MECHANICS OF SOLIDS AND STRUCTURES (Partizione B)
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- Versione italiana
- Academic year
- 2022/2023
- Teacher
- GIAMPAOLO GUERZONI
- Credits
- 9
- Didactic period
- Primo Semestre
- SSD
- ICAR/08
Training objectives
- The Course is the second of the sequence of structural teachings relating to the Structural Analysis and Design. The main objective is to stimulate the student to develop the architectural design, since the early stage of its conception, even in its structural components. The course also aims at providing the technical language and the contents the student can use in his relationships with all possible future co-workers in preparing the architectural design. The Course is still a basic Course as it completes the training on the General Principles and Methods of Structural Mechanics. At the same time it provides the necessary operational tools to easily tackle the structural design of simple architectures or to perform simple structural checks.
The student will acquire the basic knowledge of:
Deformability and stress state of a three-dimensional continuum
Equilibrium and congruence
The fundamentals of the Theory of Linear Elasticity referred to a homogeneous and isotropic continuum
The general principles of Mechanics and the fundamental theorems of Structural Mechanics
The elastic equilibrium of a one-dimensional, linear elastic, homogeneous and isotropic solid (beam)
The main building materials and their mechanical properties
The general methods to solve statically undetermined structures
Meaning and purpose of the strength criteria and their diversification according to the type of material
The main skills (i.e. the ability to apply the acquired knowledge), that the student must develop, concern study and control of the static behavior and deformation of beams and frames, with particular reference to those made with steel. In detail, the student will be able to :
Determine displacement and rotation functions in a linear beam under whatsoever applied loads and constraint conditions
Determine displacement parameters in any cross section of a statically determined structure
Solve statically undetermined structures
Check both strength and deformation in elementary structures
Check the resistance of structural elements made with no tension materials and subject to eccentric axial loads
check the possible instability of slender, axially loaded structural elements and their strength under the applied loads. Prerequisites
- The exam can be taken only by those who have passed the exam of Statics
The student is supposed to have already:
- The basics of Calculus, in particular of the matrix Algebra, differential and integral Calculus.
- The basic knowledge of Elementary Physics, in particular of Mechanics
- The main elements of Statics, in particular the methods and procedures to deal with statically determined structures (definition of constraint reactions and internal forces, checks on the structural strength in the presence of axial loads with or without eccentricity and bending moments)
- The fundamentals of Geometry of Areas and the Vector Analysis Course programme
- 1. Elements of Continuum Mechanics: stress analysis and some basic concepts of strain analysis, the undefined equilibrium equations and the Cauchy equilibrium equations on the boundary, Cauchy’s Theorem, principal stresses and principal stress directions, reciprocity Theorem for stress components, reciprocity of tangential stresses, fundamentals of Linear Elasticity with reference to homogeneous and isotropic continua, the elastic equilibrium problem, Clapeyron’s Theorem, Betti and Betti-Maxwell Theorems, the mechanical behaviour of the main building materials, strength criteria for fragile materials (Rankine and Mohr – Coulmb criteria) and for ductile materials (Hencky Von Mises criterium).
2. De Saint Venant’s Solid:
General formulation of the problem, recalls of some internal stress states (due to axial loads with and without eccentricity, bending moments) already studied in the previous Course of Statics, torsion and shear and related tangential stresses, combined stress states
3. Elements of the Technical Theory of Elastic Beams:
Euler-Bernoulli and Timoshenko models, differential equations for axial and bending deformations in statically determined and undetermined beams, thermal distorsions, elastic and non-elastic settlements, kinematic composition of displacements.
4. Theory of Structures
The Method of Congruence (Forces) and Equilibrium (Displacements) for statically undetermined beams and frames; the Principle of Virtual Works for statically determined and undetermined deformable truss structures, beams and frames, introduction to the automatic computation of statically undetermined structures, instabilty of structural elements with reference to Euler’s beam.
5. Strength controls and checks
The Hencky Von Mises Criterion to check the admissible stresses in steel structures, the “Omega” method to check the structural strength in slender steel structural elements Didactic methods
- The approach to the discipline is mainly deductive but with constant references to real phenomena and real material and structural behaviours. The operational tools, that are mainly mathematical-physical-geometric, remain strictly functional to an essential and rigorous treatment of the issues and allow handling real, even complex, problems by means of simplified mechanical models.
The course is developed through classroom lectures and exercises.
Exercises carried out by Tutors are added to those carried out by the Professor during the Course Learning assessment procedures
- The assessment of what has been learnt and of the degree of achievement of the educational goals is carried out with:
Final examination test with the purpose of assessing the level of acquisition of the issues presented during the Course, the ability to use operational tools for computations and structural checks, the acquisition of the scientific language with which the topics are treated.
The exam consists of a written test with which students are asked to analyse either statically determinate or indeterminate structures with the methods and procedures illustrated during the course and to answer a series of questions on the theoretical contents of the course and on simple structural controls
The exam is completely passed only if the test has been successful. Reference texts
- - Course Notes
- P. Casini, M. Vasta, Scienza delle Costruzioni, CittàStudi Edizioni
- A. Carpinteri, Scienza delle Costruzioni, Vol. 1-2, Pitagora
- Viola, Esercitazioni di Scienza delle Costruzioni, Vol. 2, Pitagora
- Furiozzi, Messina, Paolini, Prontuario con software didattico per il calcolo di elementi strutturali, Le Monnier, Firenze.
- Furiozzi, Messina, Paolini, Prontuario con software didattico per il calcolo di elementi strutturali, Le Monnier, Firenze.
