Use the unit displacement approach to develop the structural stiffness matrix for the structure shown in Figure $1,$ assuming that the axial stiffness of all three members are identical, i$.$e$.(\frac{AE}{L}{)}_1=(\frac{AE}{L}{)}_2=(\frac{AE}{L}{)}_3=150\frac{k}{i}n.$ Then report the force$-$displacement matrix equation that you need to solve to calculate the joint displacements. Partition the matrix equation based on unconstrained and restrained degrees of freedom, and highlight the components $F_u,R_r,{}_u,{}_r,K_{},K_{ur},K_{ru}$ and $K_{rr}.$ In this equation, show the constraints on ${}_r.$

Note

a$.$ All members are axial members so only horizontal DOFs are to be considered.

b$.$ Only showing the matrix equation will suffice for the final part. No need to solve for unknown displacements and reactions. However, feel free to compute them to get an extra credit of $10$ points!