Eccentric loading on a rectangular footing: condition to avoid tension For a rectangular footing of length L and breadth B under an axial load P with eccentricity e along the length, and allowable soil bearing capacity Q, which condition(s) must be satisfied to avoid tension in soil contact?

Introduction / Context:
Eccentric column loads cause non-uniform contact pressure beneath a footing. To prevent separation (tension) at the heel and to remain within the soil’s allowable bearing capacity, combined conditions on eccentricity and maximum pressure must be checked.

Given Data / Assumptions:

• Rectangular footing plan area A = L * B.
• Resultant load P acts with eccentricity e along length L.
• Linear pressure distribution assumption (elastic, rigid footing on Winkler-type support).
• Allowable bearing capacity (limit) = Q.

Concept / Approach:

For linearly varying pressure under eccentric load: q_max = (P/A) * (1 + 6e/L) and q_min = (P/A) * (1 − 6e/L). To avoid tension, require q_min ≥ 0 → e ≤ L/6. Also check q_max ≤ Q to meet bearing capacity limits.

Step-by-Step Solution:

Verification / Alternative check:

If e = 0, conditions reduce to P/A ≤ Q, as expected. If e approaches L/6, q_min → 0, the pressure diagram becomes triangular—still permissible if q_max ≤ Q.

Why Other Options Are Wrong:

Option (a) alone ignores capacity; (b) alone may allow tension at the heel. Option (d) ignores eccentricity-induced uplift; (e) is physically incorrect since soils cannot carry tension.

Common Pitfalls:

Using breadth B instead of length L in the 6e/L factor; neglecting to check both heel (q_min) and toe (q_max) pressures.

Final Answer:

Both (a) and (b) must be satisfied simultaneously