Mohr's circle
How to construct Mohr's circle for the two-dimensional analysis of the stress state.
Tagged: mechanics
Plane stress and plane strain
Definition of plane stress and plane strain, the form of the stress and strain tensors, and the stress–strain relations in each case.
Equilibrium equations
Derivation of the equilibrium equations in three dimensions and proof of the symmetry of the Cauchy stress tensor.
Index notation for tensors and vectors
An introduction to index notation for vectors and tensors in continuum mechanics.
Mohr's circle in three dimensions
How to construct Mohr's circle diagram in three dimensions.
Octahedral stresses
Definition of the octahedral planes and of the normal and shear stresses acting on them.
Deviatoric stress and invariants
Definition of the hydrostatic and deviatoric parts of the stress tensor and calculation of the invariants of the deviatoric stress tensor.
Principal stresses and stress invariants
Derivation of the principal stresses and the stress invariants from the Cauchy stress tensor.
Calculation of normal and shear stress on a plane
How to calculate the normal and shear stress on an arbitrary plane through a point of a body in equilibrium.
Transformation of a tensor to a new coordinate system
Rotation of a tensor into a new coordinate system, with application to the Cauchy stress tensor.