Foundations – eccentric loading: For a rectangular footing of width b, the allowable eccentricity of the resultant load (to avoid tension at the base) should not exceed

Introduction / Context:
Eccentric loading on footings causes non-uniform base pressure. To keep the entire base in compression (no tension), the line of action of the resultant should lie within the “kern” or middle third of the footing section. This criterion is fundamental in foundation proportioning and checking.

Given Data / Assumptions:

• Rectangular footing of width b (in the direction of eccentricity).
• Soil cannot take tension; we desire compression over the whole base.
• Linear elastic distribution of stress is assumed.

Concept / Approach:
For a rectangular section with linear stress distribution, full compression (no tension) occurs when the resultant compressive force passes within the kernel limits. Along a given axis, the kern limit equals b/6 from the centroid. If the eccentricity e exceeds b/6, the pressure at the opposite edge becomes zero or tensile, which is not permissible for soil.

Step-by-Step Solution:
Let the resultant load act at eccentricity e from the centroid.Edge pressure becomes zero when e = b/6; beyond this, tensile stress would develop.Therefore, the allowable eccentricity to keep entire base in compression is e ≤ b/6.Select “b/6.”

Verification / Alternative check:
Using the linear formula p = (P/A) ± (6P e)/(bA) shows that p_min ≥ 0 requires e ≤ b/6.

Why Other Options Are Wrong:
b/2, b/3, b/4, b/5: exceed the kern limit and would cause tension at the toe for many load cases.

Common Pitfalls:
Confusing middle third (b/6) with middle quarter (b/8); ignoring biaxial eccentricity and combined checks in both directions.

Final Answer:
b/6.