a$.$ Write the local stiffness matrix equations for each of the four bars.

b$.$ Assemble the stiffness matrix equations to form the global structure stiffness matrix.

c$.$ Determine the displacements of joints $1,$ and $2$ if the system is loaded by $20$ k force to right at joint $2$ and $15$ k force to right at joint $1.$

d$.$ Determine the displacements of joints $1$ and $2$ if the system is loaded by imposing the displacement of joint $3$ to be $0\mathrm{.}05$ in$,$ and of joint $5$ to be $0\mathrm{.}07$ in$.$