Checking date: 01/10/2020

Course: 2020/2021

Elasticity and strength of materials
Study: Bachelor in Industrial Technologies Engineering (256)

Coordinating teacher: BARBERO POZUELO, ENRIQUE

Department assigned to the subject: Department of Continuum Mechanics and Structural Analysis

Type: Compulsory
ECTS Credits: 6.0 ECTS


Students are expected to have completed
We strongly advise you not to take this course if you have not passed - Mecánica de Estructuras - Cálculo I y II - Álgebra
Competences and skills that will be acquired and learning results. Further information on this link
Capacity to formulate the elasticity equations, to assess the hypotheses and to interpret the results. Knowledge and application of principles of Strength of Materials Knowledge of the basic techniques for Structural Analysis of deformable bodies. Capacity of analysis and evaluation with critical sense of results of structural calculus
Description of contents: programme
CHAPTER 1. INTRODUCTION TO SOLID MECHANICS Subject 1: Kinematic of deformable bodies - Motion: Basic concepts - Strain Tensor - Infinitesimal strain - Geometrical meaning of the components of infinitesimal strain tensor - Principal Strains - Equations of compatibility Subject 2: Equilibrium in deformable bodies - Body and surface forces - Concept of stress - Stress tensor - Stress equations of equilibrium - Stationary stresses Subject 3: Constitutive equations - Behaviour laws - Hyperelastic behaviour - Linear elastic behaviour - Material symmetries - Physical meaning of the constants Subject 4: Failure criteria - Failure by yielding - Haig-Westergaard representation - Von Mises-Hencky-Nadai yield criterion - Tresca-Guest yield criterion - Equivalent stress and safety factor CHAPTER 2. INTRODUCTION TO ELASTICITY Subject 5: Formulation of Elasticity equations (I) - Elasticity equations - Boundary and contact conditions - Displacement (Navier) formulation - Stress (Michell-Beltrami) formulation Subject 6: Formulation of Elasticity equations (II) - Theorem of Virtual Works - Superposition Theorem - Saint Venant´s principle Subject 7: Two dimensional theory of Elasticity (I) - Plain Stress and Plain Strain - Plane Elasticity in term of displacement - Plane Elasticity in terms of stresses - Methods of solutions - Mohr´s circle in 2D Subject 8: Two dimensional theory of Elasticity (II) - Elasticity in polar coordinates - Plane Elasticity in term of displacement - Plane Elasticity in terms of stresses CHAPTER 4. INTRODUCTION TO STRENGTH OF MATERIALS Subject 9: Bending in beams (I) - Fundamentals concepts - External and internal forces - Equilibrium equations - Kinematic hypotheses - Normal stresses in beams Subject 10: Bending in beams (II) - Neutral axis - Shear stresses - Sections with symmetries Subject 11: Torsion - Kinematic hypotheses - Displacement formulation - Stress formulation - Circular cross sections - Thin-walled cross-sections Subject 12: Deflections of beams - Equilibrium equations of beams - Internal forces and moments equations - Deflections by integration of the internal forces- and moment-equations (Navier-Bresse equations) - Moment-area method(Mohr´s theorems) Subject 13: Analysis of hyperstatic beams - Differential equation of the deflection curve (Euler and Timoshenko beams) -- Kinematic definitions - Static definitions - Introduction to the displacement (or stiffness) method
Learning activities and methodology
In each week one lecture session (master class) and one practical session (in reduced groups) will be taught. The first is geared to the acquisition of theoretical knowledge, and the second to the acquisition of practical skills related to theoretical concepts. In addition to this sessions four laboratory practical sessions in reduced groups (maximum 20 students) will be impart. Students will have the possibility of individual tutorials.
Assessment System
  • % end-of-term-examination 60
  • % of continuous assessment (assigments, laboratory, practicals...) 40
Basic Bibliography
  • Barber, J.R. . Elasticity. Kluwer Academic Publishers. 1992
  • Garrido, J.A. y Foces, A. . Resistencia de Materiales. Secretariado de Publicaciones. Universidad de Valladolid. 1994
  • Oliver, X.; Agelet, C.. Mecánica de medios continuos para ingenieros. Edid. UPC. 2000
  • Ortiz Berrocal, L . Elasticidad. Ed. McGraw Hill. 1998
  • Paris Carballo, F. . Teoría de la elasticidad. Ed. Grupo de Elasticidad y Resistencia. 1998
  • Samartin Quiroga, A.. Resistencia de Materiales. Servicio de Publicaciones. Colegio de Ingenieros de Caminos, canales y Puertos. 1995
  • Sanmartín Quiroga, A. . Curso de Elasticidad. Ed. Bellisco. 1990
Additional Bibliography
  • Benham, P.P. y Crawford, R.J. . Mechanics of engineering materials. Longman Scientific & Technical. 1987
  • Chung T.J. . Applied continuum mechanics. Cambridge University Press. 1996
  • Doblaré Castellano, M. y Gracia Villa, L. . Fundamentos de la Elasticidad Lineal. Ed. Síntesis. 1998
  • Shames, I.H. y Cozzarelli, F.A.. Elastic and inelastic stress analysis. CRC Press. 1997
  • Wunderlich, W. y Pilkey, W.D. . Mechanics of structures: Variational and Computanional Methods. CRC Press. . 1992

The course syllabus and the academic weekly planning may change due academic events or other reasons.