divided into lectures aimed to introduce the theoretical concepts underlying Solid Mechanics and exercises for the resolution of practical problems (analysis of the stress and strain states and strength verification).

SYLLABUS/CONTENT

Introduction to Solid Mechanics - Equilibrium and stress concept according to Cauchy - The Cauchy theorem - The equilibrium equations - Principal stresses and principal stress directions - Mohr's circle for biaxial stress states - Analysis of deformation – Compatibility Equations – Principal strains and principal directions of strain - The constitutive equations - Elasticity - The Saint-Venant problem and the semi-inverse method - The Saint-Venant postulate - Stress state due to normal force and bending moment in prisms - Shear stress - Jourawski's approximate theory for shear - Torsion - Bredt's approximate theory, torsion of hollow beams - Failure criteria: Galileo-Rankine, Tresca, von Mises.

RECOMMENDED READING/BIBLIOGRAPHY

Main References

L. Gambarotta, L. Nunziante e A. Tralli, Scienza delle Costruzioni, McGraw-Hill, Publishing Group Italia, Milano, 2011

P. Casini, M. Vasta, Scienza delle Costruzioni, CittàStudi Edizioni, De Agostini Scuola SpA, Novara, 2016

E. Benvenuto, La Scienza delle Costruzioni e il suo sviluppo storico, Reprint, Edizioni di Storia e Letteratura, Roma, 2006

O. Belluzzi, Scienza delle Costruzioni, Zanichelli, Bologna, Opera edita a partire dal 1944

Exercises

F. Beer, R. Johnston , Scienza delle Costruzioni, McGraw-Hill Libri Italia srl, Milano, 1997

TEACHERS AND EXAM BOARD

Exam Board

FEDERICA TUBINO (President)

GIACOMO BATACCHI

LUIGI GAMBAROTTA

STEFANO PODESTA' (President Substitute)

LESSONS

LESSONS START

21 September 2020

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

The examination is divided into a written test and a subsequent oral exam, which must be taken within the same exam session and is normally set 2 weeks after the written exam. During the written test, only the use of an A4 format help sheet is admitted, which the student can fill in on the front and back, reporting the information he considers useful for the written test. Students who have scored 18 or more in the written test are admitted to the oral exam.

ASSESSMENT METHODS

The written test normally lasts 3 hours and consists in the solution of problems (normally 3) related to the topics addressed in the course (e.g. stress and strain analysis in the continuum, stress distribution in beams, determination of the stress state in beams in space, strength verification of beams in the plane and in space.

The oral exam is aimed at ascertaining the understanding of the theoretical knowledge of Solid Mechanics acquired by the student (stress and strain analysis in solids, constitutive equations for the continuum, Saint Venant problem - normal force and bending moment, shear, torsion -, failure criteria). The exam focuses on the formulation of the problems and the related demonstrations, which allow to derive the application tools used in the written test. The assessment will take into account the level of knowledge achieved, the degree of preparation, the ability of critical analysis and the acquisition of a correct terminology.

Exam schedule