21. Recap - Solid Mechanics
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21. Recap

21. Recap

The chapter discusses the principles of Extension, Torsion, and Inflation in a hollow cylinder, focusing on equilibrium equations, stress distribution, and deformation under various conditions. Key mathematical formulations are derived to describe the behavior of the hollow cylinder under pressure and torques, alongside graphical representations. The chapter also explores the effects of axial force and twisting moments on the structure, providing insights into material behavior in composite cylinders.

13 sections

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Sections

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  1. 1

    This section summarizes the key concepts and mathematical formulations...

  2. 2
    Mathematical Form Of U

    This section provides mathematical formulations of the displacement in a...

  3. 3
    Mathematical Form Of U

    The section dives into the mathematical representation of displacement in a...

  4. 4
    Solution For Σ And Σ

    This section explores the mathematical solution of stress components in a...

  5. 4.1
    Mathematical Form

    This section discusses the mathematical formulation of stress within a...

  6. 4.2
    Application Of Boundary Conditions

    This section outlines how to apply boundary conditions to solve for unknown...

  7. 4.3
    Final Solution

    This section provides the final solutions for stress and displacement...

  8. 5
    Final Solution For U

    The section deals with deriving the final expression for the longitudinal...

  9. 6
    Solution For U And U

    This section discusses the solutions for longitudinal and circumferential...

  10. 6.1
    Relating Torque And End-To-End Rotation

    This section examines the relationship between torque and end-to-end...

  11. 6.2
    Relating Axial Force And Axial Strain

    This section discusses how axial force relates to axial strain in the...

  12. 7
    Variation Of Γ And Τ In The Cross Section

    This section discusses the linear variation of shear strain (γ) and shear...

  13. 7.1
    Special Case: Composite Cylinder

    This section discusses the mechanical behavior of a composite cylinder made...

What we have learnt

  • The equilibrium equations reveal relationships among stress, displacement, and applied loads in a hollow cylinder.
  • Boundary conditions are crucial for solving differential equations related to stress and strain.
  • The behavior of shear stress and shear strain varies linearly in the cross-section of a twisted cylinder.

Key Concepts

-- Equilibrium Equations
Mathematical expressions that describe the balance of forces and moments in a static system.
-- Boundary Conditions
Conditions imposed on the system at the boundaries to facilitate the solution of differential equations.
-- Shear Stress and Strain
The measure of internal forces acting parallel to a surface and the deformation caused by these forces.
-- Composite Cylinder
A structure made from two or more different materials, affecting the distribution of stresses and strains.
-- Lame’s Constants
Material constants that relate to the elastic properties of materials, useful in stress-strain relationships.

Additional Learning Materials

Supplementary resources to enhance your learning experience.