A plane rigid frame with applied load is shown in Fig. $1.$ Determine the nodal displacements at node $1.$ Calculate the reactions at nodes $2$ and $3.$ Take $A_1=10i{n}^2,A_2=15i{n}^2,I_1=100i{n}^4$ and $I_2=200i{n}^4.$ Use $E=400$ksi for entire frame.By means of direct stiffness method,analyze the given problem.

Ans.: $u_{1x}=-4\mathrm{.}99in.,u_{1y}=-3\mathrm{.}29in.,{}_1=0\mathrm{.}020$rad