Lecture 11- 1page
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Transcript of Lecture 11- 1page
7/27/2019 Lecture 11- 1page
http://slidepdf.com/reader/full/lecture-11-1page 1/5
© 2007 The McGraw-Hill Companies, Inc. All rights reserved.
Vector Mechanics for Engineers: StaticsE i gh t h
E d i t i on
3 - 1
Resolution of a Force Into a Force at O and a Couple
• Force vector F can not be simply moved to O without modifying itsaction on the body.
• Attaching equal and opposite force vectors at O produces no net
effect on the body.
• The three forces may be replaced by an equivalent force vector and
couple vector, i.e, a force-couple system.
7/27/2019 Lecture 11- 1page
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© 2007 The McGraw-Hill Companies, Inc. All rights reserved.
Vector Mechanics for Engineers: StaticsE i gh t h
E d i t i on
3 - 2
Resolution of a Force Into a Force at O and a Couple
• Moving F from A to a different point O’ requires the
addition of a different couple vector M O’
F r M Or
r
r
×′='
• The moments of F about O and O’ are related,
( )F s M
F sF r F sr F r M
O
Or
r
r
r
r
r
r
r
rr
r
r
r
×+=
×+×=×+=×= ''
• Moving the force-couple system from O to O’ requires the
addition of the moment of the force at O about O’.
7/27/2019 Lecture 11- 1page
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© 2007 The McGraw-Hill Companies, Inc. All rights reserved.
Vector Mechanics for Engineers: StaticsE i gh t h
E d i t i on
3 - 3
Sample Problem 3.6
Determine the components of the
single couple equivalent to the
couples shown.
SOLUTION:
• Attach equal and opposite 20 lb forces in
the + x direction at A, thereby producing 3
couples for which the moment componentsare easily computed.
• Alternatively, compute the sum of the
moments of the four forces about an
arbitrary single point. The point D is a
good choice as only two of the forces will
produce non-zero moment contributions..
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© 2007 The McGraw-Hill Companies, Inc. All rights reserved.
Vector Mechanics for Engineers: StaticsE i gh t h
E d i t i on
3 - 4
Sample Problem 3.6
• Attach equal and opposite 20 lb forces in
the + x direction at A
• The three couples may be represented bythree couple vectors,
( )( )
( )( )
( )( ) in.lb180in.9lb20
in.lb240in.12lb20
in.lb540in.18lb30
⋅+=+=
⋅+=+=
⋅−=−=
z
y
x
M
M
M
( ) ( )
( )k
ji M r
rrr
in.lb180
in.lb240in.lb540
⋅+
⋅+⋅−=
7/27/2019 Lecture 11- 1page
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© 2007 The McGraw-Hill Companies, Inc. All rights reserved.
Vector Mechanics for Engineers: StaticsE i gh t h
E d i t i on
3 - 5
Sample Problem 3.6
• Alternatively, compute the sum of the
moments of the four forces about D.
• Only the forces at C and E contribute tothe moment about D.
( ) ( )
( ) ( )[ ] ( )ik j
k j M M Dr
rr
rrrr
lb20in.12in.9
lb30in.18
−×−+
−×==
( ) ( )
( )k
ji M r
rrr
in.lb180
in.lb240in.lb540
⋅+
⋅+⋅−=