PROBLEM 5.18
Determine the x coordinate of the centroid of the trapezoid shown in
terms of h1, h2, and a.
PROBLEM 5.19
For the semiannular area of Prob. 5.12, determine the ratio r1 to r2 so that the centroid
of the area is located at x = 2
1
2r and y = 0.
PROBLEM 5.19 (Continued)
1
PROBLEM 5.20
A composite beam is constructed by bolting
four plates to four 60 60 12-mm angles as
shown. The bolts are equally spaced along the
beam, and the beam supports a vertical load.
As proved in mechanics of materials, the
shearing forces exerted on the bolts at A and B
are proportional to the first moments with
respect to the centroidal x-axis of the red-
shaded areas shown, respectively, in parts a
and b of the figure. Knowing that the force
exerted on the bolt at A is 280 N, determine
the force exerted on the bolt at B.
PROBLEM 5.21
The horizontal x-axis is drawn through the centroid C of the area shown,
and it divides the area into two component areas A
1
and A
2
. Determine the
first moment of each component area with respect to the x-axis, and
explain the results obtained.
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PROBLEM 5.22
The horizontal x-axis is drawn through the centroid C of the area shown,
and it divides the area into two component areas A
1
and A
2
. Determine the
first moment of each component area with respect to the x-axis, and
explain the results obtained.
Area above x-axis (Area A
1
):
1
33
(25)(20 80) (7.5)(15 20)
40 10 2.25 10
QyA
33
1
42.3 10 mmQ
Area below x-axis (Area A
2
):
2
( 32.5)(65 20)QyA
33
2
42.3 10 mmQ
12
||| |,QQ
since C is centroid and thus,
0QyA
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PROBLEM 5.23
The first moment of the shaded area with respect to the x-axis is denoted by
Q
x
. (a) Express Q
x
in terms of b, c, and the distance y from the base of the
shaded area to the x-axis. (b) For what value of y is
x
Q
maximum, and what is
that maximum value?
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PROBLEM 5.24
A thin, homogeneous wire is bent to form the perimeter of the figure indicated.
Locate the center of gravity of the wire figure thus formed.
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PROBLEM 5.25
A thin, homogeneous wire is bent to form the perimeter of the figure
indicated. Locate the center of gravity of the wire figure thus formed.
PROBLEM 5.26
A thin, homogeneous wire is bent to form the perimeter of the figure indicated.
Locate the center of gravity of the wire figure thus formed.