Question
Download Solution PDFWhich of the following represents the polar modulus of the hollow shaft?
[ If Do = External diameter and Di = Internal diameter ]
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFExplanation:
The polar modulus is a geometric property of the cross section of a shaft that is used to calculate the strength of the shaft in torsion. For a hollow shaft, the polar modulus is derived from the external and internal diameters.
Polar Modulus of a Hollow Shaft:
The polar modulus (Zp) for a hollow circular shaft is given by the formula:
Zp = J / R
where J is the polar moment of inertia, and R is the outer radius of the shaft.
The polar moment of inertia (J) for a hollow circular shaft is:
J = \(\frac{\pi}{32}\) × \({Do}^4 - {Di}^4\)
where Do is the external diameter and Di is the internal diameter.
The outer radius (R) is half of the external diameter:
R = Do / 2
Now, substituting J and R into the formula for the polar modulus, we get:
∴ Zp = \(\frac{π}{16}\)Do × [ \({Do}^4 - {Di}^4\)]
Last updated on Jun 7, 2025
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