6–69.
Determine the reactions at supports Aand B.
SOLUTION
a
Ans.M
A=
43.2 kip
#
ft
+©MA=0;
MA–3(6) –3.50 a3
5b(12) =0
6ft
500lb/ft
6ft
8ft
9ft
700lb/ft
6ft
AC
D
B
SOLUTION
6–70.
Determine the horizontal and vertical components of force
at pins B and C. The suspended cylinder has a mass of 75 kg.
A
B
C
1.5 m
0.3 m
SOLUTION
6–71.
Determine the reactions at the supports A, C, and E of the
compound beam.
4 m 3 m
3 m 6 m
2 m
AD
BE
C
3 kN/m
12 kN
SOLUTION
*6–72.
Determine the resultant force at pins A, B, and C on the
three-member frame.
200 N/m
60fi
2 m
800 N
2 m
B
C
A
SOLUTION
2
6–73.
Determine the reactions at the supports at A, E, and B of
the compound beam.
3 m
900 N/m 900 N/m
4 m3 m
ACD
B
3 m
3 m
E
6–74.
The wall crane supports a load of 700 lb. Determine the
horizontal and vertical components of reaction at the pins A
and D.Also, what is the force in the cable at the winch W?
SOLUTION
Member ABC:
a
Ans.
Ans.
At D:
Ans.
Ans.Dy=2409 sin 45° =1.70 kip
Dx=2409 cos 45° =1703.1 lb =1.70 kip
Ax=1.88 kip
–Ay – 2409 cos 45° –350 cos 60° +350 –350 =0
+
:©F
x=0;
Ay=700 lb
–Ay+2409 sin 45° –350 sin 60° –700 =0+c©F
y=0;
T
BD =2409 lb
T
BD sin 45°(4) –350 sin 60°(4) #700 (8) =0+©MA=0;
4 ft
D
C
4 ft
700 lb
4 ft
6–75.
The wall crane supports a load of 700 lb. Determine the
horizontal and vertical components of reaction at the pins A
and D.Also, what is the force in the cable at the winch W?
The jib ABC has a weight of 100 lb and member BD has a
weight of 40 lb. Each member is uniform and has a center of
gravity at its center.
4ft
D
AB
C
4ft
4ft
SOLUTION
SOLUTION
By–3375
a3
5
b
=0
*6–76.
Determine the horizontal and vertical components of force
which the pins at A and B exert on the frame. 400 N/m
1.5 m
2 m
3 m
3 m
F
E
D
C
6–77.
SOLUTION
Ans.
Ans.
Member BDE:
a
Ans.
Ans.
Ans.Ey=1608 lb =1.61 kip
+c©Fy=0; –500 –120 a3
5b+2180 –Ey=0
Ex=96 lb
:
+©Fx=0; –Ex+120a4
5b=0
Dy=2180 lb =2.18 kip
+©Mg=0; 500 (8) +120a3
5b(5) –Dy(2) =0
Ay=72 lb
+c©Fy=0; –Ay+120a3
5b=0
Ax=96 lb
:
+©Fx=0; Ax–120a4
5b=0
NC=120 lb
The two-member structure is connected at Cby a pin, which
is fixed to BDE and passes through the smooth slot in
member AC. Determine the horizontal and vertical
components of reaction at the supports.
4ft
B
CD
E
500 lb
6–79.
The toggle clamp is subjected to a force Fat the handle.
Determine the vertical clamping force acting at E.
1.5 a
1.5 a
60
a/2
a/2
a/2
E
C
D
F
B
A
SOLUTION
*6–80.
When a force of 2 lb is applied to the handles of the brad
squeezer, it pulls in the smooth rod AB. Determine the force
Pexerted on each of the smooth brads at Cand D.
SOLUTION
Equations of Equilibrium: Applying the moment equation of equilibrium
about point Eto the free-body diagram of the lower handle in Fig. a,we have
Using the result of FAB and considering the free-body diagram in Fig. b,
(1)
(2)
Solving Eqs. (1) and (2) yields
4–N
C–N
D=0©F
x=0;
:
+
N
C=N
D
N
C(1.5) –N
D(1.5) =0+©MB=0;
F
AB =4 lb
2(2) –F
AB(1) =0+©ME=0;
A
C
D
2 lb
1 in.
2 lb
2 in.
2 in.
0.25 in.
1.5 in.
1.5 in.
E
B
P
P
6–81.
E
F
G
H
2m
2m1m
The hoist supports the 125-kg engine. Determine the force
the load creates in member DB and in member FB, which
contains the hydraulic cylinder H.
SOLUTION
6–82.
A5-lb force is applied to the handles of the vise grip.
Determine the compressive force developed on the smooth
bolt shank Aat the jaws.
5lb
5lb
3 in.1 in.1.5 in.
20fi
A
B
E
C
D
1in.
0.75 in.
SOLUTION
From FBD (a)
SOLUTION
22b
6–83.
Determine the force in members FD and DB of the frame.
Also, find the horizontal and vertical components of
reaction the pin at C exerts on member ABC and
member EDC.
B
A
G
F
E
D
C
2 m
6 kN
1 m
2 m1 m
SOLUTION
*6–84.
Determine the force that the smooth 20-kg cylinder exerts
on members AB and CDB. Also, what are the horizontal
and vertical components of reaction at pin A?
C
1
m
1.5 m
A
2 m
BE
D
6–85.
The three power lines exert the forces shown on the truss
joints, which in turn are pin-connected to the poles AH and
EG.Determine the force in the guy cable AI and the pin
reaction at the support H.
125ft
20 ft
AE
B
800lb
800lb800 lb
CD
20 ft20 ft
40 ft40 ft
SOLUTION
AH is a two – force member.
Joint B:
6–86.
The pumping unit is used to recover oil. When the walking
beam ABC ishorizontal, the force acting in the wireline at
the well head is 250 lb. Determine the torque Mwhich must
be exerted by the motor in order to overcome this load. The
horse-head Cweighs 60 lb and has a center of gravity at
The walking beam ABC has a weight of 130 lb and a center
of gravity at , and the counterweight has a weight of
200 lb and a center of gravity at The pitman, D, is pin
connected at its ends and has negligible weight.
G
W
.
G
B
G
C
.
G
B
20°
250 lb
70°
5ft
6ft1ft
G
w
G
C
D
AB
E
C
M
SOLUTION
From (b),
a
Ans.M=314 lb
#
ft
449.08132–200 cos 20°15.52–M=0+©M
E
=0;
F
AD
=449.08 lb
A
6–87.
Determine the force that the jaws Jof the metal cutters
exert on the smooth cable Cif 100-N forces are applied to
the handles.The jaws are pinned at Eand A, and Dand B.
There is also a pin at F.
F
15$
15$
20 mm
20 mm
30 mm 80 mm
B
J
C
D
E
A
15$
15$
400 mm
100 N
SOLUTION
*6–88.
Themachine shown is used for forming metal plates.It
consists of two toggles ABCandDEF,which are operated by
the hydraulic cylinder H.The toggles push the movable bar G
forward, pressing the plate pinto the cavity.Ifthe force which
the plate exerts on the head is determine the
force Fin the hydraulic cylinder when u=30°.
P=12 kN,
200mm
fiF
F
Pfi12 kN
H
F
G
D
E
Bp
200mm
200mm
200mm
ufi30
SOLUTION