The content of this course assumes and complements the knowledge previously acquired in the subject "Elasticity and Strength of Materials". During the development of this course it is intended that students acquire skills in solving problems of structural design and mechanical elements formed from the union of prismatic bars as well as analysis techniques to deal with deformable solids. In addition, it helps to introduce mechanical design concepts useful in the design of structures of diverse functionality.

The first topic is devoted to complete the analysis of bending, particularly unsymmetrical bending and combined bending with axial force. In the next topic, the concept of hyperstaticity in bending and its application to solving simple statically indeterminate structures by classical methods are exposed, with special emphasis on the method of forces. In the third issue the torsion theory and its application to pieces of circular cross-section is addressed. Next, two issues of considerable interest are presented: the buckling instability and the energy theorems. The program is completed with a brief exposition of the elementary theory of impact problems. With this course the student will have the basic knowledge to successfully address problems of calculation and design of solids formed by prismatic bars.

As mentioned before, this course is a continuation of the course "Elasticity and Strength of Materials" and is part of the curricular line of Mechanical Engineering. So, like that, the subject "Solid Elastic Calculation" is based on the subjects of second course "Mechanics" and "Applied Mechanics" whose knowledge and mastery are essential to understand the behavior of structures and other mechanical parts considered as deformable solids. Obviously, the student should also have a good grasp of the fundamental concepts of "Algebra" and "Calculus" studied in the first year. Another link can also be found with another subject taught in the third year, "Theory of Mechanisms and Mechanical Vibrations", a discipline that helps determine the forces undergone by the elements of a mechanism, and from which stresses and strains can be obtained by means of the "Solid Elastic Calculation". In this way a proper design ensuring system integrity can be obtained.

The knowledge acquired in this subject also form the basis of other mechanical-type subjects of the fourth year such as "Theory of Structures and Construction", where new methods are shown in the calculation of structures formed by prismatic bars. It is also evident the relationship with the subjects "Theory of Machines" and "Machine Elements", where it is essential to obtain stresses and strains and to apply the corresponding theories of failure. Finally, the "Solid Elastic Calculation" is also basic for some subjects included in several Master courses: in the "Master in Mechanical Engineering" (a continuation of the Degree in Mechanical Engineering) and in the "Master in Industrial Engineering" (a continuation of the Degree in Industrial Technology Engineering).

The competence of the subject corresponding to the module Specific Technologies, and reflected in the memory of the degree is:

- Knowledge and ability to apply the fundamentals of elasticity and strength of materials to the behavior of real solids.

As a result of learning it is expected that the students are able to:

- Understand the fundamentals of calculation of statically indeterminate structures with particular emphasis on the method of forces and master the resolution of simple structures composed of prismatic bars.

- Complete calculation of stresses and strains in structures subjected to different types of forces including torsion effects in circular prismatic bars.

- Acquire the skills to carry out the advanced analysis of bars under biaxial or unsymmetrical bending.

- Know the procedures for calculating heterogeneous sections subjected to pure bending and be able to apply the transformed section method and the static method.

- Master the analysis of elements subjected to eccentric compression, both in materials with similar behavior in tension and compression, and those that do not support tensile stresses.

- Acquire theoretical analysis methods for calculating supports against buckling under compression and become familiar with the standards-based calculation (Technical Standards for Building).

- Be able to use as an alternative energy methods to calculate both isostatic and statically indeterminate structures, understanding the meaning of the fundamental energy theorems.

- Know the method of the equivalent static load to solve impact loads on structures with both linear and nonlinear behavior.

THEORETICAL CONTENTS

ITEM 1. UNSYMMETRICAL BENDING. COMBINED BENDING AND AXIAL FORCE. HETEROGENOUS SECTIONS

ITEM 2. ANALYSIS OF BENDING IN HYPERSTATIC STRUCTURES

ITEM 3. THEORY OF TORSION

ITEM 4. INSTABILITY: BUCKLING THEORY

ITEM 5. ENERGY THEOREMS

ITEM 6. IMPACT ELEMENTAL THEORY



LABORATORY PRACTICES

PRACTICE SESSION 1. PHOTOELASTICITY

PRACTICE SESSION 2. BENDING OF BEAMS

The contents of the subject "Solid Elastic Calculation" are taught through lectures, practical classes, seminars and laboratory practice.

In the lectures the contents and theoretical concepts of each topic are presented with the aid of some specific publications available to the student and by the resolution of practical exercises.

In the practical classes problems based on structures and mechanical systems are solved in order to consolidate the concepts presented in the lectures.

Throughout the semester three seminars are held, in which larger problems as well as exams of previous editions are solved. The arrangement in small seminar groups propitiates an interactive resolution of problems between the professor and the students.

Along the course two laboratory practices are performed, the first corresponding to a photoelasticity test and the second consisting of the measurement of reactions and deformations in beams subjected to bending. The practices are carried out in the "Laboratory of Strength of Materials and Structures" of the Department of Mechanical Engineering. Previously, and depending on each practice, students individually or divided into groups initially attend a theoretical presentation and solve analytically some exercise related to the practice prior year. During the session, students are divided into smaller groups so as to carry out experimental measurements and validate their calculations. At the end of each practice, students must submit a report with the results and final conclusions.

On the virtual platform eGela, the following material is available to the students: the Student Guide, a collection of review exercises, some problems to be solved in the seminars and other problems from the examination sessions, together with the results and exam grades. All subject groups have at their disposal the same material simultaneously.

• Final Assessment System
• Tools and qualification percentages:
  • Written test to be taken (%): 95
  • Realization of Practical Work (exercises, cases or problems) (%): 5

In this subject a partial exam is proposed that allows reducing contents in the final exam. It will be assumed that by not doing or not obtaining the required grade in this partial exam the student is giving up the continuous assessment system.

The requirements for passing the course are:

1. Attend all laboratory practices.

2. Get an average rating greater than or equal to 5.0.

The laboratory practices account for 5% and the written tests for 95% of the final grade. The written tests consist of individual resolution of problems and theoretical questions. The first written test enables to pass definitively the first part of the course (for this it is necessary to obtain a rating equal to or greater than 4.0). In the second part of the course, a score equal to or greater than 3.5 should be obtained in order to be able to get a pass average. The final grade is the average of the two partial tests. Students may also make a full examination even after having passed the first of the written tests. The theoretical part of the exam is in any case one third of the mark for each exam.

According to the current regulations of the University of the Basque Country - EHU, it is sufficient for the student not to present himself to give up the corresponding call.

In the extraordinary examination a written exam including the full course will be performed. This will consist of individual resolution of problems and theoretical questions. The theoretical part accounts for one third of the exam. The final grade will be obtained by taking the laboratory practices into account.

As in the ordinary call, to give up this call it will be sufficient for the student not to present himself.

- "Cálculo Elástico de Sólidos", José Luis Alcaraz, Rubén Ansola, Javier Canales, José A. Tárrago, Estrella Veguería. Sección de Publicaciones de la E.T.S.I. de Bilbao, 2015.
- "Cálculo Elástico de Sólidos: Colección de Problemas de clase", José Luis Alcaraz, Rubén Ansola, Javier Canales, José A. Tárrago, Estrella Veguería. Sección de Publicaciones de la E.T.S.I. de Bilbao, 2016.

Basic bibliography

- "Elastikotasuna eta Materialen Erresistentzia", Rubén Ansola. UEU, Udako Euskal Unibertsitatea, 2005.

- "Resistencia de Materiales". L. Ortiz Berrocal. McGraw-Hill, 1991.

- "Mecánica de Materiales" (2ª ed.), S.P. Timoshenko y J.M. Gere. Grupo

Editorial Iberoamericana, 1986.

- "Mecánica de Materiales" (2ª ed.), F.P. Beer y E.R. Johnston. McGraw-Hill, 1993.

- "Resistencia de Materiales", V.I. Feodosiev. Mir, 1980.

- "Problemas de Resistencia de Materiales", I. Miroliúbov et al. Mir, 1978.

In-depth bibliography

- "Advanced Mechanics of Materials (6th Ed.)", A.P. Boresi y R.J. Schmidt. John Wiley & Sons, 2003.
- "Advanced Strength and Applied Elasticity", A.C. Ugural y S.K. Fenster. Prentice Hall, 1995.
- "Mechanics of Materials (2nd Ed.)", R.R. Craig Jr. John Wiley & Sons, 2000.

Journals

- Int. J. of Mechanical Sciences, Elsevier.
- Int. J. of Solids and Structures,Elsevier.
- Mechanics of Materials, Elsevier.
- Computers & Structures, Elsevier.

Web addresses

- https://egela.ehu.es/
- http://www.ehu.eus/es/web/ingenieria-mecanica
- es.scribd.com/doc/305851/Resistencia-de-materiales-Problemas-resueltos
- es.wikipedia.org/wiki/Resistencia_de_materiales