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TABLE 4.2
Loading Vector
p
i
0
of a Beam Stiffness Matrix for Applied Distributed Loading (Sign Convention 2)
Definitions
Force and Displacement Vectors
0
p
0
/
0
0
m
0
0
0
−
0
u
a
w
a
θ
u
b
w
b
θ
k
N
V
a
M
a
N
b
V
M
b
(
7
p
a
+
3
p
b
)/
2
20
(
m
a
+
m
b
)/
2
2
2
−
p
0
/
12
−
(
p
a
/
20
+
p
b
/
30
)
(
m
a
−
m
b
)/
12
p
i
0
=
p
i
0
p
0
/
0
0
v
i
=
=
2
m
0
(
3
p
a
+
7
p
b
)/
20
−
(
m
a
+
m
b
)/
2
2
0
2
−
(
m
a
−
m
b
)/
12
p
0
/
12
(
p
a
/
30
+
p
b
/
20
)
p
p
b
m
m
b
Normalised Force and
Displacement Vectors
0
0
1
0
0
−
0
0
0
0
1
/
2
7
/
20
3
/
20
1
/
2
1
/
2
u
a
w
N
a
V
a
M
a
/
N
b
V
b
M
b
/
−
1
/
12
−
1
/
20
−
1
/
30
1
/
12
−
1
/
12
p
i
0
a
θ
a
u
b
w
b
θ
b
=
p
0
m
0
0
0
0
0
0
v
i
p
i
=
=
1
/
2
1
0
3
/
20
7
/
20
−
1
/
2
−
1
/
2
1
/
12
1
/
30
1
/
20
−
1
/
12
1
/
12
Uniform Temperature
Change ∆T
M
T
b
−
M
T
a
M
T
=
M
T
=
A
TzdA
α
=
Thermal Coefficient
0
−
M
T
p
x
/
2
(
2
p
xa
+
p
xb
)/
6
−
(/
2
)α
EA
T
0
0
p
x
/
0
0
0
0
−
M
T
a
0
2
(
p
xa
+
2
p
xb
)/
6
(/
2
)α
EA
T
M
T
M
T
b
0
0
0
0
0
0
p
xa
0
M
T
a
−
1
0
0
1
0
0
21
00
00
12
00
00
−
1
0
0
1
0
0
M
T
b
p
xb
M
T
a
0
M
T
b
−
−
1
px
2
6
2
α
EA
T
M
T
a
M
T
b
Note:
This table applies to the ith element of a simple Euler-Bernoulli beam. For more complex beam elements, see Table 4.4.
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