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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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