Public University of Navarre



Academic year: 2023/2024 | Previous academic years:  2022/2023  |  2021/2022  |  2020/2021  |  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:

 

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

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Languages

This subject is taught in Spanish, Basque and English.

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Evaluation

Learning outcome Assessment activity Weight (%) It allows test resit Minimum required grade
R1,R2,R3 Midterm Unit 1 10% Yes No
R1,R2,R3 Midterm Unit 2 20% Yes No
R1,R2,R3 Ordinary Call (Unit 3, 4 and 5) 70% Yes No
    EVALUATION - Theory of Elasticity and Strength of Materials The final grade in the continuous assessment depends on the result obtained in two main activities: midterms and final exam. REQUIREMENTS In order to pass the exam, the student must attend 2 midterms that are focused on the first two units developed in the lectures: 1) Theory of Elasticity, 2) Free Body Diagram. Their weight will be 10% and 20% respectively. The ordinary call will consist in an exam focused on the contents of the other three units: 3) Axially Loaded Members, 4) Torsion and 5) Bending Moment, developed in the lectures. Their weight will be 10%, 25% and 35% respectively. The weight of the ordinary call is independent of the results obtained in the midterms. MIDTERMS The students are requested to deliver 2 midterms. Each midterm is mainly a short exam about the first 2 units of the Theory of Elasticity and Strength of Materials and their global weight on the final grade is of 30%. The grade of the individual midterms will be always computed as the average of the 2 midterms (a non delivered midterm is equivalent of a grade of zero in the midterm). The grades of the individual midterms to be performed during the lectures CANNOT BE RECOVERED in the final exams (in the ordinary calls) but they CAN BE RECOVERED in the extraordinary call. ORDINARY CALL EXAM It is an exam focused on the contents of the unit 3), 4) and 5) developed during the lectures. Its global weight on the final grade is of 70%. The single weight of the unit 3) 10%, 4) is 25%, that of the unit 5) is 35%. In order to have success in the ordinary call, it is required a final minimum grade of 5/10 (obtained as sum of both midterms and exam). EVALUATION WEIGHT MIDTERMS 30% -Unit 1 10% -Unit 2 20% EXAM Ordinary Call 70% -Unit 1 10% -Unit 4 25% -Unit 5 35% RETAKE CALL EXAM It is an exam focused on the contents of the totality of the units of Theory of Elasticity and Strength of Materials. Its weight is 100% as, after the ordinary call, the marks obtained in the midterms will be no further considered and the weights of each unit may vary. In order to have success in the extraordinary call, it is required a final minimum mark of 5/10 in this exam. EVALUATION WEIGHT EXAM Retake call 100%

 

 

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Agenda

PART I: Theory of Elasticity

1.  Introduction to the Elasticity: 
-   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:
-   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:
-   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:
-   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:
-   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
-  Safety coefficients
Load safety coefficient
Material resistive safety coefficient
-   Statically determinate and indeterminate structures
Equilibrium equations
Displacements conditions
-   Strain Energy
Definitions
Expressions

6.  Axially loaded members:
-   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:
-   Definitions and equation of equilibrium
Hypothesis
Stresses
-   Structural connections: bolts
Structural failure

8.  Torsion: 
-   Definitions and equation of equilibrium
-   Circular Bars of Linearly Elastic Materials
-   Torsional Deformations of a Circular Bar: angle of twist 
-   Transmission of Power by Circular Shafts
-   Stresses and Strains in Pure Shear
-   Statically Indeterminate Torsional Members
-   Diagram of torque
-   Diagram of torsional displacements
 
9.  Bending Moments: Stresses in beams
-   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
Collignon-Jourawski stresses
 
10. Deflections of beams:
-   Compatibility equation. Strain energy. Differential Equations of the Deflection Curve. Deflections by Integration of the Bending-Moment Equation
-   Principle of Virtual Works

11 Columns:
-   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

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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.

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