Structural Analysis I

Code:

EC0020

Acronym:

TEST1

Keywords
Classification	Keyword
OFICIAL	Structures

Instance: 2007/2008 - 1S

Active?	Yes
Web Page:	http://civil.fe.up.pt/pub/apoio/ano3/te/index.htm
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
LEC	0	Plano de estudos de transição para 2006/07	3	7	7	75	188
MIEC	330	Syllabus since 2006/2007	3	-	7	75	188
		Plano de estudos de transição para 2006/07	3	-	7	75	188

Teaching language

Portuguese

Objectives

Study of the principles of behavior of reticulate structures and development of the force and displacement method to calculate it.
Deepen the knowledge of hyperstatical structures behavior in linear regime.

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

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.

Evaluation Type

Distributed evaluation with final exam

Observations

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Working time estimated out of class: 4 hours