Core (kernel) of a circular column – location of load for wholly compressive stress To keep the stress distribution wholly compressive in a circular masonry/RC column of diameter d, the eccentric load must lie within a concentric circle (core). What is the diameter of this core circle?

Introduction / Context:
The core (or kernel) of a section is the locus of points where a resultant compressive load can act without causing tensile stress anywhere on the section. For masonry and plain concrete, keeping the stress wholly compressive is essential.

Given Data / Assumptions:

• Uniform circular cross-section of diameter d.
• Linear elastic stress distribution (no cracking in compression-only design).
• Eccentric compressive load applied.

Concept / Approach:
For a circular section, the core is also circular with radius r_core = d/4. Therefore, the core diameter is 2 * (d/4) = d/2. Any load applied within this core produces a linear stress block that remains non-tensile across the section.

Step-by-Step Solution:
For any section, core boundaries are defined by the condition that the extreme fibre stress just reaches zero.For a circle, r_core = I / (A * c) with c = radius = d/2, I = (pi/64) d^4, A = (pi/4) d^2 → r_core = [(pi/64) d^4] / [ (pi/4) d^2 * (d/2) ] = d/4.Hence core diameter = 2 * d/4 = d/2.

Verification / Alternative check:
Many design handbooks directly list the circular section core as a circle of radius d/4, confirming the computation.

Why Other Options Are Wrong:
d/3, d/4, d/8, d/10 do not match the derived size. d/4 is the core radius, not the diameter.

Common Pitfalls:
Mistaking core radius for core diameter; applying rectangular-section kernel formulas to circular sections.

Final Answer:
d/2