Structural Analysis

Code:

L.EC021

Acronym:

TE

Keywords
Classification	Keyword
OFICIAL	Structures

Instance: 2021/2022 - 1S

Active?	Yes
Web Page:	https://moodle.up.pt
Responsible unit:	Structural Division
Course/CS Responsible:	Bachelor in Civil Engineering

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
L.EC	174	Syllabus	3	-	6	65	162

Teaching language

Portuguese and english
Obs.: Turma em Inglês prevista

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

Presencial

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

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.

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 – Calculation of displacements
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 – 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.

Chapter 5 – Energy Theorems
Introduction to Energy Theorems.
Strain energy and virtual work.
Strain energy due to a system of loads. Derivation of the theorem of virtual work.
Derivation of the theorem of Betti. Maxwell’s reciprocal theorem (1st and 2nd consequences of the theorem of Betti).
Derivation 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 6 - Symmetry Simplifications
Analysis of symmetric structures. Definition of symmetric structure and of symmetric and anti-symmetric loading.
Analysis of symmetric structures. Behaviour of symmetrical structures subject to symmetrical and anti-symmetrical loading.
Symmetry simplifications.
Exercises.

Chapter 7 – Influence lines
Definition 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.  

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

Ghali, A.; Structural analysis. ISBN: 0415280923

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. 

DEMONSTRATION OF THE COHERENCE BETWEEN THE TEACHING METHODOLOGIES AND THE LEARNING OUTCOMES:

The teaching methodologies allow 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.

keywords

Technological sciences > Engineering > Civil engineering

Evaluation Type

Distributed evaluation with final exam

Assessment Components

Designation	Weight (%)
Exame	70,00
Teste	25,00
Trabalho laboratorial	5,00
Total:	100,00

Amount of time allocated to each course unit

Designation	Time (hours)
Estudo autónomo	97,00
Frequência das aulas	62,00
Trabalho laboratorial	3,00
Total:	162,00

Eligibility for exams

Achieving final classification requires compliance with attendance at the course unit, according to the MIEC assessment rules. A student is considered to attend a course if, having been regularly enrolled, he/she does not exceed the limit number of absences, corresponding to 25% of the number of presential classes planned.

Calculation formula of final grade

The final classification is defined based on a distributed assessment and a final exam. The distributed assessment, which consists of an exam to be carried out during the term and one laboratory assignment, is optional.

All assessment components are expressed on a scale of 0 to 20.

1. The final grade, CF, results from the following calculation formula:

CF = max {pPAD x cPAD + pTPL x cTPL + pEF x cEF ; cEF}

where

cPAD - grade obtained in the exam carried out during the term;
cTPL – classification obtained in the laboratory assignment;
cEF - grade obtained in the final exam.

The grades cPAD, cTPL and cEF are associated with the following weights:

pPAD = (25%)
pTPL = (5%)
pEF = (70%)

NOTE 1: All students enrolled in the course are graded according to this method.

NOTE 2: The grade associated with the distributed assessment obtained in previous years will not be considered in the current academic year.

NOTE 3: A grade higher than 17/20 can only be obtained after an oral examination.

2. Procedure for distributed assessment during the semester 

2.1. Distributed assessment exam

The distributed assessment exam will be conducted on the Moodle platform. This will be carried out according to the following rules:

a) The exam will last, at most, 50 minutes.

b) The exam will consist of theoretical and practical questions related to the topics covered until that date and will be conducted without any consultation of lecture notes (except tables and formula sheet).

2.2. Laboratory assignment

The laboratory assignment will be conducted by groups consisting of a maximum of 3 students and involves carrying out a laboratory test and the writing of a report.

Observations

English class - Mondays at 9:30: https://videoconf-colibri.zoom.us/j/83366565869?pwd=K2N6YnRqdm1NaS9rRjN3L01IRjd2Zz09

English class - Wednesdays at 10:00: https://videoconf-colibri.zoom.us/j/87157406694?pwd=WHc4Qkhsc2s4ZElReG1wUVlZaUkwZz09