For a column base subjected to axial load P and moment M, what should be the ratio M/P in order to keep the bearing pressure distribution between the base plate and concrete compressive and varying from zero to maximum?

Introduction / Context:Column bases under combined axial load and moment must ensure that the contact stress remains compressive. A linear stress distribution is assumed. To avoid uplift (tension), a geometric limit on M/P exists.

Given Data / Assumptions:

• Base plate width in bending direction = L
• Axial load = P
• Bending moment = M
• Stress varies linearly from zero to maximum

Concept / Approach:Average stress = P/A. Additional bending stress = M/Z. To avoid negative stress (tension), the maximum eccentricity e = M/P must not exceed L/6. This ensures stress ranges from 0 to 2P/A.

Step-by-Step Solution:Eccentricity e = M/PCondition for non-negative stress: e ≤ L/6Thus, ratio M/P = L/6

Verification / Alternative check:This is consistent with the middle-third rule of soil/structural mechanics.

Why Other Options Are Wrong:

• L/4 and L/2: too large, would cause tension at the edge
• L/8: smaller, overly conservative

Common Pitfalls:Confusing middle-third rule with middle-half rule; misinterpreting L as full base dimension instead of loaded dimension.

Final Answer:M/P = L/6