Problem $3$: Consider the planar frame shown below. Notice that the support at joint $3$ inhibits rotation and horizontal motion.

Use the direct stiffness method to calculate the unknown nodal displacements$/$rotations of joints $1,2,$ and $3,$ and all support reactions. You need to develop two solutions: $($i$)$ assume first that all members are axiallyrigid and have flexural rigidity of $\backslash ($ E I $\backslash )$; $($ii$)$ assume next that axial effects should be included and that the members, in addition to the flexural rigidity, they also have axial properties $\backslash ($ E A $\backslash ).$

Notice that you are not asked to compute the displacements$/$rotation of joint $4.$ Both of the requested solutions can be developed by replacing the tip$-$loaded cantilevered segment $2-4$ with equivalent loading applied at joint $2.$