Structural Analysis

Recommended Prerequisites

Linear Algebra and Analytic Geometry

Mathematical Analysis I and II

Numerical methods

Mechanics II

Continuum mechanics

Strength of Materials I and II.

Teaching Methods

The traditional blackboard lecture style is used for (1) the motivation and detailed exposition of the fundamental ideas, concepts and methods and (2) the application and illustration of the theory, by discussing the specific provisions and by working through selected examples in detail. The student is then expected to solve, under the supervision of the instructor, a collection of systematically arranged problems; the aim is (1) to suggest to him useful lines of disciplined thought in dealing with more complex problems and (2) to promote his autonomy.

Learning Outcomes

Requirements of new knowledge and capacity of understanding:

1. Understanding the basic assumptions adopted in the quasi-static linear analysis of structures

2. Understanding the main types of quasi-static actions on a structure, their modeling and effects

3. Understanding the fundamental variables of a structural problem

4. Understanding the physical meaning of the analysis procedures

5. Understanding the main characteristics of linear structural behavior

6. Understanding of structural models as physical models of reduced spatial dimension

7. Understanding the discrete nature of the models for skeletal structures

Application of new knowledge:

1. Calculation of fields of internal forces, generalized strains and displacements in the linear analysis of skeletal structures

Critic reflection / analysis:

1. Selection of the most appropriate analysis methods for a given practical application

2. Qualitative evaluation of the computed solutions.

Work Placement(s)

No

Syllabus

A) Linear elastic analysis of plane skeletal structures

1. Linear statics

1.1 Classification of the structures with respect to the type of the system of equilibrium equations

1.2 Static indeterminacy

1.3 Equilibrium relations (general solution). Isostatic bases

2. Linear kinematics

3. Force method

3.1 Generalized strains and elasticity relations

3.2 Work theorem and virtual work – compatibility relations

3.3 Calculation of displacements

3.4 Canonical equation of the force method

4. Displacement method

4.1 Discrete formulation for planar one-dimensional elements

4.2 Kinematical indeterminacy

4.3 Canonical equation of the displacement method

4.4 Potential energy

4.5 Internal constraints

5. Influence lines

B) Linear analysis of thin slabs – Kirchhoff’s theory

1. Hypotheses

2. Displacement field and generalized strains

3. Internal forces. Equilibrium relations and elasticity relations

4. Germain-Lagrange equation. Boundary conditions

5. Potential energy

6. Ritz method.

Head Lecturer(s)

Anísio Alberto Martinho de Andrade

Assessment Methods

Assessment
Frequency: 100.0%

Bibliography

[1] P. Providência e A. Andrade, Apontamentos de Teoria das Estruturas I, Universidade de Coimbra, 2019

[2] P. Providência e A. Andrade, Resolução de Provas de Teoria das Estruturas I, Universidade de Coimbra, 2018

[3] J.A. Teixeira de Freitas e C. Tiago, Análise Elástica de Estruturas Reticuladas, Universidade de Lisboa - IST, 2019

[4] V. Dias da Silva, Mechanics and Strength of Materials, Springer, 2005

[5] I. H. Shames e C. L. Dym, Energy and Finite Element Methods in Structural Mechanics, Taylor & Francis, 1985

[6] A. Borkowski, Analysis of Skeletal Structural Systems in the Elastic and Elastic-Plastic Range, Elsevier, 1988

[7] E. Arantes e Oliveira, Elementos da Teoria da Elasticidade, IST Press, 2008.