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-3.04
-2.87
-0.81
3
9
1
2
-0.65
5
7
8
A
0.48
4
6
0.48
1.44
1.06
0.65
2.22
2.76
3.38
-2.26
-2.24
-1.31
-0.87
-1.34
-0.68
-0.68
1
-0.84
8
10
3
11
12
2
5
6
7
9
B
4
0.80
1.06
2.08
2.22
3.57
3.66
-2.10
-2.10
-0.53
-0.53
1 2 3 4 5
6
9 10 11 12
13 14 15 16 17 18 19 20 21 22 23
C
7
8
1.09
1.05
2.25
2.29
3.83
3.80
FIGURE 6.7
Moment distributions, for mesh refinements A, B, and C, using the material law M
.
=−
EI
w
P 2
P 3
P 1
k w
2.0
6.0
10.0
3.0
21.0
-2.59
-1.54
-1.38
Exact
solution
1.12
1.96
2.41
-2.59
-1.54
-1.38
-0.07
-0.07
1
2
9
3
4
5
7
A
8
6
1.12
1.96
2.41
-2.59
-1.38
-1.54
-0.07
-0.07
4
7
9
10 11 12
1
2
3
5
6
B
8
1.12
1.96
2.41
-2.59
-1.54
-1.38
-0.07
-0.07
1 2 3 4 5
9 10 11 12
8
13 14 15 16 17 18
C
6
19 20 21 22 23
7
1.12
1.96
2.41
FIGURE 6.8
The exact distribution of shear force and the shear force distributions for mesh refinements A, B, and C, using
nodal forces
p i 0 . The nodal values are arbitrarily connected with straight lines.
= k i
p i
v i
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