Statics 2e 363
364 Solutions Manual
Problem 3.81
A model for a push button or key, such as on a calculator or computer keyboard,
is shown. The model has the feature that if
F
is sufficiently large, point
A
snaps through to give the user positive tactile feedback that the keystroke was
properly entered. Both springs have stiffness
2N=mm
, and when
FD0
, the
structure has the geometry shown and all springs are unstretched.
(a) Derive an expression that gives Fas a function of ı.
(b) Plot Fversus ıfor 0ı5mm.
(c) Determine the approximate largest value that Fhas for 0ı2mm.
(d)
What deficiency does this model display for representing a push button?
L:(5)
Using Eqs. (2) and (5), Eq. (1) becomes
FD 2k .LL0/2mm ı
L:(6)
Problem 3.82
The model of Prob. 3.81 is revised to include a third spring. Springs
AB
and
AC
have stiffness
2N=mm;
and spring
AD
has stiffness
0:3 N=mm
. When
FD0, the structure has the geometry shown and all springs are unstretched.
(a) Derive an expression that gives Fas a function of ı.
(b) Plot Fversus ıfor 0ı5mm.
(c) Determine the approximate largest value that Fhas for 0ı2mm.
(d) Does spring AD serve a useful purpose in this model? Explain.
Solution
Part (a)
The FBD of point
A
is shown at the right, where
PFxD0
requires
the force in springs
AB
and
AC
to be equal, and this force is denoted by
Fs
. The
Problem 3.83
The structure shown consists of three bars pinned together at point
A
, and with
socket supports at points
B
,
C
, and
D
. Force
F
acts in the
y
direction. If
FD3kN, determine the force supported by each member.
12.3kN/D 2:75 kN:(8)
12.3 kN/D4:5 kN:(9)
Partial checks of accuracy:
Problem 3.84
The structure shown consists of three bars pinned together at point
A
, and with
socket supports at points
B
,
C
, and
D
. Force
F
acts in the
y
direction. If
each of the bars have
5kN
strength in tension and
4kN
strength in compression,
determine the largest force Fthat may be supported.
Problem 3.85
The object at
D
is supported by boom
AO
and by cables
AB
,
AC
, and
AD
,
which are parallel to the
x
,
y
, and
´
axes, respectively. If the mass of object
D
is
mDD100 kg
, determine the forces supported by the boom and three cables.
Problem 3.86
In Prob. 3.85, if the cables and boom have the failure strengths given below,
determine the largest mass mDthat can be supported.
Member Strength
AO 4000 N tension & 2000 N compression
AB 1500 N
AC 1000 N
AD 2000 N
Problem 3.87
A weight
W
is supported at
A
by bars
AB
and
AD
and by cable
AC
. Bars
AB
and
AD
are parallel to the
y
and
x
axes, respectively. If
WD1000
N,
determine the forces in each bar and the cable.
Solution
Problem 3.88
In Prob. 3.87, if the cable can support a maximum force of
2kN
, and bars
AB
and
AD
can support maximum compressive forces of
1kN
and
3kN
,
respectively, determine the largest weight Wthat may be supported.
Solution
Problem 3.89
When in equilibrium, plate
BCD
is horizontal. If the plate weighs
1:6 kN
,
determine the forces in cables AB,AC , and AD.
Problem 3.90
A weight
W
is supported by bar
AO
and cables
AB
,
AC
, and
AD
. Point
A
lies in the
xy
plane. If
WD1000 lb
, determine the forces in the bar and the
three cables.
Problem 3.91
In Prob. 3.90, if the bar and cables have the strengths listed below, determine
the largest value Wmay have.
Member Strength
AO 3000 lb tension & 2000 lb compression
AB 2000 lb
AC 1500 lb
AD 2500 lb
Problem 3.92
A circular ring with weight
W
and inside radius
r
is supported by three identical
springs having stiffness
k
and that are unstretched when
dD0
. When in
equilibrium, the ring is horizontal.
(a) Derive an expression that relates the weight Wto dand r.
(b)
If
WD300 lb
,
kD25 lb=in:
, and
rD20 in:
, determine
d
(an accurate
approximate solution is acceptable).