In Fig. P. 14.5 is shown a solid shift. Find the length of an equivalent shaft of the same mater

Step 1: Identify the torsional stiffness formula for a solid shaft. The torsional stiffness (k)

In Fig. P. 14.5 is shown a solid shift. Find the length of...

Key Concepts

Equivalent Shaft

An equivalent shaft is a uniform shaft designed to have the same torsional properties as a more complex or composite shaft system. This involves ensuring that the product of the material's shear modulus and the shaft's polar moment of inertia divided by its length (which represents the torsional rigidity) is equal for both the original and the equivalent shaft.

Modulus of Rigidity

The modulus of rigidity, also known as the shear modulus, is a material property that measures the material's ability to resist shear deformations. In torsion problems, it is used to calculate the angle of twist for a given torque, influencing the overall torsional stiffness of shafts made from the same material.

Torsional Stiffness

Torsional stiffness is the measure of how resistant a shaft is to twisting under an applied torque. It is defined by the ratio of the applied torque to the resulting angular deformation and depends on both the material’s shear modulus and the geometry of the shaft, specifically the polar moment of inertia and its length.

Polar Moment of Inertia

The polar moment of inertia is a geometrical property of a cross-sectional shape that quantifies its resistance to torsion. For circular shafts, it can be calculated using the shaft’s diameter, and it plays a crucial role in determining how the applied torque is distributed over the shaft, directly impacting the torsional stiffness.

In Fig. P. 14.5 is shown a solid shift. Find the length of an equivalent shaft of the same material having the same torsional stiffoess. The diameter of the equivalent shaft is to be 75 mm .

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