Analyze a beam $($EA$,$ EI$,$ L$)$ with one end fixed and the other end vertically supported by a linear elastic spring with spring constant k $($lb$/$in$),$ as shown in Fig. P$5\mathrm{.}12.$ The beam is subjected to uniformly distributed transverse load of intensity q$0($lb$/$in$).$ Use the Euler$$Bernoulli beam element with Newton$$s iteration method. Use eight elements in the beam $(11$ in$2$ cross section, E $=30106$ psi, and L $=100$ in$)$ and k $=0,25,$ and $250($i$.$e$.$ three different cases$).$ Tabulate and plot the deflection w$($L$)$ versus the load q$0,$ with maximum load of q$0=10($lb$/$in$),$ for two separate cases: $($a$)$ horizontal movement of the free end is not restricted, and $($b$)$ the horizontal movement of the free end is restricted to zero. A load increment of $$q$0=0\mathrm{.}5($lb$/$in$)$ is suggested. Use a convergence tolerance of $=103$ and the maximum number of iterations to be ITMAX $=25$ Complete Problem $5\mathrm{.}12.$ Develop your code so that it can be run with an arbitrary

number of elements. Then run your code using $8,16,$ and $32$ elements for the three cases

outlined in Problem $5\mathrm{.}12.$ Fig. P$5\mathrm{.}12$