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Problem 5.51
The horizontal bar
ABCD
is supported by a link
BE
with the shape shown.
All pins are frictionless, and slots (if present) are loose fitting. Determine the
reactions that support bar ABCD.
Problem 5.52
The horizontal bar
ABCD
is supported by a link
BE
with the shape shown.
All pins are frictionless, and slots (if present) are loose fitting. Determine the
reactions that support bar ABCD.
NOTE:
The first printing of this book has an error in the figure for this problem; the location of point
E
was
not given. Point
E
is located
0:4
m from the vertical line passing through point
C
. This error is corrected in
the second and subsequent printings of the book.
Solution
y
x
The FBD is shown at the right. Because member
BE
is a two-force
member, the force it supports is directed along line
BE
, which provides
the orientation shown.
XMCD0W3kN .4 m/CFBE
1:2
p1:8 .1 m/8kNmD0(1)
)FBE D 4:472 kN, (2)
XFxD0WFBE
0:6
p1:8 CCxD0(3)
)CxD2kN, (4)
XFyD0W 3kN FBE
1:2
p1:8 CCyD0(5)
)CyD 1kN. (6)
Problem 5.53
The horizontal bar
ABCD
is supported by a link
BE
with the shape shown.
All pins are frictionless, and slots (if present) are loose fitting. Determine the
reactions that support bar ABCD.
Solution
Problem 5.54
The crane is supported by a pin at point
A
and a roller at point
B
. A winch
at point
C
is used to raise and lower loads. The pulleys all have
350 mm
radius, and cable segment
ED
is horizontal. Determine the support reactions if
PD10 kN and
(a) D0ı.
(b) D30ı.
Problem 5.55
The crane is supported by a pin at point
A
and a roller at point
B
. A winch
at point
C
is used to raise and lower loads. The pulleys all have
350 mm
radius, and cable segment
ED
is horizontal. Determine the support reactions if
PD10 kN and
(a) D0ı.
(b) D30ı.
Problem 5.56
Bar
ABCD
is supported by a link
BE
with circular shape and a cable wrapped
around two frictionless pulleys that have
4in:
radius. Cable segment
CF
is
horizontal, and segments
C G
and
DG
are vertical. If the weight supported by
pulley Gis WD30 lb, determine the reactions at Aand B.
p468.5 in./FBE
p468.12 in./
CT .15 in./T .36 in./T .48 in./D0(1)
)FBE D 143:5 lb (2)
Problem 5.57
The structure
ABCDE
shown is used to support two bottles of soda and one
bottle of milk. Each bottle of soda weighs
2lb
, the bottle of milk weighs
4lb
,
and the dimensioning lines shown locate the center of gravity for each bottle.
The weight of all other components is negligible. The structure is supported by
a roller at
B
, a collar at
C
that slides on a fixed frictionless vertical bar, and by
a cable
DF G
that is subjected to a
6lb
force. The portion of the cable attached
to point
D
is horizontal, and the roller and pulleys are frictionless. Determine
the support reactions.
Problem 5.58
A walkway for loading and unloading ships at a wharf is shown. The elevation
of the walkway is controlled by cable
BCD
, which is attached to a drum on
a geared motor at
B
. If the
1kip
force is vertical and is positioned halfway
between points
A
and
C
, determine the forces supported by cables
BCD
and
DE, the reactions at A, and the force supported by bar DF .
Problem 5.59
Repeat Prob. 5.58 if the 1kip vertical force is positioned at the bearing of pulley C.
Problem 5.60
In the structure shown, member
ABCD
is supported by a pin at
C
and a cable
that wraps around pulley E, which is frictionless.
(a)
Specify if member
ABCD
has complete fixity or partial fixity and whether
it is statically determinate or statically indeterminate.
(b)
Draw the FBD for member
ABCD
, and determine the cable tension in terms
of force
F
and length
L
. Comment on any difficulties that might arise in
your analysis.
Solution
Problem 5.61
In the structure shown, member
ABCD
is supported by a pin at
C
and a cable
that wraps around pulley E, which is frictionless.
(a)
Specify if member
ABCD
has complete fixity or partial fixity and whether
it is statically determinate or statically indeterminate.
(b)
Draw the FBD for member
ABCD
, and determine the cable tension in terms
of force
F
and length
L
. Comment on any difficulties that might arise in
your analysis.
Solution
Problem 5.62
In the structure shown, member
ABCD
is supported by a pin at
C
and a cable
that wraps around pulley E, which is frictionless.
(a)
Specify if member
ABCD
has complete fixity or partial fixity and whether
it is statically determinate or statically indeterminate.
(b)
Draw the FBD for member
ABCD
, and determine the cable tension in terms
of force
F
and length
L
. Comment on any difficulties that might arise in
your analysis.
Solution
Problem 5.63
An office chair has a compressed spring that allows the chair to tilt backward
when a sufficiently large force
F
is applied. When
F
is small, the stop at point
A
prevents the chair from tilting forward. If the spring has
10 lb=in:
stiffness
and
15 in:
unstretched length, determine the value of
F
that will cause the chair
to begin tilting backward.
Solution
Problem 5.64
An office chair has a prewound torsional spring that allows the chair to tilt
backward when a sufficiently large force
F
is applied. When
F
is small,
the stop at point
A
prevents the chair from tilting forward. If the spring has
100 in:lb=rad
stiffness and is prewound by 3/4 of a turn, determine the value
of Fthat will cause the chair to begin tilting backward.
Solution
Problem 5.65
The brake pedal
ABCD
for an automobile has a torsional spring at pin
C
. The
spring has
4000 Nmm=rad
stiffness and is prewound by 1/2 of a turn so that
contact is made at point
E
when
PDQD0
. If
PD100
N and the pedal has
negligible weight, determine the value of
Q
that will cause the pedal to begin
to move and the reactions at C.
Solution
Problem 5.66
The brake pedal
ABCD
for an automobile has a horizontal spring
BF
. The
spring has
5N=mm
stiffness and
110 mm
unstretched length. If
PD100
N
and the pedal has negligible weight, determine the value of
Q
that will cause
the pedal to begin to move and the reactions at C.
Solution
Problem 5.67
The geometry of a structure before the
500
N force is applied is shown, where
member
ABC
is horizontal and spring
AD
is unstretched. The pulley at
C
is frictionless. Determine the vertical displacement
d
of point
A
, the forces
supported by cable
BCD
and the spring, and the reaction between the roller
A
and the wall to the right of it, due to the
500
N force. Assume
d
is small
enough so that the geometry of the displaced structure is essentially the same
as the geometry before loads are applied.
Solution
Problem 5.68
When force
PD0
, portion
ABC
of the structure is vertical, portion
CD
is horizontal, and spring
EB
is horizontal and unstretched. When a nonzero
value of
P
is applied, points
B
,
C
, and
D
move to locations
B0
,
C0
, and
D0
,
respectively. The force
P
is always vertical, the spring has
20 lb=in:
stiffness,
the pulley at
D
is frictionless, and weight of members is negligible. Determine
the value of
P
so that portion
AB0C0
of the structure is horizontal and portion
C0D0
is vertical. Also determine the force supported by the spring and the
reactions at point A.
Solution
Problem 5.69
A truck pulling a trailer with a tractor on it is shown in Fig. P5.69(a). The trailer’s mass is
500 kg
and
the tractor’s mass is
900 kg
, with centers of gravity at points
E
and
G
, respectively. A model for the
trailer is shown in Fig. P5.69(b) where point
A
is idealized as a pin and the tires are modeled by a vertical
spring with stiffness
kD600 kN=m
. Assuming the trailer is in static equilibrium, determine the vertical
deflection of point
D
due to the weight of the trailer and tractor. Also determine the reactions at
A
and the
force supported by the spring.
Solution
Problem 5.70
A clipboard that is used for holding and writing on paper is shown. The clamp
ABC
has a torsional spring at pin
C
with stiffness
ktD2in:lb=rad
. To
release the clamp so that paper may be inserted or removed, the user applies a
vertical force
P
. Determine the pretwist of the torsional spring (in terms of the
number of turns) so that the clamp provides a clamping force of
4lb
at point
A
when
PD0
, and determine the force
P
needed to release the clamp. Assume
the contact at Ais frictionless.
