Under normal operating conditions a motor exerts a torque of...

Under normal operating conditions a motor exerts a torque of magnitude $T_{F}$ at $F$. The shafts are made of a steel for which the allowable shearing stress is $12 \mathrm{ksi}$ and have diameters $d_{C D E}=0.900$ in. and $d_{F G H}=0.800$ in. Knowing that $r_{D}=6.5$ in. and $r_{G}=4.5$ in. determine the largest allowable value of $T_{F}$

Key Concepts

Shear Stress and Allowable Stress

Shear stress in a shaft under torsion is calculated by dividing the applied torque times the radius by the polar moment of inertia. The allowable shear stress is a material property that represents the maximum stress the material can sustain without failure. Ensuring that the induced shear stress does not exceed this value is critical for safe design.

Torque Transmission and Safety Design

In mechanical design, a component such as a shaft must be capable of transmitting a specific torque while maintaining stresses below the allowable limits. This involves calculating the resulting shear stress using the relevant geometric properties and ensuring that the design adheres to the material's strength limits. Balancing these factors is key to achieving an efficient and safe design.

Torsion in Circular Shafts

This concept refers to the twisting of a structural member when subjected to a torque. In circular shafts, the applied torque creates a shear stress distribution that is highest at the outer surface and decreases linearly to zero at the center. Understanding this stress distribution is crucial for designing shafts that can safely transmit torque without failing.

Polar Moment of Inertia

The polar moment of inertia quantifies a shaft's resistance to torsion. For a circular cross-section, it is determined by the geometry (specifically, the diameter raised to the fourth power) and is calculated using J = (?/32)d^4. This parameter is essential in relating the applied torque to the resulting shear stresses in the shaft.

Transcript

Please give Ace some feedback