PROBLEM 3.86
A worker tries to move a rock by applying a 360–N
force to a steel bar as shown. If two workers attempt
to move the same rock by applying a force at A and a
parallel force at C, determine these two forces so that
they will be equivalent to the single 360–N force
shown in the figure.
PROBLEM 3.87
The shearing forces exerted on the cross section of a steel channel can be
represented by a 900-N vertical force and two 250–N horizontal forces as
shown. Replace this force and couple with a single force F applied at
Point C, and determine the distance x from C to line BD. (Point C is
defined as the shear center of the section.)
Replace the 250–N forces with a couple and move the 900–N force to Point C such that its moment about
H is equal to the moment of the couple
(0.18)(250 N)
45 N m
H
M=
= ⋅
Then
(900 N)
H
Mx=
or
45 N m (900 N)
0.05 m
x
x
⋅=
=
900 N=F
50.0 mmx=
PROBLEM 3.88
A force and a couple are applied as shown to the end of a
cantilever beam. (a) Replace this system with a single force
F applied at Point C, and determine the distance d from C to
a line drawn through Points D and E. (b) Solve part a if the
directions of the two 360-N forces are reversed.
PROBLEM 3.89
Three control rods attached to a lever ABC exert on it the
forces shown. (a) Replace the three forces with an
equivalent force–couple system at B. (b) Determine the
single force that is equivalent to the force–couple system
obtained in Part a, and specify its point of application on
the lever.
PROBLEM 3.90
A rectangular plate is acted upon by the force and couple
shown. This system is to be replaced with a single equivalent
force. (a) For
a
= 40°, specify the magnitude and the line of
action of the equivalent force. (b) Specify the value of
a
if the line
of action of the equivalent force is to intersect line CD 300 mm
to the right of D.
SOLUTION
(a) The given force-couple system (F, M) at B is
48 N=F
And
PROBLEM 3.91
While tapping a hole, a machinist applies the horizontal
forces shown to the handle of the tap wrench. Show that
these forces are equivalent to a single force, and specify, if
possible, the point of application of the single force on the
handle.
PROBLEM 3.92
A hexagonal plate is acted upon by the force P and the couple shown.
Determine the magnitude and the direction of the smallest force P for
which this system can be replaced with a single force at E.
PROBLEM 3.93
An eccentric, compressive 250–kN force P is applied to the end
of a column. Replace P with an equivalent force–couple system
at G.
PROBLEM 3.94
A 2.6–kip force is applied at Point D of the cast iron post
shown. Replace that force with an equivalent force-couple
system at the center A of the base section.
PROBLEM 3.95
Replace the 150–N force with an equivalent force-couple
system at A.