# Università degli Studi di Napoli "Parthenope"

## Teaching schedule

2020/2021
Belonging course:
Course of Bachelor's Degree Programme on CIVIL AND ENVIRONMENTAL ENGINEERING FOR THE MITIGATION OF RISKS
Location:
Napoli
Disciplinary sector:
MATHEMATICAL PHYSICS (MAT/07)
Language:
Italian
Credits:
9
Year of study:
2
Teachers:
Cycle:
First Semester
Hours of front activity:
72

Italian

### Course description

Knowledge and understanding
The Course aims to provide some fundamental concepts of the statics of structures, with particular reference to the calculation methodologies for simple structures, consisting of one-dimensional elements (beams) with linear elastic behaviour.
Applying knowledge and understanding
At the end of the Course, each student should be able to determine the safety level of the above structures.
Communication skills
At the end of the Course, each student should know all the technical words related to the topics treated.

Matematica I

### Syllabus

The extended program of the Course is as follows:
(1) Geometry of areas. Introduction. Static moment and centroid. Moments of inertia. Laws of transformation. Principal axes and moments of inertia. Mohr’s circle.
Exercises
(2) Simple (beams) and complex (frames) structural systems. Plane beams and frames. Problem of structural system equilibrium: kinematic definition of plane constraints; static definition of plane constraints (constraint reactions) and cardinal equations of statics. Framed structures: statically determinate (or isostatic); hypostatic; statically indeterminate (or hyperstatic). Principle of superposition.
Exercises
(3) Statically determinate framed structures. Three methods: cardinal equations of statics; auxiliary equations; the principle of virtual work.
Exercises
(4) Internal beam reactions. Three methods: direct method; differential method (indefinite equations of equilibrium for plane beams); the principle of virtual work. Diagrams of characteristics of internal beam reactions.
Exercises
(5) Analysis of stresses (for three-dimensional solids). Stress tensor, equations of Cauchy, law of reciprocity. Principal stress directions, Mohr’s circles. Plane stress condition and Mohr’s circle. Boundary conditions of equivalence and indefinite equations of equilibrium.
Exercises
(6) Analysis of strains (for three-dimensional solids). Rigid displacements, strain tensor. Strain components: dilatations and shearing strains. Principal strain directions. Equations of compatibility.
Exercises
(7) The theorem of virtual work (for three-dimensional solids).
Exercises
(8) Theory of elasticity (for deformable three-dimensional solids). Real work of deformation, elastic material, linear elasticity, homogeneity and isotropy, linear elastic constitutive equations.
Exercises
(9) Strength criteria. Criteria by Rankine, Grashof, Tresca, von Mises.
Exercises

The topics treated in the Course are the following ones:
(1) Geometry of areas
(2) Simple (beams) and complex (frames) structural systems
(3) Statically determinate framed structures
(4) Internal beam reactions
(5) Analysis of stresses
(6) Analysis of strains
(7) The theorem of virtual work
(8) Theory of elasticity
(9) Strength criteria

### Teaching Methods

The Course consists of theoretical lectures and practical tutorials. For each topic treated in the Course, exercises are planned so that each student can determine the solutions of the theoretical problems explained just before such practical tutorials.

### Textbooks

Recommended books:
- E. VIOLA: "Esercitazioni di Scienza delle Costruzioni", Ed. Pitagora, Bologna.
- M. CAPURSO: "Lezioni di Scienza delle Costruzioni", Ed. Pitagora, Bologna.
- V. FRANCIOSI: "Fondamenti di Scienza delle Costruzioni ", Ed. Liguori, Napoli.

### Learning assessment

The final test consists of a written test and an oral test.
Such a final test is weighted as follows:
- written test: 50% application of theoretical concepts to practical cases, i.e. exercises (practical skill);
- oral test: 40% questions on theoretical concepts (theoretical skill); 10% ability to present scientific topics (communication skill).