sm13 7

________________________________________________________________________
PROBLEM (13.7) A planar truss containing 5 members of axial rigidity AE is supported at joints 2, 3,
and 4 a shown in Fig. P13.7. What is the global stiffness matrix for each element?
SOLUTION
Table 4-1 Data for truss of Fig. P13.7.
22
145222212121
2 315 22 22 12 12 12
301010
4900 1010
5900 1010
o
o
o
o
o
Element c s c s cs θ
2
0
−
−
Equation (13.14)
11 2
uvu2 v
1
12 12 12 12
12 12 12 12
2
[]
12 12 12 12
212 12 12 12
AE
kL
−−
⎡⎤
⎢⎥
−−
⎢⎥
=⎢⎥
−−
⎢⎥
−−
⎣⎦
3
v
Similarly, for elements 2, 3, 4, and 5, we obtain
11 3
uvu
2
12 12 12 12
12 12 12 12
2
[]
12 12 12 12
212 12 12 12
AE
kL
−−
⎡⎤
⎢⎥
−−
⎢⎥
=⎢⎥
−−
⎢⎥
−−
⎣⎦
4 11 4
uv u v
3
10 10
00 00
[]
10 10
00 00
AE
kL
−
⎡⎤
⎢⎥
⎢⎥
=⎢⎥
−
⎢⎥
⎣⎦
Continued on next slide
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4422
uvuv
4
0000
0101
[] 0000
0101
AE
kL
⎡⎤
⎢⎥
−
⎢⎥
=⎢⎥
⎢⎥
−
⎣⎦
334
uvu v
4
5
0000
0101
[] 0000
0101
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.