Question #80131

The axle of a heavy duty tractor 120 K W at 600 rpm it acts as a cantilever supporting a load of 280 N located 60 cm from the fixed end. The allowable normal stress Is 137 MPa and the allowable shear stress is 62 MPa. If the axial load is negligible, find the axle diameter. A:52 mm B:50 mm C:56 mm D:54 mm

Expert's answer

**Normal stress** is given by

where "M=Fx=280N\\cdot60cm=168Nm -" the maximum bending moment,

"r=\\frac{d}{2} -" the radius of the axle,

"I=\\frac{\\pi d^4}{64}-" the moment of inertia.

Substitute

"d=\\sqrt[3]{\\frac{32M}{\\pi\\sigma}}=\\sqrt[3]{\\frac{32\\cdot168}{137\\cdot10^6\\pi}}=0.0232m=23.2mm."

**Shear stress** is given by

where "T=\\frac{P}{2\\pi n}=\\frac{120\\cdot10^3}{2\\pi\\cdot\\frac{600}{60}}=1909.86Nm-" torque,

"J=\\frac{\\pi d^4}{32}-" polar moment of inertia.

Substitute

"d=\\sqrt[3]{\\frac{16T}{\\pi\\tau}}=\\sqrt[3]{\\frac{16\\cdot1909.86}{62\\cdot10^6\\pi}}=0.0539m=53.9mm."

Thus, the axle diameter is **54 mm** (Option D).

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