# 30978 - Mechanics of Solids and Structures

• Moduli: Francesco Ubertini (Modulo 1) Luca Patruno (Modulo 2)
• Campus: Bologna
• Corso: First cycle degree programme (L) in Civil Engineering (cod. 8888)
• from Feb 21, 2024 to Jun 05, 2024

• from Feb 22, 2024 to Jun 06, 2024

## Learning outcomes

The goal of the course is to provide the students with the fundamental concepts of solid mechanics and the methodologies for structural analysis.

## Course contents

Requirements/Prior knowledge

A prior knowledge and understanding of mathematical analysis and rational mechanics is required to attend with profit this course.

Fluent spoken Italian is a necessary pre-requisite: all lectures and tutorials, and all study material will be in Italian.

Course Contents

OVERVIEW

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 and strain energy. Linear elasticity. Isotropy. The linear elastic equilibrium problem. Superposition. Uniqueness of solution. Clapeyron's, Betti's and Maxwell's theorems.

FAILURE CRITERIA

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

ST VENANT'S PROBLEM

THEORY OF STRUCTURES

Beam model and internal forces. Constraints. Static and kinematic analysis. Funicular. Truss structures. Cross section geometry properties. Structural symmetry and asymmetry. The Elastica equation. Evaluating displacements and rotations. Statically indeterminate structures: force method and displacement method. Elastic stability. Euler buckling load.

- Lecture slides and notes (https://virtuale.unibo.it).

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

- E. Viola, Esercitazioni di Scienza delle Costruzioni, Vol. 1, Pitagora Editrice Bologna, 1993.

- E. Viola, Esercitazioni di Scienza delle Costruzioni, Vol. 2, Pitagora Editrice Bologna, 1993.

## 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. The instructors will tutor the students. The course includes, also, at least one visit to the Laboratory of Structural Engineering and Geotechnics (LISG) to attend some laboratory tests of materials and structures.

## Assessment methods

There will be a final examination structured in two phases: a first written exam (2,5 hours, without using notes or books) and a subsequent oral exam. The written exam consists of a few simple exercises and will be reviewed at the presence of the students. In order to be admitted to the oral exam, students need to obtain a sufficient grade in the written test. The oral exam consists of some questions intended to assess the knowledge and understanding of the topics covered by the course. There will be also two midterm written examinations. Students who pass both of them will be only required to take the final oral exam.

To obtain a passing grade, students are required to at least demonstrate a knowledge of the key concepts of the subject and some ability for critical application.

A failing grade will be awarded if the student shows knowledge gaps in key-concepts of the subject and/or logic failures in the analysis of the subject.

## Teaching tools

The teaching tools are: whiteboard, projector and lesson recording.

Visits to the Laboratory of Structural Engineering and Geotechnics (LISG) are planned.

As concerns the teaching methods of this course unit, all students must attend Module 1, 2 [https://www.unibo.it/en/services-and-opportunities/health-and-assistance/health-and-safety/online-course-on-health-and-safety-in-study-and-internship-areas] online, while Module 3 on health and safety is to be attended in class. Information about Module 3 attendance schedule is available on the website of your degree programme.

## Office hours

See the website of Francesco Ubertini

See the website of Luca Patruno