The shaft is held by plain bearings that cannot absorb any axial loads. Given the permissible stress for the shaft, determine the smallest diameter so that the shaft can absorb the load. Use the shape change hypothesis. Given: F$1=50$N$,$ F$2=150$N$,$ F$3=100$N$,$ F$4=250$ N$,$ L $=250$mm$,$ alpha$=30\backslash$deg $,$ permissible stress $=80$MPa, r$1=150$mm$,$ r$2=100$mm