Public University of Navarre



Academic year: 2019/2020
Bachelor's degree in Industrial Engineering at the Universidad Pública de Navarra
Course code: 252404 Subject title: ELASTICITY AND STRENGTH OF MATERIALS I
Credits: 6 Type of subject: Mandatory Year: 2 Period: 2º S
Department: Ingeniería
Lecturers:
MALVE ., MAURO (Resp)   [Mentoring ]

Partes de este texto:

 

Descriptors

Mechanics, Work, Energie, Thermodynamics, Electromagnetism.

For an adequate and efficient achievement of this matter it is strongly advised a deep knowledge of the physical principles of Mechanics, Thermodynamics and Electromagnetism. Additionally, the knowledge of the different units of measurements of the main physical variables related to this subejct is necessary. The aforementioned requirements are provided in Physics I and II.

Up

Methodology

Methodology - Activity In-class hours Out of class hours
A1. Classes 30.0  
A2. Workshop, exercises 20.0  
A3. Debates 2.0  
A4. Project   10.0
A5. Review of Material   30.0
A6. Individual study   50.0
A7. Examinations and tests 6.0  
A8. Individual tutorship 2.0  
Total 60.0 90.0

Up

Languages

This subject is taught in Spanish, Basque and English.

Up

Evaluation

In order to pass the exam it is mandatory:

  • To assist to at least 51% of the individual midterms to be performed in class (usually at least 3 midterms of 5).
  • To have reached a minimum of 5 (out of 10) in the final exam (ordinary call).
  • To have reached a minimum of  5 (out of 10) in the final exam (extraordinary call) in case of fail the ordinary call.

The grades of the individual midterms to be performed in class cannot be recovered in the final exams (in both ordinary and extraordinary calls).

The grade of the individual midterms will be always computed as the average of the 5 midterms (an absence or a non delivered midterm is equivalent of a grade of zero in the midterm).

Learning Outcome Evaluation Weight (%) Recoverability
Matter specific goals. R1, R2, R3, R4, R5 Exams 85% YES
Individual midterms and tests. R1, R2, R3, R4, R5 Midterms 15% NO

Up

Agenda

PART I: Theory of Elasticity

1.  Introduction to the Elasticity: (1 hour)
-   Aims of the Elasticity
-   Principles of Solid Mechanics
Typology and characteristics.
-   Static and Elastic Equilibrium
Solving methods
Internal forces
-   Concept of Stress
Definitions
Elastic equilibrium

2.  Analysis of stresses in deformable solids: (4 hours)
-   Stress Vector. Characterization of the stress vector components
-   Stress vector in specific location and direction of a solid
-   Stress Matrix

-   Equilibrium equations
Internal equilibrium
Boundary conditions
-  Principal stress and principal directions of stress
Characteristic equation
Invariant properties
-   Mohr's circle
Construction of the Mohr's circle
Cases and special conditions
 

3.  Analysis of strains in deformable solids: (4 hours)
-   Cinematics
Translation, rotation and dilatation
-   Strains Matrix

Physical meaning of the matrix components
Principal strains and principal direction of strains. Characteristic equation
-   Strain vector
Strain vector per unit length
Characterization of the strain vector components
Correlation between stress and strain
-   Mohr's circle
          Construction of the Mohr's circle
Cases and special conditions

4.  Correlation between stress matrix and strain matrix: (3 hours)
-   Stresses-Strains diagram
Material behaviours
Uniaxial tensile test
Hooke's law. Young's Modulus E.
-   Lateral contraction
Poisson's coefficient
-   Principle of superposition
-   Hooke's law in case of triaxial tensile stress
Shear modulus of elasticity G
Correlation between E and G
-   Lamé's equations


PART II: Strength of Materials

5.  Introduction to the Strength of Materials: (4 hours)
-   Aims and scopes of the Strength of Materials
Strength, rigidity and stabity
Difference between Theory of Elasticity and Strength of Materials
-   Prismatic solid
Elastic solid
Characteristics: Gravity center, Area, Moment of Inertia and first moment of the area.
-   Equilibrium
Axial and Shear Force, Torque and Bending Moment: definitions and correlation with the stresses and strains matrix
-   General principles of the Strength of Materials
Relative rigidity principle
Superposition principle
De Saint-Venant's principle
-   Loads
Types and combination
-   Structural connections
Types
-  Security coefficients
Load security coefficient
Material resistive security coefficient
-   Statically determinate and indeterminate structures
Equilibrium equations
Displacements conditions
-   Strain Energy
Definitions
Expressions

6.  Axially loaded members: (3 hours)
-   Changes in Lengths of Axially Loaded Members
Stresses and strains
Bernoulli's hypothesis
Stress matrix
Mohr's circle
-   Stress Concentrations
Examples
-   State of strain
Strain per unit length
Strain matrix
Displacements
-  Statically Indeterminate Structures
-  Strain energy
Expressions
Principle of virtual works
-  Thermal Effects

7.  Shear Forces: (2 hours)
-   Definitions and equation of equilibrium
Hypothesis
Stresses
-   Structural connections: bolts
Structural failure

8.  Torsion: (6 hours)
-   Definitions and equation of equilibrium
-   Circular Bars of Linearly Elastic Materials
-   Torsional Deformations of a Circular Bar
-   Transmission of Power by Circular Shafts
-   Stresses and Strains in Pure Shear
-   Statically Indeterminate Torsional Members
 
9.  Stress in beams (9 hours)
-   Pure Bending and Nonuniform Bending
          Relationships Between Loads, Shear Forces, and Bending Moments
Shear-Force and Bending-Moment Diagrams
-   Definitions and equation of equilibrium
Bending types
-   Normal Stresses in Beams (Linearly Elastic Materials)
Bernouilli's hypethesis
Navier's equation
Neutral axis and neutral surface
-   Shear Stresses in Beams of Rectangular Cross Section
Colignon-Jourawsky stresses
Strain energy

10 Deflections of beams: (6 hours)
-   Differential Equations of the Deflection Curve. Deflections by Integration of the Bending-Moment Equation
-   Principle of Virtual Works

11 Columns: (3 hours)
-   Introduction. Buckling and Stability
-   Critical load. Columns with Eccentric Axial Loads
-   Columns with pinned ends and Columns with other support conditions
-   Critical stress
-   Effective Lengths of Columns

Up

Bibliography

Access the bibliography that your professor has requested from the Library.


  • "Mechanics of Materials", Gere-Timoshenko. Thomson Learning. ISBN 0-534-41793-0
  • "Elasticidad", Luis Ortiz Berrocal. Universidad Politécnica de Madrid. Escuela Superior de Ingenieros Industriales, ISBN 84-481-2046-9.
  • "Resistencia de Materiales", Luis Ortiz Berrocal. McGraw-Hill, 684pp, ISBN 84-7615-512-3
  • "Ejercicios de Resistencia de Materiales", Begoña Calvo Calzada, Jesús Zurita Gabasa. Colección Textos Docentes, Prensas Universitarias de Zaragoza, 1996, ISBN 84-7733-465-X.

Up