Question

1. using material densities from the following table. what is the total weight (in kips) of an 8-foot-tall by 25-foot-long wall that is constructed of 6-inch concrete masonry units with a layer of ½ gypsum board on each side?

Explanation:

To solve this, we need the densities of Concrete Masonry Units (CMU) and Gypsum board from the table (not provided here, but we'll assume typical values: CMU density ≈ 120 lb/ft³, Gypsum board density ≈ 2.5 lb/ft²).

Step 1: Calculate Volume of CMU Wall

First, convert the thickness of CMU from inches to feet: \( 6 \, \text{in} = \frac{6}{12} = 0.5 \, \text{ft} \).
The volume of the CMU wall is:
\[
\text{Volume}_{\text{CMU}} = \text{height} \times \text{length} \times \text{thickness} = 8 \, \text{ft} \times 25 \, \text{ft} \times 0.5 \, \text{ft} = 100 \, \text{ft}^3
\]

Step 2: Weight of CMU Wall

Using density \(
ho_{\text{CMU}} = 120 \, \text{lb/ft}^3 \):
\[
\text{Weight}_{\text{CMU}} = \text{Volume}_{\text{CMU}} \times
ho_{\text{CMU}} = 100 \, \text{ft}^3 \times 120 \, \text{lb/ft}^3 = 12,000 \, \text{lb}
\]

Step 3: Area of Gypsum Board (per side)

The area of one side of the wall is:
\[
\text{Area}_{\text{gypsum (one side)}} = \text{height} \times \text{length} = 8 \, \text{ft} \times 25 \, \text{ft} = 200 \, \text{ft}^2
\]
With 2 sides (both sides have gypsum board):
\[
\text{Total Area}_{\text{gypsum}} = 2 \times 200 \, \text{ft}^2 = 400 \, \text{ft}^2
\]

Step 4: Weight of Gypsum Board

Using density \(
ho_{\text{gypsum}} = 2.5 \, \text{lb/ft}^2 \):
\[
\text{Weight}_{\text{gypsum}} = \text{Total Area}_{\text{gypsum}} \times
ho_{\text{gypsum}} = 400 \, \text{ft}^2 \times 2.5 \, \text{lb/ft}^2 = 1,000 \, \text{lb}
\]

Step 5: Total Weight (Convert to kips)

Total weight in pounds:
\[
\text{Total Weight (lb)} = \text{Weight}_{\text{CMU}} + \text{Weight}_{\text{gypsum}} = 12,000 \, \text{lb} + 1,000 \, \text{lb} = 13,000 \, \text{lb}
\]
Convert to kips (\( 1 \, \text{kip} = 1,000 \, \text{lb} \)):
\[
\text{Total Weight (kips)} = \frac{13,000 \, \text{lb}}{1,000 \, \text{lb/kip}} = 13 \, \text{kips}
\]

Answer:

\( \boldsymbol{13} \) kips (note: this depends on the exact densities from the table; if densities differ, recalculate with the provided values).