Which of the following statements is true?
Try it first: pick an option, then read the explanation.
Correct answer: A. The sum of normal stresses is constant
Asked in SSC JE 24/01/2018 (Morning)
Detailed Explanation
When we rotate the planes through a point, the normal and shear stresses on them change. But some combinations stay the same — these are called stress invariants.
\[ \sigma_x + \sigma_y = \sigma_{x'} + \sigma_{y'} = \sigma_1 + \sigma_2 = \text{constant} \]
On Mohr's circle, this sum is twice the centre's abscissa, which does not move.
Why “The sum of normal stresses is constant” Is Correct
So the sum of normal stresses on two perpendicular planes is constant — the first stress invariant.
Why the Other Options Are Wrong
- B. The sum of normal stresses is variable: The sum does not change with orientation.
- C. The sum of normal stresses depends on the plane: Individual stresses depend on the plane, but their sum on perpendicular planes does not.
- D. None of these: Statement (a) is true.
Key Point
σx + σy = σ1 + σ2 (first invariant); Mohr's circle centre = (σx + σy)/2.
Key Concepts for Students
- Maximum shear stress = (σ1 − σ2)/2.
- Principal planes carry no shear stress.
- In 3-D, σx + σy + σz is invariant.
Practice more: this is question 34 in Stress and Strain MCQs – Part 3. Try the whole set and check every answer instantly.