# 26371 - Mechanics of Structure -

## Learning outcomes

At the end of the course the students know the basic concepts of the solid mechanics and the methodologies for the structural analysis.

## Course contents

THEORY OF STRUCTURES

Beam model and internal forces. Static and kinematic analysis. The Elastica equation. Evaluating displacements and rotations. Statically indeterminate structures: force method and displacement method. Elastic stability. Euler buckling load.

STRAIN ANALYSIS

Displacement, deformation and strain. Strain tensor and physical meaning. Principal strains and directions. Compatibility equations.

STRESS ANALYSIS

Volume and surface forces. Rigid body equilibrium. Concept of stress and stress tensor. Principal stresses and directions. Mohr's circles. Equilibrium equations.

GENERAL RELATIONSHIPS

Principle of virtual works. Weak form of equilibrium and weak form of compatibility. Applications to beams.

ELASTICITY

Behavior of materials. Testing of ductile and brittle materials. Elastic behavior. Linear elasticity. Isotropy. The linear elastic equilibrium problem. Superposition. Uniqueness of solution.

FAILURE CRITERIA

Limit states and safety factors. Tresca stress criterion. Von Mises stress criterion. Failure criteria for brittle materials.

ST VENANT'S PROBLEM

P. Casini M. Vasta Scienza delle Costruzioni, Città Studi edizioni

C. Comi e L. Corradi Dell'Acqua, Introduzione alla Meccanica Struttural, McGraw-Hill

M. Capurso, Lezioni di Scienza delle Costruzioni, Pitagora Editrice

## Teaching methods

The course content will be entirely covered by the lectures. The course includes some help sessions, which will cover the practical aspects of the lectures.

## Assessment methods

There will be a final examination structured in two phases: a first written exam and a subsequent oral exam. The written exam consists of two exercises. The first exercise deals with the resolution of an hyperstatic structure, the second one with the resolution of a cross section subjected to bending, shear force or torque moment. The marks of the written exam is 30/30, 18 are assigned to the first exercise and 12 to the second one. It is necessary to have a good evaluation in both the exercises.

The written test is predominant, during the oral the final marks can increase for a maximum of 4 points.

There will be also two midterm written examinations. Students who pass both of them will be only required to take the final oral exam.

## Teaching tools

Some notes will be available on the web.

## Office hours

See the website of Luisa Molari

See the website of Veronica Bartolomeo