Combined footing for two columns with unequal loads: The location of maximum hogging (negative) bending moment occurs at which column position?

Introduction / Context:
In foundation engineering, a combined footing supports two columns on a single slab or beam. When column loads are unequal, the soil pressure distribution and internal bending vary along the footing. Recognizing where the maximum hogging (negative) bending moment occurs is essential for correct placement and sizing of top reinforcement.

Given Data / Assumptions:

• Two-column combined footing on uniform soil with eccentricities accounted by maintaining resultant soil reaction through the centroid of footing.
• Column loads are unequal, causing different peak reactions beneath each column footprint.
• Hogging moment is negative bending at the column locations (top fibers in tension) in a typical strap/combined footing.

Concept / Approach:

The footing behaves like a continuous beam on elastic support (soil). Concentrated column reactions plus distributed soil pressure produce bending. Larger column load increases the negative moment demand at that column, because soil reactions and compatibility generate a greater curvature reversal near the heavier column.

Step-by-Step Solution:

Verification / Alternative check:

Elastic-foundation solutions and strip-method approximations show that the section over the heavier column requires greater top steel due to higher negative moment, matching design experience in combined footings and strap footings.

Why Other Options Are Wrong:

(a) Less-loaded column sees a smaller hogging moment. (c) Midway between columns is typically a sagging region. (d) and (e) confuse shear and bending locations; maximum shear and zero-shear points do not necessarily coincide with negative-moment peaks.

Common Pitfalls:

Assuming symmetric reinforcement when loads are unequal; neglecting punching and two-way shear near columns; ignoring soil pressure limits near heavily loaded column edges.

Final Answer:

Under the more-loaded column