34310 - Elements of Machines T

Learning outcomes

Students will learn elements of the theory of elasticity, basic concepts about the mechanical behavior of materials and of the theory of structures. These tools will enable students calculating the stresses in lumped parameters structural models (e.g. beams, trusses, frames). Students will also learn how to perform a static structural verification of a simple beam cross section.

Course contents

GRAPHIC STATICS: Operations on force vectors: sum of two or more forces. The funicular polygon. Composition of forces and moments.

STATICS OF BEAMS: Constraints. Examples of statically determinate, indeterminate and underconstrained structures. Calculation of the constraint reactions on statically determinate structures. Practical examples.

FORCE AND MOMENT DIAGRAMS: Tension, compression, shear, bending and torsion. Undefined equations of equilibrium. Shear and moment diagrams. The principle of superposition of effects.

CROSS SECTIONAL AND MASS PROPERTIES: Determination of the CG location in a cross-section. Moments of inertia. Theorem of Huygens-Steiner. Polar moments of inertia. Practical applications: determination of the CG location and of the moments of inertia, considering the most widely used cross-sections in engineering applications.

STRESS AND STRAIN: Normal stresses and shear stresses. The Saint Venant’s principle. Strain and angular distorsion. The elastic behaviour of materials: the Hooke's law. Mohr's circle. Principal stresses. Failure criteria: Rankine, Grashof, Tresca and von Mises.

THE FOUR LOAD CASES FOR BEAMS: Axial loading. Pure bending. Torsion. Shear.

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

Bending of bars. Distribution of stress and strain. The neutral axis. 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. Twisting angle. 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. The relationship between the Young’s modulus and the shear modulus. Jourawsky’s formula.

THE DIFFERENTIAL EQUATION OF THE ELASTIC CURVE: Integration of the differential equation of the elastic curve. The Mohr’s theorem. Composition of deflections. Examples.

STATICALLY INDETERMINATE STRUCTURES: Force method and Displacement method. Examples.

Readings/Bibliography

O. Belluzzi. Scienza delle Costruzioni. Volume Primo. Zanichelli Editore, Bologna.

E. Viola, Lezioni di Scienza delle Costruzioni, Pitagora Editrice Bologna, 2003.

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.

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

Teaching methods

The course content will be entirely covered by the lectures. Lectures are supported by many practical exercises, aimed at guiding the students towards the solution of practical problems, based on the tools acquired during the theoretical lectures.

Assessment methods

The examination consists of a written test (mandatory), and an oral test (discretionary).

Teaching tools

Lecture slides, video-projector, tablet with hand writing function.

Office hours

See the website of Massimiliano De Agostinis