03MNIMX

A.A. 2022/23

Course Language

Inglese

Course degree

Master of science-level of the Bologna process in Ingegneria Civile - Torino

Course structure

Teaching | Hours |
---|---|

Lezioni | 60 |

Esercitazioni in laboratorio | 20 |

Tutoraggio | 15 |

Teachers

Teacher | Status | SSD | h.Les | h.Ex | h.Lab | h.Tut | Years teaching |
---|---|---|---|---|---|---|---|

Cornetti Pietro | Professore Associato | ICAR/08 | 55 | 0 | 0 | 0 | 2 |

Teaching assistant

Context

SSD | CFU | Activities | Area context |
---|---|---|---|

ICAR/08 | 8 | B - Caratterizzanti | Ingegneria civile |

2022/23

The course aims to improve and deepen the basic knowledge acquired in the course of Structural Mechanics at the Bachelor Degree. The fundamental tools necessary for the advanced modeling of the mechanical behavior of materials and structures will be provided. The student will study highly statically indeterminate beam-framed structures, will learn the basic concepts for the analysis of bi-dimensional elements (plates and shells) and will face the basic concepts of dynamics of beam systems.

The course aims to improve and deepen the basic knowledge acquired in the course of Structural Mechanics at the Bachelor Degree. The fundamental tools necessary for the advanced modeling of the mechanical behavior of materials and structures will be provided. The student will study highly statically indeterminate beam-framed structures, will learn the basic concepts for the analysis of bi-dimensional elements (plates and shells) and will face the basic concepts of dynamics of beam systems.

The student will have to deepen the analytical and numerical topics presented during lectures, starting from the basic equations and choosing, for each problem, the most appropriate methodology to get the solution. The student must possess an appropriate scientific language. The knowledge of a finite element code will help the student to understand the difficulties for scientific/professional modeling.

After the course, the student is expected:
- to be able to correctly identify the structural problem at hand and to choose the most appropriate solution strategy;
- to use Finite Element programs for the solution of structural problems and to check these solutions by hand calculations, for frames, plates and shells;
- to acquire an appropriate technical and scientific language.

Fundamental notions from the bachelor mathematical courses (Mathematical Analysis 1 and 2, Geometry, Linear Algebra, Analytical Mechanics, Numerical Methods) and engineering courses (Structural Mechanics: study of isostatic and statically indeterminate structures by the force method, differential equation of the elastica) are required.

Fundamental notions from the bachelor mathematical courses (Mathematical Analysis, Geometry, Linear Algebra, Analytical Mechanics, Numerical Methods) and engineering courses (Structural Mechanics: study of isostatic and statically indeterminate structures by the force method, differential equation of the elastic curve) are required.

1. ONE-DIMENSIONAL STRUCTURES. Statically Indeterminate Structures: Method of forces, Method of displacements, mixed Method. Structural symmetry. Rotating- and translating-node frames. Thermal loads and imposed displacements. Frames with non-orthogonal beams. Stiffness matrix of the beam. Automatic computation of beam systems. Beams with curvilinear axes. Beam on elastic foundation.
2. BI-DIMENSIONAL STRUCTURES: Plane stress and plane strain. Plates loaded in their plane: plates with a circular hole; concentrated force acting on a semi-infinite plane. Plates loaded orthogonally to their plane: Sophie Germain equation for plates in bending, boundary conditions. Symmetrically loaded shells of revolution: membranes and thin shells, circular plates, cylindrical shells.
3. DYNAMICS OF STRUCTURES: Single-degree-of-freedom linear systems. Free response. Damped response. Forced response to harmonic, periodic, impulsive or generic excitations. Non-linear elastic oscillator. Elasto-plastic oscillator. Multi-degree-of-freedom linear systems: modal analysis. Continuous systems: modal analysis of deflected beams. Dynamics of beam systems.

1. ONE-DIMENSIONAL STRUCTURES. Statically Indeterminate Structures: Method of forces, Method of displacements, Mixed method. Structural symmetry. Rotating- and translating-node frames. Thermal loads and imposed displacements. Frames with non-orthogonal beams. Stiffness matrix of the beam. Automatic computation of beam systems. Beams with curvilinear axis, arches. Beam on elastic foundation.
2. BI-DIMENSIONAL STRUCTURES: Plates loaded in their plane. Plates loaded orthogonally to their plane. Sophie Germain equation for plates in bending, boundary conditions. Symmetrically loaded membranes and shells of revolution: circular plates, cylindrical and spherical shells. Domes. Pressurized tanks.
3. DYNAMICS OF STRUCTURES: Single-degree-of-freedom linear systems: undamped and damped free response; forced response to harmonic, periodic, impulsive or generic excitations. Multi-degree-of-freedom linear systems: modal analysis. Response spectrum analysis.
4. FINITE ELEMENT METHOD: fundamentals, shape functions and stifffness matrix, applications (bar, beam, plane elements). Commercial codes.

Approximately three fourth of the lectures are given in classroom (mainly at blackboard) whereas one fourth are held at LAIB to learn the use of a finite element software. This allows the student to check the results obtained analytically during the course. These lessons cover: (1) introduction of a finite element analysis on PC, thin or thick beam elements; (2) calculation of plane frames and trusses; (3) calculation of shear-type and spatial frames; (4) calculation of rectangular thin plates; (5) calculation of circular plates and hemispherical domes; (6) calculation of beam on elastic foundation and hydrostatic tanks; (7) free vibrations of a cantilever beam (mono-, bi-and tri-dimensional model); (8) modal analysis of plane and space frames; (9) Modal analysis of continuous systems (arc, circular plate, hemispherical dome).

Approximately three fourths of the lectures are given in classroom whereas one fourth are held at LAIB (Basic Information Laboratory) to teach the use of a finite element software. This allows the student to check the results obtained analytically during the course and face linear finite element analyses in general.
The LAIB lessons cover: (1) introduction to finite element analysis on PC, thin or thick beam elements; (2) analysis of plane frames and trusses; (3) analysis of shear-type and spatial frames; (4) analysis of rectangular thin plates; (5) analysis of circular plates and hemispherical domes; (6) analysis of beam on elastic foundation and hydrostatic tanks; (7) free-vibration analysis of beams and plane frames.

Official textbook:
- A. Carpinteri, "Advanced Structural Mechanics", CRC Press, 2017. (Chapter 1 to 6)
Recommended books:
– A. Carpinteri, "Structural Mechanics Fundamentals", CRC Press, 2013. (it covers what students are expected to know from the bachelor course in structural mechanics)
-A. Carpinteri, G. Lacidogna, C. Surace, "Calcolo dei telai piani – Esempi ed esercizi", Pitagora Editrice, Bologna, 2002 (useful for the written examination).
-S. Timoshenko, "Theory of Plates and Shells", McGraw-Hill, Singapore, 1959. (world-wide known structural mechanics book)
As regards numerical and analytical practice lessons, material will be uploaded on the teaching internet site.

Official textbook:
– A. Carpinteri, "Advanced Structural Mechanics", CRC Press, 2017. (Chapter 1 to 6)
Recommended books:
– A. Carpinteri, "Structural Mechanics Fundamentals", CRC Press, 2013. (it covers what students are expected to know from the bachelor course in structural mechanics)
– A. Carpinteri, G. Lacidogna, C. Surace, "Calcolo dei telai piani – Esempi ed esercizi", Pitagora Editrice, Bologna, 2002 (useful for the written examination).
– S. Timoshenko, "Theory of Plates and Shells", McGraw-Hill, Singapore, 1959. (world-wide known structural mechanics book)
As regards numerical and analytical practice lessons, material will be uploaded on the teaching internet site.

The exam is aimed at ascertaining the knowledge of the topics listed in the course syllabus and the ability to apply the theory and the relative calculation methods to the solution of structural systems (see Expected Learning Outcomes).
The exam consists in three parts: (1) the numerical solution of a structure to check the knowledge of the finite element code (see Expected Learning Outcomes), either at the Informatic Laboratory at the end of the course or at home; (2) a written exercise on statically indeterminate frames; (3) an oral examination on the theoretical topics. The overcoming of the writing part is a necessary condition to access the oral examination. During the written exam, it is forbidden to use cell phones, programmable calculators, books, texts, notes (except the formulary provided during the course). Oral questions will assess the knowledge level and the scientific language of student. The final mark will properly take into account the results obtained in both the oral and the written tests.

Gli studenti e le studentesse con disabilità o con Disturbi Specifici di Apprendimento (DSA), oltre alla segnalazione tramite procedura informatizzata, sono invitati a comunicare anche direttamente al/la docente titolare dell'insegnamento, con un preavviso non inferiore ad una settimana dall'avvio della sessione d'esame, gli strumenti compensativi concordati con l'Unità Special Needs, al fine di permettere al/la docente la declinazione più idonea in riferimento alla specifica tipologia di esame.

The exam is aimed at ascertaining the knowledge of the topics listed in the course syllabus and the ability to apply the theory and the relative calculation methods to the solution of structural systems.
The exam consists in three on-site parts:
(1) the numerical solution of a structural problem similar to those dealt with at the Lab sessions. Time: 1 hour. Evaluation: passed/failed. Passing this test is mandatory to go on.
(2) a written exercise on statically indeterminate frames, similar to the one presented in classroom lectures, to be solved by hand. The use of cell phones, programmable calculators, books, texts, notes (except the formulary provided during the course) is forbidden. Time: 1.5 h. Evaluation: 0-14 failed; 15-30 passed. Passing this test is mandatory to go on.
(3) an oral examination on the theoretical topics of the course. Oral questions will assess the knowledge level and the scientific language of student. Time: 0.5-1h. Evaluation: passed/failed. If passed, the final mark will properly take into account the results obtained in both the oral and the written tests. If not passed, the results of parts (1) and (2) remain valid.

In addition to the message sent by the online system, students with disabilities or Specific Learning Disorders (SLD) are invited to directly inform the professor in charge of the course about the special arrangements for the exam that have been agreed with the Special Needs Unit. The professor has to be informed at least one week before the beginning of the examination session in order to provide students with the most suitable arrangements for each specific type of exam.

© Politecnico di Torino

Corso Duca degli Abruzzi, 24 - 10129 Torino, ITALY

Corso Duca degli Abruzzi, 24 - 10129 Torino, ITALY