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
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