Find the moment of inertia and radius of gyration of the section of this bar about an axis parallel to x-axis going through the center of gravity of the bar. The bar is symmetrical about the axis parallel to y-axis and going through the center of gravity of the bar and about the axis parallel to z-axis and going through the center of gravity of the bar.

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Formulas
Moments of Inertia
x= [y²d
ly = fx²dA
Theorem of Parallel Axis
Ixr = 1 + d² A
* axis going through the centroid
x' axis parallel to x going through the point of interest
d minimal distance (perpendicular) between x and x'
ly₁ = 15+d²A
ỹ axis going through the centroid
y' axis parallel to y going through the point of interest
d minimal distance (perpendicular) between y and y'
Composite Bodies
1=Σ 4
All the moments of inertia should
be about the same axis.
Radius of Gyration
k=
Transcribed Image Text:Formulas Moments of Inertia x= [y²d ly = fx²dA Theorem of Parallel Axis Ixr = 1 + d² A * axis going through the centroid x' axis parallel to x going through the point of interest d minimal distance (perpendicular) between x and x' ly₁ = 15+d²A ỹ axis going through the centroid y' axis parallel to y going through the point of interest d minimal distance (perpendicular) between y and y' Composite Bodies 1=Σ 4 All the moments of inertia should be about the same axis. Radius of Gyration k=
Find the moment of inertia and radius of gyration of the section of this bar about an axis parallel to
x-axis going through the center of gravity of the bar.
The bar is symmetrical about the axis parallel to y-axis and going through the center of gravity of the
bar and about the axis parallel to z-axis and going through the center of gravity of the bar.
The dimensions of the section are:
. 1-56 mm, h-29 mm
.
The triangle: hy-11 mm, lj-16 mm
•
and the 2 circles: diameter-7.8 mm, hc-9 mm, de-6 mm.
l+
A
hr
O
A
Ľ+
l
A is the origin of the referential axis.
Provide an organized table and explain all your steps to find the moment of inertia and radius of
gyration about an axis parallel to x-axis and going through the center of gravity of the bar.
Does the radius of gyration make sense?
In the box below enter the y position of the center of gravity of the bar in mm with one decimal.
Transcribed Image Text:Find the moment of inertia and radius of gyration of the section of this bar about an axis parallel to x-axis going through the center of gravity of the bar. The bar is symmetrical about the axis parallel to y-axis and going through the center of gravity of the bar and about the axis parallel to z-axis and going through the center of gravity of the bar. The dimensions of the section are: . 1-56 mm, h-29 mm . The triangle: hy-11 mm, lj-16 mm • and the 2 circles: diameter-7.8 mm, hc-9 mm, de-6 mm. l+ A hr O A Ľ+ l A is the origin of the referential axis. Provide an organized table and explain all your steps to find the moment of inertia and radius of gyration about an axis parallel to x-axis and going through the center of gravity of the bar. Does the radius of gyration make sense? In the box below enter the y position of the center of gravity of the bar in mm with one decimal.
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