73470 - Shape Optimization Methods T

Course Unit Page


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

Zero hunger Quality education Gender equality

Academic Year 2021/2022

Learning outcomes

At the end of the course the student possesses the basic elements for evaluating the shape of an object for the purpose of its ability to withstand the mechanical stresses to which it is subjected. In particular he knows: the mechanics of shells; the geometry of masses; the relationship between material and resistance to stress.

Course contents

Review of vectors: theory of vectors (forces): sum of vectors; scalar product; Vectorial Product; mixed product; versors; projection of a vector in one direction; Cartesian representation of vectors; components of a vector; moment of a vector with respect to a pole; resultant moment of a vector system; Varignon's theorem; resultant of a vector system; equivalent systems of vectors; definition of couple; plane vector systems; polygon of subsequent resultants; plane systems of parallel vectors: graphic constructions. Introduction to the geometry of masses. Kinematics and statics of the rigid body: degrees of constraint and degrees of freedom of a material point and systems of material points; flat body: kinematic performance of flat constraints (roller, pendulum, hinge, double pendulum, fixed support); isostatic, hyperstatic and labile structures; cardinal equations of statics; flat body: static performance of flat constraints; the problem of the structural model and physical reality: definition of a structural scheme; external actions applied to bodies. Bodies subject to prevalent normal actions: the case of the constrained plane beam (curvilinear or straight axis); determination of the support reactions for a flat (restrained) beam by means of the cardinal equations of statics; stress characteristics for the flat beam; internal constraints in plane structures made up of systems of bodies; auxiliary equations for determining the constraint reactions in structures consisting of several rigid bodies constrained to each other; determination of the characteristics of the stress in flat isostatic structures formed by systems of beams; pressure curve; determination of the constraint reactions of a plane isostatic structure by means of graphical considerations. The elastic line, determination of sags and rotations in simple straight-axis beams, application to the solution of simple hyperstatic structures. Stress analysis: definition of normal tension; definition of admissible tension, resistance criterion for bodies subject to axial stress; the reticular structures; methods of resolving reticular structures; arched structures; the statics of the shells in the membrane regime; strength by shape. Bodies subject to prevalent bending actions: the cantilever beam; bending stresses; the curvature. Verification of the main sections of beams (rectangular, T and double T, C and L) subject to normal stress (centered and not), shear (determination of the shear center) and bending and twisting moment, diagrams of relative stresses. Notes on the phenomenon of "fatigue". Notes on the "buckling".

The program is completed by some lessons / meetings on the following topics of the UN Sustainable Development Goals:

1) Zero Hunger | End hunger, achieve food security, improve nutrition and promote sustainable agriculture.

2) Quality education | Ensure quality, equitable and inclusive education, and lifelong learning opportunities for all.

3) Gender equality | Achieve gender equality and empower all women and girls.


Slides and lecture notes.

Guagenti E., Buccino F., Garavaglia E., Novati G., Statica – Fondamenti di meccanica strutturale, McGraw Hill

Comi C., Corradi Dell'Acqua L., Introduzione alla meccanica strutturale, McGraw Hill

Beer F. P., Russel Johnston Jr. E., DeWolf J.T., Meccanica dei solidi- Elementi di scienza delle costruzioni, McGraw Hill

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

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

Teaching methods

Lectures and exercises in the classroom and / or online.

Assessment methods

Intermediate tests and final oral exam.

Teaching tools

Slides of the course and exercises available on the platform https://virtuale.unibo.it (evolution of IOL - Online teaching).

Office hours

See the website of Alberto Custodi

See the website of Cristina Gentilini