Structural Analysis I

Code:

EC0020

Acronym:

TEST1

Keywords
Classification	Keyword
OFICIAL	Structures

Instance: 2011/2012 - 1S

Active?	Yes
Web Page:	https://moodle.fe.up.pt/1112/course/view.php?id=2533
E-learning page:	http://moodle.fe.up.pt/
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	316	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

Eligibility for exams

1. Students’ assessment will be based on a final exam. However, students can also do three exercises that will be taken into account on the final mark. These exercises are supposed to be done in an autonomous way. Students can also opt to do a presentation related with structural analysis.
2. These exercises should follow the following rules:
2.1. In the day that the exercises are delivered to the students, it will be scheduled a date when students should deliver them. Students should have a spare copy of the exercise, so that they can correct it later.
2.2. After everyone has delivered the exercises, the professors will provide a correction. Students should follow that correction and deliver it to the professor in the next practical class. Then professors will assess the exercise.
2.3. In the following classes questions related with the exercises may be asked.
2.4. These exercises can weight two values in the final mark for students with a mark of 10 or inferior to 10 out of 20. However, it may be proportionally reduced with the mark. It may have value of 0, if the mark of the final exam is 20 out of 20.
2.5. Students can earn two more values if they do the four exercises, and if they achieve a grade better than 90% in each of the exercises. On the other hand, students can lose two values, depending on the number of exercises delivered and their mark.
2.6. Students can lose two values if they have made a big mistake in the correction or in the assessment of their exercises and if they cannot justify their decisions (see 3).
2.7. At the end of the semester, students will know how much values they will earn.
3. A presentation of an assignment related with structural analysis will be valued with the maximum of two values. The assignments can cover a vast range of themes, namely the research of a subject, a structural analysis of a specific case and presentation and discussion of an engineering work. The professor should be informed about the theme of the assignment, and it will be supervised by the professor.
4. Students who want to earn a higher grade than 17 out of 20 have to attend to an oral exam.
5. Students who have attended to 75% of the theoretical classes will earn an extra value (exercises done).
6. Students have to reach a minimum grade of 7.5 out of 20 to complete the course.

Special assessment (TE, DA, ...)

In accordance with FEUP assessment regulations.

SPECIAL RULES FOR MOBILITY STUDENTS:
Proficiency in Portuguese or in English.
In the written exams, exercises ou practical works, mobility students may use one of the following languages: Portuguese, English, Spanish and French.

Observations

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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.