Three mutually perpendicular normal stresses in a coordinate system where all shear stresses vanish defines what?

Three mutually perpendicular normal stresses in a coordinate system where all shear stresses vanish defines what?

• A. Normal Stress
• B. Principal Stress
• C. Shear Stress
• D. Hydrostatic Stress

Answer: (B)

Principal stresses are the normal stresses on the axes where all shear components vanish. In three dimensions, you can rotate the coordinate system to align with directions in which the stress tensor is diagonal; along those principal directions, the shear stresses are zero and the remaining normal stresses are the principal stresses. These are the eigenvalues of the stress tensor and represent the maximum and minimum normal stresses that can occur at a point. If all three principal stresses happened to be equal, the state would be hydrostatic stress, but in general the three perpendicular normal stresses on the principal axes define the principal stress state.

Principal stresses are the normal stresses on the axes where all shear components vanish. In three dimensions, you can rotate the coordinate system to align with directions in which the stress tensor is diagonal; along those principal directions, the shear stresses are zero and the remaining normal stresses are the principal stresses. These are the eigenvalues of the stress tensor and represent the maximum and minimum normal stresses that can occur at a point. If all three principal stresses happened to be equal, the state would be hydrostatic stress, but in general the three perpendicular normal stresses on the principal axes define the principal stress state.