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: l=55 mm, h=22 mm The triangle: hT=12 mm, lT=19 mm and the 2 circles: diameter=8 mm, hC=6 mm, dC=8 mm. 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? Enter the y position of the center of gravity of the bar in mm with one decimal.

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
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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:

  • l=55 mm, h=22 mm
  • The triangle: hT=12 mm, lT=19 mm
  • and the 2 circles: diameter=8 mm, hC=6 mm, dC=8 mm.

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?

Enter the y position of the center of gravity of the bar in mm with one decimal. 

hy
A
Ľx
.X
вт
е
L
Transcribed Image Text:hy A Ľx .X вт е L
Geometric Properties of Line and Area Elements
Centroid Location
Centroid Location
[c
b
y
L-r
r sin
0
Circular are segment
-L-20r
Quarter and semicircle ares
aA₂h (a + b)
a
C
Trapezoidal area
-b-A-3ab
Semiparabolic area
AT (++)
a-
C
}
L-at
Exparabolic area
-A-ab
10 b
A=4ab
Parabolic area
T
h
L
h
y
Circular sector area
A-0²
sin
1-17²
V
Quarter circle area
y
Semicircular area
X
Circular area
z
A-²²
X
A-bh
Triangular area
-X
Rectangular area
-A-bh
h
Area Moment of Inertia
1-¹ (0-sin 20)
1,---r¹(0+ -sin 20)
1
16
4-16
4₂
274
7774
4
1
1₂--bh³
12
12
4,--bh³
36
Formulas
Moments of Inertia
¹x = [ y²dA
ly
¹y = Sx
Theorem of Parallel Axis
1x = 1 +d² A
axis going through the centroid
x' axis parallel to x going through the point of interest
d minimal distance (perpendicular) between and x'
lyr=15+d² A
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
All the moments of inertia should
be about the same axis.
x²dA
Radius of Gyration
k =
Transcribed Image Text:Geometric Properties of Line and Area Elements Centroid Location Centroid Location [c b y L-r r sin 0 Circular are segment -L-20r Quarter and semicircle ares aA₂h (a + b) a C Trapezoidal area -b-A-3ab Semiparabolic area AT (++) a- C } L-at Exparabolic area -A-ab 10 b A=4ab Parabolic area T h L h y Circular sector area A-0² sin 1-17² V Quarter circle area y Semicircular area X Circular area z A-²² X A-bh Triangular area -X Rectangular area -A-bh h Area Moment of Inertia 1-¹ (0-sin 20) 1,---r¹(0+ -sin 20) 1 16 4-16 4₂ 274 7774 4 1 1₂--bh³ 12 12 4,--bh³ 36 Formulas Moments of Inertia ¹x = [ y²dA ly ¹y = Sx Theorem of Parallel Axis 1x = 1 +d² A axis going through the centroid x' axis parallel to x going through the point of interest d minimal distance (perpendicular) between and x' lyr=15+d² A 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 All the moments of inertia should be about the same axis. x²dA Radius of Gyration k =
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I am sorry but your values when plugging in are not the correct values. Not too sure where your values are from but can you please redo the question using the given values in this problem and not from a different problem please? (example, height is not 29, it is 22) all values do not correlate to this problem. I was also told when finding the area of triangle to use (1/2)*b*h*Ad^2 and not 1/36*b*h*Ad^2

 

 

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:

  • l=55 mm, h=22 mm
  • The triangle: hT=12 mm, lT=19 mm
  • and the 2 circles: diameter=8 mm, hC=6 mm, dC=8 mm.

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?

Enter the y position of the center of gravity of the bar in mm with one decimal. 

 

hy
A
Ľx
.X
вт
е
L
Transcribed Image Text:hy A Ľx .X вт е L
Geometric Properties of Line and Area Elements
Centroid Location
Centroid Location
[c
b
y
L-r
r sin
0
Circular are segment
-L-20r
Quarter and semicircle ares
aA₂h (a + b)
a
C
Trapezoidal area
-b-A-3ab
Semiparabolic area
AT (++)
a-
C
}
L-at
Exparabolic area
-A-ab
10 b
A=4ab
Parabolic area
T
h
L
h
y
Circular sector area
A-0²
sin
1-17²
V
Quarter circle area
y
Semicircular area
X
Circular area
z
A-²²
X
A-bh
Triangular area
-X
Rectangular area
-A-bh
h
Area Moment of Inertia
1-¹ (0-sin 20)
1,---r¹(0+ -sin 20)
1
16
4-16
4₂
274
7774
4
1
1₂--bh³
12
12
4,--bh³
36
Formulas
Moments of Inertia
¹x = [ y²dA
ly
¹y = Sx
Theorem of Parallel Axis
1x = 1 +d² A
axis going through the centroid
x' axis parallel to x going through the point of interest
d minimal distance (perpendicular) between and x'
lyr=15+d² A
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
All the moments of inertia should
be about the same axis.
x²dA
Radius of Gyration
k =
Transcribed Image Text:Geometric Properties of Line and Area Elements Centroid Location Centroid Location [c b y L-r r sin 0 Circular are segment -L-20r Quarter and semicircle ares aA₂h (a + b) a C Trapezoidal area -b-A-3ab Semiparabolic area AT (++) a- C } L-at Exparabolic area -A-ab 10 b A=4ab Parabolic area T h L h y Circular sector area A-0² sin 1-17² V Quarter circle area y Semicircular area X Circular area z A-²² X A-bh Triangular area -X Rectangular area -A-bh h Area Moment of Inertia 1-¹ (0-sin 20) 1,---r¹(0+ -sin 20) 1 16 4-16 4₂ 274 7774 4 1 1₂--bh³ 12 12 4,--bh³ 36 Formulas Moments of Inertia ¹x = [ y²dA ly ¹y = Sx Theorem of Parallel Axis 1x = 1 +d² A axis going through the centroid x' axis parallel to x going through the point of interest d minimal distance (perpendicular) between and x' lyr=15+d² A 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 All the moments of inertia should be about the same axis. x²dA Radius of Gyration k =
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