Combined footing for two equal column loads with restricted overall width: Which footing shape is generally adopted to satisfy centroidal alignment and uniform soil pressure?

Introduction / Context:
When two columns of equal load share a combined footing and site width is limited (e.g., property line constraint), the footing must still position the resultant soil reaction under the combined centroid of column loads. For equal loads at reasonable spacing, a rectangular combined footing is typically suitable and economical.

Given Data / Assumptions:

• Two columns with equal axial loads.
• Restricted overall footing width (e.g., due to boundary line).
• Uniform allowable soil bearing capacity.
• Eccentricity control needed so resultant passes through centroid.

Concept / Approach:

For equal loads and symmetric geometry, the pressure distribution is uniform when the footing centroid coincides with the load resultant. A rectangular footing centered beneath the two columns satisfies this condition if its length spans between columns and is centered along the line joining them. Trapezoidal shapes are usually adopted when loads are unequal or when a property line prevents centering the footing; triangular shapes do not suit two equal point loads well.

Step-by-Step Solution:

Verification / Alternative check:

Basic statics confirms that a symmetric rectangular area gives no net moment about the centroid line, maintaining uniform bearing. A trapezoid is warranted primarily when P1 ≠ P2 or centering is not feasible.

Why Other Options Are Wrong:

Square is only possible if spacing and allowable pressure make it viable; triangular and circular are inappropriate for two equal, spaced point loads; trapezoidal is for unequal loads or boundary constraints causing eccentricity.

Common Pitfalls:

Using a trapezoid unnecessarily; ignoring footing self-weight and overburden; failing to check punching shear near columns.

Final Answer:

Rectangular