The radius of the Mohr’s circle of stress is (where σx and σy are normal stresses, and τ is shear stress.)
- A√[((σx + σy)/2)² − τ²]
- B√[((σx − σy)/2)² + τ²]Correct
- C√[((σx − σy)/2)² − τ²]
- D√[((σx + σy)/2)² + τ²]
Solution
Concept
Mohr circle geometry
Formula
R = √[((σx − σy)/2)² + τ²]
Step-by-step solution
1. The centre of the circle is at (σx + σy)/2. 2. The point (σx, τ) is at horizontal distance (σx − σy)/2 and vertical distance τ from the centre. 3. Radius = √[((σx − σy)/2)² + τ²] = maximum shear stress.
Explanation
The radius is found by Pythagoras from the half difference of the normal stresses and the shear stress. It equals the maximum in-plane shear stress.
Why the other options are wrong
Options with a minus sign under the root or with (σx + σy) do not give the distance from the centre to the stress point.
Shortcut
R = τmax = √[((σx − σy)/2)² + τ²].
Common mistake
Using the sum instead of the difference.
Correct answer: B) √[((σx − σy)/2)² + τ²]