Structural Analysis I

Instance: 2013/2014 - 1S

Cycles of Study/Courses

Last updated on 2013-10-17.

Fields changed: Objectives, Resultados de aprendizagem e competências, Métodos de ensino e atividades de aprendizagem, Componentes de Avaliação e Ocupação, Obtenção de frequência, Programa, Observações, Fórmula de cálculo da classificação final

Teaching language

Objectives

OBJECTIVES:
Study the principles of frame structures behavior and development of the method of forces and displacements for their calculation. Increasing knowledge on the behavior of statically indeterminate structures in the linear regime. Study of energy theorems. Determination of influence lines in frame structures.

Learning outcomes and competences

SKILLS AND LEARNING OUTCOMES:
Knowledge: Identify different types of structural solutions to characterize the distribution and displacements and internal forces, due to static loads in framed structures with linear behavior and interpret the results obtained from the application of the structural analysis methods.

Working method

Program

Chapter 1 – Introduction
Objectives of Structural Analysis.
The structural problem.
Presentation and discussion of structural solutions.
General hypothesis of the structure analysis.
Structural types.
External demands/ solicitations.
Displacements, distortions and tensions.
Relations between tensions deformations.
Equilibrium relations.
Superposition-of-effects principle
General aspects of the strength method.
Chapter 2 – Displacement calculation
Theorem of virtual work
Calculation of the distortion internal work
Displacements calculation using the theorem of virtual work
Example of the displacement calculation using the theorem of virtual work. Method of Verchaguyne or method of Bonfim Barreiros 
Chapter 3 – Force method
Structural hiperestaticity degree. Internal and external hiperestaticity.
Presentation and systematization of the force method.
Final efforts in hyperstatic structures.
Calculation of displacements in hyperstatic structures using the theorem of virtual work.
Structures subject to the settlement of support and elastic support.
Relative importance of the bending part due to transversal moments and efforts.
Effect of temperature variations in structures.
Uniform and differential variations.
Evaluation of the hyperestaticity by direct inspection and a number of equilibrium equations.
Mixed structures.
Symmetrical structures with symmetrical and anti-symmetrical action. Symmetrical structures with any charge. Decomposition of a charge in a symmetrical and anti-symmetrical part.
Chapter 4 – Energy Theorems
Introduction to Energy Theorems
Distortion energy and virtual work.
Distortion energy due to a charge system. Deduction of the theorem of virtual work.
Deduction of the theorem of Betti. Maxwell’s reciprocal theorem (1st and 2nd consequences of the theorem of Betti).

Deduction of the theorem of Castigliano and its inverse. Physical interpretation of the theorem and its application to the structure analysis.
Third consequence of the Theorem of Betti. Determination of displacements in hiperestatical structures using the theorem of Castigliano.
Chapter 5 – Influence lines
Notion of influence line.
Determination of influence lines of reactions of support in isostatic structures.
Determination of influence lines of transversal efforts and bending moments in isostatic structures.
Determination of efforts in structures by influence lines
Influence lines in hyperstatic structures.

Chapter 6 – The Displacement Method to solve statically indeterminate structures
The displacement method as a dual method with respect to the Force Method. Illustration by a simple example.
Direct formulation of the displacement method in the analysis of structures.
Obtaining the configurations corresponding to null and unit displacement. Obtaining the system of equilibrium equations. Determination of the final reactions and member stress resultants; final diagrams of member generalized efforts.
Inclusion of elastic supports and settlements. Systematization of the displacement method. Solving a real pedagogic example.
Notion of stiffness matrix of a frame uniform member and transformation matrix of nodal coordinates; transformation matrix of nodal displacements and efforts of any bar of a framed plane structure, from the system of local axes to the global axis system.
Determination of efforts on the bars in the context of the displacement method, using the stiffness matrix of the bar.
General matrix formulation of the displacement method for solving planar frame structures. Grouping or assembling the stiffness matrices of the bars.
Matrix formulation of the displacement method for planar articulated structures.
Matrix formulation of the displacement method for structural grids.
Systematization of the matrix formulation of the displacement method.
Study of three-dimensional structures constituted by framed and hinged bars. Presentation of the corresponding matrix formulation.
Aspects of automatic calculation of structures. General scheme of a computer program.

Scientific content - 80%

Technological content - 20%

DEMONSTRATION OF THE SYLLABUS COHERENCE WITH THE CURRICULAR UNIT'S OBJECTIVES:
For the elaboration of structural projects is necessary to evaluate the stresses and strains distribution, due to actions proposed by codes, at all points of the structures in order to compare them with established limits. To determine stress and strain states is necessary to know the methods of structural analysis for the various types of structures and structural elements.

Mandatory literature

Teaching methods and learning activities

Presentation and discussion of all the contents in theoretical classes along with simple illustrative problems. In theoretical-practical classes is proposed and discussed a set of applications associated to theoretical issues. Four complementary individual exercises will be proposed and evaluated.

DEMONSTRATION OF THE COHERENCE BETWEEN THE TEACHING METHODOLOGIES AND THE LEARNING OUTCOMES:
The teaching methodologies permit to use methods of structural analysis to calculate the displacements and internal forces of frame structures, discuss and criticize the results of the calculation of structures in order to validate the calculation process, propose, for the methods of the forces and displacements, efficient base systems and according to the obtained results structural variants with improved behaviour.

Evaluation Type

Assessment Components

Eligibility for exams

Achieving final classification requires compliance with attendance at the course unit, according to the MIEC assessment rules. It is considered that students meet the attendance requirements if, having been regularly enrolled, the number of absences of 25% for each of the classes’ types is not exceeded.

Calculation formula of final grade

Observations

Working time estimated out of class: 4 hours

Pre-requisite knowledge: Fundamental equilibrium principles from Mechanics of Rigid Bodies statically determinate. Analysis and behaviour of statically determinte linear elastic deformable structures under actions, as presented in Strength of Materials or Mechanics of Solids or Deformable Materials, namely the determination of stresses (normal and tangencial) deformations (extensions and distortions) and generalized displacements.