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Answer:
12
12
6
12
12
6
a
b
2
2
2
2
12
6
12
6
a
k 22
a +
k 24
2
2
k
=
EI
12
12
6
12
12
6
+
+
a
b
2
2
2
2
12
6
12
6
b
k 42
b +
k 44
2
2
a
12
12 a
12
6
b +
6
a +
k 22 =
2 +
+
4
k 42 =
2 a b +
2
12
6
a +
6
b +
12
12 b
2
b
k 24 =
2 a b +
2
k 44 =
2
+
+
4
5.37 Calculate the deflection at x
=
10 ft of the beam of Fig. P5.1.
Answer: See Problem 5.1.
5.38 Find the displacement under the loads for the beam of Fig. P5.2.
Answer: See Problem 5.2.
5.39 Compute the bending moment and deflection at midspan of the beam of Fig. P5.3.
Frames
5.40 Determine the horizontal and vertical displacements of point d of the frame of Chapter
3, Fig. 3.6a. Assume numerical values as needed.
5.41 Compute the displacements of the free end of the cantilevered angle of Chapter 3,
Fig. 3.7a. Express the answer in terms of symbols, e.g., lengths, P
.
5.42 Find the force in the tie rod of the structural system of Chapter 3, Fig. 3.7b. Assign
numerical values as needed.
5.43 Calculate the deflection at the free end of the beam of Chapter 3, Fig. 3.7b. Also find
the reactions at the c antilevered end of the beam. Express your answer in terms of
symbols, e.g., E, I, P
.
5.44 Find the displacements at the nodes of the frame of Chapter 3, Fig. 3.7e. Assume all
m embers are uniform with the same E and I
.
Assign numerical values as needed for
P i ,E,I , and locations of applied loads.
5.45 A simple frame is loaded with a moment as shown in Fig. P5.45. List the element
stiffness matrices in local and global coordinates. Find the displacements o f th e nodes.
Also, find the global nodal forces, as well as the local element forces. Let M
=
1000
.
0
2 ,
2 and I
10 7
10 4
in. 4
in. lb, E
=
1
.
0
×
lb/in
.
ν =
0
.
3 ,
=
1 in., A
=
1in
.
=
1
.
0
×
.
FIGURE P5.45
A plane frame.
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