# STATICS (036AR)

#### A.Y. 2019 / 2020

Professor
Period
Second semester
Credits
6
Duration/Length
48
Type of Learning Activity
Programme specific subjects
Study Path
[PDS0-2018 - Ord. 2018] common
Syllabus
Teaching language

Italian

Learning objectives

1. Knowledge and understanding: basic principles of construction science, fundamental theorems, recognition of the types of structures, constraints and static schemes.
2. Applying knowledge and understanding: search for the resultant of a system of forces, resolution of isostatic structures and reticular systems, calculation of sectional properties.
3. Making judgments: to recognize the correct mastery of an analytical procedure applied to the calculation of structures.
4. Communication skills: acquiring the specific lexicon of building science.
5. Learning skills: to measure one's own understanding of statics through guided exercises.

Prerequisites

Propaedeutic courses: Physics
Mathematics

Contents

1. Vectorial calculus for free and applied vectors
Definitions, vector components, Cartesian representation of vectors, operations on vectors in Cartesian components. Moment of an applied vector with respect to a pole. Resulting moment of a system of applied vectors: Varignon’s theorem. Exercises.

2. Kinematics of material point systems
Point systems and relative degrees of freedom. Constraints on point systems. Stiffness constraint between material points. The rigid body. Exercises.

3. Static analysis of the rigid constrained body and structures
Cardinal equations of statics. Definition of the constraints. Definition of external actions. Static analysis of beams and isostatic beam systems. Characteristics of internal forces. Diagrams of the characteristics of the internal forces. Examples and exercises. References to real structures.

4. Geometry of masses. Definitions. Center of gravity and static moments. Barycentric and main moments of inertia. References to real, simple and compound structural elements. Exercises.

5. Reticular structures: definitions. Resolution methods: node method, Ritter’s section method. Examples and exercises. References to real structures.

6. Introduction to computational mechanics: introduction to the finite element method. Practical overview.

Teaching format

Frontal lessons
Guided exercises
Didactic seminars

Extended Programme

1. Vectorial calculus for free and applied vectors
Definitions, vector components, Cartesian representation of vectors, operations on vectors in Cartesian components. Moment of an applied vector with respect to a pole. Resulting moment of a system of applied vectors: Varignon’s theorem. Exercises.
2. Kinematics of material point systems
Point systems and relative degrees of freedom. Constraints on point systems. Stiffness constraint between material points. The rigid body. Exercises.
3. Static analysis of the rigid constrained body and structures
Cardinal equations of statics. Definition of the constraints. Definition of external actions. Static analysis of beams and isostatic beam systems. Characteristics of internal forces. Diagrams of the characteristics of the internal forces. Examples and exercises. References to real structures.
4. Geometry of masses. Definitions. Center of gravity and static moments. Barycentric and main moments of inertia. References to real, simple and compound structural elements. Exercises.
5. Reticular structures: definitions. Resolution methods: node method, Ritter’s section method. Examples and exercises. References to real structures.
6. Introduction to computational mechanics: introduction to the finite element method. Practical overview.

End-of-course test

Intermediate tests
Final exam: written and oral
Attending the entire course is compulsory; the required frequency is 75% of the frontal lessons. Who does not reach this prerequisite will not be able to access the intermediate tests during the course, if they were carried out. Registration is required on the relevant Moodle2 page as a REQUIRED CONDITION to access the exam.
Students from past academic years must agree in advance with the teacher on the frequency requirements for access to the exam sessions.
The student is required to count his own frequency independently; the fulfillment of this requirement will not be communicated to the student neither during nor at the end of the course, but used only when correcting intermediate tests. The intermediate tests of those who do not have the frequency requirement will not be considered valid.
The procedures for passing the course include:
(1) passing the written test (50% weight), or in exam session or in partial tests during the course, and
(2) the next oral test (weight 50%).
If foreseen, access to partial tests (intermediate tests) during the course requires the acquisition of the frequency, calculated at 75% of the lessons carried out up to the date of the partial test. Partial tests of those who do not have the attendance requirement will not be considered valid. Sufficiency in both test tubes is a necessary condition for their equivalence with the passing of the written test. Overcoming the written test is a necessary condition for access to the oral exam.
In the absence of intermediate tests, or if at least 1 of the 2 provided is not sufficient, the student is required to completely redo the written test, except for any recovery decided by the teacher to be carried out by the first exam session after the end of the course.

Other information
Texts/Books

E. VIOLA, Esercitazioni di scienza delle costruzioni, Vol. 1, Pitagora Ed., Bologna.
L. BOSCOTRECASE, A. DI TOMMASO, Statica applicata alle costruzioni, Patron, Bologna.
C. COMI, L. CORRADI DALL’ACQUA, Introduzione alla meccanica strutturale, McGraw-Hill, Milan
P. RUGARLI, Calcolo strutturale con gli elementi finiti, EPC Libri, Roma

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