Question

2.2.b △l = \frac{p×l}{a×e}
a = 8×8 = 7.5 in×7.5 in = 56.25 in² (nominal)
l = 12 ft = 144 in
p = 45 kips = 45,000 lb
e = 1,600,000 psi
2.2.c △l = \frac{p×l}{a×e}
e = 29,000,000 psi
a = 2 in²
l = 16 ft
△l = 0.0111 in
p = 20.5 kips = 20,500 lb

Explanation:

Step1: Identify the formula for $\Delta L$

The formula is $\Delta L=\frac{P\times L}{A\times E}$.

Step2: Solve for the first - case (2.2.B)

Given $P = 45000$ lb, $L=144$ in, $A = 56.25$ in², $E = 1600000$ psi. Substitute into the formula:
\[

$$\begin{align*} \Delta L&=\frac{45000\times144}{56.25\times1600000}\\ &=\frac{6480000}{90000000}\\ &= 0.072\text{ in} \end{align*}$$

\]

Step3: Solve for the second - case (2.2.C)

Given $E = 29000000$ psi, $A = 2$ in², $L = 16\times12 = 192$ in, $\Delta L=0.0111$ in. We need to find $P$. Rearrange the formula $\Delta L=\frac{P\times L}{A\times E}$ to $P=\frac{\Delta L\times A\times E}{L}$.
\[

$$\begin{align*} P&=\frac{0.0111\times2\times29000000}{192}\\ &=\frac{0.0111\times58000000}{192}\\ &=\frac{643800}{192}\\ &= 3353.125\text{ lb} \end{align*}$$

\]

Answer:

For 2.2.B, $\Delta L = 0.072$ in. For 2.2.C, $P = 3353.125$ lb.