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FONDAMENTI DI MECCANICA E STATICA
Academic Year 2026/2027 - 2° Year
Teaching Staff
Taught classes: 70 hours
Exercise: 26 hours
Semester: 1°
- STATICA: Francesco CANNIZZARO
- FISICA: Giovanna FERRARA
Taught classes: 70 hours
Exercise: 26 hours
Semester: 1°
STATICA
Expected Learning Outcomes
The Statics module aims to provide Architecture students with the fundamental principles of structural mechanics required for subsequent courses in Structural Analysis and Structural Design.
The course introduces the tools required for the modelling and analysis of plane structural systems and progressively develops the competencies needed to understand the static and kinematic phenomena governing the behaviour of structures.
Knowledge and understanding
At the end of the course, students will demonstrate:
- understanding of the fundamental principles governing the equilibrium of rigid bodies;
- understanding of the physical and geometrical meaning of loads and support reactions;
- understanding of the criteria used to classify structures according to their static and kinematic behaviour;
- understanding of internal actions and their graphical representations;
- understanding of the principles underlying the method of virtual work;
- knowledge of the main types of statically determinate structures;
- knowledge of the geometric properties of plane figures and their role in structural analysis;
- command of the technical terminology used in Statics.
At the end of the course, students will be able to:
- interpret real structures through appropriate simplified mechanical models;
- perform the kinematic analysis of plane structures composed of interconnected rigid bodies;
- classify structures according to their static and kinematic behaviour;
- identify and characterize external and internal constraints;
- determine support reactions using analytical methods, graphical methods and the principle of virtual work;
- determine and interpret the internal actions in statically determinate structures;
- analyse simple truss structures and identify members subjected to tension or compression;
- determine the main geometric properties of plane figures and apply the related calculation procedures;
- use simplified structural models to interpret the static behaviour of buildings and structural systems.
At the end of the course, students will be able to:
- critically evaluate the correctness of simplified structural models;
- assess the physical plausibility of obtained results;
- compare different solution strategies for static problems;
- identify conceptual and procedural errors in the analysis of statically determinate structures.
At the end of the course, students will be able to:
- use the technical language of Statics appropriately;
- describe and discuss kinematic and static analysis procedures;
- graphically represent forces, constraints and internal actions;
- clearly present and justify the solution of structural problems.
At the end of the course, students will be able to:
- independently consult textbooks and learning materials in Structural Analysis;
- further develop topics that are preparatory to subsequent structural courses;
- use learning resources and supporting tools to strengthen their competencies;
- continue the study of structural mechanics with an adequate degree of autonomy.
Course Structure
The course is organised into theoretical lectures and problem-solving sessions.
Theoretical lectures are devoted to the presentation and discussion of the fundamental concepts of Statics and make use of teaching materials prepared and made available by the lecturer.
Problem-solving sessions form an integral part of the course and are aimed at developing the practical skills required for the kinematic analysis of structures, the determination of support reactions, the evaluation of internal actions, the analysis of truss structures, and the calculation of the geometric properties of plane figures.
Throughout the semester, tutoring activities and formative assessment sessions are also provided in order to monitor students' progress and to encourage continuous learning.
Digital tools may also be employed to support teaching and learning activities.
If the course is delivered in blended or remote mode, appropriate adjustments may be made to the above, in order to ensure consistency with the syllabus.
Required Prerequisites
Students are expected to have acquired the fundamental knowledge of Calculus introduced during the first year of the degree programme, as well as the basic principles of Mechanics usually covered in introductory Physics courses.
In particular, students should be familiar with:
- basic algebraic operations and the solution of systems of equations;
- fundamental concepts of analytic geometry;
- elementary vector calculus;
- basic principles of particle mechanics and force systems.
Some topics previously introduced in the Mechanics module, such as vector operations and force representation, will be reviewed and further developed within the context of Structural Statics.
Successful completion of the prerequisite first-year courses specified in the degree programme is also strongly recommended.
Attendance of Lessons
Due to the practical nature of the topics covered and the significant amount of time devoted to problem-solving activities, regular participation in classes is considered particularly important.
Throughout the semester, formative assessment activities and tutoring sessions are also provided, allowing students to progressively monitor their level of preparation.
Attendance is not compulsory, but it is strongly recommended.
Attendance is monitored throughout the course.
Detailed Course Content
(Course material provided by the lecturer)
Review of vector algebra. Plane force systems. Force polygon. Resolution of a force along assigned directions. Moment of a force and force couples. Resultant and resultant moment of a force system. Transfer of a force couple. Elementary invariant operations. Equivalent force systems. Central axis. Funicular polygon and applications of graphical statics.
2. Kinematics of Constrained Rigid Bodies
(A. Greco, Structural Analysis, Aracne Editrice, 2012)
Particle kinematics. Definition of constraints. Kinematic characterization of external and internal constraints. Definition of rigid body. Kinematics of free and constrained rigid bodies. Mozzi’s theorem. Absolute and relative centres of rotation. Kinematic analysis of plane structures. Statically determinate, statically indeterminate and unstable systems. Articulated systems. Fundamental equation of structural kinematics. Kinematic chains. Chasles’ and Kennedy’s theorems. Compatibility conditions. Virtual displacements. Static-kinematic duality.
3. Static Analysis of Statically Determinate Structures
(A. Greco, Structural Analysis, Aracne Editrice, 2012)
Principles of dynamics. Fundamental equations of statics. Equilibrium conditions for translation and rotation. Graphical and analytical formulations of equilibrium.
Graphical and analytical determination of support reactions. Static characterization of external and internal constraints. Internal support reactions. Graphical method. Symmetric and antisymmetric systems.
Internal actions in structures. Differential equilibrium equations of plane beams. Internal force diagrams and analytical expressions.
Principle of virtual work for rigid bodies. Determination of support reactions through the principle of virtual work.
Plane trusses. Method of joints. Ritter’s method of sections. Roof trusses. Gerber beams. Arches and their static behaviour. Relationship between real structures and structural models.
4. Area Geometry
(Course material provided by the lecturer)
Centroids of discrete and continuous systems. Graphical and analytical determination of centroids. First moments of area. Moments of inertia. Huygens-Steiner theorem. Principal axes and principal moments of inertia. Central ellipse of inertia. Polarity and antipolarity with respect to the central ellipse of inertia. Kern of a section. Applications to the principal structural cross-sections.
Textbook Information
Main reference textbook
- J.L. Meriam, L.G. Kraige Statics (7th edition), Wiley
- A. Greco, Scienza delle Costruzioni, Edizioni Culc Catania, 2019.
Supplementary textbook for exercises and problem solving
- E. Viola, Esercitazioni di Scienza delle Costruzioni. Vol. 1: Strutture isostatiche e geometria delle masse, Pitagora Editrice, 1977.
Additional teaching material
- Lecture notes, solved exercises, collections of past assignments and additional teaching materials made available by the lecturer during the course.
| Author | Title | Publisher | Year | ISBN |
|---|---|---|---|---|
| Greco A. | Scienza delle Costruzioni | Edizioni Culc Catania | 2019 |
Course Planning
| Subjects | Text References | |
|---|---|---|
| 1 | Vector Theory and Graphical Statics | Provided notes |
| 2 | Kinematics of restrained rigid bodies | Provided notes |
| 3 | Static Analysis of Statically Determinate Structures | Provided notes |
| 4 | Area Geometry | Provided notes |
Learning Assessment
Learning Assessment Procedures
The assessment of the Statics module is carried out together with the assessment of the Physics module within the integrated course.
In order to pass the integrated course, students must achieve a passing grade in both modules. The final grade is determined by a weighted average of the results obtained in the two modules, with a weight of two thirds assigned to Statics and one third assigned to Physics.
The assessment of the Statics module includes the solution of practical structural problems and may include questions aimed at evaluating the understanding of the theoretical foundations of the subject.
The assessment is intended to verify the student's ability to:
- correctly model plane structural problems;
- perform the kinematic analysis of a structure;
- determine support reactions;
- determine and interpret internal actions in structures;
- analyse simple truss structures;
- determine the main geometric properties of plane figures;
- critically discuss the obtained results.
The final assessment will take into account:
- correctness in problem formulation;
- ability to construct appropriate structural models;
- correctness of calculation procedures;
- ability to critically interpret the obtained results;
- appropriate use of technical terminology.
Throughout the semester, formative assessment activities are also carried out in order to monitor the progressive acquisition of competencies and to identify possible learning difficulties.
The outcomes of these activities may be taken into account in defining the subsequent discussion related to the Statics module within the final examination of the integrated course.
To ensure equal opportunities and in compliance with current laws, interested students may request a personal interview in order to plan any compensatory and/or dispensatory measures based on educational objectives and specific needs.
Students can also contact the CInAP (Centro per l’Integrazione Attiva e Partecipata – Services for Disabilities and/or Specific Learning Disorders) referring teacher within their Department (https://www.cinap.unict.it/content/referenti).
Examples of frequently asked questions and / or exercises
- Kinematic analysis of plane structures composed of constrained rigid bodies and classification of structures as statically determinate, statically indeterminate or unstable.
- Graphical and analytical determination of support reactions in statically determinate structures.
- Application of the fundamental equations of statics and the principle of virtual work to the calculation of support reactions.
- Determination of internal actions and construction of the corresponding internal force diagrams.
- Determination of the analytical expressions of internal force distributions in plane beams.
- Analysis of truss structures using the method of joints and Ritter's method of sections.
- Study of the static behaviour of simple statically determinate structural systems.
- Calculation of the geometric properties of plane figures (centroids, moments of inertia, principal axes of inertia, radii of gyration, central ellipse of inertia and kern of a section).
- Discussion of the theoretical concepts covered during the course and interpretation of the results obtained in practical applications.
FISICA
Expected Learning Outcomes
The course aims to provide students with the conceptual, methodological, and quantitative foundations of General Physics. The primary objective of the educational program is to guide students from the understanding of fundamental physical principles to their concrete application.
Upon completion of the course, students will achieve the following learning outcomes:
Knowledge and understanding
Understanding of: principles and laws of classical mechanics.
Mastery of: formal scientific language and International System (SI) units of measurement; methodology of dimensional analysis and order-of-magnitude estimation of physical phenomena.
Applying knowledge and understanding
Ability to: identify the physical forces and stresses acting on simple elements, determining their conditions of motion or rest.
Communication skills
Ability to: communicate physical concepts and results in a clear, rigorous, and unambiguous manner.
Learning skills
Ability to: independently acquire new scientific and technological knowledge in the field of physics applied to architecture; consult and interpret scientific texts; develop the necessary skills to approach subsequent courses in the curriculum with adequate scientific preparation.
Course Structure
The teaching activity consists of lectures.
Required Prerequisites
The prerequisites required to students are the basic notions of mathematical analysis, already acquired during the first year of studies.
Attendance of Lessons
Attendance is strongly recommended.
Textbook Information
Any university-level physics text.
The teacher will provide students with copies of their notes dictated during classes. The teacher will also provide notes with typical exercises which will also be presented in the classroom.
Course Planning
| Subjects | Text References | |
|---|---|---|
| 1 | Physical quantities, their measurement and related errors. | |
| 2 | Vector calculus. | |
| 3 | Kinematics of the mass point. | |
| 4 | Concept of momentum. | |
| 5 | The forces. | |
| 6 | Angular momentum. | |
| 7 | Conservation principles. | |
| 8 | Modeling (extremely simplified) of some physical phenomena of applicative interest. |
Learning Assessment
Learning Assessment Procedures
The exam consists of a written test and an oral interview.
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