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where
=
k
11
+
k
11
k
12
k
13
3
−
2
−
1
k
21
k
22
+
k
22
+
k
22
k
23
+
k
23
K
=
−
24
−
2
−
1
−
23
k
31
k
32
+
k
32
k
33
+
k
33
+
k
33
Introduce boundary conditions:
4
U
b
U
c
0
1
−
2
=
−
23
Answer:
U
b
1
Spring Forces: Calculate
p
b
for each spring.
p
a
=−
=
1
/
4
,U
c
=
1
/
2
,p
a
=−
p
b
,p
b
=
5
,p
c
=
25
,p
c
=
0
.
0
.
0.25, and
p
c
=
.
5.12 Suppose the applied load of the spring sys
tem
of the previous problem (and Fig. P5.11)
is replaced by a prescribed displacement
U
c
0
.
5
=
.
1
Find the response variables again.
Hint:
The global equilibrium equations are
K
11
K
12
K
13
0
U
b
1
P
a
P
b
P
c
?
0
?
=
=
K
21
K
22
K
23
K
31
K
32
K
33
Partial Answer:
U
b
=
1
/
2
,P
c
=
2
5.13 If
b
∗
p
=
P
and
p
=
bP
, show that
b
∗
=
b
−
1
,
b
∗
b
I
,
and
bb
∗
=
=
I
.
Trusses
5.14 Find the vertical and horizontal displacements of joint
a
of the bar system of Chapter
3, Fig. 3.1. Also, compute the elongations of the individual bars, as well as the axial
forces in the bars.
Answer:
See Example 3.1.
5.15 Calculate the nodal displacements of the truss of Chapter 3, Fig. 3.4. Also, find the
axial forces and displacements for each member.
Answer:
See Example 3.7.
5.16 Determine the movement of joint
a
of the truss of Fig. P5.16. Assume all members
behave in a linear elastic manner.
5.17 Calculate the nodal displacements and the bar forces of the truss of Fig. P5.16. Assume
linear properties.
5.18 Compute the displacements of joint
a
of the truss of Chapter 3, Fig. 3.12a. Also find
the forces in the bars.
Answer:
See Fig. 3.13.
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