The course aims to provide the fundamental basis to perform the design and verification of structural components and mechanical systems subject to static and fatigue loads.
Topics covered, after a resume of static equilibrium concepts, are:
- evaluation of the elastic properties and the static strength of materials by tensile test and some notes on creep;
- state of stress and state of strain in mechanical elements in linear elastic conditions; combined stress failure theories; static safety factors;
- calculation of stresses in one-dimensional structural elements subjected to loads in plane and space: geometric properties of areas, de St Venant solid, equilibrium and internal forces diagrams in statically determinate systems; extensional, flexural, torsional and shear behaviour; equation of the elastic curve; elastic instability;
- definition and effect of notches: the stress concentration factor; static component verification;
- high cycle fatigue strength in terms of uniaxial stress: cyclic stress, nucleation and propagation of cracks, diagrams for the presentation of fatigue tests results; application to the verification of mechanical components, the main factors reducing the fatigue strength.

Knowledge and understanding of the mechanical properties and strength of materials
Knowledge of methods for describing the state of stress and the state of strain in linear elastic conditions
Knowledge of static failure criteria and the concept of safety factor
Knowledge of methods for assessing the state of strain, stress and displacements in one-dimensional structural elements
Understanding the phenomenon of fatigue; knowledge of diagrams that describe the high cycle fatigue behaviour of materials.
Knowledge of methods of verification of components subject to constant amplitude cycling stresses.
Ability to verify elements subject to known static stress.
Ability to calculate reaction forces of statically determinate structures.
Ability to calculate the internal forces diagrams in statically determinate elements subject to known applied loads.
Ability to assess the stresses and strain in sections of one-dimensional elements with and without notches , known the internal forces applied to the section.
Ability to perform fatigue assessment of components subject to constant amplitude cycling stresses.

Concepts of mathematics (study of functions and computation of derivatives and integrals, matrix algebra, eigenvalue / eigenvectors problems) and physics (basic concepts of kinematics and statics).

This course is organized in two parts. Lectures will give a straight presentation of relevant topics to be studied to perform a complete structural analysis of both static and fatigue behaviours of mechanical structures. Practice hours will be offered to solve examples, numerical exercises and practical cases.
Topics dealt with in this course are herein listed.

1. Statics
Basic concepts of static behaviour of structures (force, moment, rigid and deformable bodies), loading conditions, constraints, static and kinematic determinacy, equilibrium conditions and equations. Computations of reactions, internal forces, diagrams. Beams, bars, trusses. Outlines of Virtual Work Principle and application to undetermined structures.

2. Stress
Stress vector, tensor, components. Principal stress and direction, related computation. Mohr circles. Equivalent stress definition and computation.

3. Strain
Rigid body motion and strain definition in elastic body. Strain components, principal strain and direction. Stress-strain relations, Hooke’s law. Elastic properties of materials. Elastic energy storage.

4. Strength of materials
Tensile test, material behaviour and properties. Elastic coefficients. Yielding phenomeon, brittle and ductile materials. Safety factors in statics.

5. Beam theory
De Saint Venant principle, beam definition, loading conditions, axial, flexural, shear, torsional behaviours. Approximated solutions for torsion of rectangular cross section, computation of stresses, strains, displacements and rotations. Shear centre. Coupled behaviour. Buckling and elastic instability.

6. Fatigue
Definition, cycles, damage origin, propagation and rupture. Wohler, Haigh, Smith and Goodman curves. Technological and other effects affecting fatigue life. Case of variable amplitude cycles and Miner theory. Multi-axial fatigue.

Theoretical aspects presented during the lectures can be found on the following textbooks:
- D.Gross, W.Hauger, J.Schroder, W.A.Wall, N. Rajapakse - “Engineering Mechanics 1: Statics”, Springer.
- V. Da Silva - “Mechanics and strength of materials”, Springer.
- L. P. Pook - “Metal fatigue: what it is, why it matters”, Springer
- J. Beer, S.Johnston - "Solid mechanics", McGraw-Hill.

Exam consists of two parts: written test and oral exam. At the end of all the classes students will be required to attend a written test, based on three exercises to be solved. Score 18/30 will give the possibility to access to the oral examination. If the last will be evaluated sufficient, final marks will computed as an average value between the score of the written and oral exams respectively. Exam will be registered when student will show his/her notebook including all the solutions of the exercises proposed during the practice hours.