Question

The value of Shear stress along principal plane of a failure surface is

• A. Minimum
• B. Maximum
• C. Neither maximum nor minimum
• D. Zero

Hint:

Principal Plane = Plane of Zero Shear Stress.
This is a core definition in stress analysis.
The maximum normal stress (\(\sigma_1\)) and minimum normal stress (\(\sigma_3\)) occur on principal planes, but the shear stress on these specific planes is always zero.

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
This is a fundamental question in mechanics and rock mechanics, asking for the value of shear stress on a principal plane.

Step 2: Detailed Explanation:
In a stressed body, there exist three mutually perpendicular planes where the stress acting on them is purely normal (perpendicular) to the plane.
These special planes are called the

principal planes.
The normal stresses acting on these planes are called the

principal stresses (denoted as \(\sigma_1\), \(\sigma_2\), and \(\sigma_3\)).
By the very definition of a principal plane, there are

no shear stresses acting on it.
The shear stress reaches its maximum value on planes that are oriented at 45 degrees to the principal planes.
Since a principal plane is defined as a plane of zero shear stress, the value of shear stress along it must be zero.

Step 3: Final Answer:
The value of shear stress along a principal plane is zero.
This corresponds to option (D).