sm13 9

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PROBLEM (13.9) A planar truss containing 6 members of axial rigidity AE is supported at joint 2 as
shown in Fig. P13.9. What is the global stiffness matrix for each element?
SOLUTION
Table 13.9 Data for truss of truss of Fig. P13.9
22
1(1 2) 45 1 2 1 2 1 2 1 2 1 2
2(2 3),4(1 4) 45 1 2 1 2 1 2 1 2 1 2
3(3 4) 135 1 2 1 2 12 12 12
5(1 3) 2 0 1 0 1 0 0
6(2 4) 2 90 0 1 0 1 0
o
o
o
o
o
Element Length c s c s cs
L
L
L
L
L
θ
−
−− − − −
−−−−
−
−−−
For element 1:
11 2
uvu v
2
1
1111
1111
[]
1111
2
1111
AE
kL
−−
⎡⎤
⎢⎥
−−
⎢⎥
=⎢⎥
−−
⎢⎥
−−
⎣⎦
34
uv
For element 2 and 4:
uv
22 3
uvu v 22 4
24
1111 1111
1111 1111
[] []
1111 1111
22
1111 1111
AE AE
kk
LL
−− −−
⎡⎤⎡⎤
⎢⎥⎢⎥
−− −−
⎢⎥⎢⎥
==
⎢⎥⎢⎥
−− −−
⎢⎥⎢⎥
−− −
⎣⎦⎣⎦
4
For element 3:
33 4
uv u v
3
1111
1111
[]
1111
2
1111
AE
kL
−−
⎡⎤
⎢⎥
−−
⎢⎥
=⎢⎥
−−
⎢⎥
−−
⎣⎦
Continued on next slide
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For element 5:
113
uvuv
3
5
10 10
00 00
[]
10 10
200 00
AE
kL
−
⎡⎤
⎢⎥
⎢⎥
=⎢⎥
−
⎢⎥
⎣⎦
3
For element 6:
113
uvuv
6
0000
0101
[]
0000
20101
AE
kL
⎡⎤
⎢⎥
−
⎢⎥
=⎢⎥
⎢⎥
−
⎣⎦
Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or
instructional purposes only to students enrolled in courses for which the textbook has been adopted. Any other
reproduction or translation of this work beyond that permitted by Sections 107 or 108 of the 1976 United States
Copyright Act without the permission of the copyright owner is unlawful.