Unit FUNDAMENTALS OF STRUCTURAL MECHANICS
- Course
- Mechanical engineering
- Study-unit Code
- 70367206
- Curriculum
- In all curricula
- Teacher
- Giulio Castori
- Teachers
-
- Giulio Castori
- Hours
- 54 ore - Giulio Castori
- CFU
- 6
- Course Regulation
- Coorte 2024
- Offered
- 2025/26
- Learning activities
- Affine/integrativa
- Area
- Attività formative affini o integrative
- Academic discipline
- ICAR/08
- Type of study-unit
- Obbligatorio (Required)
- Type of learning activities
- Attività formativa monodisciplinare
- Language of instruction
- Italian
- Contents
- The course introduces the fundamental principles of solid and structural mechanics. Topics include: continuum mechanics, stress and strain analysis, linear elasticity, the Saint-Venant problem, basic structural analysis, beam theory, support conditions, analysis of statically determinate structures, strength criteria (Tresca and von Mises), and verification of beam cross-sections
- Reference texts
- Recommended Textbooks: 1. Angotti, F., Borri, A.: Lezioni di Scienza delle Costruzioni. Dei, 2005. Additional References: 2. Viola, E.: Esercitazioni di Scienza delle costruzioni (Volumi I e II). Pitagora, 1993. 3. Camiciotti, R., Cecchi, A.: Esercizi di Scienza delle Costruzioni (Volume III). Edizione Morelli, 1998. 4. Baldacci, R.: Scienza delle Costruzioni (Volumi I e II). UTET, 1970-76. Didactic Materials: Lecture slides, problem sets with solutions, tables, videos, and other course materials are available through the Unistudium platform.
- Educational objectives
- The main objective of the course is to provide students with a solid foundation for understanding the fundamental concepts and principles of Structural Mechanics. The course aims to equip students with the necessary tools to determine and assess the stress and strain states of structural elements, with particular focus on one-dimensional solids of various cross-sections and shapes. The expected learning outcomes include: • Acquisition of knowledge (Dublin Descriptor 1): ¿ Strain state and general compatibility equations; ¿ Stress state and equilibrium equations for continuous media; ¿ Constitutive equations and theorems of linear elastic bodies; ¿ Criteria for plasticity, strength, and safety. • Ability to apply theoretical knowledge to practical cases involving the analysis of plane elastic frame structures (Dublin Descriptor 2) and independent judgment in selecting suitable approaches for structural modelling and analysis (Dublin Descriptor 3), with particular reference to: ¿ Determination of internal force diagrams in statically determinate plane elastic frames; ¿ Calculation of stress distribution in beam cross-sections using the Saint-Venant model; ¿ Safety verification of plane elastic structures.
- Prerequisites
- In order to understand and apply most of the techniques presented in the course, students are expected to have prior knowledge of: Mathematical Analysis: function study, differentiation and integration techniques for single- and multi-variable functions; Geometry: vector spaces and linear mappings, matrices and linear transformations, linear systems, algebraic curves (conic sections); Physics and Rational Mechanics: vector calculus, and the cardinal equations of statics.
- Teaching methods
- Lectures and practical classroom exercises, during which the topics covered in the course are presented and discussed.
- Other information
- Further information is available on the Unistudium course page. The instructor is available for consultations at the end of each lecture. Additional meetings, either in person or via Microsoft Teams, can be arranged by appointment.
- Learning verification modality
- The exam consists of two parts: • A written test (approximately 2 hours and 30 minutes) involving the solution of two exercises. The first exercise concerns the analysis of a statically determinate structure (kinematic analysis, calculation of support reactions, and construction of internal force diagrams). The second exercise focuses on the stress analysis of a cross-section. • An oral examination, lasting no more than approximately 30 minutes, aimed at assessing the student’s understanding of the topics covered during the lectures. For logistical reasons, the written test will be taken prior to the oral examination, which will be held during the same exam session according to the schedule established by the Degree Programme. In exceptional and specific cases, the oral examination may be taken during a different session, subject to prior agreement with the instructor.
- Extended program
- Strain Analysis: • Strain in the neighborhood of a point; finite and infinitesimal strain tensors; linear, angular, surface, and volumetric strain; strain compatibility. Stress Analysis: • Stress in the neighborhood of a point; stress tensor; general and boundary equilibrium equations; principal stresses and directions; uniaxial, biaxial, and triaxial stress states; graphical representation of stress states (Mohr’s circle). Elastic Solid and Energy Theorems: • Constitutive equations; elastic and linear elastic materials; homogeneity and isotropy; Clapeyron’s, Betti’s, and Kirchhoff’s theorems; the problem of isotropic elastic equilibrium: Navier’s and Beltrami-Michell’s equations. The de Saint Venant Problem: • Reduction of equilibrium equations; de Saint Venant’s assumptions and postulate; axial force; pure bending; eccentric axial force; combined bending and shear; torsion. The Beam Problem: • Support conditions; beam kinematics; beam statics; internal force diagrams; internal discontinuities; analysis of statically determinate beam systems. Plasticity and Strength Criteria: • Stress-strain diagram; safety verifications (Tresca and Von Mises criteria).
- Obiettivi Agenda 2030 per lo sviluppo sostenibile
- • Goal 4: Quality Education • Goal 9: Industry, Innovation and Infrastructure