|Politecnico di Torino|
|Anno Accademico 2010/11|
Mechanics of materials
Corso di Laurea in Ingegneria Dell'Autoveicolo (Automotive Engineering) - Torino
To develop an understanding of the processes underlying yield and fracture of materials under constant and repeated loading and to familiarise students with the basis for describing mechanical properties of engineering materials. To provide the student, in a simple form, the essential fundamental knowledge of the theory of linear elasticity as the basis for stress analysis and for the design and safe use of engineering structures. To develop the load-stress relationship for beams and shafts. To introduce the students to the equation of virtual work and to the energy methods to solve statically indeterminate structures under load. The overall aim is to provide students with the ability to solve problems related to mechanical engineering.
On successfully completing this course unit, students will be able to:
- derive the rules for static determinacy of frames and to apply equilibrium conditions to analyse structures under load;
- determine stress, strains and displacements in loaded beams within frameworks;
- recall the principal analytical and graphical methods used to analyse stress and strain;
- solve simple problems involving the prediction of static and fatigue failure of engineering materials and structures under multiaxial stress and strain.
Euclidean geometry; matrix algebra; eigenvalue problems; differential and integral calculus; basic kinematics; basic mechanics including forces and moments equilibrium and equivalence, moment reduction.
- Equilibrium conditions in frames;
- Loads and constraints;
- Rules for static determinacy of frames.
- Tension test: basic definitions of stresses and strains
- Yielding: deformation under uniaxial loading, elastic and plastic deformation;
- Ductile and brittle materials;
- Tresca and von Mises criteria; maximum stress criteria;
- Safety coefficients.
Stress ans strain analysis
- Stress and strain analysis in three dimensions, principal values, maximum shear stresses;
- Mohr's circle for stress and strain;
- Yield criteria and the concept of equivalent uniaxial stress;
- Equilibrium, compatibility and constitutive equations;
- Hooke's law for three dimensions and the elastic constants.
Applications in elasticity
- Normal and bending stresses in beams: moment, stress, curvature relationship, deflections;
- Shear stresses in beams, centre of shear;
- Torsion in beams with circular and non circular sections;
- Buckling of struts and instability.
- Strain energy, equation of virtual work;
- Betti's theorem;
- Clapeyron 's theorem;
- Castigliano's theorem;
- Applications to statically indeterminate frames and deflections of beams.
- High cycle fatigue phenomenology: crack initiation and propagation;
- Fatigue strength (S-N approach)
- Effect of means stresses; multi-axial stresses;
- Fatigue limit and life; Miner's rule;
- Safety coefficient and fatigue design philosophies.
Laboratori e/o esercitazioni
During the practical exercises, which represent a fundamental component of the learning process, students will carry out exercises in the classroom on the topics dealt with during the lessons, especially regarding the verification of mechanical components. It is essential, in order to draw maximum advantage from such exercises, that the students apply the concepts and notions learned during the lessons autonomously.
Lecture notes will be made available to the students. Reference texts:
F.P. Beer, E. R. Johnston, J. T. DeWolf 'Meccanica dei solidi', McGraw-Hill
M. Rossetto 'Introduzione alla fatica dei materiali e dei componenti' Levrotto & Bella
Nash 'Resistenza dei materiali' Collana Schaum, n° 28 (exercises done)
Controlli dell'apprendimento / Modalità d'esame
The exam consists of a written paper which includes both theory and exercises. The oral test is optional.
|Orario delle lezioni|
|Statistiche superamento esami|
Programma definitivo per l'A.A.2009/10