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
2) Rigid body kinematics
3) Force and moment distributions
4) Mechanics of rigid systems in 2D
- linearized kinematics
- (internal and external) constraints
- equilibrium and reaction forces
- the principle of virtual work (PVW)
5) 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, 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
6) Limit analysis for beam frames in bending
7) Complements
- cables and arches
- shear stress: Zhuravskii formula
- notes on structural stability: Euler's critical load and column design
2) Bernardini. "Statica. Un'introduzione alla meccanica delle strutture". Città-Studi Edizioni.
Programme
1) Algebra and vector geometry (follow-up)2) Rigid body kinematics
3) Force and moment distributions
4) Mechanics of rigid systems in 2D
- linearized kinematics
- (internal and external) constraints
- equilibrium and reaction forces
- the principle of virtual work (PVW)
5) 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, 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
6) Limit analysis for beam frames in bending
7) Complements
- cables and arches
- shear stress: Zhuravskii formula
- notes on structural stability: Euler's critical load and column design
Core Documentation
1) Comi, Corradi Dell'Acqua. "Introduzione alla meccanica delle strutture". McGraw-Hill.2) Bernardini. "Statica. Un'introduzione alla meccanica delle strutture". Città-Studi Edizioni.
Reference Bibliography
Stephen Timoshenko. "History of The Strength of Materials". McGraw-Hill Book Company. Edoardo Benvenuto. "La scienza delle costruzioni e il suo sviluppo storico". Storia e Letteratura Editore. Leone Corradi Dell'Acqua. "Meccanica delle Strutture". McGraw-Hill Education. Daniel L. Schodeck. "Strutture". Pàtron Editore. Emilio Turco, et al. "Scienza delle costruzioni". McGraw-Hill Education. Luigi Gambarotta, et al. "Scienza delle costruzioni". McGraw-Hill Education. Angelo Luongo, Achille Paolone. "Scienza delle costruzioni". Casa Editrice Ambrosiana. Zanichelli distribuzione.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
Final assessment is both oral and written. Students who will attend lectures successfully, and then pass (at least two) intermediate examinations during the course, can access to the final interview directly. The final exam score is not affected by the grades obtained in the written tests. Written examinations are a 2.5-hour test, involving one exercise of the same level of tests faced during the course. In the SUMMER SESSION, the final assessment is restricted to oral examination alone. Such an examination is split in two parts, the former is a preliminary test mimicking the usual written test, the latter is a standard oral interview. The exam is in remote procedure, using Microsoft Teams, together with further specifications that will be provided by the student online convocation. 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
- 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
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
- 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.
Reference Bibliography
Stephen Timoshenko. "History of The Strength of Materials". McGraw-Hill Book Company. Edoardo Benvenuto. "La scienza delle costruzioni e il suo sviluppo storico". Storia e Letteratura Editore. Leone Corradi Dell'Acqua. "Meccanica delle Strutture". McGraw-Hill Education. Daniel L. Schodeck. "Strutture". Pàtron Editore. Emilio Turco, et al. "Scienza delle costruzioni". McGraw-Hill Education. Luigi Gambarotta, et al. "Scienza delle costruzioni". McGraw-Hill Education. Angelo Luongo, Achille Paolone. "Scienza delle costruzioni". Casa Editrice Ambrosiana. Zanichelli distribuzione.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
Final assessment is both oral and written. Students who will attend lectures successfully, and then pass (at least two) intermediate examinations during the course, can access to the final interview directly. The final exam score is not affected by the grades obtained in the written tests. Written examinations are a 3 hour test, involving one exercise of the same level of tests faced during the course. As for the summer appeal, the examination will be held exclusively in oral form on the Teams platform, as required by the rules for the COVID emergency.