A residential foundation in Hawaii requires design for volcanic ash soil with a bearing capacity of 1,500 psf. If a column load is 45,000 lbs, what minimum footing area is required?
Correct Answer
C) 30 square feet
Required area = Load ÷ Bearing capacity = 45,000 lbs ÷ 1,500 psf = 30 square feet.
Why This Is the Correct Answer
The minimum 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 fundamental footing sizing formula ensuring the soil is not overstressed.
Why the Other Options Are Wrong
Option A: 50 square feet
50 square feet is too large. That would correspond to a load of 75,000 lbs at 1,500 psf, which significantly overestimates the required area and wastes material.
Option B: 40 square feet
40 square feet is too large. It would correspond to a 60,000 lb load at 1,500 psf, overdesigning the footing for the given conditions.
Option D: 20 square feet
20 square feet is too small. It would only support 30,000 lbs at 1,500 psf, leaving 15,000 lbs unsupported and risking foundation failure.
Memory Technique
Area = Load ÷ Bearing. Think: 'A big load on weak soil needs a BIG shoe.' The shoe area = weight ÷ ground strength. 45,000 ÷ 1,500 = 30.
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A residential foundation is being constructed on volcanic ash soil with a bearing capacity of 1,500 psf. If a continuous footing must support a load of 4,200 pounds per linear foot, what is the minimum required footing width?