Core or Kernel of Section MCQ with answer and solution

Concept

For zero tension at one extreme fibre of a solid circular section, the load must act at e = D/8 from the centre. This is the boundary of the core.

Formula

σ_min = P/A − P·e/Z = 0, A = πD²/4, Z = πD³/32, e = Z/A = D/8

Step-by-step solution

1. Stress at the extreme fibre = P/A − P·e/Z. 2. For zero stress: P/A = P·e/Z, so e = Z/A. 3. Z = πD³/32 and A = πD²/4. 4. e = (πD³/32)/(πD²/4) = D/8 from the centre. 5. Distance from the periphery = D/2 − D/8 = 3D/8. 6. So the load is 3D/8 from the periphery, measured towards the centre. This matches option C.

Explanation

The core (kernel) of a solid circular section is a circle of diameter D/4, so its radius is D/8. A load placed exactly on the core boundary gives zero stress at the far extreme fibre. This point is 3D/8 from the periphery.

Why the other options are wrong

A: D/6 > D/8, so tension develops. B: D/4 > D/8, so more tension develops. D: D/3 > D/8, so large tension develops.

Shortcut

Circle core radius = D/8 (middle-quarter rule). Rectangle core = b/6 (middle-third rule).

Common mistake

Using the rectangle rule (D/6) for a circular section.