Unlock document.
This document is partially blurred.
Unlock all pages and 1 million more documents.
Get Access
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.)
SOLUTION
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.
