Combined footing fundamentals — which statements are correct? Consider the following statements about combined footings for two columns: (a) The footing is proportioned so that the centroid of the supporting area coincides with the centroid of the two column loads. (b) A combined footing may be rectangular or trapezoidal in plan. (c) Rectangular combined footings are used when column loads are equal or the interior column carries the greater load. (d) Trapezoidal combined footings may be provided under any loading without restriction. Which option correctly identifies the true statements?

Introduction / Context:
Combined footings support two columns with a single slab when isolated footings would overlap or property lines prevent symmetric layouts. Proportioning rules ensure that the soil pressure is uniform (or linearly distributed without tension), which minimizes eccentricity and prevents edge uplift.

Given Data / Assumptions:

• Two axially loaded columns on a common footing.
• Soil behaves elastically within allowable bearing pressure.
• Self-weight of footing either neglected in first sizing or added uniformly.

Concept / Approach:

The resultant of the column loads must pass through the centroid of the footing area to avoid net moment that would cause nonuniform contact pressures. Plan shapes are typically rectangular or trapezoidal. Rectangular shapes are efficient when loads are equal or when the inner column is heavier so that the load resultant lies near the geometric center. Trapezoidal shapes are usually adopted when column loads are unequal or edge constraints shift the resultant; they are not “under any loading” but selected to align centroid locations and geometric limits.

Step-by-Step Solution:

Verification / Alternative check:

Worked examples show moving from rectangular to trapezoidal when column load ratio significantly deviates or when the property line limits projection on one side, to keep the resultant through the centroid of area.

Why Other Options Are Wrong:

• (b) alone or (a)&(c) alone omit valid information; (d) is false because trapezoidal is not universal; (d) also invalidates “All of…” in option (d).

Common Pitfalls:

• Forgetting that the location of the resultant governs plan shape more than habit.
• Ignoring column dimensions and projection limits while placing the footing centroid.

Final Answer:

Only (a), (b), and (c) are correct.