PORTALE DELLA DIDATTICA

### Structural mechanics

07LLQTR

A.A. 2023/24

Course Language

Inglese

Course degree

1st degree and Bachelor-level of the Bologna process in Civil And Environmental Engineering - Torino

Course structure
Teaching Hours
Teachers
Teacher Status SSD h.Les h.Ex h.Lab h.Tut Years teaching
Teaching assistant
Context
SSD CFU Activities Area context
ICAR/08 10 B - Caratterizzanti Ingegneria della sicurezza e protezione civile, ambientale e del territorio
2021/22
The teaching aims to provide the basic knowledge needed to compute a structure and to assess its safety, by defining the parameters that describe the applied loadings and the strength of materials. The calculation methods used to assess the stress state in simple structural elements are presented, with focus on examples of civil/environmental interest (structures, infrastructures, plants) and failure under monotonic loading.
The teaching aims to provide the basic knowledge needed to compute a structure and to assess its safety, by defining the parameters that describe the applied loadings and the strength of materials. The calculation methods used to assess the stress state in simple structural elements are presented, with focus on examples of civil/environmental interest (structures, infrastructures, plants) and failure under monotonic loading.
The student will be able to determine the constraint reactions and the diagrams of internal actions (normal stress, shear stress and bending moment), and to plot the deflection curve for any plane system of isostatic beams; to calculate the stresses in the beams on the basis of De Saint Venant theory; to apply the strength criteria for generic stress states; to investigate a slender bar subjected to a buckling load.
The student will be able to determine the constraint reactions and the diagrams of internal actions (normal stress, shear stress and bending moment), and to plot the deflection curve for any plane system of isostatic beams; to calculate the stresses in the beams on the basis of De Saint Venant theory; to apply the strength criteria for generic stress states; to investigate a slender bar subjected to a buckling load.
The student must know the kinematic, static and dynamic theory of the material point, the operations on vectors (sum, multiplication by a scalar, scalar product and vector product) and on matrices, the fundamentals of linear algebra and analytic/differential geometry. For functions of one variable, he/she must know the limits, derivatives, integrals, developments in Taylor series and solutions of differential equations with constant coefficients. For functions of several variables, he/she must know Taylor's rules of derivation, integrations and development in series.
The student must know the kinematic, static and dynamic theory of the material point, the operations on vectors (sum, multiplication by a scalar, scalar product and vector product) and on matrices, the fundamentals of linear algebra and analytic/differential geometry. For functions of one variable, he/she must know the limits, derivatives, integrals, developments in Taylor series and solutions of differential equations with constant coefficients. For functions of several variables, he/she must know Taylor's rules of derivation, integrations and development in series.
STATICALLY DETERMINATE BEAM SYSTEMS: statics and kinematics, plane constraints, hypostatic systems, determination of constraint reactions with auxiliary equations and with the graphical method; internal beam reactions; indefinite equations of equilibrium for plane beams; trusses. ANALYSIS OF STRAIN AND STRESS: strain tensor; dilations and shearing strains; principal directions of strain; cubic dilation. Measures by extensometers. Stress tensor; principal directions of stress; plane stress condition; Mohr�s circle. Indefinite equations of equilibrium; boundary equations of equivalence; principle of virtual work for deformable bodies. ELASTIC CONSTITUTIVE LAW AND STRENGTH CRITERIA: experimental techniques to characterize the mechanical behavior of materials. Traction test. Linear elasticity; elastic potential; Young modulus and Poisson�s coefficient; problem of a linear elastic body: Clapeyron�s theorem; Betti�s reciprocal theorem; isotropy; Tresca�s and Von Mises� strength criteria. GEOMETRY OF AREAS: centroid, static moment, moment of inertia, product of inertia, principal axes and moments of inertia. SAINT-VENANT PROBLEM: fundamental hypotheses; centered axial force; flexure; eccentric axial force and biaxial flexure; central cores of inertia; torsion; shearing force; beam strength analysis. CALCULUS OF ELASTIC DISPLACEMENTS AND SIMPLE STATICALLY UNDETERMINATE BEAM SYSTEMS: equation of the elastica; determination of elastic displacements; method of forces; equations of congruence written with the principle of virtual works; Simpson�s integration rule. ELASTIC INSTABILITY: compressed beams with different constrain conditions.
STATICALLY DETERMINATE BEAM SYSTEMS: statics and kinematics, plane constraints, hypostatic systems, determination of constraint reactions with auxiliary equations and with the graphical method; internal beam reactions; indefinite equations of equilibrium for plane beams; trusses. ANALYSIS OF STRAIN AND STRESS: strain tensor; dilations and shearing strains; principal directions of strain; cubic dilation. Measures by extensometers. Stress tensor; principal directions of stress; plane stress condition; Mohr�s circle. Indefinite equations of equilibrium; boundary equations of equivalence; principle of virtual work for deformable bodies. ELASTIC CONSTITUTIVE LAW AND STRENGTH CRITERIA: experimental techniques to characterize the mechanical behavior of materials. Traction test. Linear elasticity; elastic potential; Young modulus and Poisson�s coefficient; problem of a linear elastic body: Clapeyron�s theorem; Betti�s reciprocal theorem; isotropy; Tresca�s and Von Mises� strength criteria. GEOMETRY OF AREAS: centroid, static moment, moment of inertia, product of inertia, principal axes and moments of inertia. SAINT-VENANT PROBLEM: fundamental hypotheses; centered axial force; flexure; eccentric axial force and biaxial flexure; central cores of inertia; torsion; shearing force; beam strength analysis. CALCULUS OF ELASTIC DISPLACEMENTS AND SIMPLE STATICALLY UNDETERMINATE BEAM SYSTEMS: equation of the elastica; determination of elastic displacements; method of forces; equations of congruence written with the principle of virtual works; Simpson�s integration rule. ELASTIC INSTABILITY: compressed beams with different constrain conditions. The course is based on lectures and classroom exercises. Lessons are intended to present the theoretical basis of the topics; classroom exercises show the solutions of sample problems. Lectures and classroom exercises are given by means of the dashboard. One lecture is supposed to be held at the Laboratory Mastrlab of DISEG, where students can attend some experimental tests to assess material strength.
The course is based on lectures and classroom exercises. Lessons are intended to present the theoretical basis of the topics; classroom exercises show the solutions of sample problems. Lectures and classroom exercises are given by means of the dashboard. One lecture is supposed to be held at the Laboratory Mastrlab of DISEG, where students can attend some experimental tests to assess material strength.
Notes, exercises, formularies will be downloadable from the website of the course. Optional textbooks: A. Carpinteri (2013) Structural mechanics Fundamentals, CRC Press.
Notes, exercises, formularies will be downloadable from the website of the course. Optional textbooks: A. Carpinteri (2013) Structural mechanics Fundamentals, CRC Press. A. Carpinteri, A. (1992) Scienza delle Costruzioni, Voll. 1 e 2, Pitagora Editrice, Bologna. S. Lenci (2009) Lezioni di Meccanica Strutturale, Pitagora Editrice, Bologna.
Modalit� di esame: Prova scritta (in aula); Prova orale obbligatoria;
Exam: Written test; Compulsory oral exam;
... Written exam on paper lasting 2 hours and classroom supervision (for students in presence) Oral exam in person.
Gli studenti e le studentesse con disabilit� o con Disturbi Specifici di Apprendimento (DSA), oltre alla segnalazione tramite procedura informatizzata, sono invitati a comunicare anche direttamente al/la docente titolare dell'insegnamento, con un preavviso non inferiore ad una settimana dall'avvio della sessione d'esame, gli strumenti compensativi concordati con l'Unit� Special Needs, al fine di permettere al/la docente la declinazione pi� idonea in riferimento alla specifica tipologia di esame.
Exam: Written test; Compulsory oral exam;
Written exam on paper lasting 2 hours and classroom supervision (for students in presence) Oral exam in person.
In addition to the message sent by the online system, students with disabilities or Specific Learning Disorders (SLD) are invited to directly inform the professor in charge of the course about the special arrangements for the exam that have been agreed with the Special Needs Unit. The professor has to be informed at least one week before the beginning of the examination session in order to provide students with the most suitable arrangements for each specific type of exam.