Civil Engineering Reference
In-Depth Information
For element 2, the same procedure in sequence gives
U
1
U
2
U
5
U
6
0
0
u
(2)
1
u
(2)
2
1000
0010
10
−
4
=
R
(2)
0
10
−
3
=
=
in
.
0
5333
1
.
0
.
5333
.
731
10(10
6
)
10
−
3
1
40
1
40
0
(2)
=
≈
133 lb/in
.
2
−
.
0
5333
f
(2)
1
f
(2)
2
u
(2
1
u
(2
2
k
2
75(10
5
)
1
10
−
3
−
200
200
lb
−
k
2
−
1
0
=
=
3
.
=
−
k
2
−
.
k
2
11
0
5333
also indicating tension.
The finite method is intended to be a general purpose procedure for analyzing prob-
lems for which the general solution is not known; however, it is informative in the exam-
ples of this chapter (since the bar element poses an exact formulation) to check the
solutions in terms of axial stress computed simply as
F
/
A
for an axially loaded member.
The reader is encouraged to compute the axial stress by the simple stress formula for each
example to verify that the solutions via the stiffness-based finite element method are
correct.
3.7 COMPREHENSIVE EXAMPLE
As a comprehensive example of two-dimensional truss analysis, the structure de-
picted in Figure 3.6a is analyzed to obtain displacements, reaction forces, strains,
and stresses. While we do not include all computational details, the example
illustrates the required steps, in sequence, for a finite element analysis.
Y
6000 lb
U
4
U
8
U
12
40 in.
40 in.
3
4
7
4000 lb
U
3
U
7
U
11
6
2
40 in.
2
4
6
8
U
2
U
6
U
10
1
5
2000 lb
U
1
U
5
U
9
X
1
3
5
2000 lb
(a)
(b)
Figure 3.6
(a) For each element,
A
= 1.5 in.
2
,
E
= 10 × 10
6
psi. (b) Node, element, and global displacement notation.
