You are framing a residential structure with 2x10 floor joists spaced 16 inches on center. The span is 14 feet with a live load of 40 psf and dead load of 10 psf. What is the total load per linear foot on the supporting beam?
Correct Answer
A) 66.7 pounds per linear foot
Total load = (40 psf + 10 psf) × 16 inches ÷ 12 inches = 50 psf × 1.33 ft = 66.7 pounds per linear foot.
Why This Is the Correct Answer
Option A is correct because the total load per linear foot on the supporting beam equals the combined live and dead loads multiplied by the joist spacing. Total load = (40 psf + 10 psf) × (16 inches ÷ 12 inches) = 50 psf × 1.333 ft = 66.7 pounds per linear foot. This accounts for the tributary area that each linear foot of beam supports.
Why the Other Options Are Wrong
Option B: 50 pounds per linear foot
This answer only accounts for the total load per square foot (50 psf) without considering the joist spacing. It fails to multiply by the tributary width of 16 inches (1.33 feet) that each linear foot of beam supports, resulting in an incomplete calculation.
Option C: 100 pounds per linear foot
This answer appears to double the correct load calculation or may result from incorrectly using the full span distance instead of the joist spacing. The calculation should use 16-inch spacing, not other dimensional factors that would yield 100 plf.
Option D: 133.3 pounds per linear foot
This answer doubles the correct result, likely from incorrectly applying the joist spacing twice in the calculation or using an incorrect conversion factor. The proper calculation yields 66.7 plf, not 133.3 plf.
Memory Technique
Remember 'LOTS': Load × On-center spacing × Tributary area = Support load. Total psf times spacing in feet gives pounds per linear foot.
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