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FIGURE 6.17
Loading on the model of Fig. 6.14b.
For elements 3 and 4 of Fig. 6.14, the loading vectors of Eqs. (6.42) and (6.43) become
00000
1
3
T
a
1
6
·
p
0
p
30
=−
0
2
(5)
00000
5
6
T
a
·
2
3
p
0
p
40
=−
0
2
The global loading vector for the whole system is developed from the element loading
vector similarly to the development of the system stiffness matrix. Table 6.3
pr
ovid
e
s the
equation numbers of the loading components in the global loading vector
P
0
=
P
. For
element 3, where only
p
y
3
and
p
y
4
are non-zero in (5), we find from Table 6.3 that
Loading Vector Component
On the element level
On the global level
p
y
3
p
16
=
1
/
3
(
ap
0
/
2
)
p
14
=
/
(
ap
0
/
)
p
y
4
1
6
2
Similarly, for element 4,
Loading Vector Component
On the element level
On the global level
p
y
3
p
18
=
5
/
6
(
ap
0
/
2
)
p
y
4
p
16
=
2
/
3
(
ap
0
/
2
)
Assemble the element loading vectors in the same manner as the stiffness matrices to form
the global loading vector
12345678910111213 14 151617
18
P
0
6]
T
ap
0
=
P
=−
[000000000 0 0 0 0 1
/
6010 5
/
/
2
=
After the boundary conditions are imposed, the global loading vector, with
p
0
100 kN/m,
becomes
12345678910 1 1213
14
6]
T
a
P
=−
[000000000 0 1
/
6015
/
·
p
0
/
2
(6)
6]
T
kN
=−
[000000000 0 50
/
60 0 0
/
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