Course Unit Page


This teaching activity contributes to the achievement of the Sustainable Development Goals of the UN 2030 Agenda.

Quality education Industry, innovation and infrastructure

Academic Year 2021/2022

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.


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

Teaching tools

Tablet, slide projector.

Office hours

See the website of Giorgio Olmi