Polar Moment Of Inertia Of Hollow Shaft

The rigidity comes from the object s cross sectional area only and does not depend on its material composition or shear modulus.

Polar moment of inertia of hollow shaft. ʃ r 2 d a where r is the distance from an axis of an infinitesimal area da integrated over the whole area. π 16 d d b. To determine the polar moment of inertia we use. π 16 d d c.

Similarly for a hollow shaft j d 4 d 4 32 where d is the outer diameter of the shaft and d is the inner diameter of the shaft. Combining 2 and 3b for a hollow shaft. For a solid shaft j d 4 32. J π r 4 2 π d 2 4 2 π d 4 32 3 where.

The greater the polar moment of inertia the smaller the shear stress required to produce a given torque. The greater the polar moment of inertia the more torque is require to turn the shaft by a certain angle. This method may be used to find the approximate value of the polar section modulus of sections that are nearly round. They are as follows.

The polar moment of inertia of a hollow shaft of outer diameter d and inner diameter d is a. The greater the magnitude of the polar moment of inertia the greater the torsional resistance of the object. Polar moment of inertia j is mathematically equal to second moment of area which will help you understand it. The polar section modulus also called section modulus of torsion z p for circular sections may be found by dividing the polar moment of inertia j by the distance c from the center of gravity to the most remote fiber.

J hollow π r 0 4 r 1 4 2 frac pi left r 0 4 r 1 4 right 2 2 π r 0 4 r 1 4 r 1 and r o inner and outer radius of the hollow shaft. π 32 d d. For a tubular shaft the polar moment of inertia is i p π d 4 d 4 32 where d is the outside diameter and d is the inner diameter of the tube shaft g is the modulus of rigidity torsional modulus of elasticity in n m 2 and l is the active length of the shaft. It is given by.

D shaft outside diameter m in. There are three main types of cross section polar moment of inertia. The polar moment of inertia of the hollow shaft is 1 125 x 10 6 m4. To determine the polar moment of inertia we use.