Example Problem Description
Consider the minimum weight design of the four bar truss shown in Figure 1. For
the sake of simplicity we assume that members 1 through 3 have the same area A
1
and
member 4 has an area A
2
. The constraints are limits on the stresses in the members and on
the vertical displacement at the right end of the truss. Under the specified loading the
member forces and the vertical displacement
δ
at the end are found to be
We assume the allowable stresses in tension and compression to be 8.74 x 10
4
E and
4.83 x 10
4
E, respectively, and limit the displacement to be no greater than 3 x 10
3
l
. The
minimum weight design subject to stress and displacement constraints can be formulated in
terms of nondimensional design variables
Figure 1. Four bar statically determinate truss.
.
3
3
6
,
3
2
,
4
,
,
5
2
1
4
3
2
1
+
=

=
=

=
=
A
A
E
pl
p
f
p
f
p
f
p
f
d
.
0
17
.
7
,
0
73
.
5
,
0
3
6
18
3
3
3
,
10
,
10
2
3
1
2
2
1
1
2
1
2
3
2
1
3
1
≥

=
≥

=
≥


=
+
=
=
=


x
g
x
g
x
x
g
to
subject
x
x
OBJ
Minimize
p
E
A
x
p
E
A
x
A
1
A
1
A
2
2P
P
1
2
3
4
l
l
3
l
A
1
Member
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