Mechanical Engineering for the Green Transition

1. Geometry of Areas (moments of inertia, transfer and rotation formulas, principal moments of inertia, central ellipse of inertia) 2. Kinematics of Rigid Bodies (rigid displacements, kinematic characterization of constraints, the kinematic problem) 3. Statics of Rigid Bodies (static characterization of constraints, the static problem, static-kinematic duality, lattice structures) 4. Beam Kinematics (displacements and rotations, measures of deformation, implicit congruence equations, the kinematic problem) 5. Beam Statics (indefinite equilibrium equations, static problem, laws and diagrams of stress characteristics) 6. Constitutive Material (linear elastic bond for one-dimensional beam, thermal distortions, linear thermal variations, constitutive equations for one-dimensional beam) 7. The Elastic Problem for the Beam 8. Displacement Method (elastic line equations) 9. Virtual Work Theorem (congruent system, balanced system, TLV demonstration, calculation of displacements and rotations in statically determinate structures) 10. Force Method (hyperstatic systems, Muller-Breslau equations) 11. Three-dimensional Continuum (definition of deformation, definition of stress, principal directions of stress and deformation, Cauchy's theorem, indefinite equilibrium equations, Mohr's circle) 12. Linear Elastic Bond 13. Saint Venant Problem (problem position, semi-inverse method, static equivalence) 14. Centered normal force, straight bending 15. Deviated bending, flexure-tension, flexure-compression 16. Uniform torsion 17. Bending and Shear

In order to participate in and successfully follow the course, it is important to have a strong background in certain specific areas of mathematics and physics. Advanced skills in mathematical analysis, geometry, and physics are required. Additionally, students should have a good understanding of fundamental concepts in finite-dimensional vector spaces, linear differential equations, and mechanics of rigid bodies.

R.C. Hibbeler, Mechanics of Materials, Pearson L. Corradi Dell’Acqua, Meccanica delle strutture – il comportamento dei mezzi continui, McGraw-Hill M. Capurso, Lezioni di Scienza delle Costruzioni, Pitagora Editrice A. Luongo, A. Paolone, Scienza delel Costruzioni- Il continuo di Cauchy, Casa Editrice Ambrosiana A. Luongo, A. Paolone, Meccanica delle strutture. Sistemi rigidi ad elasticità concentrata, Casa Editrice Ambrosiana

Although not mandatory, attendance in classes is strongly recommended.

The final test includes a written and an oral test. The written test requires the solution of a series of problems concerning: - diagrams of axial force, shear a bending moment of a statically undetermined system of deformable beams - application of strength criteria to the cross-section of a beam. Passing the written test is a necessary but not sufficient condition to pass the exam, which includes also an oral test. In the oral test, students have to demonstrate their ability to discuss and present the written test, enunciate and demonstrate theorems, define mechanical quantities and principles that rule statics and kinematics of deformable bodies.

Teaching activities include ex cathedra lectures and classroom tutorials. They evolve so that students are able to achieve learning outcomes. Ex cathedra lectures present the theoretical subjects listed in the program. Each lecture contains discussion of examples or case studies with increasing difficulty, in such a way that students attending the course would be eventually able to solve the problems assigned in the final test. Classroom tutorials strengthen the students' ability to solve target problems described in section "Modalità di valutazione".