Core or Kernel of Section MCQ with answer and solution

Concept

Kernel of a Solid Circular Section

Formula

e = D/8 = r/4

Step-by-step solution

1. For a circular column with radius r, the diameter is D = 2r. 2. For no tension condition, the maximum allowable eccentricity is e = D / 8. 3. Substitute D = 2r into the formula: e = 2r / 8 = r / 4.

Explanation

To avoid any tension in a solid circular column, the eccentric load must lie within the middle-fourth region (the core/kernel of the section). For a circular cross-section with diameter D (or radius r), the maximum allowable eccentricity for no tension is e = D/8. Substituting D = 2r gives e = 2r/8 = r/4.

Shortcut

For circular sections, remember the "Middle-Fourth Rule": the kernel diameter is D/4, so the maximum eccentricity from the center is half of that, which is D/8 or r/4.

Common mistake

Confusing the formula in terms of diameter (e = D/8) and selecting Option D (r/8), or mistaking the kernel diameter (D/4) for eccentricity.