8.12 Applications of Geometric Programming 533subject to
8. 62 R−^1 L^3 ≤ 1 (E 13 )The solution of this one-degree-of-difficulty problem can be found asR∗= 1. 2 9,L∗=
0 .53,andf∗= 61 .2.
Example 8.13 Design of a Two-bar Truss [8.33] The two-bar truss shown in Fig. 8.3
is subjected to a vertical load 2P and is to be designed for minimum weight. The
members have a tubular section with mean diameterdand wall thicknesstand the
maximum permissible stress in each member (σ 0 ) is equal to 60,000 psi. Determine the
values ofhanddusing geometric programming for the following data:P= 33 ,000 lb,
t= 0 .1 in.,b=30 in.,σ 0 = 06 ,000 psi, andρ(density)=0.3 lb/in^3.
SOLUTION The objective function is given by
f (d, h)= 2 ρπ dt√
b^2 +h^2= 2 ( 0. 3 )π d( 0. 1 )√
900 +h^2 = 0. 188 d√
900 +h^2 (E 1 )The stress constraint can be expressed as
σ=P
πdt√
900 +h^2
h≤σ 0or
33 , 000
π d( 0. 1 )
√
900 +h^2
h≤ 60 , 000
Figure 8.3 Two-bar truss under load.