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TABLE 4.5
Loading Vactor
z
i
for the Transfer Matrix of a Beam.
∗
(Sign Convention 1)
z
i
u
b
w
b
b
b
b
0
0
P
0
0
p
0
1
EI
0
0
−
N
4
4
24
EI
−
(
4
p
a
+
p
b
)
0
b
3
1
6
E
I
−
2
1
2
EI
M
M
−
120
EI
−
(
3
p
a
+
p
b
)
3
p
0
3
6
EI
0
0
b
N
b
V
b
M
b
θ
2
1
2
EI
0
−
P
1
EI
0
0
M
24
EI
0
−
(
p
a
+
p
b
)
2
−
(
2
p
a
+
p
b
)
N
0
0
−
p
0
P
2
−
p
0
2
−
P
1
2
6
b
Uniform
Temperature
Change
T
α
=
Thermal
Coefficient
z
i
0
u
b
w
2
2
EA
0
0
2
6
EA
(
α
T
p
x
−
0
2
p
xa
+
p
xb
)
−
2
EI
M
Ta
3
0
b
(
3
m
a
+
m
b
)
24
EI
0
0
0
0
0
−
2
+
3
M
T
0
0
−
(
p
xa
+
p
xb
)
2
0
0
EI
M
Ta
0
b
N
b
V
b
M
b
θ
−
2
(
2
m
a
+
m
b
)
+
2
M
T
6
EI
0
0
−
(
m
a
+
m
b
)
2
−
p
x
0
0
0
0
0
∗
This table applies to the
i
th element of Euler-Bernoulli beams with uncoupled extension. For more complex beam elements, see Table 4.3.
Definitions:
M
T
=
A
E
α
TzdA
M
T
b
−
M
Ta
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