Introduction to Structural Analysis

Introduction to structural analysis (251 - 15336)
Study: Bachelor in Aerospace Engineering
Semester 2/Spring Semester
2ND Year Course/Lower Division

*Considered lower division; however, please note the course prerequisites.

Students are expected to have completed:

Calculus II
Linear Algebra
Physics I
Introduction to Mechanics of Flight

We strongly advise you not to take this course if you have not passed Physics I and Introduction to Mechanics of Flight

Compentences and Skills that will be Acquired and Learning Results:

- 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:

CHAPTER 1. INTRODUCTION TO SOLID MECHANICS (Nº of sessions: 3)

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. ELASTICITY (Nºof sessions: 3)

Subject 4: Formulation of Elasticity

- Elasticity equations
- Boundary and contact conditions
- Theorem of Virtual Works
- Theorem of Minimum Potential Energy
- Reciprocity Theorems
- General Principles

Subject 5: Failure criteria

- Failure by yielding
- Haig-Westergaard representation
- Von Mises-Hencky-Nadai yield criterion
- Tresca-Guest yield criterion
- Alternate yield criteria
- Equivalent stress and safety factor

Subject 6: 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

CHAPTER 3. STRENGTH OF MATERIALS (Nºof sessions: 7)

Subject 7 and 8: Reaction and internals forces
- External degrees of freedom in a mechanical system
- External link in a mechanical system
- External degree of static indeterminacy
- Internal link
- Internal degree of static indeterminacy
- Total degree of static indeterminacy
- Computation of reactions

Subject 9: Introduction to beam theory

- Definition of a beam
- Types of loads acting in beams
- Internal forces and moments in beams

Subject 10 and 11 : Bending and shear in beamss
- Normal stresses in beam
- Neutral axis
- Sections with symmetries
- Shear stresses due to shear force
- Sections with symmetries
- Shear stresses due to torque

Subject 12: Deflections of beams
- Equilibrium equations of beams
- Internal forces and moments equations
- Deflections by integration of the internal forces (Navier-Bresse equations)
- Moment-area method(Mohr´s theorems)

Subject 13: Isostatically indeterminate structures
- Kinematic definitions
- Introduction to the force (or flexibility) method
- Application to continuum beams

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. Additionally, students will complement the classes with work at home, using material provided on Aula Global.

In addition to these sessions, four laboratory practical sessions in reduced groups (maximum 20 students) will be impart. These practices are mandatory.

At the end of the semester tutorial session will be held. Students also have the possibility of individual tutorials.

Assessment System:

Final exam (obligatory): 60%
Continuum evaluation: 40%
- Laboratory report: 25%
- Evaluation controls: 15%
If the mark obtained in the final exam is lower than 4.5, the final mark of the student will be computed only with the final exam.

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. Ed. UPC. 2000
Ortiz Berrocal, L . Elasticidad. Ed. McGraw Hill. 1998
Paris Carballo, F.. Teoría de la elasticidad. Grupo de Elasticidad y Resistencia. 1998
Pilkey, W.D. y Wunderlich, W. . Mechanics of structures. Variational and Computational Methods. CRC Press. 1994
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