## 21010036-1 - SOLID MECHANICS

Knowledge of the qualitative behavior and relative mathematical modeling of several structures: 2D and 3D frames, 2D and 3D pin-jointed trusses, shear-type frames and Vierendeel beams, Grid of beams under bending, arches, walls and load bearing partitions. Setting up a preliminary structural project. Notes on the classification, resistance and deformability of geotechnical materials.

Canali

teacher profile | teaching materials

Programme

1. Introductory classes
Introduction to structural design:
a) systems with simply or multiple supported span,
b) systems with structural overhang,
c) the structure of a multi-storey building.

2. Solid mechanics and beam model.
Statically determinate beam systems.
The Cauchy stress.
Introduction to mechanics of materials: steel, wood, reinforced concrete, glass. Characteristics strength and design strength. Basic concepts: elasticity and inelasticity, isotropy and anisotropy, fragility and ductility.
Bernoulli’s beam model and displacement fields in elastic beams.

3. Between Structural Mechanics and Structural Design.
Loads on structural elements: area of influence of a beam and a pillar.
Preliminary design of beams and a pillars. Stress and displacement analysis of simple beams, design checks. Cantilevers with variable section.
Design of a steel truss in 3D.
Statically indeterminate structures framed resolution methods: integration of the elastic line, force method and stiffness method. Features and benefits of the three methods. Applications of the force method and of the stiffness method. Shear-type frames – Vierendeel beams. Bracing systems: concepts and comparisons. The centre of a system of parallel vectors. The stiffness centre of a braced deck. Grid of beams under bending. Arches: circulars, parabolic. Concept of funicularity. Arch thrust and thrust elimination methods.
Introduction to 3D frames. Center of rigidity. Center of mass.
Introduction to structural dynamics. Resonance. Introduction to modal analysis. Applications to the preliminary design of framed structures.

4. Lessons of the software SAP2000 for modeling and analysis of the structures presented in the course.

Core Documentation

for the theoretical part of strength of materials:
Capecchi D., "Scienza delle Costruzioni", Ed. CISU, 1995 (in Italian)

for the structural design part:
Schodek D.L., “Strutture”, 4a ed., Patron Ed., Bologna, 2008 (in Italian)
Sandaker B.N., Eggen A.P., Cruvellier M.R., “The structural basis of architecture”, 2nd ed., Routlege, Taylor and Francis, 2011

course website from which students can download additional teaching material and perform the delivery of the assigned homework:

Reference Bibliography

Any additional teaching material will be indicated by the teacher during the classes and it will be pubblished on course website: https://sites.google.com/view/meccstru-r3

Type of delivery of the course

The course is developed through lectures, work and structural-design reviews and specific seminars. Two software for structural modeling will be explained and used. The Mathematica software for the qualitative solution of the problems related to the theoretical part. This tool allows students to understand the proposed physical-mathematical models as well as focus on the conceptualization of a structural problem. The SAP2000 software will be used to conceptualize and implement a structural model of the architectural project, and to evaluate the numerical response, once the design loads have been defined. This allows students to have a tool for the design of structural elements.

Attendance

students who do not have at least 75% attendance will not be admitted to the final exam. The attendance is verified in class by the teacher

Type of evaluation

Three/Four individual homework are assigned during the course, to be delivered in written form and for which each student will be evaluated. The oral exam will focus on the theoretical topics, developed in class, and on the discussion of the project. The final project concerns the structural modeling and study of a selected part of an architectural project, in agreement with the teacher. It is delivered with drawings and a small report on the numerical model and structural analysis. Instructions for exams in remote mode: - the final project will be delivered in PDF format within the day before the exam. - The exam is carried out as an individual remote meeting with Microsoft Teams or other video conferencing platform. - It is necessary for the student to be able to share the screen, in order to show (if required) the ability to use the SAP2000 software and the Mathematica software. He / she must also be able to show (live streaming - with any useful platform, or by writing on a graphic tablet) a blank sheet on which he / she writes and explains the formulations required for the theoretical part, draws the structural schemes useful for the discussion and possibly draw analytical diagrams (deformed configurations and stress diagrams).

teacher profile | teaching materials

Programme

1. Introductory classes
Introduction to structural design:
a) systems with simply or multiple supported spans;
b) systems with structural overhang;
c) the structure of a multi-storey building.

2. Solid mechanics and beam model.
Statically determinate beam systems.
The Cauchy stress.
Introduction to mechanics of materials: steel, wood, reinforced concrete, glass. Characteristics strength and design strength. Basic concepts: elasticity and inelasticity, isotropy and anisotropy, fragility and ductility.
Bernoulli beam model and displacement fields in elastic beams.

3. Between Structural Mechanics and Structural Design.
Loads on structural elements: area of influence of a beam and a pillar.
Preliminary design of beams and a pillars. Stress and displacement analysis of simple beams, design checks. Cantilevers with variable section.
Design of a steel truss in 3D.
Statically indeterminate structures framed resolution methods: integration of the elastic line, force method and stiffness method. Features and benefits of the three methods. Applications of the force method and of the stiffness method. Shear-type frames – Vierendeel beams. Bracing systems: concepts and comparisons. The centre of a system of parallel vectors. The stiffness centre of a braced deck. Grid of beams under bending. Arches: circulars, parabolic. Concept of funicularity. Arch thrust and thrust elimination methods.
Introduction to 3D frames. Center of rigidity. Center of mass.
Introduction to structural dynamics. Resonance. Introduction to modal analysis. Applications to the preliminary design of framed structures.

4. Lessons of the software SAP2000 for modeling and analysis of the structures presented in the course.

Core Documentation

The course lecture notes can be found on the interactive portal http://design.rootiers.it/strutture/. The minimum list of these notes to be studied is the following:

1. Basics of the three-year degree:
Forze_e_asse_centrale.pdf
Vincoli monolateri.pdf
Sezioni di Ritter.pdf
travi isostatiche_richiami.pdf
tensione_dimensionamento_trave_part I.pdf
tensione_dimensionamento_trave_part II.pdf

2. Hyperstatic structures and arches:
11.metodo degli spostamenti_richiami.pdf
linea elastica.pdf
il metodo delle forze.pdf
sul concetto di rigidezza e sul metodo.pdf
dispensa archi corretta 20_06_2013.pdf

3. Structural morphology:
Ad astra per aspera- Si fa presto a dire aggetti.pdf
Gli edifici non volano-1.pdf
Gli edifici non volano-2.pdf

4. SAP2000:
Sap2000.pdf

In addition, there is a list of online videos on the YOUTUBE platform, in the two channels "Portale di Meccanica" (42 videos) and "Corso di recupero di Meccanica Strutturale" (7 videos).

and also two online versions of the course on the YOUTUBE platform.

Reference Bibliography

Schodek D.L., “Strutture”, 4a ed., Patron Ed., Bologna, 2008 Sandaker B.N., Eggen A.P., Cruvellier M.R., “The structural basis of architecture”, 2nd ed., Routlege, Taylor and Francis, 2011

Type of delivery of the course

The course consists of lessons, exercises and design applications. The lessons are ex-cathedra, the exercises and the design applications are guided by the teacher and the assistant teacher. The course also consists of a part of recovery of the contents of structural mechanics of the three-year degree. This content is retrieved through distance learning, with the help of two YouTube Channels, named as "Portale di Meccanica" and "Corso di recupero di Meccanica Strutturale".

Attendance

Attendance of the course is mandatory, because most of the work is done in the classroom, especially in relation to the design exercises. Mandatory attendance means attendance of at least 75% lessons.

Type of evaluation

1. How to carry out the exams in the traditional way (in presence): The exam consists of three tests: a) a discussion on structural design choices, carried out through the examination of graphic designs and a short technical report; b) a practical test of the detailed knowledge of SAP2000, of its modeling skills, but also of the reading and interpretation of the results produced by the software; c) an oral test, on the theoretical contents of the course, with exercises performed on the impression and theoretical demonstrations carried out with symbolic language. 2. How to carry out the exams remotely in the event of a health emergency (on the Teams platform): a) for discussion on the project, direct via Teams with screen sharing, if the connection allows it. Where it is not possible, the project is sent two days before to the teacher, or is uploaded to the web 2.0 mechanical portal (http://design.rootiers.it/strutture/), and its evaluation weighs 1/3 of the evaluation. overall exam; b) the practical test of knowledge of SAP2000 is carried out with screen sharing via Teams and the evaluation of this test weighs for one third of the exam; c) the oral test is an individual test and is carried out with the joint use of teams and whatsapp in camera mode, and its evaluation weighs a third in the overall assessment of the exam.