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cross-section of depth
h
would be
p
i
0
h
]
T
=
[0
−
EI
α
T
/
h
0
EI
α
T
/
is the coefficient of thermal expansion.
5.31 Set up a displacement method computer routine to find the displacements of the beam
of Fig. P5.4. Find the displacements at
b
an
d
c
for:
Case 1: Concentrated loads only with
P
where
α
=
500 N,
M
b
=
0,
M
c
=
100 Nm
20
◦
C,
10
−
6
/
◦
C
Case 2: Thermal loading only with
T
=
α
=
12
×
Answer:
Case 1:
θ
c
]
T
10
−
5
10
−
4
rad]
T
[
w
b
θ
b
=
[0
.
0117 mm
−
0
.
670
×
rad
0
.
268
×
Case 2:
c
]
T
10
−
3
10
−
3
rad]
T
[
w
θ
θ
=
[
−
0
.
183 mm
0
.
183
×
rad
−
0
.
733
×
b
b
5.32 Use the displacement method to find the displacements at the supports of the beam
of Fig. P5.5. Use the numerical geometrical and physical values given in Problem 5.5.
Answer:
See Problem 5.5.
5.33 Find the slopes of the beam of Fig. P5.6 at nodes
b
and
c
.
Answer:
44
θ
.
0
b
=
1
/(
0
.
11
EI
)
θ
−
30
.
4
c
5.34 Calculate the bending moments at nodes
a, b
, and
c
of the beam of Fig. P5.7.
Answer:
(for
EI
=
1)
.
M
a
M
b
M
c
244
0
=
−
186
.
9
72
.
6
5.35 Find the maximum deflection and bending stress in the overhanging beam of Fig. P5.8.
Answer:
See Problem 5.8.
5.36 Derive a 4
×
4 stiffness matrix for the beam of Fig. P5.36.
FIGURE P5.36
A beam with rigid end segments.
Hint:
1
w
w
b
θ
b
1
w
w
a
θ
a
−
b
01
a
01
a
b
=
=
θ
θ
a
b
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