The angle between a principal plane and the plane of maximum shear is:
Try it first: pick an option, then read the explanation.
Correct answer: B. 135°
Asked in SSC JE 29/01/2018 (Morning)
Detailed Explanation
Shear on a plane is ((σ₁ − σ₂)/2) sin 2θ, which is maximum when sin 2θ = ±1, i.e. θ = 45° or 135° from a principal plane.
Why “135°” Is Correct
The maximum shear planes lie at 45° and 135° to the principal planes (the two describe the same pair of perpendicular planes). Since 45° is not listed, 135° is correct.
Why the Other Options Are Wrong
- A. 90°: 90° separates the two principal planes from each other.
- C. 60°: At 60°, sin 2θ = 0.87 — not the maximum.
- D. none of these: 135° is listed and correct.
Key Point
Max shear planes at 45°/135° to principal planes (90° apart on Mohr's circle).
Key Concepts for Students
- Angles on Mohr's circle are double the actual angles.
- Two principal planes are 90° apart.
- Normal stress on max-shear planes = (σ₁ + σ₂)/2.
Practice more: this is question 8 in Principal Stress and Principal Planes MCQs – Part 1. Try the whole set and check every answer instantly.