Which one of the following statements is not correct regarding principal stresses and planes ?
- AThe planes on which shearing stresses are zero are called principal planes and the stresses normal to principal planes are known as principal stresses.
- BThe principal planes are the planes of maximum or minimum normal stresses.
- CThe planes of extreme shearing stresses are at 90° to the principal planes.Correct
- DThe sum of normal stresses in any two mutually perpendicular directions is constant in case of a general two-dimensional stress.
Solution
Concept
Properties of principal planes
Formula
σx + σy = σ₁ + σ₂ (invariant)
Step-by-step solution
1. Principal planes carry zero shear and have extreme normal stresses (a, b true). 2. The sum σx + σy is an invariant (d true). 3. Planes of maximum shear are at 45° to the principal planes, not 90°. Statement (c) is wrong.
Explanation
On the Mohr circle, the principal stresses are at the ends of the horizontal diameter and the maximum shear at the top and bottom of the circle, which is 90° on the circle = 45° in the body.
Why the other options are wrong
Statements (a), (b) and (d) are standard true properties of principal stresses.
Shortcut
Principal planes ↔ max shear planes: 45° apart.
Common mistake
Confusing 90° on the Mohr circle with 90° in the body.
Correct answer: C) The planes of extreme shearing stresses are at 90° to the principal planes.