Docente
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ARENA ANDREA
(programma)
Lecture 1.
1.1 Introduction to structural and continuum mechanics. Summary of basic tensor and vector
algebra. Summary of basic calculus. Examples.
Lecture 2.
2.1Kinematics of three-dimensional continua. The infinitesimal strain tensor and the
mechanical meaning of its components. Principal strains and principal directions.
Lecture 3.
3.1 Statics of three-dimensional Cauchy continua. The Cauchy theorem. Equilibrium equations.
Principal stresses and principal directions.
Lecture 4
4.1Exercises developed in class.
Lecture 5.
5.1The octahedral shear stress and the maximum shear stress in 3D continua.
5.2The Mohr’s circles and their application to plane stress-states.
5.3Exercises developed in class.
Lecture 6.
6.1Constitutive behaviors for 3D continua.
6.2Linear elastic behavior of isotropic homogeneous materials. The elastic problem in 3D
continua
6.3Yield surfaces: the von Mises criterion and the Tresca yield surface. Examples.
Lecture 7.
7.1The Saint-Venant problem
7.2Geometric properties of surfaces. Thin-walled sections.
Lecture 8.
8.1Exercises developed in class
Lecture 9.
9.1 Global equilibrium equations of the Saint-Venant solid: stress resultants and strain
resultants. The S-V sub-problems.
Lecture 10.
10.1 The axial problem: theory and applications. The one-axis bending problem and the
two-axes bending problem: theory and applications. The case of eccentric axial forces:
theory and applications.
Lecture 11.
11.1 Exercises developed in class
Lecture 12.
12.1 The shear problem and the Jourawsky theory.
12.2 The shear center.
Lecture 13.
13.1 Exercises developed in class
Lecture 14.
14.1 Torsion of thin-walled open sections.
14.2 Exercises developed in class
Lecture 15.
15.1 Torsion of thin-walled closed sections.
15.2 Exercises developed in class
Lecture 16.
16.1 Kinematics and statics of rigid bodies systems.
16.2 The constraints and their kinematic and static meaning
16.3 The kinematic and the static problems
Lecture 17.
17.1 Exercises developed in class: solution of the kinematic problem, the isokinematic
case
Lecture 18.
18.1 Exercises developed in class: solution of the static problem, the isostatic case.
Lecture 19.
19.1 The beam theory: the in-plane problem
19.2 Kinematics of the beam.
19.3 Statics of the beam
Lecture 20.
20.1 Systems of beams, the case of isostatic systems: stress resultants diagrams.
Lecture 21.
21.1 The elastic beam problem and the Euler-Bernoulli beam model.
Lecture 22.
22.1 Solution of the elastic problem for Euler-Bernoulli beams subjected to different
boundary conditions.
Lecture 23.
23.1 Exercises developed in class
Appunti presi in aula dallo studente
Dispense del docente
Testi:
R.C. Hibbeler
Mechanics of Materials, Ninth edition
R.C. Hibbeler
Statics, Thirteenth Edition
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