sm13 1

PROBLEM (13.1) The truss element 5-3 of length L and diameter d is oriented at an angle
θ
counterclockwise from the x axis (Fig. P13.1). Determine:
(a) The global stiffness matrix of the element.
(b) The axial strain in the element.
Given: d = 1 in., L = 3 ft,
θ
= 120o , E = 10 x 106 psi
u = -0.01 in., = -0.005 in., u
5
v5 = 0.02 in., = 0.03 in.
3
v
SOLUTION
We have
22
(1) 0.785
44
Ad
π
π
== =
6
0.785(10 10 )
312
AE
L
×
=×
3
218.166(10 ) .lb in=
F53 =F35
5
3
F35 d=1 in.
1
cos120 sin120 3 2
2
oo
cs==−==
(a) Equation (13.14):
3
14 34 14 34
34 34 34 14
[ ] 218.166(10 ) 14 34 14 34
34 14 34 34
e
k
⎡
⎤
−−
⎢
⎥
−−
⎢
⎥
=
⎢
⎥
−−
⎢
⎥
⎢
⎥
−−
⎣
⎦
from which
0.25 0.433 0.25 0.433
0.433 0.75 0.433 0.25
[ ] 218.166 .
0.25 0.433 0.25 0.433
0.433 0.25 0.433 0.75
e
k kip in
−
⎡⎤
⎢⎥
−−
⎢⎥
=⎢⎥
−−
⎢⎥
−−
⎣⎦
(b) Equation (13.15) with i=5 and j=3:
153
0.02 0.01
13
218.166 0.03 0.005
22
FF ⎡⎤
+
⎧
⎫
== −
⎨
⎬
⎢⎥
+
⎩⎭
⎣⎦ 3.34 kips
=
Continued on next slide
x
L
=3 ft 120o
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Thus
1
13.34 4.255
0.785
Fksi
A
σ == =
3
16
4.255(10 ) 425.5
10 10
ε
μ ==
×
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.