Problem 5.138
Beam
ABCD
is supported by a vertical bar
AE
, a pin at point
B
, and a vertical
cable C G. The weights of all members are negligible.
(a)
If the value of
P
is known, is beam
ABCD
statically determinate or
statically indeterminate? Explain.
(b)
Let bar
AE
and cable
C G
be modeled by springs with stiffnesses
kAE D
10;000 lb=in:
and
kC G D14;000 lb=in:
, respectively. If
PD2000 lb
,
determine the forces supported by the bar and cable, and the reactions at
point B.
Problem 5.139
Member ABCD has negligible weight.
(a)
If member
ABCD
is to be a two-force member, which (if any) of
FB
,
FD, and MCmust be zero?
(b)
If member
ABCD
is to be a three-force member, which (if any) of
FB
,
FD, and MCmust be zero?
(c)
If
FDD0
,
MCD0
, and
FB> 0
, draw the FBD for member
ABCD
and sketch the force polygon corresponding to PE
FDE
0.
Problem 5.140
Draw the FBD for each object shown, and specify whether it has partial tixity
or full tixity and whether it is statically determinate or statically indeterminate.
Assume that cables are in tension.
Problem 5.141
Draw the FBD for each object shown, and specify whether it has partial tixity
or full tixity and whether it is statically determinate or statically indeterminate.
Assume that cables are in tension.
Problem 5.142
Boom
OABC
is supported by a socket at
O
, cable
EABF
that passes through
small frictionless loops at
A
and
B
, and a cable at
C
that supports a force
T1
and whose line of action is directed toward
D
. The distances between points
O
and A,Aand B, and Band Care equal.
(a) If T1D0, qualitatively describe the equilibrium position of the boom.
(b)
For the static equilibrium position shown, determine the value of
T1
, the
force
T2
supported by cable
EABF
, and the reactions at
O
.Hint: A
numerical solution of the equilibrium equations is recommended.
Problem 5.143
Frame
ABCDE
consists of four bars welded together to form a single object.
Bar
CD
is parallel to the
x
axis, bars
AB
and
DE
are parallel to the
y
axis, and
bar
BC
is parallel to the
´
axis. The frame is supported by a ball and socket
at point
A
, a frictionless surface at
E
that lies in the
x´
plane, cable
BF
, and
cable
EF
. The frame has negligible weight and supports an object
G
with mass
mG
. If the cables have the allowable loads listed below, and assuming the other
members are sufticiently strong, determine the largest value mGmay have.
Member Allowable load
BF 8 kN
EF 12 kN
Problem 5.144
The landing gear for an airplane is shown just prior to landing. Frame
ABCDE
lies in the
y´
plane. The
150 lb
weight of the wheel and frame acts at point
D
in the
y
direction, and the
250 lb
force due to drag acts at point
D
in the
x
direction. The frame is supported by a self-aligning thrust bearing at
A
,
and a self-aligning bearing at
B
. A torsional spring is installed at
C
; it has
20 in:lb=degree
stiffness, and the moment it produces is zero when the landing
gear is fully raised (i.e., frame
ABCDE
rotates about the positive
´
axis until it
lies in the
x´
plane). The force
P
applied at point
E
has
x
,
y
, and
´
direction
cosines of
3=5
,
0
, and
4=5
, respectively. Assuming the landing gear is in
static equilibrium, determine the value of Pand all support reactions.
5.15 in./C250 lb.15 in./Bx.37 in./D0; (7)
5.12 in./D0; (9)
)ByD 54:50 lb, (10)
Statics 2e 795
Problem 5.145
A machine for sawing concrete is shown. It is supported by a cutting disk
at point
C
and two wheels at points
A
and
B
(the wheel at
B
is not shown).
The wheels at
A
and
B
are separated by a
0:8 m
distance along the
x
axis.
Determine the dimension
d
where the cutting disk should be located so that the
force supported by wheel Ais 20% of the force supported by wheel B.
Problem 5.146
A structure consists of a thin flat plate and two short bars with bearing supports
at
A
and
B
, where the bearing at
B
is self-aligning. The plate is loaded at its
center by a
100 lb
vertical force and by a
40 lb
force in the
x
direction at one of
the corners.
(a)
Does the plate have complete tixity or partial tixity, and is it statically
determinate or statically indeterminate? Explain.
(b) Determine all reactions at Aand B.
Problem 5.147
Bar
ABCD
is supported by a cable
AED
, which passes over a frictionless
pulley at point E, and a collar Bthat slides without friction on a vertical shaft
with square cross section. If the tip
A
is subjected to a
5kN
vertical force,
determine the tension in the cable and all support reactions at collar B.
7.3m/D0: (9)
Problem 5.148
The FBDs for two objects are shown. The forces and moments act at the points
indicated, in the directions indicated, and have positive values; i.e.,
F1> 0
,
F2> 0
,
:::
,
M1> 0
, and so on. Assuming the forces and moments have
the proper values, select one of the choices below to indicate whether these
bodies
could be
or
could never be
in equilibrium. If a body could never be in
equilibrium, explain why.
(a) Object 1 could be in equilibrium; Object 2 could be in equilibrium.
(b)
Object 1
could never be
in equilibrium; Object 2
could never be
in
equilibrium.
(c)
Object 1
could be
in equilibrium; Object 2
could never be
in equilib-
rium.
(d)
Object 1
could never be
in equilibrium; Object 2
could be
in equilib-
rium.
(e) Cannot determine without additional information.
Note: Concept problems are about explanations, not computations.
Problem 5.149
The FBDs for two objects are shown. The forces and moments act at the points
indicated, in the directions indicated, and have positive values; i.e.,
F1> 0
,
F2> 0
,
:::
,
M1> 0
, and so on. Assuming the forces and moments have
the proper values, select one of the choices below to indicate whether these
bodies
could be
or
could never be
in equilibrium. If a body could never be in
equilibrium, explain why.
(a) Object 1 could be in equilibrium; Object 2 could be in equilibrium.
(b)
Object 1
could never be
in equilibrium; Object 2
could never be
in
equilibrium.
(c)
Object 1
could be
in equilibrium; Object 2
could never be
in equilib-
rium.
(d)
Object 1
could never be
in equilibrium; Object 2
could be
in equilib-
rium.
(e) Cannot determine without additional information.
Note: Concept problems are about explanations, not computations.
Problem 5.150
The FBDs for two objects are shown. The forces and moments act at the points
indicated, in the directions indicated, and have positive values; i.e.,
F1> 0
,
F2> 0
,
:::
,
M1> 0
, and so on. Assuming the forces and moments have
the proper values, select one of the choices below to indicate whether these
bodies
could be
or
could never be
in equilibrium. If a body could never be in
equilibrium, explain why.
(a) Object 1 could be in equilibrium; Object 2 could be in equilibrium.
(b)
Object 1
could never be
in equilibrium; Object 2
could never be
in
equilibrium.
(c)
Object 1
could be
in equilibrium; Object 2
could never be
in equilib-
rium.
(d)
Object 1
could never be
in equilibrium; Object 2
could be
in equilib-
rium.
(e) Cannot determine without additional information.
Note: Concept problems are about explanations, not computations.
Problem 5.151
The FBDs for two objects are shown. The forces and moments act at the points
indicated, in the directions indicated, and have positive values; i.e.,
F1> 0
,
F2> 0
,
:::
,
M1> 0
, and so on. Assuming the forces and moments have
the proper values, select one of the choices below to indicate whether these
bodies
could be
or
could never be
in equilibrium. If a body could never be in
equilibrium, explain why.
(a) Object 1 could be in equilibrium; Object 2 could be in equilibrium.
(b)
Object 1
could never be
in equilibrium; Object 2
could never be
in
equilibrium.
(c)
Object 1
could be
in equilibrium; Object 2
could never be
in equilib-
rium.
(d)
Object 1
could never be
in equilibrium; Object 2
could be
in equilib-
rium.
(e) Cannot determine without additional information.
Note: Concept problems are about explanations, not computations.