An A$-$shaped truss structure is used to support a roof in a garage as shown in Figures $1$ and $2.$ For simplicity, assume each truss is constructed of wood with cross$-$section dimensions of $0\mathrm{.}1$ m x $0\mathrm{.}25$ m and the truss structure is supported by a pin on the left bearing wall and a roller on the right bearing wall.

The garage owner realized on installation that installing the hoist at location C doesn't make much sense because member AB gets in the way. The owner of the garage is now interested in installing a $5-$ton hoist on the bottom chord $($i$.$e$.,$ horizontal member $"$AB$")$ to lift car engines and complete other vehicle repairs. Member AB has length, a$,$ of $8\mathrm{.}5$ m and the truss has a height, b$,$ of $3\mathrm{.}5$ m$.$ The hoist would be capable of lifting a weight of $2,000$ kg$.$ The hoist is proposed to be constructed at location Z$,$ which is the mid span distance between points A and B$.$ An example of the hoist is provided in Figure $3.$

The amount of deflection, calculated in Question $1,$ of the bottom chord for the A$-$shaped truss structure shown in Figure $2$ was considered too large by the garage owner. The garage owner is interested in installing a supporting post $($called a king post, as shown in Figure $5,$ to limit the deflection at location Z$.$ The king post would have the same cross$-$section dimensions as the other members. The elastic modulus of the king post is $10$ GPa.

Using the method of joints, determine the absolute value of the force, in units of kN$,$ in member BC for the roof structure depicted in Figure $4.$ You can assume that the joint at Z now acts like a pin. Complete the following and use $3$ significant figures in your answer.

Apply a sign convention that forces acting up and to the right are positive and clockwise moments are positive.

Note$-$ Figure $2$ is not used in Question $2.$Question $2(1$ point$)$

Chord

Figure $3.$ Example $5$ ton hoist.

Figure $1.$ A frame timber roof.

Figure $2.$ A schematic representation of the frame timber roof.