Analysis of Structures I


The course aims to provide the knowledge of fundamental structural analysis methods and to to further develop the students'' ability to reason, think and to apply them to solve statically indeterminate structures, establishing the basis for the finite element method and of the thin plates using classical methods.

By the completion of this course the students should be able to:
Formulate the flexibility and stiffness matrices of truss, beam and frame elements and of the plate problems.

Perform linear analysis of the reticulated hyperstatic structures (manually) to calculate displacements, reactions and internal stresses subject to various combinations of loading conditions (applied loads, temperature effects or foundation settlement) and to build compatible and statically admissible solutions in slabs.

Understand how the principles of virtual work relate to the force and direct stiffness method of structural analysis.

Model a structure with elastic supports, inclined supports, or member end releases (hinges).

Develop the ability to make engineering judgment about structural behaviors.

General characterization





Responsible teacher

Corneliu Cismasiu, Ildi Cismasiu


Weekly - 5

Total - 75

Teaching language



Basic knowledge of Strenght of Materials I and II


Bibliografia principal:

1. A. Ghali, A. M. Neville and T.G. Brown. Structural Analysis. A unified classical and matrix approach. E & FN Spon, 6th edition, 2009

2. J.A. Teixeira de Freitas e Carlos Tiago, Análise elástica de estruturas reticuladas, IST, Lisboa, 2010.

3. C. Cismasiu, I. Cismasiu Apontamentos das aulas teóricas (disponíveis na página da disciplina)

Bibliografia secundária:

1. Kenneth M. Leet and Chia-Ming Uang and Anne M. Gilbert. Fundamentals of Structural Analysis. McGraw Hill, 3rd ed. 2008  

2. R. C. Hibbeler. Structural Analysis. Prentice Hall, 5th edition, 2001

3. W. McGuire, R. H. Gallagher, and R. D. Ziemian.Matrix structural analysis. John Wiley & Sons, Inc., 2nd edition, 2000

4. T. R. G. Smith. Linear Analysis of Frameworks. Ellis Horwood Series in Engineering Science. Prentice Hall Europe, 1983.

Teaching method

The teaching methods are based on student-centered teaching approach, theoretical -practical
 classes and continuos evaluation process.
The theoretical-practical clasees introduce the fundamental concepts of the curricular unit related to each topic followed by simple practical example, complemented b solving a larger set of problems involving a reduced complexity that can be manually solved. The further objective of the working classes to give a more practical insight about theoretical concepts and encourage the students'' initiative and their active participation. Individual work, outside of the presencial classes, will be stimulated, by the resolution of a set problems.
Analysis and problem-solving skills are assessed continuously during the practical classes and through unseen written examinations.

Evaluation method

Assessment Method (2019-2020) 

(em construção)

The assessment methods of the course are in accordance with the current Assessment Regulations.

Analysis and problem-solving skills are assessed continuously during the classes and through three unseen written examinations corresponding to the three modules of the curricular unit.

1. Theoretical and practical evaluation:

For the theoretical and practical evaluation the subject matter will be divided into three parts (parts A, B and C). The different parts correspond, as a rule, to the logical division of the taught subject.

  • Test 1 (NA – 6.5 val) - (aprox. 1.5 hours): Part A: Force Method and symmetry

  • Test 2 (NB – 7.0 val) - (aprox. 1.5 hours): Part B: Displacment Method and symmetry

  • Test 3 (NC – 6.5 val) - (aprox. 1.5 hours) : Part C: - Theory of plates

2. Summative assessment:

The MTP grade of the summative assessment will be obtained on written resolution of various problems during the class, the attendance of students and the appreciation of the teacher.


          NAP = 0 a 20 valores e NATP = 0% a 100%

Several problems will be solved in class, some of which will be randomly chosen for summative assessment.

The NAP assessment will consist of the classification of the resolutions of the chosen problems and the appreciation of the teacher.

The NATP assessment will consist of student attendance and teacher appreciation.

3. Frequency

The frequency will be obtained in accordance with Article 6 of the Evaluation Regulation. To obtain frequency you need to have:

attendance in at least 2/3 of classes

Frequency waiver will be granted in regulated special cases (TE, AAC, DA, etc.).

4. Época Normal

NE = NA + NB + NC ≥ 7.5 ( scale 0 a 20)

5. Época de Recurso

 Exame de Recurso: NE ≥ 7.5  (scale 0 a 20)

6. Classificação Final

NFinal = 0.85xNE + 0.15xMTP ≥ 9.5

Students who have special regulated status (TE, AAC, DA, etc.) must take a test to obtain the MTP summative grade on a scheduled date.

Students with a final grade higher than 16 will have to take an oral exam to confirm the grade. In this case, the student''s classification will be the oral exam classification. If not, the final grade will be 16 values.

Registration for continuous assessment tests is required, otherwise the rules of Article 5 (10) of the current assessment rules apply.

8. Examination Dates

 Test 1 - xx  de Outubro de 2019

 Test 2 - xx de Novembro de 2019

 Test 3 - xx de Dezembro de 2019

Subject matter

1. Introduction to Structural Analysis.

2.Structural Symmetry

Symmetric structures subjected to general loading

3. Force Method

Structural indeterminacy. Released structure

Description of the method.  Revison of pincipals of complementary virtual work. Flexibility matrix.

Analysis for different loading conditions

4. Displacement Method

Fundamental solutions of bars and beams

Kinematic indeterminacy. Kinematic ally determinate structure

Description of the method. Direct formulation.

Revison of pincipals of complementary virtual work. Alternative definition of the stiffness matrix

Analysis for different loading conditions

5. Comparison of Force and Displacement Methods

Duality between the force method and the displacement method

5. Theory of Plates

          Introduction to the linear elastic anlysis of thin (Kirchhoff) plates

Fundamental relations, Lagrange equations and boundary conditions

Some analytical solutions (Navier, Lévy, cylindrical flexion)

Analysis of the plates by  simplified methods