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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

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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%.