Kernel (core) of a square masonry pillar – side of the core square A short masonry pillar has a 60 cm × 60 cm square cross-section. The kernel (core) for zero-tension loading is a square (rotated 45°) inside the section. What is the side length of this core square?

Introduction / Context:
For masonry or plain concrete compression members, the resultant load must lie within the kernel (core) to avoid tensile stress at the edges. For a rectangular section b × d, the kernel is a rhombus with diagonals b/3 and d/3. A square section makes this rhombus a square rotated 45°.

Given Data / Assumptions:

• Square section: b = d = 60 cm.
• Kernel (core) rhombus diagonals = b/3 and d/3.
• Linear elastic stress distribution and compression-only requirement.

Concept / Approach:
For a square, both kernel diagonals are equal: D = 60/3 = 20 cm. A rhombus with equal diagonals is a square. The side s of a square relates to its diagonal D by D = s * sqrt(2). Therefore, s = D / sqrt(2) = 20 / sqrt(2) ≈ 14.14 cm.

Step-by-Step Solution:
Compute diagonals: D_1 = D_2 = 60/3 = 20 cm.Recognize rhombus becomes a square (equal diagonals).Convert diagonal to side: s = 20 / sqrt(2) = 14.142 cm (≈ 14.14 cm).

Verification / Alternative check:
Kernel coordinates for a rectangle are within ±b/6 and ±d/6 from the centroid along principal axes; for b = d = 60 cm, limits are ±10 cm. The inscribed square's half-diagonal equals 10 cm → full diagonal 20 cm → side 14.14 cm.

Why Other Options Are Wrong:
17.32, 20.00, 22.36, 25.22 cm do not satisfy D = s * sqrt(2) for D = 20 cm.

Common Pitfalls:
Confusing kernel bounds (±b/6, ±d/6) with the side of the inscribed square; mixing up diagonal and side relations.

Final Answer:
14.14 cm