For all the problems below solve using Matlab. For each problem $1)$ make a neat and clear diagram of the problem with node numbers and element numbers labeled as well as any element orientation angles. Check your answers as indicated and show this work by hand. For your matrix method solutions include a table giving the displacement of all nodes and the stresses and forces in each element. Zip all your Matlab files into a single file and submit that file through MS Teams along with a pdf of your final report.

Solve the following problem using two $1$D rod elements. Check your results for the axial force in each member and the displacement at Point C using mechanics of material approach. In the figure below a $4-$ft section of aluminum pipe of cross$-$sectional area $1\mathrm{.}75i{n}^2$ rests on a fixed support at $A.$ The $\frac{5}{8}-$in$.-$diameter steel rod $BC$ hangs from a rigid bar that rests on the top of the pipe at B$.$ Knowing that the modulus of elasticity is $29{10}^6$ psi for steel and $10\mathrm{.}0{10}^6$ psi for aluminum, determine the deflection of point $C$ when a $15-$kip force is applied at $C.$

Solve the $2$ d truss problem below for all the element axial forces using $2$D truss elements. Use the method of joints to check your results for the member AF$.$ All members are aluminum and have a cross sectional area of $1,000m{m}^2$ all vertical and horizontal members are $1$ m long.

Solve a $2$ d truss problem of your own construction. The only requirement is that it have at least $8$ members and use members with at least two different cross$-$sectional areas. You should check the