sm13 8

________________________________________________________________________
PROBLEM (13.8) A plane truss containing 5 members with axial rigidity AE is supported at joints 1
and 4 as shown in Fig. P13.8. Determine the global stiffness matrix for each element.
SOLUTION
Table P13.8 Data for the truss of Fig P13.8
5.05.05.0707.0707.013525.45
0010105.44
10010905.43
00101062
36.048.0639.06.08.09.365.71
)( 22
−−
o
o
o
o
o
scscscftLengthElement θ
Apply Eq.(13.14):
uvu
112
v
2
1
0.639 0.48 0.639 0.48
0.48 0.361 0.48 0.361
[] 0.639 0.48 0.639 0.48
7.5
0.48 0.361 0.48 0.361
AE
k
−−
⎡⎤
⎢⎥
−−
⎢⎥
=⎢⎥
−−
⎢⎥
−−
⎣⎦
uv uv
11 33
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎣
⎡
−
−
=
0000
0101
0000
0101
0.6
][ 2AE
k
uvuv
2233
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎣
⎡
−
−
=
1010
0000
1010
0000
5.4
][ 3AE
k
uvuv
3344
Continued on next slide
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instructional purposes only to students enrolled in courses for which the textbook has been adopted. Any other
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⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎣
⎡
−
−
=
0000
0101
0000
0101
5.4
][ 4AE
k
uv u v
22 4 4
5
0.5 0.5 0.5 0.5
0.5 0.5 0.5 0.5
[] 0.5 0.5 0.5 0.5
4.5 2 0.5 0.5 0.5 0.5
AE
k
−−
⎡⎤
⎢⎥
−−
⎢⎥
=⎢⎥
−−
⎢⎥
−−
⎣⎦
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.