Problem $1$: MATLAB $2$D Truss Problem

An overhang truss is shown below. The left end of the bridge is fixed, and the right end is free. All truss members are considered linear elastic bars, with a circular cross section of diameter $5$ cm $.$ The vertial and horizontal trusses are of length $1$ m $.$ The material is steel $(\backslash (\backslash$mathrm$\{$E$\}-210\backslash$mathrm$\{$GPa$\}\backslash )).$ The vertical force F has a magnitude of $10$ c $3$ N $.$

$1.$ Using the methods from lecture $13$ write Matlab code to solve for the unknown displacements of this system. Provide a printout of the the full displacement vectore once solved.

$2.$ Solve for the force vector and provide a printout.

$3.$ Solve for the stress and strain in each element. Which element is undergoing the largest tensile $($positive$)$ stress? Which is undergoing the largest compressive stress?

$4.$ Make a plot of the original and the deformed truss structure. You will need to choose an appropriate scale factor to magnify the displacement by$.($In my solution I used $5$e$2).$

$5.$ Is Member $6$ in tension or compression? Explain.

$6.$ Repeat the analysis but switch the orientation of the diagonal truss members $1,6$ ad $10.($i$.$e$.$ element $2$ would be connected to nodes $1$ and $8$ for instance$).$ Does this change in design lower or increase the absoluted maximum stress in the truss?