Problem 6.92a
Given:
a) Calculate the nodal loads at all
three nodes of the bar element
considered in Problem 6.101b
Solution:
From Problem 6.10b, a uniformly
distributed axial load of intensity q
acts along the entire bar.
The consistent nodal loads are given by:
r
e
1
−
1
ξ
N
T
q
⋅
J
⋅
⌠
⎮
⌡
d
=
From Eq. 6.14
N
1
1
2
ξ
−
ξ
2
+
()
⋅
=
N
2
1
ξ
2
−
=
N
3
1
2
ξξ
2
+
⋅
=
From Eq. 6.16
J
1
2
1
−
2
ξ
⋅
+
⋅
2
−
ξ
⋅
1
2
12
ξ
⋅
+
⋅
⎡
⎣
⎤
⎦
0
L
2
L
⎛
⎜
⎜
⎜
⎝
⎞
⎟
⎟
⎟
⎠
⋅
=
simplify
J
L
2
=
→
q
L
2
⋅
1
−
1
ξ
1
2
ξ
−
ξ
2
+
⋅
⌠
⎮
⎮
⌡
d
⋅
Lq
⋅
6
→
r
e
1
−
1
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This note was uploaded on 01/11/2011 for the course MAE 5020 taught by Professor Folkman during the Fall '10 term at Utah State University.
 Fall '10
 Folkman

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