Structural Mechanics

Code:

L.EM022

Acronym:

ME

Keywords
Classification	Keyword
OFICIAL	Applied mechanics

Instance: 2022/2023 - 1S

Active?	Yes
Responsible unit:	Applied Mechanics Section
Course/CS Responsible:	Bachelor in Mechanical Engineering

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
L.EM	261	Syllabus	3	-	6	52	162

Teaching language

Portuguese

Objectives

Analysis and dimensioning structures: beams, trusses and reticulate structures. The determination of internal forces, stresses and deformation allows the validation of the structural system proposed. First determinate structures are treated and then appropriate approaches for the analysis of redundant structures. Section Design in steel structures using Ultimate Stress and Ultimate Service Criteria.
Analysis of structures using numerical methods and based on the mechanics of solids.
Specific goals: to know, to understand and to analyse the Displacement Method and the Finite Element Method (formulated based on the displacement methods) applied to solving analysis problems of elastic linear structures. It is assumed that the students should be acquainted with the principles of Displacement method and be capable of using on a spreadsheet the stiffness matrix and the solicitation vector of a structure under the action of several types of loading. Students should also know how to introduce boundary conditions that simulate the connections to the exterior of a structure and to determine the nodal displacement vector. And should also know how to calculate the stress that act on critical sections of a structure. By the end of the semester, students should be acquainted with the principles of the Finite Element Method, be capable to establish the stiffness matrix and the solicitation vector of a finite element, isoparametric (with triangular or quadrangular geometry), with a linear/quadratic approximation, to analyse linear elastic structures. From the nodal displacements, be capable of calculating: deformations and stresses in the interior of a finite element.

 

Learning outcomes and competences

Students must acquire skills to carry out analysis and design of structures.

Working method

Presencial

Pre-requirements (prior knowledge) and co-requirements (common knowledge)

Knowledge of Statics (static equilibrium, reactions, stress diagrams) and concepts of Elasticity Theory (Stress and Deformation Tensor), the relationship between internal stresses and stresses for simple loads are essential.

Program

- Column Stability. Critical buckling load (Euler Problem). Design of steel sections subject to axial compressive loading by using the European Rules.

- Static Equilibrium in determinate structures; Reaction and internal forces, shear force and bending moment diagrams in beams and planar frames. Analysis of planar trusses.

- Energy theorems: Deformation Energy, Virtual Work theorem. Principle of complementary virtual work. Unit load method.

- Force Method. Coefficient of flexibility, canonical equation, symmetry simplification.

- Displacement Method: Theoretical principles, stiffness coefficients and stiffness matrices. Stiffness matrix of a beam in local and global axis. Assembly of elementary stiffness matrices; solicitation vector. Resolution of global system of equations.

- Finite Element Method: Overview; discrete and continuous problems. Linear elastic analysis by using the finite element method (FEM). Equilibrium of a 2D domain; decomposition in three node triangular elements; displacement fields, stress fields. System of nodal forces, equilibrium of the finite element; equilibrium of the whole domain. Interpolation functions and shape functions. Deformation matrix (B), elasticity matrix (D), stiffness matrix (K), solicitation vector. Parametric transformation: isoparametric elements, numerical integration.

Mandatory literature

Carlos Reis Gomes; Mecânica das Estruturas, 2010
Filipe Miguel Horta e Vale Teixeira-Dias; Método dos elementos finitos. ISBN: 978-972-8480-25-7

Complementary Bibliography

Beer, Ferdinand P.; Resistência dos materiais. ISBN: 85-346-0344-8
A. Ghaly and A. M. Neville; Structural Analysis , Chapman & Hall
António Joaquim Mendes Ferreira; Problemas de elementos finitos em MATLAB. ISBN: 978-972-31-1329-7

Teaching methods and learning activities

Theoretical presentation of themes and subjects followed by a set of examples to be solved and discussed.
The sessions are of2h+2h per week.

Software

MATLAB

keywords

Technological sciences > Engineering > Civil engineering > Structural engineering

Evaluation Type

Distributed evaluation with final exam

Assessment Components

Designation	Weight (%)
Exame	50,00
Teste	50,00
Total:	100,00

Amount of time allocated to each course unit

Designation	Time (hours)
Estudo autónomo	102,00
Frequência das aulas	60,00
Total:	162,00

Eligibility for exams

According to General Evaluation Rules of FEUP.

Calculation formula of final grade

The evaluation is based on two exams of equal weight (50% each one):

-one will be held during the semester and it will be related with the first part of contents,
-another one to be performed in January exclusively containing the second part of the contents.

In each of these assessments will be a minimum grade of 6.5 values.

The students:

-that have not gotten an average of 10;

-that have obtained a final average of 10, but have not obtained the referred minimum grade (6.5);

-that have missed at least one of the assessments,

may perform the appeal examination that will evaluate all the contents of the CU.

Students with a final classification greater than 17 on the written examination can be subjected to an oral exam.

 

Special assessment (TE, DA, ...)

These kind of evaluation will be obtained with a final exam.

Classification improvement

Students who which to improve their mark are allowed an “appeal Exam”, according to General Evaluation Rules of FEUP.