Universidad de Jaén

Block A: THEORY OF ELASTICITY 

LESSON I.- INTRODUCTION TO ELASTICITY 

    Introduction to the mechanics of continuous media. 
    The elastic solid. Properties. . 
    Hypothesis and principles of elasticity. 

LESSON II.- Stress 

    The stress concept. 
    Conditions of equilibrium. 
    Principal stresses. Invariant properties. 
    Plane Stress. 
    Graphic representation of stresses. Mohr's circles. 

LESSON III.-Strain. 

    Changes of volume and shape. 
    The strain concept. 
    The strain matrix. Properties. 
    Compatibility equations. 
    Plane Strain. 

LESSON IV.- Stress- strain relationship. 

    The tensile test. 
    Lateral strain. Poisson's coefficient. 
    Stress-strain relationship. Hooke's law. 
    Lame's equations. 

LESSON V.- The Energy approach of elasticity. 

    Strain energy. 
    Strain energy expressions. 
    Castigliano's theorem. 
    Yielding criteria. von Mises's stress. 

LESSON VI.- Thin-walled Vessels 

    Thin-walled Vessels. 
    Cylindrical and Spherical vessels subjected to internal pressure. 
    Cylindrical open liquid tanks. 
    Cylindrical pipes subjected to pressure. 

Block B: Strength of Materials 

LESSON VII.- Basic Concepts of Strength of Materials. 

    Structural members. 
    Cross Section stresses. Definitions. 
    General principles of strength of materials. 
    External and cross section equilibrium. 
    Types of supports. Support reactions. 
    Isostatic and hyperstatic bars. 

LESSON VIII.- Tension and Compression. 

    Stress by uniaxial tension or compression. 
    Axial force laws and diagrams. 
    Deformation due to axial force. 
    Tension or compression produced by own weight of members 
    Strain energy related to axial force. 

LESSON IX.- General Theory of Bending. 

    Simple Bending. Navier's law. 
    Relationship between shear force and bending moment. 
    Bending moment and shear force laws and diagrams. 
    The ten elemental beams analysis. 
    Stress produced by shear force. Collignon's theorem. 
    Principal stresses and von Mises's stress in bending. 

LESSON X.- Deflection produced by bending. 

    Differential equation of the bend line. 
    The double integration method. 
    Mohr's theorems in bending. 
    Strain energy related to simple bending. 
    Deflection produced by shear force. 

LESSON XI.- Biaxial Bending with and without axial force. 

    Biaxial bending. Neutral axis. 
    Deflection produced by biaxial bending. 
    Bending with axial force or eccentric tension/compression. Pressure centre. 
    Neutral Axis and Kernel in biaxial bending with axial force. 

LESSON XII.- Buckling. 

    Stability of Columns. 
    Euler´s formula. 
    Buckling Critical Load according to end conditions. 

LESSON XIII.- Torsion. 

    Pure Torsion. Circular shaft subjected to torsion. 
    Determination of torque. 
    Strain energy related to torque. 

Practices (the student will take each year 4 out of 7) 

Practice 1: Solving problems of Elasticity using MATLAB.  

Practice 2: Mechanical behaviour of different materials. Stress-Strain curves. 

Practice 3: Electric Extensometry: Tension/Compression. Torsion and Bending. 

Practice 4: Stress and strain in cylindrical shells subject to inner pressure. 

Practice 5: Bending. Experimental determination of the bend line. Principle of superposition in bending. 

Practice 6: Numerical analysis of stress in beams using software. 

Practice 7: Biaxial bending with axial force. 

Practice 8: Buckling. Critical load according to end conditions.

LECTURES

During the lectures, the different sections included in the course's syllabus will be developed. Student participation may take place at any time and doubts will be solved at the time. During lectures the problems of the course included in the collections of problems will be solved in a participatory way and discussion of results and resolution methods will be exposed. Selected exercises and practical cases will be solved at the end of each chapter, along with some exams problems. 

To complement the learning process, the student will have at hand notes and slides with some of the content of classes. Additionally, collections of problems and previous exams will be also available. 

For selected lessons, an aproach of flipped classroom might be followed, whereby the students would prepare the lesson initially, with help of the support material provided by the teacher. After that, some practical problems would be tackled at class to consolidate the learning process. 

LAB SESSIONS

Practices will be held in the laboratory of the area of mechanics of continuous media and theory of structures or in computers room. Lab session will be divided in two parts: first, there will be a theoretical introduction along with some exhibition, where the teacher will explain the tasks to be performed using lab equipment or computational scripts; then, student must work on their own and collect data to ellaborate a final report, to be submitted after a few days.

Notes concerning the lab sessions will be available beforehand at the web site of the course. The content of such notes is considered selfcontained, and will allow the student to learn about the theoretical aspects and practical exercises and equipment before going to the lab. 

SEMINARS

Additonal tutor hours and seminars may be organized to present practical applications of the theoretical contents of lessons. 

OTHER INFORMATION

Students with special educational needs should contact the Student Attention Service (Servicio de Atención y Ayudas al Estudiante) in order to receive the appropriate academic support.

Students with special educational needs should contact the Student Attention Service (Servicio de Atención y Ayudas al Estudiante) in order to receive the appropriate academic support

At the final exam, the score of both theoretical and operating contents of course must be greater than zero in each of part, to pass the exam. 

In particular, the theoretical contents' weigth in the final exam is 30%, while the remaining 70% concerns operational exercices (problems) 

Additionally, the student is required to pass independently both final exam and lab sessions, in order to pass the course. The learning process associated to the lab sessions will be evaluated by means of a virtual test at the end of the semester, which will ask about content and practical tasks performed by the student at the practices. Additionally, the student will have to turn it the files containing calculations and notes from the lab sessions.