Structural Analysis

Code:

L.EC021

Acronym:

TE

Keywords
Classification	Keyword
OFICIAL	Structures

Instance: 2025/2026 - 1S

Active?	Yes
Web Page:	https://moodle.up.pt
Responsible unit:	Department of Civil and Georesources Engineering
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	157	Syllabus	3	-	6	65	162

Teaching language

Portuguese

Objectives

JUSTIFICATION: For the execution of structural design in construction projects, it is necessary to predict the distribution of deformations and stresses, caused by regulatory actions, at all points of the structures in order to compare them with limit values. To determine the state of stress and deformation, it is essential to master the methodologies of structural analysis for various types of structures and structural elements.

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.

Comprehension: Identify the steps of structural analysis methods, the force method, and the displacement method, to be adopted for different types of structural solutions.

Application: Use structural analysis methods to calculate displacements and forces in frame structures.

Analysis: Discuss and critique the results of the structural calculations with a view to validating the calculation process.

Synthesis: Propose efficient base systems within the framework of the force and displacement methods, and based on the results, find structural variants with better performance.

Engineering Design: Analyze real structures in order to align the structural models with scenarios that closely resemble design conditions.

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
1.1. Objectives of Structural Analysis.
1.2. The structural problem. Presentation and discussion of structural solutions.
1.3. General hypothesis of the structure analysis. Structural types.
1.4. External demands/ solicitations. Displacements, distortions and tensions.
1.5. Relations between tensions deformations. Equilibrium relations.
1.6. Superposition-of-effects principle.
1.7. General aspects of the strength method.

Chapter 2 – Calculation of displacements
2.1. Theorem of virtual work. Calculation of the deformetion internal work.
2.2. Displacements calculation using the theorem of virtual work.
2.3. Example of the displacement calculation using the theorem of virtual work.
2.4. Method of Verchaguyne or method of Bonfim Barreiros.

Chapter 3 – Force method
3.1. Structural hiperestaticity degree. Internal and external hiperestaticity.
3.2. Presentation and systematization of the force method.
3.3. Final efforts in hyperstatic structures.
3.4. Calculation of displacements in hyperstatic structures using the theorem of virtual work.
3.5. Structures subject to the settlement of support.
3.6. Structires with elastic supports.
3.7. Relative importance of the bending part in the deformation due to moments and shear efforts.
3.8. Effect of temperature variations in structures. Uniform and differential variations.
3.9. Evaluation of the hyperestaticity by direct inspection and a number of equilibrium equations.
3.10. Trussed structures.
3.11. Composite structures.

Chapter 4 – The Displacement Method
4.1. The displacement method as a dual method with respect to the Force Method. Illustration by a simple example.
4.2. 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.
4.3. Inclusion of elastic supports and settlements.
4.4. Systematization of the displacement method. Solving a real pedagogic example.
4.5. 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.
4.6. Determination of efforts on the bars in the context of the displacement method, using the stiffness matrix of the bar.
4.7. General matrix formulation of the displacement method for solving planar frame structures. Grouping or assembling the stiffness matrices of the bars.
4.8. Matrix formulation of the displacement method for planar trussed structures.
4.9. Matrix formulation of the displacement method for structural grids. Systematization of the matrix formulation of the displacement method.

Chapter 5 – Energy Theorems
5.1. Introduction to Energy Theorems.
5.2. Derivation of the theorem of Betti.
5.3. Theorem of Elastic Displacements' reciprocity or Maxwell’s theorem (1st consequence of Betti's theorem).
5.4. Theorem of Forces' reciprocity or Complementar Maxwell’s theorem (2nd consequence of Betti's theorem).
5.5. Theorem of Muller-Breslau (3rd consequence of Betti's theorem) and its utility for obtaining influence lines.
5.6. Exercises.

Chapter 6 - Symmetry Simplifications
6.1. Analysis of symmetric structures. Definition of symmetric structure and of symmetric and anti-symmetric loading.
6.2. Analysis of symmetric structures. Behaviour of symmetrical structures subject to symmetrical and anti-symmetrical loading.
6.3. Symmetry simplifications.
6.4. Exercises.

Chapter 7 – Influence lines
7.1. Definition of Influence Line.
7.2. Determination of influence lines of reactions of support in isostatic structures.
7.3. Determination of influence lines of transversal efforts and bending moments in isostatic structures. Determination of influence lines for axial forces and displacements in isostatic structures.
7.4. Determination of efforts in structures by influence lines.
7.5. 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 without final exam

Assessment Components

Designation	Weight (%)
Teste	90,00
Trabalho laboratorial	10,00
Total:	100,00

Amount of time allocated to each course unit

Designation	Time (hours)
Estudo autónomo	89,00
Frequência das aulas	65,00
Trabalho laboratorial	8,00
Total:	162,00

Eligibility for exams

Approval in the course unit implies meeting the attendance requirement, which is considered fulfilled if the student, having been regularly enrolled, does not exceed the maximum number of absences corresponding to 25% of the scheduled in-person classes for each type of session. In addition to the cases provided for in the regulations currently in force at FEUP, students who obtained a final grade equal to or greater than 6 (on a scale of 0–20) in the same course unit during the immediately preceding academic year are exempt from the attendance requirement.

Calculation formula of final grade

The final grade is set based on a distributed assessment consisting of 3 tests to be taken during the semester and an optional laboratory assignment.

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

1. The final mark (CF) is calculated using the following formula:

CF = max {30% x cPAD1 + 40% x cPAD2 + 20% x cPAD3 + 10% x cTPL;  3/9 x cPAD1 + 4/9 x cPAD2 + 2/9 x cPAD3}

where:
cPAD1 - grade obtained in Distributed Assessment Test 1;
cPAD2 - grade obtained in the Distributed Assessment Test 2;
cPAD3 - grade obtained in Distributed Assessment Test 3;
cTPL - grade obtained in the laboratory assignment;

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

NOTE 2: The Distributed Assessment Tests (PAD1, PAD2 and PAD3) are compulsory. If the student fails one or more of these exams or wishes to improve their grades, they must take the retake exam scheduled during the exam period.

NOTE 3: Any (or all) of the three distributed assessments (one, two, or all) can be retaken or improved in the retake period.

NOTE 4: A zero mark will be awarded if any of the three distributed assessments have not been taken, either during the semester or in the retake period.

NOTE 5: For the retake period, each student may choose to be assessed on the subject of:

(i) only PAD1, (ii) only PAD2 or (iii) only PAD3;

(iv) only PAD1 + PAD2, (v) only PAD1 + PAD3 or (vi) only PAD2 + PAD3;

(vii) the whole subject (PAD1 + PAD2 + PAD3).

NOTE 6: The classification for the retake period will result from the formula above, considering for cPAD1, cPAD2 and cPAD3 the classifications obtained in the period of appeal or, if the student has chosen not to recover/improve a certain component(s) of the assessment, the respective classifications obtained in the tests carried out under the distributed assessment system will be considered.

NOTE 7: The grades for the distributed assessment component obtained in previous years will not be considered in the current academic year.

NOTE 8: To obtain a final grade higher than 17, it is necessary to take an additional oral exam.

2. Procedure for the distributed assessment

2.1 Distributed assessment tests

The distributed assessment tests will be carried out according to the following rules:

a) Each test will have a maximum duration of 50 minutes.

b) Each test will consist of questions (theoretical and practical) related to the subjects covered up to the date of the test and will be carried out without consultation (except tables/forms).

2.2 Practical laboratory work

Practical laboratory work will be carried out by groups of no more than four students and involves carrying out a test in the laboratory and writing a report.

Internship work/project

Observations