To provide knowledge of the rudiments of mechanics for rigid body and the beam models, with application to simple cases of isostatic and hyperstatic systems articulated in two dimensions. Course topics are in particular: introduction of rigid body kinematics and concepts of constraints; distributions, equivalence and reduction of systems of forces; the balance equations and the methods of calculations of reaction forces; the beam model kinematics linea rizzata; the contact actions; the balance equations; the Navier formula; the resolution of simple isostatic and hyperstatic systems.
Canali
teacher profile teaching materials
- provide basics knowledge in structural mechanics, focusing on both rigid and elastic bodies
- introduce students to the study and learning skills required for the analysis of simple structures (beams, frames, trusses, cables and arches), using the most commonly adopted models in structural mechanics
Program
Algebra and vector geometry (follow-up)
Force and moment distributions
Mechanics of rigid systems in 2D
- linearized kinematics
- (internal and external) constraints
- equilibrium and reaction forces
- the principle of virtual work (PVW)
Mechanics of elastic beam systems in 2D
- beam equilibrium equations
- evaluation and diagrams of internal forces
- equilibrium in truss systems
- stress and strain (outline and definition)
- construction materials: steel, basic production processes, experimental evidences (tensile test), notes on safety assessment analysis
- linear elastic behavior: relationships of stress-strain and force-displacements
- straight beam:
axial and bending behavior
basic design criteria for trusses and frames
- internal work and PVW
Complements
- cables and arches
- statically indeterminate beams
- shear stress: Jourawski formula
- notes on the elastic-plastic behavior
- notes on structural stability: Eulerian critical load and column design
STRUTTURE'. MCGRAW-HILL.
2) DAVIDE BERNARDINI. 'STATICA. UN'INTRODUZIONE ALLA MECCANICA
DELLE STRUTTURE'. CITTÀSTUDI EDIZIONI.
Programme
Contents- provide basics knowledge in structural mechanics, focusing on both rigid and elastic bodies
- introduce students to the study and learning skills required for the analysis of simple structures (beams, frames, trusses, cables and arches), using the most commonly adopted models in structural mechanics
Program
Algebra and vector geometry (follow-up)
Force and moment distributions
Mechanics of rigid systems in 2D
- linearized kinematics
- (internal and external) constraints
- equilibrium and reaction forces
- the principle of virtual work (PVW)
Mechanics of elastic beam systems in 2D
- beam equilibrium equations
- evaluation and diagrams of internal forces
- equilibrium in truss systems
- stress and strain (outline and definition)
- construction materials: steel, basic production processes, experimental evidences (tensile test), notes on safety assessment analysis
- linear elastic behavior: relationships of stress-strain and force-displacements
- straight beam:
axial and bending behavior
basic design criteria for trusses and frames
- internal work and PVW
Complements
- cables and arches
- statically indeterminate beams
- shear stress: Jourawski formula
- notes on the elastic-plastic behavior
- notes on structural stability: Eulerian critical load and column design
Core Documentation
1) COMI, CORRADI DELL'ACQUA. `INTRODUZIONE ALLA MECCANICA DELLESTRUTTURE'. MCGRAW-HILL.
2) DAVIDE BERNARDINI. 'STATICA. UN'INTRODUZIONE ALLA MECCANICA
DELLE STRUTTURE'. CITTÀSTUDI EDIZIONI.
Type of delivery of the course
The course is taught by lectures and practical exercises. Teaching bases on regular interaction between teacher and students. Guided practice and intermediate practice tests are scheduled during the duration of the course. Experimental tests in Lab can be provided by appointment only.Attendance
Students are strongly encouraged to attend to their class for both theory and practice.Type of evaluation
written and oral exams teacher profile teaching materials
FORCE AND MOMENT DISTRIBUTIONS
MECHANICS OF RIGID SYSTEMS IN 2D
- LINEARIZED KINEMATICS
- (INTERNAL AND EXTERNAL) CONSTRAINTS
- EQUILIBRIUM AND REACTION FORCES
- THE PRINCIPLE OF VIRTUAL WORK (PVW)
MECHANICS OF ELASTIC BEAM SYSTEMS IN 2D
- BEAM EQUILIBRIUM EQUATIONS
- EVALUATION AND DIAGRAMS OF INTERNAL FORCES
- EQUILIBRIUM IN TRUSS SYSTEMS
- STRESS AND STRAIN (OUTLINE AND DEFINITION)
- CONSTRUCTION MATERIALS: STEEL, BASIC PRODUCTION PROCESSES, EXPERIMENTAL EVIDENCES (TENSILE TEST), NOTES ON SAFETY ASSESSMENT ANALYSIS
- LINEAR ELASTIC BEHAVIOR: RELATIONSHIPS OF STRESS-STRAIN AND FORCE-DISPLACEMENTS
- STRAIGHT BEAM:
- AXIAL AND BENDING BEHAVIOR
- BASIC DESIGN CRITERIA FOR TRUSSES AND FRAMES
- INTERNAL WORK AND PVW
COMPLEMENTS
- CABLES AND ARCHES
- STATICALLY INDETERMINATE BEAMS
- SHEAR STRESS: JOURAWSKI FORMULA
- NOTES ON THE ELASTIC-PLASTIC BEHAVIOR
- NOTES ON STRUCTURAL STABILITY: EULERIAN CRITICAL LOAD AND COLUMN DESIGN
Programme
ALGEBRA AND VECTOR GEOMETRY (FOLLOW-UP)FORCE AND MOMENT DISTRIBUTIONS
MECHANICS OF RIGID SYSTEMS IN 2D
- LINEARIZED KINEMATICS
- (INTERNAL AND EXTERNAL) CONSTRAINTS
- EQUILIBRIUM AND REACTION FORCES
- THE PRINCIPLE OF VIRTUAL WORK (PVW)
MECHANICS OF ELASTIC BEAM SYSTEMS IN 2D
- BEAM EQUILIBRIUM EQUATIONS
- EVALUATION AND DIAGRAMS OF INTERNAL FORCES
- EQUILIBRIUM IN TRUSS SYSTEMS
- STRESS AND STRAIN (OUTLINE AND DEFINITION)
- CONSTRUCTION MATERIALS: STEEL, BASIC PRODUCTION PROCESSES, EXPERIMENTAL EVIDENCES (TENSILE TEST), NOTES ON SAFETY ASSESSMENT ANALYSIS
- LINEAR ELASTIC BEHAVIOR: RELATIONSHIPS OF STRESS-STRAIN AND FORCE-DISPLACEMENTS
- STRAIGHT BEAM:
- AXIAL AND BENDING BEHAVIOR
- BASIC DESIGN CRITERIA FOR TRUSSES AND FRAMES
- INTERNAL WORK AND PVW
COMPLEMENTS
- CABLES AND ARCHES
- STATICALLY INDETERMINATE BEAMS
- SHEAR STRESS: JOURAWSKI FORMULA
- NOTES ON THE ELASTIC-PLASTIC BEHAVIOR
- NOTES ON STRUCTURAL STABILITY: EULERIAN CRITICAL LOAD AND COLUMN DESIGN
Core Documentation
Introduzione alla meccanica delle strutture. Teoria ed Esercizi. Bernardini Davide, CittàStudi Edizioni (2012)Reference Bibliography
Schodek D.L., “Strutture”, 4a ed., Patron Ed., Bologna, 2008Type of delivery of the course
The course is carried out through theoretical classes, on the basis of the topics listed in the course outline and a hands-on part, consisting of guided classroom exercises concerning: the equilibrium problem of two-dimensional beam systems, the design of simple structural elements and resistance or deformability verifications. Seminar classes on the introduction to structural modeling and experimental lessons will be organized. A weekly office time will be made available for individual clarifications.Attendance
Attendance is required for at least 75% of the lessonsType of evaluation
Two mid term tests are proposed during the semester of the course, for the purpose of evaluating the practical part. The final exam will be carried out with a written test, in which the student will have to independently solve exercises such as those presented in the classroom. Having a good evaluation to the written test the student will take an oral test with discussion of the topics of the theoretical classes. During the oral exam, each student is asked to bring and discuss a paper on a structural theme, in which one starts from an existing architecture to arrive at the simplified structural scheme of the selected project.