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 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.

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.

Modalità di esame: Prova scritta (in aula); Elaborato scritto individuale; Prova scritta in aula tramite PC con l'utilizzo della piattaforma di ateneo;

Exam: Written test; Individual essay; Computer-based written test in class using POLITO platform;

... Written exam on paper lasting 2 hours and classroom supervision (for students in presence) Oral exam in person.

Gli studenti e le studentesse con disabilità 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'Unità Special Needs, al fine di permettere al/la docente la declinazione più idonea in riferimento alla specifica tipologia di esame.