Solid Mechanics | 10. Mohr’s Circle Recap by Abraham | Learn Smarter
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10. Mohr’s Circle Recap

10. Mohr’s Circle Recap

The chapter delves into Mohr's circle, discussing its application in determining principal stresses and shear stress in various planes. It also covers stress invariants, octahedral stress components, and the decomposition of the stress tensor into hydrostatic and deviatoric parts. Key examples illustrate the graphical methods of analysis and the limitations associated with Mohr's circle.

9 sections

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Sections

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  1. 1
    Mohr’s Circle Recap

    This section recaps the concepts surrounding Mohr’s Circle, its significance...

  2. 1.1
    Planes Of Principal Stresses In Mohr’s Circle

    This section discusses how to determine the orientation of principal stress...

  3. 1.2

    This section explores an example using Mohr's circle to determine principal...

  4. 2
    Mohr’s Stress Plane

    This section discusses Mohr's stress plane, defining the concept and...

  5. 2.1
    Special Case I

    This section discusses special cases of the Mohr’s stress plane when...

  6. 2.2
    Special Case Ii

    Special Case II discusses scenarios where all principal stress components...

  7. 3
    Stress Invariants

    This section delves into stress invariants, demonstrating how certain stress...

  8. 4
    Octahedral Stress Components

    This section introduces octahedral stress components, detailing their...

  9. 5
    Hydrostatic And Deviatoric Parts In Stress Tensor

    This section explains how to decompose the stress tensor into hydrostatic...

What we have learnt

  • Mohr's circle is a graphical representation of the state of stress at a point.
  • Stress invariants are quantities related to the stress matrix that remain unchanged under coordinate transformations.
  • The stress tensor can be decomposed into hydrostatic and deviatoric parts to analyze stress more effectively.

Key Concepts

-- Mohr's Circle
A graphical method used to represent the state of stress at a point, allowing for the determination of principal stresses and maximum shear stress.
-- Principal Stress
The maximum and minimum normal stresses acting on certain planes, which are derived from the eigenvalues of the stress matrix.
-- Stress Invariants
Quantities derived from the stress tensor characteristics that do not change when the coordinate system is altered.
-- Octahedral Stress Components
Stress components acting on the octahedral faces of a cubic volume element, essential in certain failure theories.
-- Hydrostatic Stress
Stress state where all normal stresses are equal, resulting only from pressure with no shear stresses.
-- Deviatoric Stress
Stress components that represent the distortion of a material, independent of the hydrostatic stress.

Additional Learning Materials

Supplementary resources to enhance your learning experience.