Consider the following statements regarding Mohr’s circle of stress 1. The coordinates of any point on the circumference represent the normal and shear stress on a specific plane. 2. The center of the Mohr’s circle always lies on the normal stress (σ) axis. 3. The radius of the Mohr’s circle represents the maximum principal stress. Which of the statements given above are correct?
- A1 and 2 onlyCorrect
- B2 and 3 only
- C1 and 3 only
- D1, 2 and 3
Solution
Concept
Properties of Mohr's Circle
Formula
Center = (σx + σy)/2, Radius = τmax = √[((σx - σy)/2)² + τxy²], Principal Stresses = (σx + σy)/2 ± √[((σx - σy)/2)² + τxy²]
Step-by-step solution
1. Analyze Statement 1: Any point on the circumference of Mohr's circle gives the normal and shear stress acting on a plane, so Statement 1 is correct. 2. Analyze Statement 2: The shear stress at the center of Mohr's circle is zero, placing its center on the horizontal normal stress (σ) axis, so Statement 2 is correct. 3. Analyze Statement 3: The radius of Mohr's circle equals the maximum shear stress (τ\_max), not the maximum principal stress, so Statement 3 is incorrect. 4. Conclude that Statements 1 and 2 are correct, making Option (a) the correct answer.
Explanation
Statement 1 is correct because every point on the circumference of Mohr's circle gives the normal stress and shear stress acting on a plane inclined at a specific angle. Statement 2 is correct because shear stress at the center of Mohr's circle is zero, placing its center strictly on the normal stress axis. Statement 3 is incorrect because the radius of Mohr's circle represents the maximum shear stress, not the maximum principal stress. Therefore, Option A (1 and 2 only) is correct.
Shortcut
To remember the key properties of Mohr's Circle, use the mnemonic "C-C-R" (Circumference, Center, Radius): - Circumference: Any point on the circle gives the Stresses (normal and shear) on a plane. - Center: Always sits on the Horizontal Axis (normal stress σ axis, where shear stress τ = 0). - Radius: Equals the Maximum Shear Stress (τmax), NOT the maximum principal stress (Principal Stress = Center + Radius).
Common mistake
A common mistake is selecting Option D by confusing the radius of Mohr's circle with the maximum principal stress. In reality, the radius represents the maximum shear stress, while the maximum principal stress is equal to the distance from the origin to the center plus the radius.
Correct answer: A) 1 and 2 only