Question

The sum of normal stresses on any two mutually perpendicular planes is

• A. Variable depending on the angle \(\theta\)
• B. Constant value
• C. Equal to the maximum shear stress
• D. Always zero

Hint:

The quantity \[ \boxed{ \sigma_x+\sigma_y } \] is called the stress invariant and remains constant for all plane orientations. It is equal to twice the center of Mohr's Circle.

Answer 1

The Correct Option is B

Step 1: Recall the stress transformation equation. For stresses acting on two mutually perpendicular planes, \[ \boxed{ \sigma_{x'}+\sigma_{y'} = \sigma_x+\sigma_y. } \]

Step 2: Interpret the result. Since \[ \sigma_x+\sigma_y \] is independent of the orientation angle, \[ \boxed{ \text{the sum of the normal stresses remains constant.} } \] Therefore, \[ \boxed{\text{Constant value}} \] is the correct answer. Thus, \[ \boxed{(B)} \] is the correct answer.