The course introduces the basic principles and methodological aspects of theoretical and applied mechanics, by adopting the tools of mathematical physics. The linear models for the static, kinematic and elastic behaviour of solids and structures are introduced to establish the fundamentals of the structural design. The student develops the engineering confidence and the operational skills to deal with elastic problems of increasing difficulty.
OBJECTIVES. Understanding of the theoretical foundations of mechanics (kinematic compatibility, quasi‐static force equilibrium, laws of virtual works and energy conservation). Acquisition of the mathematical tools employed in the formulation of the physical models describing the mechanical behaviour of structural elements and complex structures (discrete models of rigid bodies, continuous models of mono‐ and tri‐ dimensional deformable beams, continuous and discrete models of planar frames). Development of the engineering awareness required for the formulation of structural analysis problems of increasing complexity, and attainment of sufficient proficiency in the practical application of the related solution techniques, focused on the structural design in the elastic field through the allowable stress method.
ABILITIES. Upon successful completion of the course, the student will have gained the engineering awareness and operational skills for (a) the formulation and solution of elastic problems for planar frames of deformable beams in the presence of external forces, ground displacements and thermal effects, with focus on the kinematic (generalized displacement and deformation variables) and static unknowns (generalized stress variables); (b) the formulation and solution of the elastic problem for three dimensional deformable prismatic solids, with focus on the kinematic (strain tensor) and static unknowns (stress tensor); (c) the structural design through the allowable stress method.
The teaching activities are carried out in the form of theoretical lessons, accompanied by illustration of application examples and, on specific request of the students, by guided exercises to the solution of typical problems and case-studies.
PART I (10 hours): physical mathematical models of rigid bodies, quasi‐static forces, bilateral holonomic time‐independent constraints, static problem and kinematic problem for rigid bodies. PART II (20 hours): one‐dimensional continuum model of deformable beams (Euler‐Bernoulli and Timoshenko models); static problem, kinematic problem and linear elastic constitutive law for deformable beams; elastic problem and law of virtual works for deformable beams; force method and displacement method for the solution of planar frames of deformable beams. PART III (10 hours): three‐dimensional continuum model of deformable solids (Cauchy model); static problem, kinematic problem and linear elastic constitutive law for the deformable solids; elastic problem for deformable solids. PART IV (20 hours): three‐dimensional continuum model of deformable prismatic solids (De Saint Venant model); elastic problem for the deformable prismatic solids and semi‐inverse method of solution; elementary problems of uniform extension, uniform and non‐uniform flexion, torsion. COMPLEMENTARY: structural design according to the method of allowable stresses; stability of equilibrium.
Ricevimento: Tuesday, 5 pm at the teacher's office in Villa Cambiaso
PAOLO BLONDEAUX (President)
MARCO LEPIDI (President)
GIOVANNA VITTORI (President)
GIOVANNI BESIO
FRANCESCO ENRILE
MARCO MAZZUOLI
GIUSEPPE PICCARDO
GAETANO PORCILE
RODOLFO REPETTO
NICOLETTA TAMBRONI
FEDERICA TUBINO
Written final examination (eventually distinguished in two partial examinations) followed, upon successful completion, by an oral examination. (see also the "Guide to the Exam" downloadable from the Aulaweb page)
