# Principles of structural design for industry

## Learning outcomes of the course unit

To develop the threshold skills required, the student is asked to

demonstrate knowledge on the following points:

• Knowledge and understanding.

o To know the basic theory of solid and structural mechanics

o To know and embrace the concepts of stress state, strain state,

constitutive relationship

o To know the response of elastic, plastic, elasto-plastic and viscoelastic

materials

o To understand relations governing the internal action and the elastic

curve of a beam

o To understand the response of elasto-plastic beam elements under

tension/compression, bending, shear, and torsion

o To understand the response of 2-dimensional structural elements

• Applying knowledge and understanding.

To be able to:

o apply the basic concepts of solid and structural mechanics

MANAGEMENT ENGINEERING STUDENTS

o determine the stress state, starting from the strain state, and viceversa

o interpret simple programs for the determination and drawing of the

internal action diagrams and of the elastic curve of a beam

o describe the stress and strain state of an elasto-plastic beam subjected

to tension/compression, bending, shear, and torsion

o describe and classify buckling phenomena

o use the acquired knowledge for autonomously studying and deepening

of issues related to solid and structural mechanics

MECHANICAL ENGINEERING STUDENTS

o determine the stress state, starting from the strain state, and

viceversa, for solids with different material response

o write simple programs for the determination and drawing of the internal

action diagrams and of the elastic curve of a beam

o determine and calculate the stress and strain state of an elasto-plastic

beam subjected to tension/compression, bending, shear, and torsion

o classify buckling phenomena and evaluate the related critical loads

o use the acquired knowledge for autonomously studying and deepening

of issues related to solid and structural mechanics, and for the design of

structural elements

• Making judgements

o to evaluate the applicability of structural models to describe real

structures and elements

o to evaluate the applicability of the beam theory and of numerical

methods

MANAGEMENT ENGINEERING STUDENTS

o to assess and compare independently the engineering solutions of a

problem with limited complexity

MECHANICAL ENGINEERING STUDENTS

o to assess and compare independently the engineering solutions of a

problem

o to analyze a problem related to solid and structural mechanics,

choosing autonomously the right approach and the appropriate tools for

its solution

• Communication skills

o to communicate effectively in written and/or oral form in the context of

solid and structural mechanics

MANAGEMENT ENGINEERING STUDENTS

o to know and know how to use the specific scientific / technical

terminology of solid and structural mechanics

MECHANICAL ENGINEERING STUDENTS

o to know and know how to use the specific scientific / technical

terminology of solid and structural mechanics, possibly also in English

o to be able to properly use the mathematical language to describe the

treated issues

• Learning skills

o to catalog, schematize and elaborate the acquired knowledge

o to correlate the different topics one other and with the basic and

related disciplines

o to autonomously use and apply the acquired knowledge

At the end of the course, students will have acquired the basic knowledge of the mechanics of deformable elastic bodies, with particular reference to the technical theory of beams.

The student will be able to perform the design and verification of some simple structural elements.

## Prerequisites

It is essential to have a basic knowledge of calculus, linear algebra,

physics and of solids and structural mechanics

It is essential to have a basic knowledge of calculus, linear algebra and physics.

## Course contents summary

The expertise are related with the study of the behavior of structures and

structural elements under the effect of various types of actions. In

particular, the course deepens issues treated in the courses “Structural

Mechanics” (for mechanical engineering students) and “Planning and

design of industrial components - module 2” (for management

engineering students), and addresses new issues.

The first part of the course is devoted to the study of Solid Mechanics,

and concerns stress and strain analysis and constitutive relations (linear

and nonlinear elasticity, elastoplasticity and viscoelasticity). The second

part is focused on Structural Mechanics. First, the theory of statically

determined and undetermined beams will be used to develop numerical

codes for the determination of the internal action diagrams and of the

elastic curve. The following issues will be the response of beam elements,

made of an elastoplastic material, under tension/compression, bending,

shear and torsion, the study of plane structural elements under in-plane

(membrane response) and out-of-plane (flexural response) loading, and

stability and buckling.

The last part of the course will be devoted to development, deepening

and implementation of different themes addressed during the course by

the students, through Project Works.

The expertise are related with the study and the use of theoretically mathematical and physical models describing the behavior of structures and structural elements under the effect of various types of actions. The course aims to provide a unified treatment of the main aspects of the mechanical behavior of structures, as well as the basic aspects of mechanical design.

## Course contents

1. Constitutive relations

1.1. Revision of analysis of Stress and Strain. Mohr’s circles, classification of stress states.

1.2. Constitutive models for engineering materials. Linear and non-linear elasticity, elasto-plasticity

1.3. Anisotropic materials

1.4. Viscoelasticity

2. Elastoplastic Analysis of beams

2.1. Axially Loaded Members. Plastic deformations

2.2. Pure Bending. Plastic deformations and residual stress. Plastic hinges. Moment-curvature relationship

2.3. Torsion. Plastic deformations and residual stress. Relationship between torque and angle of twist.

2.4. Shear

3. 2-dimensional flat elements

3.1. plane structural elements under in-plane loading. Plane stress state, Airy function

3.2. plane structural elements under out-of-plane loading (flexural response). Kirkhhoff-Love plate theories

3.3. tensioned membranes

4. Stability and buckling

4.1. Buckling of compressed elements. Euler’s critical load.

4.2. Structures with concentrated elasticity

4.3. Flexural and torsional instabilities. Local instabilities.

5. Development of numerical codes for the determination of the elastic curve

5.1. Introduction to matlab

5.2. Revision of Calculus of statically indeterminate structures, internal action relationships and diagrams, moment-curvature relationship, governing differential equation for the elastic curve.

5.3. Development of numerical codes (in Matlab) for the determination of the internal action diagrams

5.4. Development of numerical codes (in Matlab) for the determination of the elastic curve

## Recommended readings

F. P. Beer, E. R. Johnston, J. T. DeWolf, D. F. Mazurek, "Meccanica dei

solidi - Elementi di scienza delle costruzioni", MCGraw-Hill, 4° edizione (in

italian, available also in english).

Other suggested books:

• S. H. Crandall, N. C. Dahl, T. J. Lardner, “Introduction to the Mechanics

of Solids”, McGraw-Hill, 2° Edizione.

• O. Belluzzi, “Scienza delle Costruzioni”, Zanichelli (in italian).

F. P. Beer, E. R. Johnston, J. T. DeWolf, D. F. Mazurek, "Meccanica dei solidi - Elementi di scienza delle costruzioni", MCGraw-Hill, 4° edizione.

## Teaching methods

Lectures and exercises on the blackboard. As a rule, lectures will follow

as much as possible the recommended text. Homework exercises will be

assigned. The teaching material will be uploaded on Elly platform weekly.

In the second part of the course, student will be asked to autonomously

develop and deeply study issues related to solid and structural

mechanics, and/or to perform design exercises based on the content of

the course, with particular reference to mechanical and industrial

applications. This will be developed individually or in small groups (up to

3 students). The topics can be chosen by students from those proposed

by the teacher, or proposed by the students themselves. The teacher will

guide and support students at this stage. The report will be discussed in

the exam.

The teacher is available for clarification during office hours or by

appointment.

Lectures and exercises on the blackboard. As a rule, lectures will follow as much as possible the recommended text. Homework exercises will be assigned; clarification will be given during office hours.

## Assessment methods and criteria

The exam is based on

• a written test (lasting 2 hours), where the student will be asked to solve

a few exercises of the same type as those carried out in the classroom

during recitation. During the written test, the student can use calculator,

self- written formulary, as well as pens, pencils, etc. The evaluation is on

0-30 scale and students are admitted to the oral exam if at least 18

points are achieved. The marks will be published on Elly platform.

• an oral test, consisting in the discussion of the project developed by the

student (develop and deeply study of particular issues related to solid

and structural mechanics, and/or design exercises based on the content

of the course, with particular reference to mechanical and industrial

applications). During the oral examination will be verified that the student

knows and has successfully used the knowledge of the mechanics of

solids and structures, applied to a problem chosen by him/herself, and

can communicate procedures and obtained results properly using the

scientific/technic terminology. For teamworks, it will be verified that each

member of the group master all the work in its entirety and explicit parts

that he personally developed. The evaluation is on 0-30 scale and the

mark is communicated to the student at the end of the oral exam.

The final mark is the average of written and oral marks. “30 cum laude”

is given to students who achieve the highest score on each item and use

precise vocabulary.

The exam is based on a written test (the student will be asked to solve a few exercises of the same type as those carried out in the classroom during recitation) and an oral test, aimed at verifying the learning of the basic theoretical knowledge.

The possibility of replacing the oral examination with the presentation and discussion of a group project will be considered.