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Statics 2e 705
Problem 5.71
A model for a 110 V electrical wall switch is shown where force
Q
that
operates the switch is perpendicular to line
BCD
. If the spring has stiffness
kD1:5 N=mm
, determine the unstretched length of the spring
L0
so that the
switch begins to move when QD2N.
Solution
Problem 5.72
A stiff fiberglass antenna is supported by a coiled spring at point
A
that has torsional
stiffness
ktD50 Nm=rad
. Force
F
at point
B
is always horizontal and models
wind forces on the antenna. Determine the rotation of the antenna if
(a) FD5N.
(b) FD50 N.
(c)
Discuss why the answer for Part (b) is not 10 times greater than the answer for
Part (a).
Hint: When appropriate in this problem, you should use the original geometry when
writing equilibrium equations. When this simplification is employed, you should
discuss its validity.
Solution
Problem 5.73
Draw the FBD for the structure shown. Then write the four equilibrium equa-
tions
PFxD0
,
PFyD0
,
PMCD0
, and
PMDD0
. If possible, solve
these equations to determine the support reactions. Discuss the difficulties that
arise.
Solution
Problem 5.74
Draw the FBD for the structure shown. Then write the four equilibrium equa-
tions
PFxD0
,
PFyD0
,
PMCD0
, and
PMDD0
. If possible, solve
these equations to determine the support reactions. Discuss the difficulties that
arise.
Solution
Problem 5.75
The I beam shown is statically indeterminate. Under certain circumstances,
it may be appropriate to use a model where the I beam is rigid and the roller
supports at points
B
and
C
are replaced by vertical springs of equal stiffness so
that the support reactions may be determined. Do this and find the reactions at
points A,B, and C.
Solution
Problem 5.76
The I beam shown in Fig. P5.76(a) is statically indeterminate. Under certain circumstances, it may be
appropriate to use the model in Fig. P5.76(b) where the I beam is rigid, the built-in support at point
A
is
replaced by a pin and torsional spring with stiffness
kt
, and the roller support at point
C
is replaced by a
vertical spring with stiffness
k
. Use this model to determine the reactions at points
A
and
C
. Express your
answers in terms of parameters such as F,L,k,kt, etc.
2.ktCkL2/;(9)
2.ktCkL2/i:(10)
With ıbeing given by Eq. (9), is determined from Eq. (5) as
2.ktCkL2/; MADFL
2h1kL2
ktCkL2i:(12)
Problem 5.77
For each object shown, specify whether it has partial fixity or full fix-
ity and whether it is statically determinate or statically indeterminate.
Assume that cables are in tension and rollers are in compression.
Problem 5.78
For each object shown, specify whether it has partial fixity or full fix-
ity and whether it is statically determinate or statically indeterminate.
Assume that cables are in tension and rollers are in compression.
Problem 5.79
Without solving, speculate on the difficulty of each of Probs. 5.80 through 5.82.
Solution
Problem 5.80
Repeat Example 5.7 on p. 308, using the actual geometry when writing the equilibrium equations to
determine the lift and drag forces
L
and
D
. Assume
L
is vertical and
D
is horizontal. In your opinion, are
the differences between your answers here and those in Example 5.7 acceptable? Describe some ways the
design of the wind tunnel of Example 5.7 could be changed so that these differences are reduced (e.g.,
change of dimensions, spring stiffnesses, etc.).
Problem 5.81
In Example 5.7 on p. 308, if
LD2N
and
DD0:3 N
, determine
ı
and
, using the original geometry
when writing the equilibrium equations.
Problem 5.82
In Example 5.7 on p. 308, if
LD2N
and
DD0:3 N
, determine
ı
and
, using the actual geometry when
writing the equilibrium equations. Assume Lis vertical and Dis horizontal.
Problem 5.83
Can the solution to Prob. 5.34 on p. 294 be obtained by superposing the solutions to Probs. 5.32 and 5.33?
Explain. Note: Concept problems are about explanations, not computations.
Solution
then using the results for load cases 1-3, the results for Problem 5.34 (where WD65 lb, PD200 lb,
Problem 5.84
Consider the structure from Example 5.8 on p. 309, shown again here where
Wis the weight of the structure with center of gravity at point H.
(a)
If
WD2kip
, determine the support reactions due to the weight of
the structure only (i.e., PD0).
(b)
Use superposition of the results from Part (a) and Example 5.8 to
determine the total values of the support reactions when
WD2kip
and PD3kip.
(c)
Use superposition of the results from Part (a) and Example 5.8 to
determine the total values of the support reactions when
WD1:8 kip
and PD4kip.
Problem 5.85
For each of the support schemes shown in Fig. 5.17 on p. 302, apply a vertical downward force
P
at
location
B
, as shown in Fig. 5.18, and specify if the object is a two-force, three-force, or general multiforce
member.
Solution
Part (a) Three-force member.
Part (b) Multiforce member.
Problem 5.86
Identify each of the members cited below as a zero-force, two-force, three-force, or multiforce member.
Members ABC and BD in Example 5.1 on p. 282.
Problem 5.87
Identify each of the members cited below as a zero-force, two-force, three-force, or multiforce member.
Member ABCD in Example 5.2 on p. 284.
Problem 5.88
Identify each of the members cited below as a zero-force, two-force, three-force, or multiforce member.
Door ABDE and strut BC in Example 5.3 on p. 285.
Problem 5.89
Identify each of the members cited below as a zero-force, two-force, three-force, or multiforce member.
Plate ABCDE in Example 5.4 on p. 286.
