PROBLEM 4.134 (Continued)
//
(0.5 m) ; (1 m) ; (268 N)
BA CA
ririPj
To eliminate the reactions at A and D, we shall write
// /
0: ( ) ( ) ( ) 0
AD AD B A BG AD B A BH AD C A
MrTrTrP
(1)
Substituting for terms in Eq. (1) and using determinants,
PROBLEM 4.135
The bent rod ABDE is supported by ball-and-socket joints
at A and E and by the cable DF. If a 60-lb load is applied
at C as shown, determine the tension in the cable.
SOLUTION
Free-Body Diagram:
16 11 8 21 in.
(16 11 8)
21
DF DF
DE T
TDF
ijk
Tijk
PROBLEM 4.136
Solve Problem 4.135, assuming that cable DF is replaced
by a cable connecting B and F.
PROBLEM 4.135 The bent rod ABDE is supported by
ball-and-socket joints at A and E and by the cable DF. If a
60-lb load is applied at C as shown, determine the tension
in the cable.
SOLUTION
Free-Body Diagram:
/
/
9
910
BA
CA
ri
rik
PROBLEM 4.137
Two rectangular plates are welded together to form the
assembly shown. The assembly is supported by ball-and-
socket joints at B and D and by a ball on a horizontal
surface at C. For the loading shown, determine the reaction
at C.
SOLUTION
First note:
22 2
(6 in.) (9 in.) (12 in.)
(6) (9) (12) in.
1(6 9 12)
16.1555
ij k
ij k
BD
PROBLEM 4.138
The pipe ACDE is supported by ball-and-socket joints at A and E
and by the wire DF. Determine the tension in the wire when a
640-N load is applied at B as shown.
SOLUTION
Free-Body Diagram:
Dimensions in mm
480 160 240
560 mm
480 160 240
560
AE
AE
AE
AE
AE
ijk
ijk
λ
PROBLEM 4.139
Solve Problem 4.138, assuming that wire DF is replaced by a
wire connecting C and F.
PROBLEM 4.138 The pipe ACDE is supported by ball-and-
socket joints at A and E and by the wire DF. Determine the
tension in the wire when a 640-N load is applied at B as shown.
SOLUTION
Free-Body Diagram:
Dimensions in mm
480 160 240
560 mm
AE
AE
ijk
PROBLEM 4.140
Two
24–ft
plywood panels, each of weight 12 lb, are nailed
together as shown. The panels are supported by ball-and-
socket joints at A and F and by the wire BH. Determine
(a) the location of H in the xy plane if the tension in the wire
is to be minimum, (b) the corresponding minimum tension.
SOLUTION
Free-Body Diagram:
424 6ft
1(2 2 )
3
ijk
λij k
AF
AF AF
PROBLEM 4.140 (Continued)
Projection of T on /
()
AF B A
λr
is constant. Thus, min
T
is parallel to
/
11
(2 2 ) 4 ( 8 4 )
33
AF B A
λrijkijk
Corresponding unit vector is
1
5
(2 ).jk
min
1
(2 ) 5
TT
jk (2)
PROBLEM 4.141
Solve Problem 4.140, subject to the restriction that H must lie
on the y-axis.
PROBLEM 4.140 Two
24–ft
plywood panels, each of weight
12 lb, are nailed together as shown. The panels are supported
by ball-and-socket joints at A and F and by the wire BH.
Determine (a) the location of H in the xy plane if the tension
in the wire is to be minimum, (b) the corresponding minimum
tension.
SOLUTION
Free-Body Diagram:
424
1(2 2 )
AF
AF
ijk
λij k
PROBLEM 4.141 (Continued)
From Eq. (1):
/21/2
212
()400 32
3(32 )
44
AF B A
T
Ty
y
λr
PROBLEM 4.142
A 3200-lb forklift truck is used to lift a 1700-lb crate.
Determine the reaction at each of the two (a) front wheels A,
(b) rear wheels B.
SOLUTION
Free-Body Diagram:
PROBLEM 4.143
The lever BCD is hinged at C and attached to a control rod at B. If
P 100 lb, determine (a) the tension in rod AB, (b) the reaction at C.
SOLUTION
Free-Body Diagram:
PROBLEM 4.144
Determine the reactions at A and B when (a) 0,h
(b)
200 mm.h
SOLUTION
Free-Body Diagram:
PROBLEM 4.145
Neglecting friction and the radius of the pulley,
determine (a) the tension in cable ADB, (b) the reaction
at C.
SOLUTION
Free-Body Diagram:
Dimensions in mm
Geometry:
Distance:
22
(0.36) (0.150) 0.39 mAD
PROBLEM 4.146
Bar AD is attached at A and C to collars that can move
freely on the rods shown. If the cord BE is vertical (
0),
determine the tension in the cord and the reactions at A and
C.
SOLUTION
Free-Body Diagram:
PROBLEM 4.147
A slender rod AB, of weight W, is attached to blocks A and B
that move freely in the guides shown. The constant of the spring
is k, and the spring is unstretched when
0.
(a) Neglecting the
weight of the blocks, derive an equation in W, k, l, and
that
must be satisfied when the rod is in equilibrium. (b) Determine
the value of
when 75 lb,W 30 in.,l and
3 lb/in.k
SOLUTION
Free-Body Diagram: