Question

Principal stresses occur where the shear stress is

• A. Maximum
• B. Minimum
• C. Zero
• D. Constant

Hint:

Principal Stresses and Planes. Principal stresses (\(\sigma_1, \sigma_2, \sigma_3\)) are the maximum and minimum normal stresses at a point. They act on principal planes, on which the shear stress is zero.

Answer 1

The Correct Option is C

Principal stresses are the maximum and minimum normal stresses acting at a point within a stressed body.
These stresses act on specific planes called principal planes.
A defining characteristic of principal planes is that the shear stress acting on these planes is zero.
When transforming the stress state to different orientations, the normal stress varies, and the shear stress also varies.
The orientations where the normal stress reaches its maximum and minimum values are the principal planes, and on these specific planes, the shear stress components are identically zero.
The maximum shear stress occurs on planes oriented typically 45 degrees relative to the principal planes.