In the steel structure $(E=200$GPa $)$ shown, an $18$ mm diameter pin is used at A $,$ and $25$ mm diameter pins are used at B and D$.$ Knowing that the ultimate shearing stress is $400$ MPa at all connections and that the ultimate normal stress is $150$ MPa in each of the two links joining $B$ and $D,$ determine the allowable load $P$ if an overall factor of safety of $2\mathrm{.}5$ is desired. Due to the load $P,$ calculate the vertical displacement of Point $C$ if the length of BD is $200$ mm $.$