6 credits during the 2nd year of 8694 Sciences of architecture (L-17) GENOVA

**Sciences of architecture 8694 (coorte 2019/2020)**- MATHEMATICS 1 56394

## OVERVIEW

This is the first course introducing the Students to the engineering structures and to their behavior, namely the way they support the applied loads. One aim is to make the Students aware of the key role of structural engineering in different branches of engineering. The goal of the course is understanding the behavior of the structures made up of rods and beams, including frames and trusses, through the quantitative and qualitative descriptions, a process that will be completed in Module 2.

## AIMS AND CONTENT

LEARNING OUTCOMES

This is the first course that introduces the Students to the engineering structures and to their behavior, namely the way they support the applied loads. One aim is to make the Students aware of the key role of structural engineering in different branches of engineering. The main goal of the course is understanding the behavior of the structures made up of rods and beams, including frames and trusses, through the quantitative and qualitative descriptions, a process that will be completed in Module 2. The mentioned goals will be pursued according to the engineering approach based on the identification and adoption of structural quantitative model, to be applied as basic tool for the structural design. The model is conceived as a rigorous conceptual tool, mathematically based, able to relate causes and effects, applied forces, internal forces, structural displacements. The student will be acquainted that structural model representative of the construction and its structure has to be obtained through simplifying hypotheses concerning the mechanical description of the empirical behavior of single structural members and of structural assemblages.

AIMS AND LEARNING OUTCOMES

At the end of the course Students should be able to:

- Analyze the equilibrium of restrained rigid bodies, beams, frames, trusses, and their classification as statically determinate/indeterminate or statically impossible systems;
- Determine the reaction forces in statically determinate beams, frames and trusses together with the representation of the free body diagram;
- Determine the axial and shearing forces and bending moment at any section and construct the diagrams of internal forces for statically determinate beams, frames with internal partial releases and to explain the relationship between them;
- Determine the axial forces in statically determinate trusses;
- Make use of the structural symmetry and of the principle of superposition when appropriate to obtain the above mentioned statical data;
- Determine the deflection of elastic beams due to applied loads, thermal loads and support settlement; explain curvature and how it changes in an elastic beam when bending changes;
- Determine the displacement or rotation at a section of a statically determinate beam, frame or truss due to generalized applied forces, thermal loads, support settlement; understand the application of the equation of virtual work; explain the deformed configuration of beams and frames on account of the curvature within it;
- Solve statically indeterminate structures through the force method to obtain reactions, internal forces, displacements and qualitative deformation of the structure.

TEACHING METHODS

The course is taught through lectures explaining the basic principles and theory of the discipline. Exercises are focused on practical topics presented in lectures.

This course is taught in Italian. The final oral exam may be given in English. The students who would like to be examined in English must inform the teacher.

SYLLABUS/CONTENT

**1. Introduction and Aims of the Course**

**2. Equilibrium of points and rigid bodies: **

Forces, moments and couples; resultants; static equivalence of systems of generalized forces; distributed forces, pressure and hydrostatic loads;

Equations of equilibrium of points and rigid bodies; constrained rigid bodies: supports and reaction forces;

The equilibrium of constrained rigid bodies; discussion on the efficiency of the constrains: statically determinate/indeterminate bodies, statically impossible systems;

Statically determinate rigid bodies: evaluation of the reaction forces;

**4. Statically determinate beams, frames and trusses**

The structural model of straight beam; generalized applied forces; supports and reactions; equilibrium equation of the in-plane loaded beam; static discussion on the efficiency of the supports; evaluation of the reaction forces;

Internal forces in the beam: axial, shearing forces and bending moment; the diagrams of the internal forces; local equation of equilibrium; plane frames and internal releases; static equation of the release; multiple connected structures; plane trusses: the method of joints and the method of sections (Ritter);

**5. Elastic beam and frames**

The in-plane deformation of beams; displacements; the strain measures: elongation, shearing and curvature; the equation of compatibility; constitutive equations: experiments and definitions;

The displacement formulation of the equilibrium of the elastic beam: the Timoshenko and the Euler-Bernoulli models; the differential equations of the deflection curve; the effect of support settlement on statically determinate and indeterminate beams and frames; the analogy of O. Mohr to evaluate generalized displacement of statically determinate beams;

The virtual work theorem; thermal effects on the deformation of beams; qualitative description of the deformed configuration of beams and frames from the diagram of the curvature; evaluation of displacements in plane trusses;

How to simplify the structural analysis taking into account the structural symmetry and the principle of superposition for linear systems;

**6. Statically indeterminate structures**

Evaluation of the grade of redundancy of frames and trusses; the force method to solve in-plane loaded statically indeterminate structures; the equations of Muller-Breslau; the effects of thermal variation and support settlement on the statics of redundant beams, frames and trusses; symmetric structures.

RECOMMENDED READING/BIBLIOGRAPHY

L. Gambarotta, L. Nunziante, A. Tralli. Scienza delle Costruzioni, 3a Edizione, McGraw-Hill, 2011.

## TEACHERS AND EXAM BOARD

**Office hours:** Monday 8.30-10.00 at the Teacher's office DAD Santa Croce building

Exam Board

LUIGI GAMBAROTTA (President)

ANDREA BACIGALUPO

GIUSEPPE PICCARDO (President Substitute)

## LESSONS

TEACHING METHODS

The course is taught through lectures explaining the basic principles and theory of the discipline. Exercises are focused on practical topics presented in lectures.

This course is taught in Italian. The final oral exam may be given in English. The students who would like to be examined in English must inform the teacher.

Class schedule

## EXAMS

EXAM DESCRIPTION

The exam consists of a written and an oral test. Furthermore, during the Course, there will be two written tests. The students that will pass them, will be enabled to access directly the oral exam.

ASSESSMENT METHODS

The written test is based on the resolution of problems similar to those carried out during the course. In such a test is proven the ability to solve three problems. In the oral exam is assessed the understanding of the concepts and reasoning skills acquired by the students and the knowledge of the theoretical part of the program.

The exams are given in Italian. The final oral exam may be given in English. The students who would like to be examined in English must inform the teacher.

Exam schedule

Date | Time | Location | Type | Notes |
---|---|---|---|---|

13/01/2021 | 08:30 | GENOVA | Scritto | |

10/02/2021 | 08:30 | GENOVA | Scritto | |

12/04/2021 | 08:30 | GENOVA | Scritto | |

15/06/2021 | 08:30 | GENOVA | Scritto | |

06/07/2021 | 08:30 | GENOVA | Orale | |

13/07/2021 | 08:30 | GENOVA | Scritto | |

20/07/2021 | 08:30 | GENOVA | Orale | |

07/09/2021 | 08:30 | GENOVA | Scritto |