30978 - Mechanics of Solids and Structures

Learning outcomes

Basics of solid and structure mechanics, with applications to elementary cases of recurrent structures.

Course contents

REQUIRED KNOWLEDGE

 Mathematical Analysis T. Geometry and Algebra T.

 

GEOMETRY OF MASSES

Polarity and antipolarity relationships. The central ellipse of inertia. The kern of a cross-section.

 

STRAIN ANALYSIS

The linearized first-order theory of displacements. Physical parameters of strain. Infinitesimal strain tensor. Kinematically admissible displacement-strain system. Principal components of strain and strain invariants; principal directions of strain. Uniaxial and biaxial strain.

 

STRESS THEORY

Undeformed free-body equilibrium. Stress tensor. Principal components of stress and stress invariants; principal planes and directions of stress. Mohr’s circles. Uniaxial and biaxial stress. Statically admissible stress field.

 

FUNDAMENTAL IDENTITY AND PRINCIPLES IN SOLID MECHANICS

Theorem and Principle of Virtual Work for deformable bodies. Strain energy and complementary strain energy. Clapeyron’s theorem.

 

ELASTIC SYSTEMS

Elastic energy and complementary elastic energy. Homogeneous and non-homogeneous materials. Isotropic and anisotropic materials. Hooke’s generalized laws. Linear homogeneous-isotropic elastic equilibrium problem. Superposition of effects principle. Kirchhoff’s principle.

 

SAINT-VENANT'S PROBLEM

Boussinesq and Saint-Venant’s postulates. Setting the Saint-Venant problem. Simple tension/compression load. Pure bending. Biaxial bending. Eccentric normal load. Pure torsion (elements). Combined bending and shear.

 

MECHANICS OF MATERIALS

Uniaxial and triaxial tests on brittle materials. Failure planes in brittle materials subjected to pure shear. Mohr/Coulomb failure criterion. Uniaxial tensile and compression test on steel bars. Prandtl’s constitutive model. Tresca and von Mises failure criteria.

 

THEORY OF STRUCTURES

The beam. Constraints. Internal actions. Indefinite equilibrium equations. Solution of statically determinate structures: graphical and analytical methods. Kinematic chain procedure. Calculation of displacement components in statically determinate structures. Solution of statically indeterminate structures: force method, movable node frame method, Principle of Virtual Works.

Readings/Bibliography

• A. DI TOMMASO, FONDAMENTI DI SCIENZA DELLE COSTRUZIONI, PARTE I, 1981; PARTE II, 1993, PATRON ED., BOLOGNA

• E. VIOLA, ESERCITAZIONI DI SCIENZA DELLE COSTRUZIONI, 1/ STRUTTURE ISOSTATICHE E GEOMETRIA DELLE MASSE, 2/ STRUTTURE IPERSTATICHE E VERIFICHE DI RESISTENZA, PITAGORA ED., BOLOGNA, 1993

Teaching methods

Classroom lectures.

Assessment methods

Written and oral examinations.

Teaching tools

The teacher handles a course and e-learning website.

Office hours

See the website of Elena Ferretti