Question

An element is subjected to a pure shear stress of magnitude \(\tau\). Which of the following statement is incorrect regarding the Mohr's Circle for this stress state?

• A. The center of the Mohr's Circle coincides with the origin \((0,0)\)
• B. The maximum principal stress is equal in magnitude to the applied shear stress
• C. The radius of the Mohr's Circle is equal to \(\tau\)
• D. The maximum normal stress acting on the element is \(2\tau\)

Hint:

For pure shear, \[ \boxed{ \begin{aligned} \sigma_1&=+\tau, \sigma_2&=-\tau, R&=\tau, \text{Center}&=(0,0). \end{aligned} } \]

Answer 1

The Correct Option is D

Step 1: Recall the Mohr's Circle for pure shear. For a pure shear state, \[ \sigma_x=\sigma_y=0, \] \[ \tau_{xy}=\tau. \] Hence, \[ \boxed{ \text{Center}=(0,0), } \] and \[ \boxed{ \text{Radius}=\tau. } \]

Step 2: Determine the principal stresses. The principal stresses are \[ \sigma_1=+\tau, \] \[ \sigma_2=-\tau. \] Therefore, the maximum normal stress is \[ \boxed{\tau,} \] not \[ 2\tau. \] Hence, \[ \boxed{\text{The statement "Maximum normal stress is }2\tau\text{" is incorrect}.} \] Thus, \[ \boxed{(D)} \] is the correct answer.