Part $2(10$ points$)$: Define normalized length $\stackrel{}{x}=\frac{x}{L}.$ Using this definition, normalize your solution

for the axial displacement field $u(x)$ and the internal axial force $N(x)$ by defining:

$\frac{?}{\text{b}\text{a}\text{r}}(u)(\stackrel{}{x})=\frac{u(x)}{L}\frac{?}{b}$

$ar(N)(\stackrel{}{x})=\frac{N(x)}{AE}$

We define $\frac{?}{\text{b}\text{a}\text{r}}(u)(\stackrel{}{x})$ and $\frac{?}{\text{b}\text{a}\text{r}}(N)(\stackrel{}{x})$ as normalized axial displacement field and the normalized internal

force.