15211 - MECHANICS OF MATERIALS AND STRUCTURES

Learning outcomes

The course aims at instructing about basics of mechanics of materials and structures.  At the end of the course the student is expected to be able to:
- Solve mechanical problems (statics)
- Compute the state of stress and strain in loaded structures
- Design and verify mechanical structures
- Understand failure modes

Course contents

Summary of main mechanical concepts:
  - Forces, moments;
  - Constraints, degrees of freedom;
  - Equilibrium equations.
 
Mechanics of solids:
  - Internal forces;
  - Concepts of stress (normal and shear);
  - Uniaxial state of stress; triaxial state of stress; stress tensor;
  - Equilibrium equations;
  - Displacement and strain; Small and large strain; Strain tensor;
  - Stress-strain relation for linear elastic materials;
  - Strain energy (uniaxial and multiaxial)  

Fundamentals of mechanics of structures:
  - Saint-Venant beam: stress and strain distribution for axial load, shear load, torsion and bending;
  - Other structures with closed-form solution;
  - Stress concentrations;
  - Buckling.

Triaxial laods:
  - Mohr circle for stress;
  - Principal stress;
  - Mohr circle for strain;
  - Principal strain;
  - Equivalent stress; failure criteria for brittle and ductile materials.

Mechanical characteristics of materials:
  - Material testing; Stress-strain curves;
  - Constitutive equations;
  - Elasticity (Hooke's law, Poisson's coefficient);  
  - Plasticity;
  - Viscoelasticity (creep, relaxation, hysteresis: very briefly).

Failure criteria:
  - Instantaneous and delayed failure;
  - Failure (ductile and brittle; energy to failure);
  - Excessive deformation, Yielding;
  - Fatigue;
  - Wear;
  - Creep, relaxation.

Properties of materials:
  - Composition, micro- and macro-structure;
  - Classification and mechanical properties of materials: polymers, metals, ceramics, composites.


Laboratory activity:
The course includes theoretical and practical labs. This includes preparation of technical reports on the experiments carried out.

Readings/Bibliography

Official textbook:  
- Beer F.P., Johnston E.R., DeWolf J.T.. (2002): "Meccanica dei solidi: Elementi di scienza delle costruzioni" McGraw-Hill Publ. (edizione italiana, con sito web dedicato) 
- Or the equivalent original (in English): Beer F.P., Johnston E.R., DeWolf J.T.. (2002): "Mechanics of Materials" McGraw-Hill Publ. (English Edition, with dedicated website)  
- Additional slides made available by the lecturer.

Additional examples and exercises can be downloaded from the Publisher's website:   http://www.ateneonline.it/beer/areastudenti.asp  


Further (optional) readings: 
- Wulff J. "Struttura e proprietà dei materiali",  vol. 1, 2, 3 Ed. Ambrosiana,  Milano (scienza dei materiali) - Pietrabissa R. "Biomateriali per protesi e organi artificiali" Patron ed. (biomaterials) 
- Nordin M., Frankel V.H. "Basic biomechanics of the musculoskeletal system" Lea & Febiger Publ.(exercises and examples in biomechanics) 
- Bronzino J.D. "The Biomedical engineering handbook" CRC Press - IEEE Press (general handbook) 
- Palastanga et al. "Anatomy and human movement" Butterworth-Heinemann Publ. (functional anatomy)

Teaching methods

Theoretical lectures are supported, in parallel, by a series of numerical examples, practical demonstrations and experiments in the lab, and a visit to a lab specialized in material testing.

Assessment methods

To be agreed with the lecturer.

Teaching tools

Projector, blackboard, practical testing in the lab.

Office hours

See the website of Luca Cristofolini