Portale di Ateneo - En.Unibs.it

Borrowed courses

SOLID AND STRUCTURAL MECHANICS

INGEGNERIA PER L'AMBIENTE E IL TERRITORIO

comune

Other Courses of the Study Programme

Course year: 1

ALGEBRA AND GEOMETRY - 9 credits - Basic
ARCHITECTURAL BASIC DRAWING - 9 credits - Characterising
ELEMENTS OF COMPUTING - 6 credits - Basic
EXPERIMENTAL PHYSICS 1 (MECH., TERM.) - 9 credits - Basic
GENERAL CHEMISTRY - 9 credits - Basic
HISTORY OF ANCIENT AND MODERN ARCHITECURE - 9 credits - Related/Supplementary
INTRODUCTION TO BASIC MATTERS - MATHEMATICS - Student's own choice
MATHEMATICAL ANALYSIS I - 9 credits - Basic
TEST OF ENGLISH - 3 credits
TEST OF FRENCH - 3 credits
TEST OF GERMAN - 3 credits
TEST OF SPANISH - 3 credits

Course year: 2

ARCHITECTURAL DRAFTING 2 - 6 credits - Student's own choice
ENGINEERING GEOLOGY - 9 credits - Characterising
ETHICS OF ENVIRONMENTAL SUSTAINABILITY - 3 credits - Student's own choice
EXPERIMENTAL PHYSICS II (ELECTROMAG., OPTICS, WAVES) - 9 credits - Basic
Investment valuation and project management - 6 credits - Characterising
LABORATORY OF SPECTROSCOPY - 3 credits - Student's own choice
MATHEMATICAL ANALYSIS II - 9 credits - Basic
RATIONAL MECHANICS - 9 credits - Basic
SURVEYING - 9 credits - Characterising
TECHNOLOGY OF MATERIALS - 9 credits - Student's own choice
URBAN AND REGIONAL SURVEYS - 9 credits - Student's own choice
WORKPLACE SAFETY - 3 credits - Student's own choice

Course year: 3

APPLIED MECHANICS - 9 credits - Student's own choice
BUILDING TECHNOLOGY - 9 credits - Characterising
ELECTRICAL ENGINEERING - 6 credits - Student's own choice
ETHICS OF ENVIRONMENTAL SUSTAINABILITY - 3 credits - Student's own choice
FINAL THESIS - 3 credits - Language/Final Examination
HYDRAULICS - 9 credits - Characterising
HYDROLOGY - 9 credits - Student's own choice
INTRODUCTION TO THERMODYNAMICS AND HEAT TRANSFER - 9 credits - Related/Supplementary
LABORATORY OF SPECTROSCOPY - 3 credits - Student's own choice
MAINTENANCE MANAGEMENT AND ENERGY - 6 credits - Student's own choice
SANITARY-ENVIRONMENTAL ENGINEERING - 9 credits - Characterising
SOLID AND STRUCTURAL MECHANICS - 9 credits - Characterising
TECHNOLOGY OF MATERIALS - 9 credits - Student's own choice
TRAINING ACTIVITY/INTERNSHIP 6 CREDITS - UNDERGRADUATE LEVEL - 6 credits - Student's own choice
TRAINING ACTIVITY/INTERNSHIP 9 CREDITS - UNDERGRADUATE LEVEL - 9 credits - Student's own choice
URBAN PLANNING - 9 credits - Characterising
WORKPLACE SAFETY - 3 credits - Student's own choice

SOLID AND STRUCTURAL MECHANICS

Single discipline educational activity

Course Sheet

Academic Year of enrolment:

2018/2019

Academic Year of provision:

2020/2021

Type of Course:

Characterising

Degree:

Bachelor's Degree Programme in CIVIL ENGINEERING

Disciplinary Sector:

Construction Science

Language:

Italian

Grouping type:

Credits:

Programme Year:

Professor and Collaborators:

PANTEGHINI Andrea Professor

FANTONI Francesca Collaborator

ALIPRANDI Claudio Collaborator

Cycle:

First semester

Hours of classroom activity:

108

Hours of individual study:

117

Analisi Matematica 2
Meccanica Razionale

Educational Goals

The student must master some basic concepts of structural engineering (stress, strain, elasticity); he or she must be able to obtain the diagrams of internal actions in planar beam systems; he or she must be able to determinate the stress in a beam section subjected to bending, torsion and/or shear; he or she must be able to determine the internal actions and displacements in statically indeterminate planar beam systems, also subjected to prescribed anelastic deformation fields or elasic constraints; he or she must master the basic concepts of strucural instability and of the classical strenght criteria.

Content

Solid and strucutral mechanics is an engineering field that studies the mechanical respose of loaded structures.
The course deals with 1) the determination of internal actions (axial force, shear, and bending moment) in statically determinate planar beam systems; 2) the general theory for isotropic linear elastic Cauchy solids; 3) the de Saint-Venant problem; 4) the determination of internal actions and displacements in statically indeterminate planar beam systems; 5) the strength criteria; 6) the determination of the buckling limit for Euler beams.

Extended Syllabus

Kinematic analysis of planar beam systems. Degrees of freedom and virtual displacements. The constraints.
Iperstatic, isostatic and ipostatic beam systems.
Determination of reaction forces and internal actions (axial force, shear, and bending moment) in statically determinate planar beam systems. Anomalous cases.
Planar system of trusses statically determined

THE CAUCHY'S CONTINUUM
Description of the problem.
The postulate of the additional constraints.

STRESS ANALYSIS
Cauchy's definition of tensions and stress
The Cauchy's theorem
Reference system rotation: rotation of a vector and of a tensor.
Stress components in different reference system.
Principal stresses, principal directions, and invariants
Decomposition of stresses in volumetric and deviatoric part
Plane stress. The Mohr's Circle for plane stress

STRAIN ANALYSIS
Small strain kinematics in a continuum medium: the displacement gradient tensor.
Rigid body motion and deformations.
The equations of external compatibility
Physical interpretation of the components of the tensor of small strains
Principal strains, principal strain directions and invariants of strain.
The equations of internal compatibility

PRINCIPLE OF VIRTUAL WORKS FOR CONTINUUM MEDIUMS

ELASTICITY
Uniaxial tensile test
Definition of Grenn's elasticity
The linear elastic homogeneous and isotropic material
The inverse relations
Physical meaning of the elastic constants: Young's modulus, Poisson's coefficient, shear modulus and bulk modulus. Thermodynamic limits of the elastic constants.

THE LINEAR ELASTIC PROBLEM
The principle of the effects superposition
Uniqueness and existence of the solution: the Kirchhoff Theorem.

THE SAINT VENANTS' PROBLEM
General formulation.
The Saint Venants' postulate

BENDING
The solution. Infinitesimal virtual work in bending
Tension and compression.
Structural constitutive relations for axial loads.
Neutral axis.
Right bending.
General bending
Bending and tension/compression. Structural constitutive relations for bending.
Bending and tension or compression.
The central intertia core for polygonal sections.

TORSION
Torsion in cylindrical circular beams
General solution.
Hydrodynamic analogy
Torsion in small thickness beams with closed hollow sections.
Torsion in beams with rectangular section.
Torsion in small thickness open beam

SHEAR
Approximate shear stress evaluation: computations of the average shear stress along a generic segment
Bending and shear symmetric in beams with shear parallel to the symmetry axis
Bending and shear symmetric in small thickness open beam.
The center of shear

The equation of the elastic line
Computation of displacements and hyperstatics in beams.
Non elastic effects
Elastic boundary conditions

Applications of the Principle of Virtual Works for planar beams
Computation of displacements
Computation of hyperstatics

Strength criteria
Von Mises and Tresca Criterion for ductile materials.
The Galileo criterion for brittle materials.

Instability
Computation of the Euler collapse load.

Recommended Bibliography

A. Panteghini. Lezioni di Scienza delle Costruzioni. Ed. Snoopy.
L. Bardella. Sistemi piani di trave staticamente determinati. Ed. Snoopy
E. Benvenuto. La scienza delle Costruzioni e il suo sviluppo Storico. Ed. Storia e Letteratura
M. Capurso. Lezioni di Scienza delle Costruzioni. Pitagora Editrice, 1998;8837100477

Methods of Provision

Conventional

Teaching Methods

Lessons and exercitations

Assessment Methods

The exam is aimed at verifying the knowledge of the topics listed in the official Program of the Course and the ability to apply the theory and its methods to the solution of exercises. For each student, the exam consists of a written part and a subsequent mandatory oral part. The evaluations of the writings are expressed by judgment (excellent, good, discrete, sufficient, insufficient). The oral part is evaulated in thirtieths. The final evaluation is determined taking into account both the written and oral tests.
WRITTEN: The written test concerns the analysis of statically determined structures. During the written test it is not possible to bring books or course notes. The use of a non-programmable calculator may be allowed.
The written exam is aimed at verifying the ability to analyze and resolve a statically determined 2D structure.
The written exercises will have a level of difficulty not higher than the level of the exercises carried out during the lessons and will be inspired by the
exercises and examples of the textbook used by the teacher. The books will be indicated by the teacher at the beginning of the course.
ORAL: to access the oral candidates must report in the written test a judgment equal to or better than "sufficient". The oral exam is considered sufficient with a score of at least 18/30. To pass the exam, the final grade, which takes into account the written and oral part, must be greater than or equal to 18/30. The oral will be mainly aimed at ascertaining an adequate knowledge of the program of the course, and will cover both aspects related to the theory and the exercises. The topics discussed during the course are reported in the Course Program.

Assessment:

Final Mark

Programme of Educational Activities

Start date of teaching period:

Monday, September 14, 2020

End date of teaching period:

Friday, December 18, 2020