Educational guide
IDENTIFYING DATA 2024_25
Subject THEORY OF STRUCTURES Code 00708026
Study programme
0708 - GRADO EN INGENIERÍA MECÁNICA
Descriptors Credit. Type Year Period
6 Compulsory Third Second
Language
Castellano
Prerequisites
Department TECN.MINERA,TOPOGRAF. Y ESTRUC
Coordinador
CIFUENTES RODRÍGUEZ , JAIME
E-mail jcifr@unileon.es
jvale@unileon.es
Lecturers
CIFUENTES RODRÍGUEZ , JAIME
VALLEPUGA ESPINOSA , JOSÉ
Web http://
General description
Tribunales de Revisión
Tribunal titular
Cargo Departamento Profesor
Presidente TECN.MINERA,TOPOGRAF. Y ESTRUC BALADRON GAITERO , GONZALO
Secretario ING.MECANICA,INFORMAT.AEROESP. UBERO MARTINEZ , IVAN
Vocal TECN.MINERA,TOPOGRAF. Y ESTRUC ORTIZ MARQUES , ALMUDENA
Tribunal suplente
Cargo Departamento Profesor
Presidente ING.MECANICA,INFORMAT.AEROESP. PEREZ GARCIA , HILDE
Secretario INGENIERIA Y CIENCIAS AGRARIAS AGUADO RODRIGUEZ , PEDRO JOSE
Vocal INGENIERIA Y CIENCIAS AGRARIAS GUERRA ROMERO , MANUEL IGNACIO

Competencias
Code  
A18160
A18161
B5634
B5635
B5643
B5644
C2 CMECES2 That students know how to apply their knowledge to their work or vocation in a professional manner and possess the skills that are usually demonstrated through the development and defense of arguments and the resolution of problems within their area of study.
C4 CMECES4 That students can transmit information, ideas, problems and solutions to both a specialised and non-specialised audience

Learning aims
Competences
Knows and applies their knowledge to their work or vocation in a professional manner and possesses the competencies typically demonstrated through the development and defense of arguments and problem-solving within their area of study. C2
Communicates information, ideas, problems, and solutions to both specialized and non-specialized audiences C4
Knows basic and technological subjects, enabling them to learn new methods and theories, and has versatility to adapt to new situations. B5634
Handles problems with initiative, decision-making, creativity, critical reasoning, and effectively communicates and conveys knowledge, skills, and abilities in the field of Industrial Engineering. B5635
Understands and applies the fundamentals of elasticity and strength of materials to the behavior of real solids. A18160
Knows and calculates industrial structures and constructions A18161
Analyzes, synthesizes, solves, and makes decisions regarding the problems proposed in Structural Theory II. B5643
Communicates and interprets the results with initiative, creativity, and critical and self-critical reasoning. B5644

Contents
Topic Sub-topic
BLOCK I: DIRECT STIFFNESS METHOD 1. Direct Stiffness Method. Flat Continuous Structures
1.1 Stresses due to node movements in a bar with 6 d.o.f.;
1.2 Stiffness matrix of a bar with 6 d.o.f.;
1.3 Stresses due to node movements in a bar with 5 d.o.f.;
1.4 Stiffness matrix of a bar with 5 d.o.f.;
1.5 Stiffness matrix in global coordinates;
1.6 Structure stiffness matrix. Assembly;
1.7 Problem formulation;
1.8 Exercises

2. Direct Stiffness Method. Displacements, Stresses, and Reactions
2.1 Node displacements;
2.2 Stresses at the ends;
2.3 External reactions;
2.4 Exercises

3. Direct Stiffness Method. Loads applied on bars
3.1 General approach;
3.2 Exercises

4. Direct Stiffness Method. Flat Articulated Structures
4.1 Introduction;
4.2 Stiffness matrix of articulated bar;
4.3 Displacements, stresses, and reactions; 4.4 Case of loads applied on bars;
4.5 Exercises

5. Direct Stiffness Method. Specific Boundary Conditions
5.1 Case of non-matching supports;
5.2 Case of uniform temperature increments and length defects;
5.3 Case of elastic supports;
5.4 Exercises

6. Direct Stiffness Method. Solved Problems
BLOCK II: FINITE ELEMENT METHOD 7. Finite Element Method. Basic Concepts of Elasticity
7.1 Equilibrium equations;
7.2 Stress-strain relationships;
7.3 Strain-displacement relationships;
7.4 The elastic problem;
7.5 Virtual work theorem

8. Finite Element Method. Fundamentals
8.1 Introduction;
8.2 Types of elements;
8.3 Displacement vector;
8.4 Element stiffness matrix;
8.5 Complete stiffness matrix of the structure;
8.6 Structure response

9. Finite Element Method. Nodal Approximations of Functions
9.1 Polynomial approximations;
9.2 Shape functions;
9.3 Natural coordinates;
9.4 Isoparametric elements

10. Finite Element Method. Two-Dimensional Elasticity
10.1 Plane stress and plane strain;
10.2 Equilibrium, compatibility, and behavior;
10.3 Three-node triangular element;
10.4 Stiffness matrix of the three-node triangular element;
10.5 Nodal equivalent forces of the three-node triangular element;
10.6 Complete stiffness matrix with three-node triangular element;
10.7 Response with three-node triangular element;
10.8 Four-node rectangular element;
10.9 Stiffness matrix of the four-node rectangular element;
10.10 Nodal equivalent forces of the four-node rectangular element

Planning
Methodologies  ::  Tests
  Class hours Hours outside the classroom Total hours
Problem solving, classroom exercises 22 33 55
 
Tutorship of group 2 3 5
 
Lecture 30 45 75
 
Mixed tests 6 9 15
 
(*)The information in the planning table is for guidance only and does not take into account the heterogeneity of the students.

Methodologies
Methodologies   ::  
  Description
Problem solving, classroom exercises Software programs will be used for problem solving, and their usage will be explained to the students beforehand. Each student must be capable of solving any type of structure using the software.
Tutorship of group The doubts that the student may have regarding both the theoretical part and its application will be resolved
Lecture In the theoretical classes, the content of the subject will be presented in a reasoned manner. At the end of each section, simple exercises directly applying the explained theory will be conducted

Personalized attention
 
Tutorship of group
Description
The focus will primarily be on addressing any doubts that may arise during the course.

Assessment
  Description Qualification
Others There will be four types of written tests:
T1: Final exam covering the entire subject.
T2: A partial exam.
T3: Individual project/work.
T4: Individual test(s) conducted using software programs.		 T1: 50 %
T2: 25 %
T3: 10 %
T4: 15 %
 
Other comments and second call

It will be mandatory to complete T4 in order to take the final exam. To pass the course, a minimum grade of 3.5 out of 10 must be obtained in T1. The course is passed if the final grade is equal to or greater than 5 points.

In the second examination period, the results of the tests taken throughout the semester will be valid.

It will be mandatory to have completed T4.

There will be a final exam that will vary between: 50% if T2 and T3 have been completed, and 85% if T2 and T3 have not been completed.

Sources of information
Access to Recommended Bibliography in the Catalog ULE

Basic , Apuntes de Cálculo de Estructuras, ,
Eugenio Oñate, Cálculo de Estructuras por el Método de Elementos Finitos Análisis Estático Lineal. Vols. 1 y 2, CIMNE,
Manuel Vázquez, Cálculo Matricial de Estructuras, Colegio de Ingenieros Técnicos de Obras Públicas de Madrid, 1992
Ramón Argüelles Álvarez, Cálculo Matricial de Estructuras, Bellisco, 2005
Manuel Vázquez y Eloísa Lopez, El Método de los Elementos Finitos aplicado al análisis estructural, Noela, 2001
, Problemas de Examen de Cálculo de Estructuras, ,

Complementary Federico París Carballo, Cálculo Matricial de Estructuras, Ediuno, 2006
Ángel Aragón Torre y Jesús Manuel Alegre Calderón, Cálculo matricial de estructuras. Teoría y ejemplos, Colección de Ingeniería y Arquitectura nº3, 2005


Recommendations


Subjects that it is recommended to have taken before
PHYSICAL FUNDAMENTALS / 00708003
STRENGTH OF MATERIALS I / 00708011
CLASSICAL MECHANICS / 00708014
STRENGTH OF MATERIALS II / 00708019
THEORY OF STRUCTURES I / 00708021