Example $2$

For the truss shown, use the stiffness method to:

$($b$)$ Determine the end forces of each member and reactions at supports.

$($a$)$ Determine the deflections of the loaded joint.

The support $B$ settles downward $2\mathrm{.}5mm.$ Temperature in member $BD$ increase $20C.$ Take $=12\frac{{10}^{-6}}{}C,AE=8({10}^3)kN.$