sm13 15

________________________________________________________________________
PROBLEM (13.15) Resolve Problem 13.14 for the planar truss supported and loaded as shown in Fig.
P13.15. Take AE = 10 MN for each element.
SOLUTION
Table P13.15 Data for the truss of Fig.P13.15
22
()
1 5 53.13 0.6 0.8 0.36 0.48 0.64
2 4 180 1 0 1 0 0
o
o
Element Length m c s c cs s θ
−
( a ) Use Eq.(13.14):
uv u
11 2
v
2
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎣
⎡
−−
−−
−−
−−
=
64.048.064.048.0
48.036.048.036.0
64.048.064.048.0
48.036.048.036.0
5
][ 1AE
k
uv uv
22 3 3
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎣
⎡
−
−
=
0000
0101
0000
0101
4
][ 2AE
k
( b ) Global Stiffness Matrix
uvu vu
112 23
v
3
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎣
⎡
−
−−
−−−
−−
−−
=
000000
025.0025.000
00128.0096.0128.0096.0
025.0096.0322.0096.0072.0
00128.0096.0128.0096.0
00096.0072.0096.0072.0
][ AEK
Continued on next slide
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( c )
2
2
0 0.322 0.096
6000 0.093 0.128
u
AE v
⎧
⎫
⎧⎫⎡ ⎤
=
⎨⎬ ⎨
⎢⎥
−
⎩⎭⎣ ⎦
⎩⎭
⎬
23
6
2
43 0 1.8
1(10 )
3 10.063 6000 6.04
10(10 )
um
v−
−
⎧⎫ ⎡⎤⎧⎫⎧⎫
==
⎨⎬ ⎨ ⎬⎨ ⎬
⎢⎥
−−−
⎣⎦⎩⎭⎩⎭
⎩⎭
( d )
12
12
3
0.072 0.096 4.5024
0.096 0.128 6.0032
0.25 0 4.5
x
y
x
Ru
R
AE kN
v
R
−−
⎧⎫ ⎡ ⎤ ⎧ ⎫
⎧⎫
⎪⎪ ⎪ ⎪
⎢⎥
=− − =
⎨⎬ ⎨⎬⎨ ⎬
⎢⎥
⎩⎭
⎪⎪ ⎪ ⎪
⎢⎥
−−
⎩⎭ ⎣ ⎦ ⎩ ⎭
( e ) Use Eq.(13.15)
[] []
26)
12 2
0.0018
0.6 0.8 10(10 0.6 0.8 37.5 ( )
0.00604
u
FAE kNC
v
⎧⎫ ⎧⎫
== =−
⎨⎬ ⎨ ⎬
−
⎩⎭
⎩⎭
[] []
26)
23 2
0.0018
1 0 10(10 1 0 18 ( )
0.00604
u
FAE kNT
v
−−
⎧⎫ ⎧⎫
=− = − =
⎨⎬ ⎨ ⎬
−⎩⎭
⎩⎭
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.