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=51 mm, h=29 mm The triangle: hT=15 mm, lT=18 mm and the 2 circles: diameter=7.4 mm, hC=8 mm, dC=7 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? In the box below enter the y position of the center of gravity of the bar in mm with one decimal.
Use the given values in problem to answer the following:
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=51 mm, h=29 mm
- The triangle: hT=15 mm, lT=18 mm
- and the 2 circles: diameter=7.4 mm, hC=8 mm, dC=7 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?
In the box below enter the y position of the center of gravity of the bar in mm with one decimal.
![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
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.X
вт
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