Foundation design for boundary walls: to keep the soil reaction on an offset footing fully compressive (no tension anywhere), where should the resultant line of action or C.G. of the applied load fall on the base?

Introduction / Context:
For masonry boundary walls on offset or eccentric footings, avoiding tensile contact stress under the base is essential. Classical foundation theory uses the middle-third rule to ensure a linear, fully compressive pressure distribution and to prevent uplift or cracking at the heel or toe.

Given Data / Assumptions:

• Rigid footing on a linear-elastic soil idealization with resultant load acting at some eccentricity e from the centroid.
• Pressure distribution under the base remains linear (no soil tension allowed).
• We seek the condition on the load's line of action (C.G.).

Concept / Approach:
For a rectangular base of breadth B with an applied vertical load W at eccentricity e, the contact pressure varies linearly. If e ≤ B/6 (i.e., resultant lies within the middle third), the pressure at both edges remains nonnegative. If e > B/6, tensile stress appears at one edge, violating the “fully compressive” requirement.

Step-by-Step Solution:
Define middle-third range: centroidal zone bounded by ±B/6 about the geometric centre.Require zero tension: enforce e ≤ B/6 so p_min ≥ 0.Therefore, the C.G. must fall within the middle third of the base.

Verification / Alternative check:
Using the linear pressure formula p(x) = W/B ± 6W e/(B^2) at edges shows p_min ≥ 0 only if e ≤ B/6, directly giving the middle-third rule.

Why Other Options Are Wrong:

• At the centre: sufficient but not necessary; the whole middle third is acceptable.
• Middle fifth: overly restrictive and not required by theory.
• Neither: contradicts the established middle-third criterion.

Common Pitfalls:

• Confusing serviceability limits (tilt) with strength/pressure limits (tension avoidance).

Final Answer:
within the middle third of the base