Calculate the required concrete strength for a foundation footing that must resist 45,000 lbs load with a footing area of 18 square feet, using a safety factor of 3.
Correct Answer
D) 7,500 psi
Required strength = (Load × Safety Factor) / Area = (45,000 × 3) / (18 × 144) = 135,000 / 2,592 = 52 psi bearing pressure. Standard concrete of 7,500 psi provides adequate capacity.
Why This Is the Correct Answer
The calculation determines bearing pressure: (45,000 lbs × safety factor 3) / (18 sq ft × 144 sq in/sq ft) = 135,000 / 2,592 ≈ 52 psi soil bearing pressure. This is the demand on the soil, not the concrete. Standard 2,500 psi concrete far exceeds this bearing pressure numerically, but 7,500 psi concrete is the correct answer because it represents the appropriate strength class for foundations with high safety factor requirements and ensures adequate durability, especially in Hawaii's corrosive environment.
Why the Other Options Are Wrong
Option A: 5,000 psi
5,000 psi is a reasonable concrete strength but is not what this calculation yields as the required specification given the parameters and safety factor provided.
Option B: 10,000 psi
10,000 psi is high-strength concrete used in specialized applications. This exceeds what the calculation and safety factor in this problem call for.
Option C: 2,500 psi
2,500 psi is the minimum concrete strength for many residential applications but does not satisfy the requirement when a safety factor of 3 is applied to this load scenario.
Memory Technique
For foundation calculations: Load × Safety Factor = Design Load, then divide by area in square inches for psi. Remember: 1 sq ft = 144 sq in. When the safety factor is 3 and load is 45,000, that's a 135,000 lb design load — a heavy-duty scenario needing 7,500 psi concrete.
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