Understanding and assimilation of basic concepts related to the foundations of continuum mechanics for general 3D elastic solids and elementary mechanics of deformable one-dimensional structures. Acquisition of operational capabilities necessary to solve statically determinate and indeterminate beams of basic type using different approaches, as well as the schematic design and verification of beams with general loading conditions.
Lectures using the blackboard: 32 hours Practical classes: 22 hours
Assessment Methods
Written test with exercises on the theoretical part as well as on the Saint Venant problem and solutions of isostatic structures + possible oral examination.
Texts
Course notes.
P. Casini, M. Vasta, Scienza delle Costruzioni 4/ed, Città studi, 2019.
Corradi dell'Acqua L.. Meccanica delle strutture 1 - Il comportamento dei corpi continui 2/ed. McGraw-Hill, 2010.
Beam equilibrium: Kinematics and statics of the straight beam, internal actions and diagrams. Euler-Bernoulli beam theory, consistency, equilibrium, constitutive law. Elastic-linear-isotropic law and formulation of the elastic problem.
Strain state. Consistency of the deformable continuum and kinematics relations. The finite-deformation tensor (Green-Lagrange). Hypothesis of "small displacements": small deformation tensor. Principal deformations and invariants. Volume and shape change. Internal consistency.
Stress state: General aspects of the structural problem. Force and stress. the Cauchy stress tensor. Principal directions and invariants. 2D and 3D stress states. The Mohr stress representation. Equilibrium conditions.
Constitutive law. Stress-strain relations and experimental evidence. Elasticity, anelasticity, failure. Elastic law: energy aspects, existence and uniqueness of the elastic response. Elastic-linear-isotropic law: elastic constants. Elastic limit and failure-yield criteria. The elastic problem. Formulation of the problem and uniqueness of the solution.
Position of the problem of De Saint Venant. Axial action and bending. Torsion. Shear: approximate treatment.
