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단면 2차 모멘트-고리모양, Second moment of area for annulus cross section

작성자 Uploader : ezcivil 작성일 Upload Date: 2017-02-27변경일 Update Date: 2019-03-26조회수 View : 1340

The 2nd moment of area, also known as moment of inertia of plane area, area moment of inertia, or second area moment, is a geometrical property of an area which reflects how its points are distributed with regard to an arbitrary axis. The second moment of area is typically denoted with either an I for an axis that lies in the plane or with a J for an axis perpendicular to the plane. In both cases, it is calculated with a multiple integral over the object in question. Its unit of dimension is meters to the fourth power, m^4.

In the field of structural engineering, the second moment of area of the cross-section of a beam is an important property used in the calculation of the beam′s deflection and the calculation of stress caused by a moment applied to the beam.

Consider an annulus whose center is at the origin, outside radius is r2, and inside radius is r1. Because of the symmetry of the annulus, the centroid also lies at the origin. We can determine the polar moment of inertia, Jz, about the z axis by the method of composite shapes. This polar moment of inertia is equivalent to the polar moment of inertia of a circle with radius r2 minus the polar moment of inertia of a circle with radius r1, both centered at the origin. First, let us derive the polar moment of inertia of a circle with radius r with respect to the origin. In this case, it is easier to directly calculate Jz as we already have r^2, which has both an x and y component. Instead of obtaining the second moment of area from Cartesian coordinates as done in the previous section, we shall calculate Ix and Jz directly using Polar Coordinates.

*** 참고문헌[References] ***

https://en.wikipedia.org/wiki/Second_moment_of_area
https://en.wikipedia.org/wiki/List_of_second_moments_of_area

Ix = (π / 4) * (r2^4 - r1^4)

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변수명 Variable	변수값 Value	변 수 설 명 Description of the variable

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현재 위치

단면 2차 모멘트-고리모양, Second moment of area for annulus cross section

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