Universitat Internacional de Catalunya

Structural Calculation I

Structural Calculation I
First semester
Technical Module
Structures 1
Main language of instruction: English

Other languages of instruction: Spanish

Teaching staff

Monday: 09.00 to 10.00, or, Wednesday: 10.00 to 11.00. By appointment at the following email addresess.

Dr. Pedro Casariego: pcasariego@uic.es 

Dr. Roger Señís: rsenis@uic.es

Dr Josep Ramón Solé: jrsole@uic.es 


The subject of Structures I is taught in the second year of the degree course. Therefore, it is a subject that extends the concepts of Physics, and provides the student with the necessary tools to understand and deal with the content of structure subjects that are covered in third and fourth years of the degree.

Intuitively, we know that each material has its own characteristics, so it is logical to think that different materials will behave differently depending on the state of their loads. There is a series of parameters that permit us to know the principal characteristics of the materials and, therefore, the behaviour of the material when submitted to a load bearing state.

Knowledge of these parameters is required to evaluate if a material, and therefore a structure, can withstand the loads which are applied to it.

On this basis, the subject of Structures I, is to focus on the characteristics and strength of materials, and introduces the student to structural analysis.

Knowledge of these parameters, common to all materials, makes it easier to undertake the study of a particular material such as concrete or steel, both of which are taught in third and fourth year of the degree.

The subject of Structures I, is divided into two blocks.

The FIRST BLOCK covers the basic concepts of the strength of materials and the behaviour of structures.

This block provides the student with the necessary tools to analyze the internal forces produced in a structure in a load bearing state, and to determinate if this structure can then withstand the loads.

This block, which has both theoretical and practical elements, will allow the student to carry out a pre-dimension of the structure, and verify and quantify the required effort by a structural element under a load bearing state, taking into account, of course, the rules governing the strength of materials.

The SECOND BLOCK is totally practical.

Students should apply the knowledge gained in the first block to check, and if is necessary modify, the structure of a building they have planned themselves in the designing assignment studied in the same year.

In order to do this, students will be introduced to the most common types of construction and the current regulation, the Technical Code for Construction (CTE) will be explained, specifically  CTE-AE and CTE-SE , with the objective that students are guided in their  actions when constructing  and establish structural security according to what is laid down in the CTE.

Pre-course requirements

Learning about structures is a continuous process throughout the degree. Each course extends the concepts from the previous one. Therefore, it is strongly recommended that the student has passed Physics.

Otherwise, students must be clear about the fundamental concepts covered in Physics. Knowledge of how to obtain the diagrams of internal forces of isostatic structures is essential.


Students should learn to work correctly with the main standard design code CTE, specifically CTE-AE and CTE-SE, and should be able to guarantee the structural safety of a building.

Students should be able to analyze structures, and produce correct diagrams showing the internal forces.

Finally, students should acquire a knowledge of the resistance of materials. Students should be able to pre-dimension and analyze the loads that a structure must withstand.


  • 12-T - Ability to conceive, calculate, design, integrate in buildings and urban complexes and execute building structures
  • 15-T - Ability to conceive, calculate, design, integrate in buildings and urban complexes and execute foundation solutions
  • 17 - Ability to apply building and technical standards
  • 24 - To acquire adequate knowledge of the mechanics of solids, continuous medium and soil as well as the plastic, elasticity and resistance properties of materials for structural works

Learning outcomes

Knowledge of the main standard design code CTE, specifically, CTE-SE-AE and CTE-SE.

Ability to design and carry out a pre-dimensional analysis of a structure with calculations based on the concepts of the strength of the materials.


Block 1

Theme 1. Introduction and general concepts.

1.1. – Strength of materials. General concepts

1.2. – Typology of internal forces. Classification.

1.3. Stress-strain diagram.

1.3.1. – Obtaining a stress-strain diagram.

1.3.2. – Introduction to the concepts of stress and strain.

1.3.3. – Elastic and plastic behaviour of materials.

1.3.4. – Interpretation of the stress-strain diagram for steel.  Young Modulus.  Hooke’s law. Ductility. Fragility. Yielding.

1.3.5. – Interpretation of the stress-strain diagram of other materials, concrete, ceramic and wood.

1.4. – Premises for the resistance of materials.

1.5. – Exercises.

Theme 2. Geometry of masses.

2.1. – Centre of gravity.

2.2. – Area.

2.3. – Static moment. First moment of an area.

2.4. – Moment of inertia. Second moment of an area.

2.5. – Steiner’s theorem.

2.6. – Section modulus.

2.7. – Torsional constant.

2.8. – Radius of gyration.

2.9. – Product of inertia

2.10. - Exercises.

Theme 3. Axial force.

3.1. – Definition of axial force.

3.2. – Stress design.

3.3. – Strain design. Hooke’s law.

3.4. – Thermal loads.

3.5. – Young Modulus and Coulumb Modulus. Poisson’s effect.

3.6. – Characteristic parameters of the behaviour of material.

3.7. – Isostatic and hyperstatic structures. Mechanisms.

3.8. – Exercises.

Theme 4. Pure bending.

4.1. – Definition of pure bending. Neutral line.

4.2. – Pure bending.

4.3. – Stress design in pure bending. Navier´s hypothesis. Section modulus.

Theme 5. Simple bending.

5.1. – Definition of simple bending.

5.2. – Normal force Vs normal stress. Tangential force Vs  tangential stress.

5.3. – Shear force. Relationship between bending and shear.

5.4. – Shear stress design . Jourawski - Colignon. Cauchy’s law.

5.5. – Particular cases of shear force. Rectangular section, circular section, hot rolled steel section.

5.6. – Bending typologies.

5.7. – Shear typologies.

5.8. –Exercises.

Theme 6. Axial force and bending moment.

6.1. – Definition.

6.2. – Typologies. Eccentric axial force, oblique axial force, axial force and wind, containment wall, post-tensioned concrete and prestressed-concrete.

6.3. – Stress design.

6.3. – Neutral axis equation.

6.6. – Exercises.

Theme 7. Axial force and two bending moments.

7.1. – Definition.

7.2. – Typologies. Eccentric load, roof beams, supports, etc.

7.3. – Stress design.

7.4. – Neutral axis equation.

7.5. – The central core. Properties. Obtaining the central core. Generic cases: rectangular, circular, hot rolled steel section

7.6. – Bending cases. Common elements in construction.

7.7. – Exercises.

Theme 8. Torsion.

8.1. – Definition.

8.2. – Typologies.

8.3. – Internal diagrams.

8.4. – Stress design. Circular sections

8.5. – Strain design. Circular sections. Torsional rotation.

8.6. – Uniform and non-uniform torsion.

8.7. – Sections Vs torsion. Torsional rigidity of sections.

8.8. –Structural design of elements submitted to torsion.

8.9. – Exercises


Block 2.

Theme 1. Introduction to the standard technical code of construction (CTE).

1.1. – Common types of construction. – DB SE. Basic Document. Structural Safety.

1.2. – DB SE-AE. Basic Document. Structural Safety. Loads in construction.

Theme 2. Basic notes for designing structures in two dimensions.

Guide made by the teacher to design structures in two dimensions.

Teaching and learning activities

In blended

The methodology and training activities are presented as a hybrid system (virtual and face-to-face). In this way, if the situation requires it, both student and teacher will be prepared to move to a fully face-to-face or totally virtual system, without any loss of time.

Classes take place on Mondays from 10.00h to 12:00h and Wednesdays from 11:00h to 14:00h

Monday: Fully virtual. Theoretical or master classes interspersed with a participatory class in which exercises will be carried out.

On the UIC's Moodle platform (intranet), available in all subjects of the University, the student will find all the necessary resources to follow up online without having to download any program or application. Programs such as the Collaborate or tools such as "Homework", among others, allow online classes to be sent and exercises to be sent back to students, privately and independently for their grade. It is also feasible to carry out tests and / or multiple-choice exams to assess the student continuously.

Wednesday: Fully face-to-face. Participatory classes and fully practical classes will be taught. In the participatory classes the teacher and the student will solve exercises together. In the practical classes, the student will have to solve the proposed exercises.

Participatory classes will be carried out directly on the blackboard.

The practical classes will be held in three classrooms, each with a teacher, where the students will have the appropriate safety distance. In these classes, the student has to solve exercises individually and ask any questions he or she has in relation to carrying out the exercises. Based on this, students can upload their questions or exercises to Moodle, which will be projected on the screen for teacher supervision. In this way the doubts of the students will be solved with the appropriate safety distance through the use of "Tablets". Blackboard will also be used when no exchange of information is required between teacher and student.

Class exhibition
12-T 15-T 17 24 0,6
Class participation
12-T 15-T 17 24 0,6
Clase practice
12-T 15-T 17 24 0,6
12-T 15-T 17 24 0,6
Individual or group study
12-T 15-T 17 24 2,5

Evaluation systems and criteria

In blended

The course is passed with a 5 out of 10 of average between exam and practical work.

Structures I Evaluation:

  1. In-person Final Exam: 60% of the final grade.
  2. Online Delivery work: 40% of the final grade.

Exam dates:

  1. In-person Final exam: Friday, January 13, 2023 from 09:00h. to 12:00h. Online: Thursday, January 26, 2023 at 15:30h
  2. In-person Second call: Friday, June 16, 2023 from 18:00 to 21:00. Online: Tuesday, July 04, 2023 at 15:30h.

Bibliography and resources

Compulsory bibliography:

Mecánica de estructuras. Libro 1. Resistencia de materiales. Miguel Cervera Ruiz y Elena Blanco Díaz. Ediciones UPC.

Mecánica de estructuras. Libro 2. Resistencia de materiales. Miguel Cervera Ruiz y Elena Blanco Díaz. Ediciones UPC.

Resistencia de Materiales. Timoshenko S. Editorial Espasa-Calpe, S.A.

Elementos de Resistencia de Materiales. Timoshenko S, Young, D.H. Editorial Limusa

Estructuras o por qué las cosas no se caen. J.E. Gordon.

Supplementary bibliography:

Estructuras para arquitectos. Salvadori, M, Heller, R. Editorial CP67

Razón y ser de los tipos estructurales. Eduardo Torroja Miret.

Calcul d´estructures. Introducció. Frances López Almansa y Jorge Urbano Salido. Edicions UPC.

Estática. William F. Riley y Leroy D. Sturges. Editorial Reverté, S.A.

Mecánica Vectorial para Ingenieros. Estática. Ferdinand P. Beer, E. Russell Johnston Jr. Editorial McGraw-Hill.