A solid $4340$ HR Steel tie rod of length Lrod$=900$mm is employed to compress a Naval Brass bushing of length Lbushing$=600$mm as shown. The tie rod has a solid circular cross section with diameter drod$=27\mathrm{.}5$mm$.$ The bushing has a hollow circular cross section with outer diameter do$=70$mm$,$ inner diameter di$,$ and wall thickness t$.$ If F$=47\mathrm{.}5$kN$,$ determine the minimum wall thickness of the bushing based on the below design requirements:

the displacement of the bottom of the tie rod with respect to the fixed horizontal surface may not exceed total$=1$mm

the normal stress of the bushing may not exceed the yield strength of the bushing material