Learning objectives
Knowledge and understanding
The Course presents basic concepts related to equilibrium of forces and
to structural mechanics. Such concepts are needed to understand the
main aspects of the structural design and, after examining the
constitutive laws of the mechanical behaviour of materials, aims at
describing in depth the concepts of equilibrium and deformation for
elastic solids.
Applying knowledge and understanding
At the end of the Course, each student should be able to model simple
structural systems (elastic frames), to determine their equilibrium
conditions, to describe the mechanical behaviour of statically
determinate elastic frames and the mechanical behaviour of statically
indeterminate elastic frames, and to identify, to formulate and to solve
the structural problems of the architectural design.
Communication skills
At the end of the Course, each student should know all the technical
words related to the topics treated.
Prerequisites
To be able to successfully attend the course, the student has to acknowledge the contents
of the courses of Fondamenti di analisi matematica e geometria and Analisi di curve e superfici per l'architettura
Course unit content
The topics treated in the Course are the following ones:
(1) Systems of forces
(2) Geometry of areas
(3) Simple (beams) and complex (frames) structural systems
(4) Statically determinate framed structures
(5) Internal beam reactions
(6) Analysis of stresses (for three-dimensional solids)
(7) Analysis of strains (for three-dimensional solids)
4) Risoluzione dei sistemi isostatici di travi
- Equazioni cardinali della statica; equazioni ausiliarie
Esercizi
5) Azioni interne (o sforzi o caratteristiche della sollecitazione)
- Metodo diretto
- Convenzioni sui segni e sul tracciamento dei diagrammi
Esercizi
6) Analisi dello stato di tensione (per solidi tridimensionali)
- Definizione di tensione
- Tensore locale degli sforzi
- Equazioni di Cauchy
- Principio di reciprocità
- Direzioni principali di tensione
- Cerchi di Mohr
- Stato tensionale piano e cerchio di Mohr relativo
- Equazioni d'equilibrio al contorno ed equazioni indefinite di equilibrio
Esercizi
7) Analisi dello stato di deformazione (per solidi tridimensionali)
- Componenti di spostamento rigido
- Tensore locale di deformazione
- Componenti di deformazione: dilatazioni e scorrimenti
- Direzioni principali di deformazione e dilatazioni principali
Esercizi
8) Teorema dei lavori virtuali (per solidi tridimensionali deformabili)
Esercizi
9) Leggi dell'elasticità (per solidi tridimensionali deformabili)
- Equazioni costitutive o di elasticità
10) Criteri di resistenza
- Criterio di Rankine
- Criterio di Grashof
- Criterio di Tresca
- Criterio di von Mises
11) Il problema di De Saint-Venant
- Ipotesi fondamentali
- Casi trattati : sforzo normale centrato, flessione retta, flessione deviata,
sforzo normale eccentrico, torsione, flessione e taglio
Esercizi
12) Risoluzione di sistemi iperstatici semplici di travi
- Teorema dei lavori virtuali: strutture sottoposte a carichi (concentrati e
distribuiti) e coazioni (cedimenti vincolari e distorsioni termiche)
Esercizi
(8) The theorem of virtual work (for three-dimensional solids).
(9) Theory of elasticity (for deformable three-dimensional solids)
(10) Strength criteria. Criteria by Rankine, Grashof, Tresca, von Mises
(11) The problem of De Saint-Venant
(12) Statically indeterminate framed structures
Full programme
(1) Systems of forces
- Introduction
- Decomposition of forces
- Definition of forces and couples, both distribuited and concentrated
- Funicular curve
Exercises
(2) Geometry of areas
- Introduction
- Static moment and centroid
- Moments of inertia
- Laws of transformation
- Principal axes and moments of inertia
- Mohr’s circle
Exercises
(3) 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
(4) Statically determinate framed structures
Cardinal equations of statics; auxiliary equations
Exercises
(5) Internal beam reactions
- Direct method
- Diagrams of characteristics of internal beam reactions
Exercises
(6) 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
(7) Analysis of strains (for three-dimensional solids)
- Rigid displacements, strain tensor
- Strain components: dilatations and shearing strains
- Principal strain directions
Exercises
(8) The theorem of virtual work (for three-dimensional solids)
Exercises
(9) Theory of elasticity (for deformable three-dimensional solids)
- Linear elastic constitutive equations
Exercises
(10) Strength criteria
- Criteria by Rankine
- Criteria by Grashof
- Criteria by Tresca
- Criteria by von Mises
(11) The problem of De Saint-Venant
- Fundamental hypotheses
- Centred axial force, flexure (bending moment), biaxial flexure, eccentric
axial force, torsion, bending and shearing force
Exercises
(12) Statically indeterminate framed structures
- Theorem of virtual work: structures subjected to loads and constraints
(like thermal distortions and constraint settlements)
Exercises
Bibliography
Recommended books:
- A. Carpinteri, “Scienza delle Costruzioni” Vol.1, Pitagora Ed., Bologna
- A. Carpinteri, “Scienza delle Costruzioni” Vol.2, Pitagora Ed., Bologna
- M. Capurso, "Lezioni di Scienza delle Costruzioni", Ed. Pitagora, Bologna
- E. Viola, “Esercitazioni di Scienza delle Costruzioni – Vol.1: Strutture
isostatiche e geometria delle masse”, Pitagora Ed., Bologna
- E. Viola, “Esercitazioni di Scienza delle Costruzioni – Vol.2: Strutture
iperstatiche e verifiche di resistenza”
- L. Boscotrecase, A. Di Tommaso, “La statica applicata alle costruzioni”,
Patron, Bologna
All books are available by the library (Biblioteca Politecnica di Ingegneria
e Architettura).
Additional educational material:
- Documentation provided by the teacher (ELLY)
Teaching methods
The Course consists of theoretical lectures and practical tutorials. For
each topic treated in the Course, exercises are solved so that each
student can determine the solutions of the theoretical problems
explained just before such practical tutorials.
The theoretical lectures are delivered by employing transparencies,
which the students can get at the Documentation Office.
For each theoretical topic treated, practical tutorials are planned
according to two modes:
- at first, by employing transparencies (which the students can get at the
Documentation Office) to explain the solution methods;
- then, students solve some exercises in the lecture hall, and a common
discussion on the difficulties to solve them follows.
Assessment methods and criteria
The final test of the Course of Structural Mechanics consists of a written test which is weighted as follows:
- 20% definition of the solving method (knowledge)
- 70% application of theoretical concepts to practical cases, i.e. exercises
(applying knowledge and understanding)
- 10% ability to present scientific topics with the right technical words
(communication skill)
Other information
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