Chemical Engineering

1. Geometry of Areas (moments of inertia, transport 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, strain measurements, implicit congruence equations, the kinematic problem) 5. Statics of the beam (indefinite equations of equilibrium, 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 (the elastic line equations) 9. Virtual work theorem (congruent system, balanced system, TLV proof, calculation of displacements and rotations in isostatic structures) 10. Method of forces (hyperstatic systems, Muller-Breslau equations) 11. The three-dimensional continuum (definition of strain, definition of tension, principal directions of tension and strain, Cauchy's theorem, indefinite equilibrium equations, Mohr's circle) 12. The linear elastic constitutive equation 13. Saint Venant's Problem (position of the problem, semi-inverse method, static equivalence) 14. Centered normal force, straight bending 15. Deflection deflection, tensoflexion, pressoflexion 16. Uniform torsion 17. Flexion and Shear

In order to participate and successfully follow the course, it is important to have a solid background in some specific areas of mathematics and physics. In particular, advanced skills in mathematical analysis, geometry and physics are required. It is also necessary for students to have a good understanding of the fundamental concepts of finite-dimensional vector spaces, linear differential equations, and rigid-body mechanics.

Notes provided by the lecturer in class Recommended texts (but not required) Krenk, S. & Høgsberg, J. Statics and Mechanics of Structures. (Springer Netherlands, 2013). P. Casini, M. Vasta. Scienza delle Costruzioni. Città Studi Edizioni.

Lecture attendance is highly suggested

The examination consists of an oral test that is accessed after passing a 3-hour written test.

The classes will take place exclusively in person with weekly online office hours (optional and upon students' request).