Università di Pavia - Offerta formativa

FUNDAMENTALS OF MECHANICS OF MATERIALS AND STRUCTURES

Enrollment year

2020/2021

Academic year

2021/2022

Regulations

DM270

Academic discipline

ICAR/08 (CONSTRUCTION SCIENCE)

Department

DEPARTMENT OF ELECTRICAL,COMPUTER AND BIOMEDICAL ENGINEERING

Course

INDUSTRIAL ENGINEERING

Curriculum

Meccanica

Year of study

2°

Period

2nd semester (07/03/2022 - 17/06/2022)

ECTS

6

Lesson hours

54 lesson hours

Language

Italian

Activity type

WRITTEN AND ORAL TEST

Teacher

Prerequisites

Calculus 1, Physics 1, Mathematical Physics, Algebra

Learning outcomes

Understanding and assimilation of basic concepts related to the foundations of continuum mechanics for general 3D elastic solids and elementary mechanics of deformable one-dimensional structures. Acquisition of operational capabilities necessary to solve statically determinate and indeterminate beams of basic type using different approaches, as well as the schematic design and verification of beams with general loading conditions.

Course contents

Basic concepts: force, moment, couple, vector/tensor operations, notations

Beam equilibrium: Kinematics and statics of the straight beam, internal actions and diagrams.

Euler-Bernoulli beam theory, consistency, equilibrium, constitutive law. Elastic-linear-isotropic law and formulation of the elastic problem.

Strain state. Consistency of the deformable continuum and kinematics relations. The finite-deformation tensor (Green-Lagrange). Hypothesis of "small displacements": small deformation tensor. Principal deformations and invariants. Volume and shape change. Internal consistency.

Stress state: General aspects of the structural problem. Force and stress. the Cauchy stress tensor. Principal directions and invariants. 2D and 3D stress states. The Mohr stress representation. Equilibrium conditions.

Constitutive law. Stress-strain relations and experimental evidence. Elasticity, anelasticity, failure. Elastic law: energy aspects, existence and uniqueness of the elastic response. Elastic-linear-isotropic law: elastic constants. Elastic limit and failure-yield criteria. The elastic problem.

Formulation of the problem and uniqueness of the solution.

Position of the problem of De Saint Venant. Axial action and bending. Torsion. Shear: approximate treatment.

Beam equilibrium: Kinematics and statics of the straight beam, internal actions and diagrams.

Euler-Bernoulli beam theory, consistency, equilibrium, constitutive law. Elastic-linear-isotropic law and formulation of the elastic problem.

Strain state. Consistency of the deformable continuum and kinematics relations. The finite-deformation tensor (Green-Lagrange). Hypothesis of "small displacements": small deformation tensor. Principal deformations and invariants. Volume and shape change. Internal consistency.

Stress state: General aspects of the structural problem. Force and stress. the Cauchy stress tensor. Principal directions and invariants. 2D and 3D stress states. The Mohr stress representation. Equilibrium conditions.

Constitutive law. Stress-strain relations and experimental evidence. Elasticity, anelasticity, failure. Elastic law: energy aspects, existence and uniqueness of the elastic response. Elastic-linear-isotropic law: elastic constants. Elastic limit and failure-yield criteria. The elastic problem.

Formulation of the problem and uniqueness of the solution.

Position of the problem of De Saint Venant. Axial action and bending. Torsion. Shear: approximate treatment.

Teaching methods

Lectures: 32 hours

Practical classes: 22 hours

Practical classes: 22 hours

Reccomended or required readings

Course notes.

P. Casini, M. Vasta, Scienza delle Costruzioni 4/ed, CittÃ studi, 2019.

Corradi dell'Acqua L.. Meccanica delle strutture 1 - Il comportamento dei corpi continui 2/ed. McGraw-Hill, 2010.

P. Casini, M. Vasta, Scienza delle Costruzioni 4/ed, CittÃ studi, 2019.

Corradi dell'Acqua L.. Meccanica delle strutture 1 - Il comportamento dei corpi continui 2/ed. McGraw-Hill, 2010.

Assessment methods

Written test with exercises (on person or remotely) + possible oral examination.

Further information

Written test with exercises (on person or remotely) + possible oral examination.

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