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Structural Mechanics

Code:

MEC134

Sigla:

ME

Áreas Científicas
Classificação	Área Científica
OFICIAL	Estruturas

Ocorrência: 2021/2022 - 1S

Ativa?	Yes
Unidade Responsável:	Mecânica e Estruturas
Curso/CE Responsável:

Ciclos de Estudo/Cursos

Sigla	Nº de Estudantes	Plano de Estudos	Anos Curriculares	Créditos UCN	Créditos ECTS	Horas de Contacto	Horas Totais
MEC	10	Study Plan	1	-	6,5	60	175,5

Língua de trabalho

Portuguese

Objetivos

The subject of Structural Mechanics is presented here through a modern approach that, giving the student a global and integrated view of the formal and practical aspects of discretization, both direct and indirect, to make him able to develop discrete models for the various physical systems, whose solution requires the application of the finite element method. These physical systems will fundamentally focus on elasticity problems of linear elastic behaviour. In terms of plastic behaviour, the plastic limit analysis of frames and slabs is a good complement to the previous knoweledge. Finally, the geometrically nonlinear problems of frame structures are addressed. During the training, the student will also have the ability to verify modeling errors and other types of custom errors in applying the software.

Resultados de aprendizagem e competências

The student's learning of the generic concepts of three-dimensional elasticity is fundamental for the use of the finite element method, namely the interaction between kinematic relations, equilibrium relations and material constitutive relations. Subsequently, the finite element method is progressively introduced, starting with one-dimensional elements (truss bar, beam, frame bar and column beam), up to two-dimensional elements (plane states of stress and deformation, slab, and joint elements). For each of the elements, the appropriate displacement approximation functions are adopted, gradually more complex and with their particularities, the constitutive relationships are considered according to the physical problem in question, and applying the Principle of Virtual Works, the balance is achieved. The entire approach will be made in a matrix form as it translates into greater versatility among the different types of finite elements discussed here. Naturally, the boundary conditions, rigid and elastic, will be discussed, the different types of actions will be modeled (load on the boundary and in the domain, support settlement, temperature and initial stresses). The student will be introduced to the h, p, r and adaptive refinement methods. The student will be alerted to the different types of errors in approximation, physical modeling, etc. The finite elements used have linear elastic behavior. In addition, the plastic analysis of frames and slabs, the kinematic, static and uniqueness theorems, the identification of critical sections, yield load and the various collapse mechanisms (multiple or partial) are treated. The matrix formulation will also be presented as it constitutes a good systematization of the methods. The geometrically non-linear analysis and Bifurcational Instability will be presented exclusively for application in planar reticulated structures. The structure of the curricular unit is coherent, given that there is an evolution in the topics presented, in terms of the complexity of elements, material behavior and geometric behavior. With this curricular unit, the student will acquire the necessary skills to use the finite element method and plastic limit analysis in the remaining curricular units within the scope of the theory of structures and structural design.

Modo de trabalho

Presencial

Programa

Plane Elasticity: Introduction to Elasticity. Plane States of Stress and Deformation; Finite Element Method: Introduction to the Method. Bar and two-dimensional elements. Matrix formulation. Approximation Functions. Plane Elasticity. Elastic supports. Settlements and Supporting Reactions. Inclined Supports. Formulation of slab elements;
Limit Plastic Analysis: Basic concepts: Critical Sections. Mechanisms. Yield, flow and parity conditions. Static and Kinematic Admissibility. Limit analysis theorems. Statically and kinematically admissible solutions. Matrix formulation. Multiple and partial mechanisms. Interaction of efforts. Application in 2D frames and slabs;
Geometrically Nonlinear Analysis and Bifurcation Instability: Limit Point Instability. Geometrically non-linear analysis of plane lattice structures. Critical load.

Bibliografia Obrigatória

Docentes; Apontamentos dos docentes
Francisco Virtuoso; Análise Plástica Limite, 2008
Luis Castro; Elementos Finitos para Análise Elástica de Lajes, 2007
Orlando Pereira; Introdução ao Método de Elementos Finitos, 2005

Bibliografia Complementar

Portela, A., Charafi, A.; Finite Elements Using Maple –A Symbolic Programming Approach, 2002
G. Kennedy, C.H. Goodchild; Practival Yield Line Design, 2004

Métodos de ensino e atividades de aprendizagem

Presentation of classes using PowerPoint slides, which are provided at the beginning of the week in a pdf file to students. The theoretical presentation of each theme is followed by the exemplification with an exercise already solved. Autonomous resolution of other exercises using programs (e.g. SAP2000).

Software

SAP 2000

Tipo de avaliação

Distributed evaluation with final exam

Componentes de Avaliação

Designation	Peso (%)
Teste	50,00
Trabalho escrito	50,00
Total:	100,00

Componentes de Ocupação

Designation	Tempo (Horas)
Frequência das aulas	52,50
Trabalho escrito	61,50
Estudo autónomo	61,50
Total:	175,50

Obtenção de frequência

Not applicable

Fórmula de cálculo da classificação final

Continueous Ev.: 50% Test + 50% Written report
Exam 1st/2nd season: 100% Exam
Special season exam: 100% Exam