a. Moment of Inertia Against Horizontal axis (XX)
Moment of inertia of the cross section to a line that is the number of cross-sectional area (element) multiplied by the square of the smallest normal distance to the EAM, or cross-sectional area multiplied by the square of the distance. If the cross-sectional area is the smallest elements DA1, DA2, dA3 …. and and the distance of the cross section to the XX line is y1, y2, y3 …… yn, then the cross-sectional moment of inertia about the line XX can be written by the following equation:
Ix = AY 2
See the following picture
Figure 5.2 The moment of inertia about the axis x
b. Moment of Inertia Against Lines Vertical axis (YY)
If the cross-sectional area is the smallest elements DA1, DA2, dA3 …. and and the distance of the cross section to line YY is the X1, X2, X3 …… Xn, then the cross-sectional moment of inertia about the line YY can be written by the following equation:
Iy = AX 2
See the following page image
Figure 5.3 The moment of inertia about the axis y
c. Polar Moment of Inertia
Namely polar moment of inertia of the cross-sectional moment of inertia of a point or the intersection of the axes of XX and YY axis, the amount is calculated based on the number-smallest cross-sectional area multiplied by the square of the radius or distance of the point normal weight. If the cross-sectional area is the smallest elements DA1, DA2, dA3 …. and the cross-section and the distance from the cut point to axis X, Y are r1, r2, r3 …… rn, then the polar moment of inertia can be written by the following equation:
Ip = Ar 2
L Ihat picture following page.
Figure 5.4 polar moment of inertia
According Phitagoras:
r 2 = x 2 + y 2
Then
Ix = Iz + A. A 2
Figure 5.5 The moment of inertia of a cross-section
Description :
Iz = moment of inertia of its own cross-section through the EAM
Ix = moment of inertia to a line xx in units CM4.