# Engineering method for determining the axial moment of inertia of a circular segment

## Authors

• Andrii Moltasov E.O. Paton Electric welding institute of NASU, Ukraine
• Mykola Koval E.O. Paton Electric welding institute of NASU, Ukraine
• Mykhaylo Malgin E.O. Paton Electric welding institute of NASU, Ukraine
• Andrii Levchuk E.O. Paton Electric welding institute of NASU, Ukraine

## Keywords:

geometric characteristics of plane sections, bending, axial moment of inertia, central axis, circular segment, semicircle

## Abstract

The work is devoted to the analytical study of the geometric characteristics of a circular segment, in particular the moment of inertia relative to its central axis, which does not pass through the center of the circle. It is proved that the formula given in the literature for determining the studied characteristic is incorrect, therefore the purpose of the work is to determine the cause of the error and clarify this formula. The paper identified the cause and determined the member of the existing formula that led to the error. On the basis of the dependences between the moments of inertia during the parallel transfer of axes, a new formula was obtained for determining the moment of inertia of a circular segment relative to its central axis. It was established that at the maximum value of the central angle on which the segment rests, the proposed formula is identical to the formula for determining the moment of inertia of a semicircle relative to the corresponding axis available in the literature. Based on the proposed formula, calculations of the reduced moment of inertia at different values of the central angle were carried out. As a result, it was found that as the central angle increases, the moment of inertia increases, reaching its limit value, which corresponds to a semicircle. A graph of dependence is constructed, which is convenient to use to determine the value of the investigated moment of inertia when the central angle changes from ⁓ 20 to 180°.

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2024-06-27

## How to Cite

[1]
A. Moltasov, M. Koval, M. Malgin, and A. Levchuk, “Engineering method for determining the axial moment of inertia of a circular segment”, Mech. Adv. Technol., vol. 8, no. 2(101), pp. 178–181, Jun. 2024.

Mechanics