For a mat foundation on soft clay with bearing capacity of 2,000 psf, what is the maximum building load if the foundation is 40 ft × 60 ft?
Correct Answer
A) 4,800 kips
Maximum load = bearing capacity × area = 2,000 psf × (40 ft × 60 ft) = 2,000 × 2,400 = 4,800,000 lbs = 4,800 kips.
Why This Is the Correct Answer
Maximum allowable load = allowable bearing pressure × foundation area. Area = 40 ft × 60 ft = 2,400 sq ft. Load = 2,000 psf × 2,400 sq ft = 4,800,000 lbs. Converting: 4,800,000 lbs ÷ 1,000 = 4,800 kips. This is a direct application of the bearing capacity formula with no partial safety factors or other adjustments needed because the problem provides the allowable (design) bearing capacity directly.
Why the Other Options Are Wrong
Option B: 6,000 kips
6,000 kips would result from using a bearing capacity of 2,500 psf (2,500 × 2,400 = 6,000,000 lbs = 6,000 kips) — a 25% overestimate. This is not the value given, and using it would allow a load that exceeds the safe capacity, risking foundation settlement or failure.
Option C: 3,200 kips
3,200 kips corresponds to approximately 1,333 psf bearing capacity with the 2,400 sq ft area, or alternatively using only part of the foundation area. This result does not match any logical rounding of the given values and represents an arithmetic error.
Option D: 7,200 kips
7,200 kips would require 3,000 psf bearing capacity (3,000 × 2,400 = 7,200,000 lbs = 7,200 kips). Using 3,000 psf when the problem states 2,000 psf is a 50% overestimation error, which would significantly underdesign the foundation.
Memory Technique
The formula is simple: P_max = q_allow × A. Always do it in three steps: (1) Calculate area in sq ft, (2) Multiply by bearing capacity in psf to get pounds, (3) Divide by 1,000 to convert to kips. Write it as: '2,000 × 2,400 = 4,800,000 lb = 4,800 kips.' The clean numbers make this calculation exam-friendly.
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