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7/25/2019 L10 - Centroids of Composite Bodies (1)
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February 5, 2015
ECOR 1101 Mechanics I
Sections D and E
Jack an den !er"
Lecture 10 Centroids of Composite Bodies
(Chapter 5 Section 5.2)
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Centroid of Composite Bodies
A composite body consists of a number of connected shapes orbodies (usua y of simp er shapes).!he simp er shapes maybe rectan"u ar# trian"u ar# semi$circu aretc.%f the &ei"ht and centre of "ra'ity of the simp er shapes are
no&n &e can determine the centre of "ra'ity of the composite
&ithout inte"ration
2ECOR1101 Mechanics I
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Centroid of Composite Bodies
3ECOR1101 Mechanics I
or composite bodies# rather than
account for the infinite differentia&ei"hts &e consider the simp ershapes of the body.
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*rob em 5$+
Locate the centroid yc of the beam,s cross$sectiona area.
4ECOR1101 Mechanics I
7/25/2019 L10 - Centroids of Composite Bodies (1)
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Samp e *rob em
-i'ide composite into simp er components &here the
centroids of the components are no&n.Because of symmetry# the centroid ies on the y$a is.
5ECOR1101 Mechanics I
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6ECOR1101 Mechanics I
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Samp e *rob em
-etermine the distance h to &hich a ho e must be bored into the
cy inder so that the centre of mass of the assemb y is ocated at xc = 64 mm . !he materia has a density of +#000 kg/m 3.
7ECOR1101 Mechanics I
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Samp e *rob em
8ECOR1101 Mechanics I
( )
C
2 2
C 2 2
2 2 2
2 2
2
1
2
xdm x dVx
dm dV
h60 40 120 20 h
2x 6440 120 20 h
160 40 120 20 h
2
64 40 120 20 h
h 128h 3840 0
h 48 mm
h 80 mm
= =
= =
=
+ ===
% %
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/a or f oor oadin"s in a shop are caused by the &ei"hts of
the ob ects sho&n. ach force acts throu"h itsrespecti'e centre of "ra'ity . Locate the centre of"ra'ity ( xc , yc) of a these components.
9
Samp e *rob em
ECOR1101 Mechanics I
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10ECOR1101 Mechanics I
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*rob em 5$3
11
Locate the centroid of the wire bent in the shape shown.
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*rob em 5$4
12
Locate the centroid of the beams cross-sectional area. se two
methods! additi"e and s#btracti"e.
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*rob em 5$11
13
Locate the center of mass of the homo$eneo#s solid bloc%.