Consider the truss shown in the figure. All $E=29{10}^6.$ Areas $)$ are in parentheses. A horizontal force of $86k$ is applied to the right at joint $4$ and the support at joint $3$ settles $0\mathrm{.}17$ inches.

Element Connectivity

$\backslash$table$[[$Element$,$End $i,$End $j,],[1,,,1],[2,,3,4],[3,,2,3],[4,,1,4],[5,,4,2]]$

a$.$ Form the element stiffness matrices $\frac{k^{(i)}}{2x^2},i=1,$dots,$5$ in local coordinates.

b$.$ Form the element coordinate transformation matrices, ${}^{(i)},i=1,$dots,$5.$

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c$.$ Form the element global stiffness matrices, $k_g^{(i)},i=1,$dots,$5.$

d$.$ Form the $K_{-},K_r,K_{rr}$ sub$-$matrices of the partitioned

global stiffness matrix. Use the global variable numbering scheme shown in the table at the right.

e$.$ Solve for the unrestrained global displacements and reactions. Show them on a figure. whether member $2$ is in tension or compression.