Structural Analysis I

Code:

EC0020

Acronym:

TEST1

Keywords
Classification	Keyword
OFICIAL	Structures

Instance: 2012/2013 - 1S

Active?	Yes
Web Page:	https://moodle.fe.up.pt/1213/course/view.php?id=541
Responsible unit:	Structural Division
Course/CS Responsible:	Master in Civil Engineering

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
MIEC	339	Syllabus since 2006/2007	3	-	7	75	188

Teaching language

Suitable for English-speaking students

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.

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.

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
“Bonfim Barreiros Method”
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 – Displacement Method
The displacement method as strength method’s dual method. Illustration by a simple example.
Direct formulation of the displacement method in the structure analysis.
Obtaining of configurations correspondent to null and unit displacement. Obtaining of an equation system. Determination of the final efforts.
Notion of stiffness matrix of a beam
Discussion of the minimum number of unknowns to consider in the base system set up.
Application of the displacement method in the case of structures with beams with despicable axial deformability. Use of the principal of virtual work to determine the fixation forces in structures with beams with despicable axial deformation
Determination of the mobility degree of a structure with beams with despicable axial deformation

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.
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

Distributed evaluation with final exam

Assessment Components

Description	Type	Time (hours)	Weight (%)	End date
Attendance (estimated)	Participação presencial	65,00
	Total:	-	0,00

Eligibility for exams

“Achieving final classification requires compliance with attendance at the course unit. 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.
The following cases are exempted from the attendance requirements: i) cases prescribed by law, including
student workers; ii) students who were admitted to exams in the previous academic year.”

Special assessment (TE, DA, ...)

Observations

........................................................
Working time estimated out of class: 4 hours

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.