Risorse bibliografiche
 Risorsa bibliografica obbligatoria Risorsa bibliografica facoltativa
 Scheda Riassuntiva
 Anno Accademico 2016/2017 Scuola Scuola di Architettura Urbanistica Ingegneria delle Costruzioni Insegnamento 096455 - MATHEMATICS AND MECHANICS OF SOLID Docente Cremonesi Massimiliano , Turzi Stefano Simone Cfu 8.00 Tipo insegnamento Corso Integrato

Corso di Studi Codice Piano di Studio preventivamente approvato Da (compreso) A (escluso) Nome Sezione Insegnamento
Arc - Urb - Cost (Mag.)(ord. 270) - MI (1018) ARCHITETTURA - PROGETTAZIONE ARCHITETTONICAADLAZZZZ096455 - MATHEMATICS AND MECHANICS OF SOLID

 Programma dettagliato e risultati di apprendimento attesi
 MATHEMATICS: This part provides the conceptual tools needed for an introduction to the mechanics of linearly elastic solids. Tensor algebra. Vectors and tensors. Dot, cross and triple products. Components and dyadic products. Symmetry and skew-symmetry. Principal invariants: trace and determinant. Eigenvalues and eigenvectors. Characteristic equation. Diagonalisation of a symmetric tensor, spectral decomposition theorem. Multivariable calculus and kinematics of deformations. Two-variable functions. Limits, continuity and partial derivatives. Tangent plane, unit normal to a surface. Vector fields. Gradient and divergence of a vector field. Infinitesimal deformations and strain tensor. Normal strain, shear strain and dilatation. Geometrical interpretation of the strain tensor. Principal strains. Double integrals and moments of inertia. Double integrals, simple regions, iterated integrals. Applications of double integrals: centre of mass, moment of inertia. Inertia tensor for a plane region. Huygens-Steiner theorem. Principal moments and principal axes of inertia. Surfaces. Parametric surfaces, coordinate lines and coordinate vectors. Surface integrals and divergence theorem.     MECHANICS: The course aims to give the students the deeper knowledge about the mechanical behavior of structures with respect to the basis acquired in the bachelor degree. Program of the lectures The course is organized in lessons ex-cathedra and exercises. The covered topics are: Review of kinematics and statics and internal forces of a rigid plane beam subjected to concentrated and distributed forces. The transmission of forces. The traction vector and the stress tensor. The Mohr circle The linear elastic constitutive theory The cases of de Saint Venant: axial force, bending moment, shear and torsion The strength criteria for fragile and ductile materials The principle of virtual work for studying isostatic and hyperstatic structures

 Note Sulla Modalità di valutazione
 There are separate exams for Mathematics and Mechanics. Each examination comprises a written tests, with exercises and theoretical questions, and an oral exam. The oral examinations are usually optional, but you may be asked to sit a compulsory oral exam in some cases.

 Bibliografia
 Mathematics: Lecture Notes selected by the teacherNote:Notes are posted on Beep, and are available for download. R.A. Adams, C. Essex, Calculus: Several Variables, Editore: Pearson Education Canada, ISBN: 978-0321549297 Steen Krenk and Jan Hgsberg, Statics and Mechanics of Structures, Editore: Springer, Anno edizione: 2013 Keith D. Hjelmstad, Fundamentals of Structural Mechanics, Editore: Springer, Anno edizione: 2004 Russel C. Hibbeler, Statics and Mechanics of Materials, Editore: Pearson Prentice Hall, Anno edizione: 2004 Claudia Comi and Leone Corradi dell'Acqua, Introduzione alla meccanica strutturle, Editore: McGraw-Hill, Anno edizione: 2016, ISBN: 9788838615412

 Software utilizzato
 Nessun software richiesto

 Mix Forme Didattiche
Tipo Forma Didattica Ore didattiche
lezione
80.0
esercitazione
28.0
laboratorio informatico
0.0
laboratorio sperimentale
0.0
progetto
0.0
laboratorio di progetto
0.0

 Informazioni in lingua inglese a supporto dell'internazionalizzazione
 Insegnamento erogato in lingua Inglese Disponibilità di materiale didattico/slides in lingua inglese Disponibilità di libri di testo/bibliografia in lingua inglese Possibilità di sostenere l'esame in lingua inglese Disponibilità di supporto didattico in lingua inglese
 schedaincarico v. 1.8.3 / 1.8.3 Area Servizi ICT 03/12/2023