Structural theory  A (students A-L) 

annual course


Prof. Giulio Zuccaro






The course aims to provide the basic elements of Mechanics of materials and structures and develop the critical sense of structural modeling, through the resolution of equilibrium problems of solids and rigid and elastic structural systems, with particular reference to beams systems and 2D problems in linear elasticity.

Elements of the Vectors Theory
Generality. Scalar and vector products. Applied vectors. Elements of graphics.

Elements of kinematics of rigid bodies
Basic definitions. Rigid motions. Constraint devices. Distortions. Congruence conditions. Compatibility conditions. Flat motion for one-dimensional structures. Absolute and relative centers of rotation. Theorems of kinematics. Kinematic chains. Isostatic, lability and hyperstaticity conditions. Analytical detection. Synthetic recognition.

Elements of Geometry of areas
Moments of first and second order. Center of gravity definition. Directions and main moments of inertia. Applications to simple sections.

Elements of Statics of rigid systems
Basic definitions. Dynamics principles. Conditions of equilibrium of material points, rigid bodies and rigid bodies systems. Cardinal equations of statics. Cutting principle. Action-reaction principle. Constraints reactions. Internal forces. Mechanical stress. 2D systems of generalized forces. Lagrange principle. Research of constraints reaction through: Cardinals Equations of Statics, Graphical method and Lagrange principle. Funicular polygon and Culmann Theorem. Research on the characteristics of internal stress through the equilibrium conditions and Lagrange principle. Laws of variation and diagrams of the internal stress characteristics. Applications trusses and inflected structures.

Elements of the elastic solid mechanics
Fundamentals of analysis of stress and strain. Mechanical behavior of main materials of constructions.

Elements of Beam theory
Normal stress. Bending and shear. Study of the structural models. Linear structures: general principles. Principle of Virtual Work. The displacement method. The method of forces. stiffness and deformability matrices of structural elements. Assembly of matrices. Matrices of stiffness and deformability. Release conditions. Trusses. Framed structures.

Determination of displacements in isostatic beams through: equation of the elastic line; congruence equations; Mohr corollaries; principle of superposition of the effects; and method of the displacements composition.
Resolution of hyperstatic structures by: equation of the elastic line; and congruence equations.
Determination of displacements in hyperstatic beams through: the principle of virtual work and the construction of the stiffness matrices.

The activity of the mono-disciplinary course in Theory of Structures develops in two semesters.
The course consists of theoretical lessons, for about 30 hours per semester, and practical exercises, for about 10 hours per semester (characterized by classroom exercises concerning the topics of the course).
In the former semester, the topics of Theory of vectors and Kinematics and Statics of rigid systems. will be illustrated.
In the latter semester, the topics of Geometry of areas, Elastic solids Mechanics and Beam Theory will be analyzed.
The final examination will focus on the course contents.
The examination consists of one written test on resolution of structures and questions of theory. In the same day, the students will be examined through an oral test.
Exceptionally, in case of overcrowded sessions, the examination could take place according to a different modality, through a written and an oral test, at a distance of not more than seven days apart.
The registration to the written test will be made through the unina portal, following the link address.
The list of registration for the examination, indicating the classroom and time of the test, will be available on line at (prof. Giulio Zuccaro) .
Each student can participate to one test every two months.

V. Franciosi. Problemi di Scienza delle Costruzioni Vol. 1, Liguori editore, Napoli 1982.
E. Viola. Esercitazioni di scienza delle costruzioni Vol.1. Pitagora Editore, 1993.
E. Viola. Esercitazioni di scienza delle costruzioni Vol.2. Pitagora Editore, 1985.
C. Anselmi. Appunti di Teoria delle Strutture. Dispensa libera.