When the $21$ kip force is applied to the rigid block ABCD at $B$ it moves horizontally

without being able to rotate because of the roller supports at $C$ and $D.$ The connections

of all springs to the supports and to the rigid block are pinned. Use the units of kips and

inches and perform the following.

$(8$ points$)$ Find the global stiffness matrix, K$,$ for the system shown based on

$[F_1$;$F_2$;$F_3$;$F_4$;$F_5]=K^{**}[u_1$;$u_2$;$u_3$;$u_4$;$u_5],$ using the basic method of elements and joints

equilibrium. Use the equations obtained to find $u_2,F_1,F_3,F_4,$ and $F_5.$ Consider

the rigid block as node number $2.$

$(2$ points$)$ Use the results of part $1$ to find the vertical reactions of the rollers at

C and D$.$

$(3$ points$)$ Find the global stiffness matrix, K$,$ for the system shown based on

$[F_1$;$F_2$;$F_3$;$F_4$;$F_5]=K^{**}[u_1$;$U_2$;$U_3$;$U_4$;$U_5],$ using the potential energy method.

$(2$ points$)$ Write a MATLAB code that finds all unknown reactions,

displacements, and element forces for element $3-2.$ Use the direct stiffness

method.

Solve $1-3.$