A bracket attached to a fixed member by four identical bolts and weld, which experiences a fluctuating force which varies between $0$ and $20$ N$.$ Because of safety considerations, SAE class $8\mathrm{.}8$ steel bolts and a minimum safety factor of $3($based on proof strength$)$ are to be used. Showing all relevant steps, determine an appropriate bolt diameter and required weld height h $.$ Neglect friction forces between the bracket and fixed member. The allowable shear stress in the weld throat is $120$ MPa $.$

Sut$=600$ MPa, Sy$=500$ MPa $($welding material$)$

Sut$=400$ MPa, Sy$=300$ MPa $($Bracket and fixed member$)8$