The shaft shown with length $11$a $($a$=10$cm$)$ and circular full cross section is supported at point B by a roller bearing and at point E by a ball bearing. The load is applied across three disks at positions A$,$ C and D by the forces F$=200$N$,$ P$=300$N and R$=250$N as shown in the figure. Given allowable stress $=100$ Mpa, determine the smallest possible allowable diameter d so that the shaft can withstand the load. Consider bending and torsion stress when sizing the shaft diameter. Use Tresca's comparative stress hypothesis in your calculation.