To determine whether 2x10 boards are appropriate given the load requirement and the room dimensions, we should follow these steps:
1. Convert Room Dimensions to Inches:
- Length: 13 feet 2 inches
- Convert to inches: [tex]\( (13 \times 12) + 2 = 156 + 2 = 158 \)[/tex] inches
- Width: 11 feet 7 inches
- Convert to inches: [tex]\( (11 \times 12) + 7 = 132 + 7 = 139 \)[/tex] inches
2. Understand the Load Requirement:
- The load requirement specified is 60 pounds per square foot (psf).
- The joist spacing is 16 inches.
3. Check the Table for Maximum Load Capacity:
- For a load requirement of 60 psf at a joist spacing of 16 inches, from the table, we need to find the appropriate span.
- For 16-inch spacing, a load of 60 psf indicates that 2x10 boards can support spans of 10 feet 10 inches.
4. Compare Room Dimensions with the Allowable Span:
- Convert the allowable span from the table into inches for direct comparison:
- Allowable span: [tex]\( (10 \times 12) + 10 = 120 + 10 = 130 \)[/tex] inches
5. Assessment:
- The length of the room is 158 inches (greater than 130 inches), so the 2x10 boards at 16 inches spacing are not sufficient to support this span.
- The width of the room is 139 inches (greater than 130 inches), so the 2x10 boards at 16 inches spacing are not sufficient to support this span either.
Therefore, the final determination:
- Are [tex]\( 2 \times 10 \)[/tex] boards appropriate?
- No, because [tex]\( 2 \times 10 \)[/tex] boards at 16 inches spacing are only suitable for supporting a length or width of up to 130 inches, both of which are less than the dimensions of the room.
Based on the given information, the correct answer is:
C. No, because [tex]$2 \times 10$[/tex] boards can support only the width of the room (in this case, they actually cannot support the width either, but this option is the closest, highlighting the limitation in span support).
