You are designing footings for a structure on loose sand with a bearing capacity of 1,500 psf. The column load is 45,000 pounds. What is the minimum required footing area?
Correct Answer
B) 30 sq ft
Required area = Load ÷ Bearing capacity = 45,000 lbs ÷ 1,500 psf = 30 square feet minimum.
Why This Is the Correct Answer
Option B (30 sq ft) is correct because the required footing area is calculated by dividing the column load by the soil bearing capacity: 45,000 lbs ÷ 1,500 psf = 30 square feet. This is the minimum area needed to spread the load without exceeding the soil's allowable bearing pressure.
Why the Other Options Are Wrong
Option A: 35 sq ft
Option A (35 sq ft) is incorrect. While a larger footing is structurally safe, the question asks for the MINIMUM required area. Using 45,000 ÷ 1,500 = exactly 30 sq ft — 35 sq ft exceeds the minimum and represents over-design.
Option C: 25 sq ft
Option C (25 sq ft) is incorrect. A 25 sq ft footing would produce a bearing pressure of 45,000 ÷ 25 = 1,800 psf, which exceeds the allowable 1,500 psf bearing capacity of the loose sand. This would cause excessive settlement or footing failure.
Option D: 40 sq ft
Option D (40 sq ft) is incorrect for the same reason as Option A — it is larger than the minimum required. The minimum is exactly 30 sq ft; 40 sq ft is oversized and not the answer sought.
Memory Technique
Think of soil bearing capacity as a 'weight limit per square foot.' To find how many square feet you need, divide total load by the limit per foot: A = L ÷ BC. Visualize spreading 45,000 pounds evenly across tiles where each tile holds 1,500 pounds — you need exactly 30 tiles.
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