Project ForgeA shaft AC rotating at a constant speed carries a thin pulley of radius r=0.4 m at the end C which drives a belt. A motor is coupled at the end A of the shaft such that it applies a torque Mz about the shaft axis without causing any bending moment. The shaft is mounted on narrow frictionless bearings at A and B where AB=BC=L=0.5 m. The taut and slack side tensions of the belt are T1=300 N and T2=100 N, respectively. The allowable shear stress for the shaft material is 80 MPa. Neglecting shock and fatigue loading and assuming maximum shear stress theory, the minimum required shaft diameter is ________ mm (round off to 2 decimal places).
Explanation
Torque transmitted: Mz=(T1−T2)r=(300−100)(0.4)=80 N·m, constant throughout the shaft. The belt's resultant transverse load T1+T2=400 N acts at the overhung end C; since C is beyond bearing B (order A-B-C), the maximum bending moment occurs at B: M=400×L=400×0.5=200 N·m. By maximum shear stress theory, equivalent torque Te=√(M²+T²)=√(200²+80²)=√46400≈215.41 N·m. d³=16Te/(πτallow)=16(215406 N·mm)/(π×80)≈13714 mm³, giving d≈23.94 mm.
Source: GATE ME 2022 Session 2 (ME-2) (2022)
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