Question

With respect to the plane of maximum shear stress, which of the following statements is INCORRECT?

• A. The normal stress on this plane is zero.
• B. The maximum shear stress is equal to the largest of the one half the difference of principal stresses.
• C. The plane of maximum shear stress occurs at \( 45^\circ \) to the principal planes.
• D. The magnitude of the maximum shear stress is equal to the largest of the radius of the Mohr's circles.

Hint:

In the plane of maximum shear stress, the shear stress is at its maximum value, and the normal stress is not zero, contrary to what is often misunderstood.

Answer 1

The Correct Option is A

The plane of maximum shear stress occurs at \( 45^\circ \) to the principal planes, where the normal stress is zero and the shear stress is maximized. The maximum shear stress is half the difference between the principal stresses.

Step 1: Incorrect Statement.
Statement (A) is incorrect because the normal stress on the plane of maximum shear stress is not zero; it is in fact half of the sum of the principal stresses. This is why statement (A) is the wrong answer.

Step 2: Correct Analysis.
The maximum shear stress occurs at a \( 45^\circ \) angle, and it is equal to half of the difference between the maximum and minimum principal stresses. Thus, the incorrect statement is (A).

Final Answer: (A)