Complements of building science

Learning objectives

The main objective of the course is to provide the student with the theoretical foundations for the study of two-dimensional solids (plates and shells), developing the knowledge acquired during the course of Construction Science. Each structural model is analyzed with the aim of obtaining the indefinite congruence equations, the elastic bond equations and the indefinite equilibrium equations. Part of the course is also devoted to the study of the stability of the elastic equilibrium of discrete systems and continuous systems. Finally, the theory of plasticity is also covered.

Expected learning outcomes

At the end of the course, the student learns advanced tools of Structural Mechanics and extends the knowledge of Building Science for the treatment of structural problems relating to two-dimensional flat and curved solids.

Course content

1. Plane stress and strain problems (Recall of three-dimensional elasticity theory; Plane strain problem; Plane stress problem).

2. Rectangular plate (Reissner-Mindlin kinematic hypothesis; Kirchhoff-Love kinematic hypothesis).

3. Circular plate (Membrane regime and flexural regime; Reissner-Mindlin kinematic hypothesis; Kirchhoff-Love kinematic hypothesis; Axi-symmetry hypothesis).

4. Cylindrical shells (Reissner-Mindlin kinematic hypothesis; Kirchhoff-Love kinematic hypothesis; Membrane behavior of cylindrical shells).

5. Shells of revolution (Flexural and membranous regime of shells of revolution).

6. Stability of elastic equilibrium (Fundamental definitions and stability criteria; Discrete and continuous systems).

7. Plasticity (Introduction to the theory of incremental elasto-plasticity; Limit analysis theorems; Plasticity of sections for ductile elements).

Prerequisites

There are no prerequisites or propaedeutics. However, students are advised to at least have previously attended the following courses: Mathematical Analysis, Geometry, Rational Mechanics and Construction Science.

Bibliography

Erasmo Viola, “Theory of structures. First volume. Stress states and plates”, Pitagora Editrice, Bologna, 2010.
Erasmo Viola, “Theory of structures. Second volume. Shells of revolution”, Pitagora Editrice, Bologna, 2010.
Leone Corradi Dell'Acqua, "Mechanics of structures", vol. 3, McGraw-Hill, Milan, 1994.
Alberto Carpinteri, "Construction science 2", Pitagora Publishing, Bologna, 1992

Teaching methods and tools

The course program will be entirely covered during class hours.

Assessment methods and criteria

The learning assessment is done through an oral exam, aimed at ascertaining the acquisition of the expected knowledge and skills. The oral exam is based on three questions to be answered in written form without the help of notes or books, and their discussion.