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.
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Sections
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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
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