Course: 2022/2023

Elasticity and strength of materials

(15509)

Requirements (Subjects that are assumed to be known)

We strongly advise you not to take this course if you have not passed
- Mecánica de Estructuras
- Cálculo I y II
- Álgebra

Skills and learning outcomes

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
CHAPTER 2. INTRODUCTION TO ELASTICITY
Subject 4: Formulation of Elasticity equations
- Elasticity equations
- Boundary and contact conditions
- Displacement and Stress formulations
- Theorems and general principes.
Subject 5: Two dimensional theory of Elasticity
- 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
- Elasticity in polar coordinates
- Plane Elasticity in term of displacement
- Plane Elasticity in terms of stresses
Subject 6: Failure criteria
- Failure by yielding
- Plastification criteria
- Equivalent stress and safety factor
CHAPTER 4. INTRODUCTION TO STRENGTH OF MATERIALS
Subject 7: Bending in beams
- Fundamentals concepts
- External and internal forces
- Equilibrium equations
- Kinematic hypotheses
- Normal stresses in beams
- Neutral axis
- Shear stresses
- Sections with symmetries
Subject 8: Torsion
- Kinematic hypotheses
- Displacement formulation
- Stress formulation
- Circular cross sections
- Thin-walled cross-sections
Subject 9: 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 10: 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
- F.P. Beer, E.R. Johnston, J.T. DeWolf, D.F. Mazurek. . Mechanics of Materials. McGraw-Hill.. 2013
- J.M. Gere, S. Timoshenko. . Mechanics of Materials. Cengage Learning. 2009

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
- 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

Detailed subject contents or complementary information about assessment system of B.T.

The course syllabus may change due academic events or other reasons.