15211 - MECHANICS OF MATERIALS AND STRUCTURES

Learning outcomes

The aim of this course is to introduce the methods for stress, strain and deflection calculation in elementary structures like straight beams, arches and axial-symmetrical shells, loaded in tension/compression, bending, torsion and shear. Many practical applications are presented and discussed.

Course contents

- Static of beams. Supported and fixed ends. Support reactions in straight beams and in circular arches.

- Tension, compression, shear, bending and torsion. Undefined equations of equilibrium. Shear and moment diagrams.

- Static moments. Determination of the barycenter location in a cross-section. Moments of inertia. Theorem of Huygens-Steiner. Polar moments of inertia. Practical applications: determination of the barycenter location and of moments of inertia (with respect to barycenter axis or to any other axis), considering the most widely used cross-sections in engineering applications.

- Stresses. Normal stresses and shear stresses. Normal strains and shear strains. Elastic behaviour of materials: the Hook's law. Mohr's circle. Principal stresses. Resistance criteria: Rankine, Grashof, Tresca and Von Mises.

- Tension and compression. Elongation of beams. Strain energy. Stress concentrations. Tension in two directions.

- Flexure of bars. Distribution of stress and strain. The neutral axis. The maximum fibre stress. Strain energy.  Convenient shapes of the cross-section. Stress concentrations. Beam not loaded in plane of symmetry.

- Torsion. Straight bar of uniform circular section under pure torsion. The angle of twist. Strain energy. Thin-walled sections. Principal stresses in pure torsion. Torsion in rectangular sections.

- Shear. Elementary theory of shear. Shear in rectangular sections. Shear in circular sections. Shear strain. Riveted structures.

- Combined loading. The principle of superposition. Examples. 

- Elastic stability of straight beams. The Eulero's and Johnson Criteria.

- The elastic curve. Differential equation of the elastic curve. The Mohr theorem. Composition of deflections.

- Statically indeterminate beams. The principal beam. Examples.

Readings/Bibliography

Handouts by the Professor.

D. Croccolo, M. De Agostinis, G. Olmi,  Esercizi di Comportamento Meccanico dei Materiali ed Elementi delle Macchine. Società Editrice Esculapio, Bologna, 2013. ISBN: 9788874886319.

D. Croccolo, N. Vincenzi, Lezioni di fondamenti e tecnica della progettazione meccanica. Società Editrice Esculapio, Bologna, 2013. ISBN: 9788874883080.

E. Viola, Esercitazioni di Scienza delle Costruzioni, Vol. 1, Pitagora Editrice Bologna, 1993.

E. Viola, Esercitazioni di Scienza delle Costruzioni, Vol. 2, Pitagora Editrice Bologna, 1993.

A. Somà, Fondamenti di meccanica strutturale, Editore Quine, Milano, 2019. ISBN: 8831284010.

Teaching methods

Explanations supported by Tablet. Numerical exercises.

Assessment methods

The final test is taken by the EOL (EsamiOnLine) dashboard, https://eol.unibo.it/

The student assessment is performed by a written test, consisting of three numerical exercises, dealing with the following issues (which are very common in the practice of a Mechanical or Aerospace Engineer):

• Solution of an isostatic structure, with required calculation of its safety coefficient.
• Determination of the centroid and of the moments of inertia of a structure cross-section. Computation of normal and shear stresses due to a bending moment and a shear force acting on the structure.
• Solution of a hyperstatic structure, with required calculation of its safety coefficient.

The overall duration of the written test is three hours and thirty minutes.

During the exam, students are permitted to use books, lecture notes downloaded from Virtuale, and formula sheets (subsets of the lecture notes). Additionally, Excel (installed on the PC used during the test) may be used to perform calculations. Conversely, internet browsing or network-connected resources are strictly prohibited.

In accordance with the University Code of Ethics, students are reminded to maintain the utmost integrity. Any activity aimed at improperly altering the exam results (e.g., copying, plagiarism, accessing online learning resources, using unauthorized AI tools) is forbidden. Please note, in particular, that the mere possession of unauthorized equipment or material during the exam will result in the immediate cancellation of the test and a report to the competent offices.
Conduct that violates this prohibition may lead to disciplinary proceedings or reports to the relevant authorities if criminally relevant; in the latter case, the students involved risk facing criminal prosecution.

Each exercise is assigned a maximum score of 10.5/30.

The exam is considered passed if both of the following conditions are simultaneously met:

• Achieving a score of at least 6 (six) points on the first exercise (Isostatic Structure). This exercise focuses on knowledge deemed necessary to reach the minimum learning objectives.
• Achieving a total score (the sum of the partial scores) of at least 18/30.

If the sum of the partial scores results in a grade strictly greater than 31, the exam outcome is "30 cum laude" (30 e lode). If the total score is between 30 and 31 (included), the final grade is 30.

In accordance with Art. 16, paragraph 5 of the Teaching Regulations, the grade obtained in the written exam can be rejected only once.

For students enrolled in the Integrated Course (C.I.) "Mechanics of Machines and Materials":

The final overall grade will be officially recorded once the exams for both this course and "Applied Mechanics to Machines" have been passed. The order in which the two exams are taken does not matter, and the assigned grades do not expire.

The overall grade to be recorded is calculated as follows:

• A grade of "30 cum laude" obtained in "Mechanical Behavior of Materials" and/or "Applied Mechanics to Machines" is assigned a score of 31.
• The average of the scores from the two exams is calculated.
• If this average is greater than or equal to 30, the overall grade is upgraded to "30 cum laude".

Teaching tools

Tablet, slide projector. At the end of each lecture, usually within 24 hours, the professor will make available to students (on virtuale.unibo.it) the slides annotated on the tablet during class (including any improvements and additions).

Office hours

See the website of Giorgio Olmi