Problem 4.28
Structure
OAB
is built in at point
O
and supports two forces of magnitude
F
parallel to the
y
and
´
axes. If the magnitude of the moment about point
O
cannot exceed 1:0 kNm, determine the largest value Fmay have.
Solution
Problem 4.29
Repeat Prob. 4.28 if the
x
component of the moment (torsional component) at
point
O
may not exceed
0:5 kNm
and the resultant of the
y
and
´
components
(bending components) may not exceed
0:8 kNm
(i.e.,
qM2
yCM2
´0:8 kNm
).
Problem 4.30
Forces of 3 kN and 200 N are exerted at points
B
and
C
of the main rotor of a
helicopter, and force
F
is exerted at point
D
on the tail rotor. The 3 kN forces
are parallel to the
´
axis, the 200 N forces are perpendicular to the main rotor
and are parallel to the xy plane, Fis parallel to the yaxis, and ˛D45ı.
(a)
Determine the value of
F
so that the
´
component of the moment about
point Oof all rotor forces is zero.
(b)
Using the value of
F
found in Part (a), determine the resultant moment
of all rotor forces about point O.
(c)
If
˛
is different than
45ı
, do your answers to Parts (a) and (b) change?
Explain.
Solution
Problem 4.31
The moment of force
E
F
about point
A
can be computed using
E
MA;1 D ErAB E
F
or using
E
MA;2 D ErAC E
F
, where
B
and
C
are points on the line of action of
E
F
.
Noting that ErAC D ErAB C ErBC , show that E
MA;1 DE
MA;2.
Problem 4.32
Consider the moment of force
E
F
about points
A
and
B
, namely
E
MA
and
E
MB
. If
E
MADE
MB, what can be said about the locations of points Aand B?
Problem 4.33
An electrical power transmission line runs between points
A
,
B
, and
C
, as
shown, and a new power transmission line between points
B
and
D
is to be
constructed. The coordinates of points
A
,
C
, and
D
are
A.6000; 1000; 500/ ft
,
C.700; 4500; 900/ ft
, and
D.2000; 400; 1400/ ft
. Use the tip given in the mar–
gin note on p. 211 to determine the smallest length possible for the new power
line. Assume that power lines ABC and BD are straight.
Problem 4.34
The steering wheel of a Ferrari sports car has circular shape with
190 mm
radius, and it lies in a plane that is perpendicular to the steering col-
umn
AB
. Point
C
, where the driver’s hand applies force
E
F
to the
steering wheel, lies on the
y
axis with
y
coordinate
yCD 190 mm
.
Point
A
is at the origin of the coordinate system, and point
B
has
the coordinates
B .120; 0; 50/ mm
. Determine the moment of
E
F
about
line AB of the steering column if
(a) E
F
has
10
N magnitude and lies in the plane of the steering wheel and
has orientation such that its moment arm to line
AB
is
190 mm
. Also
determine the vector expression for this force.
(b) E
FD.10 N/18 O{3O|C14 O
k
23 .
(c) E
FD.10 N/12 O{5O
k
13 .
Problem 4.35
A rectangular piece of sheet metal is clamped along edge
AB
in a machine
called a brake. The sheet is to be bent along line
AB
by applying a
y
direction
force
F
. Determine the moment about line
AB
if
FD200 lb
. Use both vector
and scalar approaches.
Problem 4.36
In Prob. 4.35 determine Fif the moment about line AB is to be 2000 in.lb.
Solution
Problem 4.37
In the pipe assembly shown, points
B
and
C
lie in the
xy
plane, and force
F
is
parallel to the
´
axis. If
FD150 N
, determine the moment of
F
about lines
OA and AB. Use both vector and scalar approaches.
Problem 4.38
In the pipe assembly shown, points
B
and
C
lie in the
xy
plane and force
F
is
parallel to the
´
axis. If a twisting moment (torque) of
50 Nm
will cause a pipe
to begin twisting in the flange fitting at
O
or at either end of the elbow fitting at
A, determine the first fitting that twists and the value of Fthat causes it.
Problem 4.39
A chocolate candy bar is molded in the shape of a thin rectangular slab with
deep grooves. The deep grooves are represented in the figure by the dashed
lines
AB
,
AD
, and
BC
, and these grooves allow small bite-size pieces of
candy to be easily broken off. Groove
AB
breaks when the moment about this
line is
5in:lb
, and grooves
AD
and
BC
break when the moment about these
lines is
4in:lb
. The candy bar is held along the edge of a table, as shown, and
a force
F
acting in the
´
direction is applied at point
D
. Determine the force
F
required to break off a piece of candy and which of the grooves
AB
,
AD
, or
BC will break. Neglect the thickness of the candy bar.
Problem 4.40
For the candy bar described in Prob. 4.39, the manufacturer wishes to design
the strength of the grooves so that:
Groove
BC
will break when a force
FD3lb
is applied in the
´
direction at point D, as shown in Fig. P4.40, and
Groove
AB
will break when
FD0
and a force
QD4lb
is applied in
the
´
direction at the midpoint of line segment
CD
(this force is not
shown in Fig. P4.40).
If this design is possible, determine the strengths of grooves
AB
and
BC
,
namely Mstrength
AB and Mstrength
BC , where these have units of in:lb.
Problem 4.41
Determine the moment of force Fabout line AB as follows.
(a)
Determine the moment of
F
about point
A
,
E
MA
, and then determine the
component of this moment in the direction of line AB.
(b)
Determine the moment of
F
about point
B
,
E
MB
, and then determine the
component of this moment in the direction of line AB.
(c)
Comment on differences and/or agreement between
E
MA
,
E
MB
, and the
moment about line
AB
found in Parts (a) and (b). Also comment on the
meaning of the sign (positive or negative) found for the moment about
line AB.
Solution
With the information provided in the problem statement, the following position vectors may be written
Statics 2e 517
Problem 4.42
Determine the moment of force Fabout line AB as follows.
(a)
Determine the moment of
F
about point
A
,
E
MA
, and then determine the
component of this moment in the direction of line AB.
(b)
Determine the moment of
F
about point
B
,
E
MB
, and then determine the
component of this moment in the direction of line AB.
(c)
Comment on differences and/or agreement between
E
MA
,
E
MB
, and the
moment about line
AB
found in Parts (a) and (b). Also comment on the
meaning of the sign (positive or negative) found for the moment about
line AB.
Statics 2e 519
Problem 4.43
The moment of force
E
F
about line
AB
can be computed using
MAB;1
or
MAB;2
where
MAB;1 D.ErAC E
F / ErAB
jErAB j; MAB;2 D.ErBC E
F / ErAB
jErAB j;
where
C
is a point on the line of action of
E
F
. Noting that
ErAC D ErAB C ErBC
,
show that MAB;1 DMAB;2.
Solution