Lecturer: Fabio Carli  

Course name: Fundamentals Of Mechanics Of Materials and Structures
Course code: 502471
Degree course: Ingegneria Industriale
Disciplinary field of science: ICAR/08
University credits: CFU 6
Course website: n.d.

Specific course objectives

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.

Course programme

LECTURES

Stress state
General aspects of the structural problem. Force and stress: the stress tensor. Principal directions and invariants. 2D and 3D stress states. The Mohr stress representation. Equilibrium conditions.

Strain state
Consistency of the deformable continuum. Kinematics relations. Small displacements and the tensor of small deformations. Principal deformations and invariants. Volume and shape change. Internal consistency.

Constitutive law
Stress-strain relations and experimental evidence. Elasticity, anelasticity, failure and time dependent phenomena. 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. Energy aspect of the elastic phenomena. Position of the problem of De Saint Venant. Axial action and bending. Torsion. Shear: approximate treatment.

Theory of beams
Kinematics and statics of the straight beam. Elastic-linear-isotropic law and formulation of the elastic problem. The elastic equation. Principle of virtual work. Energy aspects. Force and displacement based methods. Axially loaded beams: removing the assumption of "small-displacement".

Elastic stability of equilibrium
Formulation of the problem. Discrete elastic systems. The Euler beam.

PRACTICAL CLASS
Kinematics: infinitesimal motions and constraints. Statics: external forces and reaction forces. Determinate structures: kinematics and statics. Analytical solution methods and graphics solutions. Internal actions and assessment of the stress condition. Trusses. Simple structural systems. Complex structural systems and their synthesis. Tracking charts of the internal actions. Kinematics of indeterminate systems. Elastic equation. Mohr's analogy. Force methods. Energy methods. Verification of sections and principles of beam design. Thermal load. Design of columns subjected to centered and eccentric axial load.

Course entry requirements

Calculus 1, Physics 1, Mathematical Physics, Algebra

Course structure and teaching

Lectures (hours/year in lecture theatre): 36
Practical class (hours/year in lecture theatre): 18
Practicals / Workshops (hours/year in lecture theatre): 0

Suggested reading materials

Track of lectures.

Corradi dell'Acqua L.. Meccanica delle strutture Vol.1. McGraw-Hill, 1992.

F.P. Beer, E. Russell Johnston Jr., J.T. DeWolf. MECCANICA DEI SOLIDI: Elementi di Scienza delle Costruzioni. McGraw-Hill, 2002.

Testing and exams

The examination mode include two alternative types of assessment:
- No.2 written "ongoing-tests" + oral exam reserved to the sufficient-results in the tests.
- Written test + oral exam in the same day (for those not included in the previous case)