The shaft is held by bearings A and B$,$ which only exert reactions on the shaft in the x and z directions. Given the allowable stress for the shaft, determine the smallest diameter so that the shaft can accommodate the gear load. Use the shape change hypothesis. Given: F$\_$cx$=200$ N$,$ F$\_$Ex$=250$N$,$ F$\_$Dz $=50$N$,$ L$=8$cm$,$ r$=4$cm$,$ permissible stress $=110$Mpa