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Statics 2e 383
Part (b)
With the values
WD300 lb
,
kD25 lb=in:
, and
rD20 in:
given in the problem statement,
Eq. (8) contains one unknown, namely
d
. Two strategies for determining the value of
d
that satisfies Eq. (8)
are described.
Problem 3.93
In the cable system shown, point
D
lies in the
y´
plane and force
P
is parallel
to the
´
axis. If
PD500 lb
, determine the force in cables
AB
,
AC
,
AD
, and
AE.
Problem 3.94
In the cable system shown, point
D
lies in the
y´
plane and force
P
is parallel
to the
´
axis. If cables
AB
and
AC
have
500 lb
breaking strength, and cables
AD
and
AE
have
1000 lb
breaking strength, and if all cables are to have a
factor of safety of
1:5
against failure, determine the largest force
P
that may be
supported.
D3
815
12PD15
32P;
(7)
FAC D15
(14)
Only the smallest of the above values of
P
will satisfy all four failure criteria. Hence, the largest value
P
Problem 3.95
Repeat Prob. 3.93 with point Ahaving coordinates A.1; 8; 0/ ft.
Problem 3.96
Repeat Prob. 3.94 with point Ahaving coordinates A.1; 8; 0/ ft.
(11)
Only the smallest of the above values of
P
will satisfy all four failure criteria. Hence, the largest value
P
Problem 3.97
Force
P
is supported by two cables and a bar. Point
A
lies in the
y´
plane,
and points
B
and
C
lie in the
x´
plane. If
PD3kip
, determine the forces
supported by the cables and bar.
Problem 3.98
Force
P
is supported by two cables and a bar. Point
A
lies in the
y´
plane, and
points
B
and
C
lie in the
x´
plane. The compressive load that causes the bar to
buckle and the breaking strength of each cable are specified below. If factors of
safety against failure (see the footnote of Prob. 3.94) of
1:7
and
2:0
are to be
used for cables and bars, respectively, determine the allowable force
P
that can
be supported.
Member Strength
AO 3000 lb compression
AB 6000 lb
AC 5000 lb
Problem 3.99
A photograph of the NASA Apollo 16 Lunar Module
(abbreviated by NASA as the LM) is shown on the
surface of the Moon. Such spacecraft made six
Moon landings during 1969–72. A simplified model
for one of the four landing gear assemblies of the LM
is shown. If the LM has
15;000 kg
mass, and rests on
the surface of the Moon where acceleration due to
gravity is
1:62 m=s2
, determine the force supported
by members
AB
,
AC
, and
AD
. Assume the weight
of the LM is uniformly supported by all four landing
gear assemblies, and neglect friction between the
landing gear and the surface of the Moon.
4.15;000 kg/1:62 m
s2D6075 N:(4)
Vector expressions for the forces are
E
TAB DTAB ErAB
rAB DTAB 1O{1O|C2:2 O
k
2:615 ;(5)
k
Problem 3.100
When in equilibrium, plate
ACDE
is horizontal. The plate weighs
1200 lb
and
is supported by cables
ABC
,
BD
,
BE
, and
BH
. As shown, cable
ABC
wraps
around ring
B
, which has negligible friction. If the coordinates of point
B
are
B .40; 20; 80/ in.
, determine the forces in the four cables. Remark: The system
of equations can be solved manually, but solution by calculator or computer is
recommended.
Solution
B
A
x
z
C
D
E
y
TBH
TBD
TAB
TBC TBE
The FBD for point
B
is shown where all cable forces are positive in
tension. By inspection (or by drawing a FBD of the entire system and
enforcing equilibrium of forces in the vertical direction),
TBH D1200 lb:(1)
Using the geometry provided in the problem statement, the following
position vectors may be written
ErBA D.50 O{C20 O|80 O
k/ in:; (2)
ErBC D.20 O{20 O|80 O
k/ in:; (3)
ErBD D.40 O{20 O|80 O
k/ in:; (4)
ErBE D.40 O{C20 O|80 O
k/ in:(5)
Vector expressions for the forces are
E
TBA DTAB ErBA
rBA DTAB
50 O{C20 O|80 O
k
96:44 ;(6)
E
TBC DTAB ErBC
rBC DTAB
20 O{20 O|80 O
k
84:85 ;(7)
E
TBD DTBD ErBD
rBD DTBD 40 O{20 O|80 O
k
91:65 ;(8)
E
TBE DTBE ErBE
rBE DTBE 40 O{C20 O|80 O
k
91:65 ;(9)
E
TBH D1200 lb O
k: (10)
Note that in writing Eqs. (6) and (7) that the magnitudes of the two forces are the same, namely
TAB
. The
equilibrium equations are
Problem 3.101
Member
OA
buckles when the compressive force it supports reaches
400
N.
Cables
AC
and
AD
each have
300
N breaking strength. Assuming the cabling
between
A
and
B
is sufficiently strong, determine the force
T
that will cause
the structure to fail. Assume the pulleys are frictionless with diameters that are
small enough so that all cables between Aand Bare parallel to line AB.
Problem 3.102
A portable tripod hoist for moving objects into and out of a manhole is shown.
The hoist consists of identical-length bars
AB
,
AC
, and
AD
that are connected
by a socket at
A
and are supported by equal
8ft
length cables
BC
,
BD
, and
CD
to prevent ends
B
,
C
, and
D
of the bars from slipping. Cable FAE passes
around a frictionless pulley at
A
and terminates at winch
E
, which is fixed to
bar
AB
. Idealize points
A
and
E
to be particles where all bar and cable forces
pass through these points. If the tripod is erected on level ground and is
7ft
high, and the object being lifted in the manhole weighs 300 lb,
(a)
Determine the forces in bars
AC
and
AD
and in portion
AE
of bar
AB
.
(b) Determine the force in portion EB of bar AB.
Hint: Define an
xy´
coordinate system where the
x
and
y
directions
lie in the plane defined by points B,C, and
D
, and where the
x
or
y
direction coincides with one of cables
BC
,
BD
, or
CD
. Then de-
termine the coordinates of points
B
,
C
, and
D
. The
x
and
y
coordi-
nates of point
A
are then the averages of the coordinates of points
B
,
C
,
and D.
Problem 3.103
A worker standing on a truck uses rope
AB
to slowly lower object
B
down a
chute. The object weighs
100 lb
and fits loosely against the walls of the chute
and slides with no friction. In the position shown, the center of object
B
is
halfway down the chute. The person’s hand
A
lies in the
xy
plane, and the
chute lies in a plane parallel to the y´ plane.
(a)
Determine the tension in rope
AB
and the reactions between the object
and the chute.
(b)
If the worker wishes to slowly pull the object up the chute, explain how
your answers to Part (a) change.
Problem 3.104
Due to a poorly designed foundation, the statue at point
A
slowly slides
down a grass-covered slope. To prevent further slip, a cable is attached
from the statue to point
B
, and another cable is attached from the
statue to point
C
. The statue weighs
1000 lb
, and idealize the surface
on which the statue rests to be frictionless. Determine the minimum
tensile strength each cable must have, and the magnitude of the reaction
between the statue and the slope.
Problem 3.105
Channel
AB
is fixed in space, and its centerline lies in the
xy
plane. The plane
containing edges
AC
and
AD
of the channel is parallel to the
x´
plane. If the
surfaces of the channel are frictionless and the sphere
E
has
2kg
mass, determine
the force supported by cord
EF
, and the reactions
RC
and
RD
between the
sphere and sides Cand D, respectively, of the channel.
