B1975 - FONDAMENTI DI COSTRUZIONE DI MACCHINE P

Learning outcomes

At the end of the course, the student knows the fundamentals of machine construction, including the concepts of tension and deformation. Furthermore, he/she has knowledge of the mechanical behaviour of materials and the main strength criteria. The student can dimension and verify simple mechanical structures such as beams, plates and shells of small thickness.

Course contents

The course provides the methodologies and tools to study the basic elements to which many of the mechanical elements of machines can be traced: beams, plates and shells. The methods and calculation tools provided are appropriately framed within the perspective of designing and constructing machine elements using composite materials. In this respect, emphasis is placed on beams and plates with both simple and composite structures. In addition, many case studies are introduced in which problems with thermal loads and the combination of these with mechanical loads are addressed. The problems of internal deformations and residual stresses arising in beams and plates with composite sections as a result of the application of both uniform and thickness-varying thermal loads are also addressed. The structure of the topics to be covered in the lecture is given below. The topics are structured in sections, and each section will be developed in approximately one week of classes. The lessons about each section will be accompanied by an adequate number of in-class examples, and students will be given an appropriate number of exercises to do at home.

1. Introduction to rigid and elastic bodies and the main geometries
   • Definition of rigid and elastic bodies
   • Simple and composite solid bodies
   • Definition of beam
   • Definition of shell
   • Definition of plate
2. Classification of forces on bodies:
   • Forces applied at a point
   • Forces acting on lines
   • Forces acting on areas
   • Volume forces
3. The Geometry of Masses and Areas
   • Barycentre
   • Moments of inertia
   • Matrix of moments of inertia and principal axes of inertia
4. Statics of Rigid Bodies
   • Free body diagram
   • Constraint conditions and the calculation of constraint reactions
   • Equilibrium of beams in the plane
   • Equilibrium of beams in space
5. Internal actions in beams and stress diagrams
   • Normal stress
   • Shear
   • Bending moment
   • Torsion
6. Springs and elements of matrix calculation
   • The link between cause and effect
   • Imposed force problems
   • Imposed displacement problems
   • Mixed condition problems
7. Tension and deformation
   • Tension and deformation
   • Analysis of the state of tension
   • Deformation state analysis
   • Constitutive equation: Hooke's law
   • Triaxial stress state
   • Triaxial state of deformation
   • Generalised Hooke's law
   • Plane states of tension and deformation
8. Tension and deformation in beams
   • Normal stress
   • Pure bending moment
   • Torsion
   • Shear
9. Compound stresses in beams
   • Normal force and bending
   • Shear and torsion
   • Bending and shear
   • Flexion and torsion
   • Thermal and mechanical loads
10. The main components
    • Main stresses
    • Principal deformations
11. Strength criteria
    • Von Mises (maximum deviatoric tension)
    • Tresca criterion (maximum tangential tension)
    • Rankine tension (maximum principal tension)
12. Small thickness vessels subject to internal pressure
    • Membrane theory
    • Flexural theory
13. Study of the mechanical behaviour of flat plates
14. Elastic instability of beams

• The problem of beam instability
• The Euler critical load
• The effect of constraint conditions on beam buckling

Readings/Bibliography

1. Notes of the teacher

2. James M. Gere, Barry J. Goodno, Mechanics of Materials, Cengage Learning, 2012

3. Sanjay Govindjee, Engineering Mechanics of Deformable Solids, Oxford University Press, 2013

4. R. C. Hibbeler, Statics, Pearson Prentice Hall, 2016

5. R. C. Hibbeler, Mechanics of Materials, Pearson Prentice Hall, 2016

6. R. C. Hibbeler, Dynamics, Pearson Prentice Hall, 2016

7. Robert C. Juvinall, Kurt M. Marshek, Fundamentals of Machine Component Design, John Wiley & Sons, 2012

Teaching methods

Frontal teaching in the classroom with use of slides and videos.

The course is developed both providing theoretical concepts and carrying out and assigning theoretical exercises and applications related to construction aspects of Automatic Machines.

To students are assigned exercises to be carried out autonomously and individually (only if specified by the teacher some exercises may be carried out in groups and, in this case, the names and surnames of the students who participated in the group must be specified in the homework book). These exercises must be collected, in an orderly manner, in a homework book that the students must bring to the exam for oral discussion.

Assessment methods

The examination will take place through an oral interview with the teacher. During the oral exams the student will have to demonstrate the knowledge of the concepts exposed during the course and will have to discuss the exercises of the exercise book. In addition, the teacher will ask the student transversal and reasoning questions related to the topics and exercises covered in class. Typically, 4 questions will be asked during the oral examination. In order to pass the exam, the student must answer at least 3 of the 4 questions correctly and thoroughly.

Teaching tools

PowerPoint presentations and audiovisual.

Office hours

See the website of Andrea Zucchelli