348
Along AB,
a=0.
Then Eq (1) becomes
*4–120. Continued
Ans:
349
SOLUTION
Equivalent Resultant Force. Referring to Fig. a
As indicated in Fig. a,
Location of Resultant Force. Referring to Fig. a
4–121.
Replace the loading on the frame by a single resultant force.
Specify where its line of action intersects a horizontal line
along member CB, measured from end C.
1 m
B
A
y
0.5 m
1 m
0.5 m
400 N
600 N
54
3
400 N
900 N
1.5 m
x
5
4
3
350
4–121. Continued
Ans:
351
4–122.
SOLUTION
Equivalent Resultant Force: Forces F1and F2are resolved into their xand y
components,Fig. a. Summing these force components algebraically along the xand
yaxes,
The magnitude of the resultant force FRis given by
The angle of FRis
u
Replace the force system acting on the post by a resultant
force, and specify where its line of action intersects the post
AB measured from point A.
250 N
500 N
0.2 m
0.5 m
3
4
5
300 N
1 m
30
1 m
1 m
A
B
352
Ans:
4–123.
Replace the force system acting on the post by a resultant
force, and specify where its line of action intersects the post
AB measured from point B.
SOLUTION
Equivalent Resultant Force: Forces F1and F2are resolved into their x and y
components,Fig.a. Summing these force components algebraically along the x and
y axes,
250 N
500 N
0.2 m
0.5 m
3
4
5
300 N
1m
30
1m
1m
A
B
The magnitude of the resultant force is given by
FR
353
Ans:
*4–124.
Replace the parallel force system acting on the plate by a
resultant force and specify its location on the x–z plane.
SOLUTION
Resultant Force: Summing the forces acting on the plate,
1m
0.5 m
5kN
z
2kN
354
Ans:
4–125.
Replace the force and couple system acting on the frame by
an equivalent resultant force and specify where the
resultant’s line of action intersects member AB, measured
from A.
SOLUTION
4ft
3
5
4
2ft
150 lb
A
355
Ans:
4–126.
SOLUTION
Replace the force and couple system acting on the frame by
an equivalent resultant force and specify where the
resultant’s line of action intersects member BC, measured
from B.
4ft
3
5
4
2ft
150 lb
A
356
4–127.
750mm
z
xy
650 mm
100 mm
150 mm
600 mm
700 mm
100 mm
150 mm
8kN
6kN
F
A
F
B
O
metsys ecrof eht tneserper, fI
acting on the corbels by a resultant force, and specify its
location on the x–y plane.
FA
=7 kN and
FB
=5kN
SOLUTION
Point of Application: By equating the moment of the forces shown in Fig. aand FR,
Fig. b, about the xand yaxes,
Ans:
357
*4–128.
Determine the magnitudes of and so that the
resultant force passes through point Oof the column.
F
B
F
A
750 mm
z
xy
650 mm
100 mm
150 mm
600 mm
700 mm
100 mm
150 mm
8kN
6kN
F
A
F
B
O
SOLUTION
Equivalent Resultant Force: By equating the sum of the forces in Fig. aalong the z
axis to the resultant force ,Fig.b,
Point of Application: Since is required to pass through point O, the moment of
about the xand yaxes are equal to zero.Thus,
FR
FR
FR
4–129.
SOLUTION
The tube supports the four parallel forces. Determine the
magnitudes of forces and acting at Cand Dso that
the equivalent resultant force of the force system acts
through the midpoint Oof the tube.
FD
FC
z
A
D
C
O
400 mm
500 N
600 N
F
C
F
D
359
Ans:
SOLUTION
Equivalent Resultant Force. Sum the forces along z axis by referring to
4–130.
The building slab is subjected to four parallel column
loadings. Determine the equivalent resultant force and
specify its location (x, y) on the slab. Take F1
=
8 kN and
F2
=
9 kN.
y
x
6 kN
12 kN
6 m
4 m
16 m
12 m
8 m
z
F1F2
360
Ans:
SOLUTION
Equivalent Resultant Force. Sum the forces along z axis by referring to Fig. a,
4–131.
The building slab is subjected to four parallel column
loadings. Determine F1 and F2 if the resultant force acts
through point (12 m, 10 m).
y
x
6 kN
12 kN
6 m
4 m
16 m
12 m
8 m
z
F1F2
361
Ans:
*4–132.
If , determine the magnitude
of the resultant force and specify the location of its point of
application (x, y) on the slab.
FA
=
40 kN and FB
=
35 kN
2.5 m
2.5 m
0.75 m
0.75 m
0.75 m
3m
3m
0.75 m 90 kN
30 kN
20 kN
x
y
z
F
A
F
B
SOLUTION
Equivalent Resultant Force: By equating the sum of the forces along the zaxis to
the resultant force ,Fig. b,
Point of Application: By equating the moment of the forces and , about the xand
FR
FR
362
Ans:
4–133.
If the resultant force is required to act at the center of the
slab, determine the magnitude of the column loadings
and and the magnitude of the resultant force.FB
FA
2.5 m
2.5 m
0.75 m
0.75 m
0.75 m
3m
3m
0.75 m 90 kN
30 kN
20 kN
x
y
z
F
A
F
B
SOLUTION
Equivalent Resultant Force: By equating the sum of the forces along the zaxis to
the resultant force FR,
Point of Application: By equating the moment of the forces and , about the xand
yaxes,
FR
Solving Eqs.(1) through (3) yields
363
Ans:
4–134.
Replace the two wrenches and the force, acting on the pipe
assembly, by an equivalent resultant force and couple
moment at point O.
SOLUTION
Force And Moment Vectors:
Equivalent Force and Couple Moment At Point O:
AB
O
z
Cy
x
100 N
100N·m
300 N
0.6 m 0.8 m
0.5 m
364
SOLUTION
Resultant Force. Referring to Fig. a
The magnitude of
FR
is
The direction of
FR
is defined by
4–135.
Replace the force system by a wrench and specify the
magnitude of the force and couple moment of the wrench
and the point where the wrench intersects the x–z plane.
z
O
x
y
0.5 m
3 m
200 N
400 N
2 m
200 N
5
3
4
365
Ans:
Referring to Fig. a, where the origin of the
x′, y′, z′
axes is the point where the
wrench intersects the xz plane,
4–135. Continued
366
SOLUTION
Resultant Force. Referring to Fig. a
Then the magnitude of
FR
is
The direction of
FR
is defined by
Resultant Moment.
The line of action of
MR
of the wrench is parallel to that of
FR
. Also, assume that
MR
FR
*4–136.
Replace the five forces acting on the plate by a wrench.
Specify the magnitude of the force and couple moment for
the wrench and the point P(x, z) where the wrench intersects
the x–z plane.
y
x
z
4 m
400 N
800 N
300 N
600 N
200 N
4 m
2 m
2 m
367
Ans:
Referring to Fig. a,
*4–136. Continued