© 2007 Pearson Education South Asia Pte Ltd Teaching Slides – Free-Body Diagrams Chapter 6:...
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Transcript of © 2007 Pearson Education South Asia Pte Ltd Teaching Slides – Free-Body Diagrams Chapter 6:...
© 2007 Pearson Education South Asia Pte Ltd Teaching Slides – Free-Body DiagramsTeaching Slides – Free-Body Diagrams
Chapter 6: Chapter 6: Structural AnalysisStructural Analysis
© 2007 Pearson Education South Asia Pte Ltd Teaching Slides – Free-Body DiagramsTeaching Slides – Free-Body Diagrams
Example 6.3
Determine the force in each member of the truss. Indicate whether the members are intension or compression.
© 2007 Pearson Education South Asia Pte Ltd Teaching Slides – Free-Body DiagramsTeaching Slides – Free-Body Diagrams
Example 6.3
)(10.4
0)30sin10.4(2;0
600
0)4(600)3(400)6(;0
600
0600;0
TkNF
FF
NA
mNmNmAM
NC
CNF
DB
DBy
y
yC
x
xx
A
B C
Cy
Cx
600N
Ay
400N
6m
3m
4m
© 2007 Pearson Education South Asia Pte Ltd Teaching Slides – Free-Body DiagramsTeaching Slides – Free-Body Diagrams
Example 6.3
A
B C
Cy
Cx
600N
Ay
400N
6m
3m
4m
600N
Cy
FAD
)(750
054
600
;0
)(450
0)750(53
;0
CNF
FN
F
TNF
NF
F
AB
AB
y
AD
AD
x
y
xA
© 2007 Pearson Education South Asia Pte Ltd Teaching Slides – Free-Body DiagramsTeaching Slides – Free-Body Diagrams
Example 6.3
A
B C
Cy
Cx
600N
Ay
400N
6m
3m
4m
FDB
600N
y
xD
450N
FDC
)(200
0)250(54
;0
)(250
250
060053
450
;0
CNF
NF
F
TNF
NF
NFN
F
DC
DC
y
DB
DB
DB
x
© 2007 Pearson Education South Asia Pte Ltd Teaching Slides – Free-Body DiagramsTeaching Slides – Free-Body Diagrams
Example 6.3
A
B C
Cy
Cx
600N
Ay
400N
6m
3m
4m
600NC
y
xFCB
200N
200N )(0200200
;0
)(600
0600
;0
checkNN
F
CNF
NF
F
y
CB
CB
x
© 2007 Pearson Education South Asia Pte Ltd Teaching Slides – Free-Body DiagramsTeaching Slides – Free-Body Diagrams
Example 6.4
Using the method of joints, determine all the zero-force members of the Fink roof truss. Assume all joints are pin connected.
© 2007 Pearson Education South Asia Pte Ltd Teaching Slides – Free-Body DiagramsTeaching Slides – Free-Body Diagrams
Example 6.4 5 kN
2 kN
A
B
C
H G F E
D
G
y
xFGH
FGCFGF
0;0 GCy FF
Joint G
© 2007 Pearson Education South Asia Pte Ltd Teaching Slides – Free-Body DiagramsTeaching Slides – Free-Body Diagrams
Example 6.4 5 kN
2 kN
A
B
C
H G F E
D
x
D
yFDF
FDC
FDE
Joint D
0;0 DFx FF
© 2007 Pearson Education South Asia Pte Ltd Teaching Slides – Free-Body DiagramsTeaching Slides – Free-Body Diagrams
Fx
y
Example 6.4 5 kN
2 kN
A
B
C
H G F E
D
Oθ
FFEFFG
FFC Joint F
0,90
0cos;0
FC
FCy
F
FF
© 2007 Pearson Education South Asia Pte Ltd Teaching Slides – Free-Body DiagramsTeaching Slides – Free-Body Diagrams
B
x
y
Example 6.4 5 kN
2 kN
A
B
C
H G F E
D
FBH
FBA
FBC
Joint B
)(2
02;0
CkNF
FkNF
BH
BHx
2 kN
© 2007 Pearson Education South Asia Pte Ltd Teaching Slides – Free-Body DiagramsTeaching Slides – Free-Body Diagrams
Example 6.7
Determine the force in member EB of the roof truss. Indicate whether the member are in tension or compression.
© 2007 Pearson Education South Asia Pte Ltd Teaching Slides – Free-Body DiagramsTeaching Slides – Free-Body Diagrams
Example 6.7 1000 N
A
F
E
B C
D
1000 N3000 N
1000 N
4000 N2000 N
© 2007 Pearson Education South Asia Pte Ltd Teaching Slides – Free-Body DiagramsTeaching Slides – Free-Body Diagrams
Example 6.7 1000 N
A
F
E
B C
D
1000 N3000 N
1000 N
4000 N2000 N
FED
FEB
FAB
FFB
FEDcos30°
FEDsin30°
)(2000 ;0
)(3000 ;0
)(3000 ;0
TNFF
CNFF
CNFM
EBy
EFx
EDB
© 2007 Pearson Education South Asia Pte Ltd Teaching Slides – Free-Body DiagramsTeaching Slides – Free-Body Diagrams
Example 6.8
Determine the forces acting in the members of the space truss. Indicate whether the members are in tension or compression.
© 2007 Pearson Education South Asia Pte Ltd Teaching Slides – Free-Body DiagramsTeaching Slides – Free-Body Diagrams
Example 6.8
Joint A
0577.0577.0577.04
0
;0
)577.0577.0577.0(
,,}4{
kFjFiFkFjFj
FFFP
F
kjiF
rr
FF
kFFjFFkNjP
AEAEAEACAB
AEACAB
AE
AE
AEAEAE
ACACABAB
z
y
x
A
FAB
FAC
FAE
P = 4 kN
© 2007 Pearson Education South Asia Pte Ltd Teaching Slides – Free-Body DiagramsTeaching Slides – Free-Body Diagrams
Example 6.8 z
y
x
B
RAB
FBD
FBEJoint B
0
show, To
)(2
)(66.5
0707.02;0
045sin4;0
0707.045cos;0
CEDCDE
BD
BEB
BEBDz
By
BEBx
FFF
CkNF
TkNFR
FFF
RF
FRF
FAB = 4kN
2 kN
45°
© 2007 Pearson Education South Asia Pte Ltd Teaching Slides – Free-Body DiagramsTeaching Slides – Free-Body Diagrams
Example 6.21
The 100kg block is held in equilibrium by means of the pulley and the continuous cable system. If the cable is attached to the pin at B, compute the forces which this pin exerts on each of its connecting members
© 2007 Pearson Education South Asia Pte Ltd Teaching Slides – Free-Body DiagramsTeaching Slides – Free-Body Diagrams
Example 6.21
B
By490.5 N
Bx
490.5 N
45°
Pulley B
NB
NNBF
NB
NBF
y
yy
x
xx
3.837
05.49045sin5.490;0
8.346
045cos5.490;0
© 2007 Pearson Education South Asia Pte Ltd Teaching Slides – Free-Body DiagramsTeaching Slides – Free-Body Diagrams
Example 6.21
B
By
490.5 N
Bx
Pin B
NB
NNBF
NB
NBF
y
yy
x
xx
3.837
05.49045sin5.490;0
8.346
045cos5.490;0
FAB
FCB