Chapter 2, Problem 1P

To determine

Calculate the dead weight of a 1-ft-long segment of a pre-stressed beam.

Answer to Problem 1P

The dead weight of a 1-ft-long segment of a pre-stressed beam is $\underset{\_}{900\text{lb}/\text{ft}}$.

Explanation of Solution

Given information:

The unit weight of the lightweight concrete $\left(\gamma \right)$ is $120\text{lbs}/{\text{ft}}^{\text{3}}$.

Calculation:

Sketch the cross section of the beam as shown in Figure 1.

Refer to Figure 1.

Calculate the area of cross section as shown below.

$\begin{array}{c}A=\left(6\times 72+2\times \left(\frac{1}{2}\times 32\times 6\right)+30\times 8+12\times 18\right)\text{in}{\text{.}}^2\times {\left(\frac{1\text{ft}}{12\text{in}\text{.}}\right)}^2\\ =7.5{\text{ft}}^2\end{array}$

Calculate the dead weight of a 1-ft-long segment of a pre-stressed beam as shown below.

$\begin{array}{c}\text{Dead weight}=\gamma A\\ =120\times 7.5\\ =900\text{lb}/\text{ft}\end{array}$

Therefore, the dead weight of a 1-ft-long segment of a pre-stressed beam is $\underset{\_}{900\text{lb}/\text{ft}}$.