ELEMENTI DI MECCANICA DEI SOLIDI

The course aims to provide basic knowledge of the statics and kinematics of rigid and deformable bodies and to analyze the structural response and stability of structures composed of solid beams. The knowledge acquired will provide the basis for the technical skills necessary for the design of safe, sustainable, and resilient structures and infrastructures in accordance with points 4, 9, and 11 of the 2030 Agenda.

Specifically, the expected learning outcomes are:

DD1 Knowledge of scientific terminology, the scientific method, common mechanical quantities, and fundamental concepts of equilibrium, stress, and strain within the context of the mechanics of elastic solids.

DD2 Ability to apply acquired knowledge of mechanics to understand the methodologies for the analysis and design of civil structures.

DD3 Ability to critically evaluate calculation results and approximations arising from underlying assumptions, and to make decisions based on one's structural knowledge and understanding.

DD4 Ability to communicate knowledge effectively, both in writing and orally, using appropriate terminology. Ability to present the results of an exercise clearly and concisely, using graphs, equations, reaction diagrams, and/or other visual representations. Ability to work in a group, effectively communicating one's own ideas and listening to those of others.

DD5 Ability to self-assess the learning skills required to undertake further studies with a high degree of autonomy.

The following courses are required as prerequisites: Linear Algebra and Geometry, Mathematical Analysis I and II, and Physics I.

KINEMATICS OF RIGID BODIES: Rigid displacements in space and the plane, constraints, kinematic characterization of structures.

STATICS OF RIGID BODIES: Static characterization of constraints in the plane, analytical calculation of constraint reactions; considerations regarding equilibrium in non-isostatic structures.

THE PRINCIPLE OF VIRTUAL WORK FOR RIGID STRUCTURES: Derivation of the cardinal equations of statics using the principle of virtual work.

ISOSTATIC STRUCTURES COMPOSED OF RIGID BEAMS: Internal force resultants, differential equilibrium equations for an infinitesimal element, diagrams of internal force resultants, governing laws for internal force resultants, application of the principle of superposition.

STRESS ANALYSIS: The concept of stress, Cauchy’s tetrahedron and the stress tensor, principal stresses and principal stress directions, classification of stress states, Mohr’s circles, differential equilibrium equations.

STRAIN ANALYSIS: Displacement vector, infinitesimal strain tensor, volumetric strain.

LINEAR ELASTIC CONSTITUTIVE RELATIONSHIP: Tensile test, mechanical properties of materials, linear elastic constitutive relationships, limits of validity for elastic constants.

ENERGY ASPECTS OF DEFORMABLE SOLIDS: The principle of virtual work for deformable bodies, strain energy, Clapeyron’s theorem, the principle of superposition.

FUNDAMENTALS OF AREA GEOMETRY: First moments of area and centroid, moments of inertia,principal axes of inertia, polar moment of inertia, and radii of gyration. ANALYSIS OF DEFORMABLE STRUCTURES: Elastic change in length of axially deformable beams; elastic curvature of beams subject to bending; application of the principle of virtual work to calculate displacements and rotations in systems of deformable beams; thermal strains; support settlements; introduction to the analysis of statically indeterminate structures.

THE PROBLEM OF ELASTIC EQUILIBRIUM

DE SAINT-VENANT BEAM THEORY: Stress states; solution to the De Saint-Venant problem; centric axial force; simple bending; combined bending; torsion; shear; shear center.

STRENGTH CRITERIA FOR CONSTRUCTION MATERIALS: Tresca criterion; von Mises criterion.

STRENGTH VERIFICATION OF ELASTIC STRUCTURES

STABILITY OF EQUILIBRIUM AND CRITICAL LOAD

During the course, interim assessments may be held; passing these allows students direct access to a simplified oral exam. Eligibility to take these interim assessments is contingent upon meeting class attendance requirements.

Students who do not take or do not pass the interim assessments may take the exam via a single written test followed by an oral test. The exam is evaluated based on the following criteria: level of knowledge regarding the required topics; clarity of expression and command of language; ability to apply knowledge to simple case studies; and ability to connect different themes within the syllabus, in accordance with indicators DD1, DD2, DD3, DD4, and DD5 (as described in the "Learning Methods" section).

Exam registration procedure: Booking via the university portal. Eight exam sessions are scheduled throughout the year, in accordance with the academic calendar.