Given the state of stress σx = σy = − σ₀ (where σ₀ > 0) and τxy = 0 as shown in the figure, which one of the following statements is not correct ? (Refer to the Mohr diagram.)
- AThe radius of the Mohr circle R = 0.
- BNo shear stress exists on any plane passing through this point.
- CThe state of stress shown here is called a state of ‘Pure Shear’.Correct
- DThe normal stress is same for all planes passing through this point.
Solution
Concept
Hydrostatic (isotropic) stress state
Formula
σx = σy, τxy = 0 → Mohr circle is a point (R = 0)
Step-by-step solution
1. Equal normal stresses and no shear give R = (σx − σy)/2 = 0. 2. The Mohr circle degenerates into a point, so every plane has the same normal stress −σ₀ and zero shear. 3. This is a hydrostatic state, not pure shear. So (c) is incorrect.
Explanation
Pure shear is the state with σx = σy = 0 and τ ≠ 0 (or σ₁ = −σ₂). Here the stress is equal in all directions and shear is absent everywhere.
Why the other options are wrong
Statements (a), (b) and (d) correctly describe an isotropic stress state.
Shortcut
Point circle = hydrostatic. Circle centred on origin = pure shear.
Common mistake
Calling any special state pure shear.
Correct answer: C) The state of stress shown here is called a state of ‘Pure Shear’.