FINITE ELEMENT METHOD 321
The assembled matrix K is
123 45678
K = 10
12 6 – 12 6 0 0 0 0
64 –6 2 0 0 0 0
–12 –6 12+6 –6+3 –6 3 0 0
62–6+34+2 –3 1 0 0
0 0 –6 –3 6+12 –3+3 –12 3
0 0 3 1 – 3 + 3 2 +1 – 3 0.5
00 0 0 –12 –312–3
0 0 0 0 3 0.5 – 3 1
6
⎡
⎣
⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢
⎢⎢
⎤
⎦
⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥
1 2 3 4 5 6 7 8
12 34 5 67 8
or K = 10
126–1260000
64–620000
–12 –6 18 – 3 – 6 3 0 0
62–36–31 0 0
0 0 – 6 – 3 18 0 – 12 3
003103–30.5
000 0–12–312–3
0 0 0 0 3 0.5 – 3 1
1
2
3
6
⎡
⎣
⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢
⎤
⎦
⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥
44
5
6
7
8
ΕΙ =^54
× 105 Nm^2
EI = 10 × 105 Nm^2
50 kN
100 kN
EI = 5 × 105 Nm^2
1 m 1 m 0.5 m
(a)
1 Element 1^23 Element 2 Element 3
4
(b)
Figure 11.8 (a) A composite beam model and (b) the finite element model