Engineering Optimization: Theory and Practice, Fourth Edition

3.2 Applications of Linear Programming 121

Figure 3.1 Rigid frame.

Figure 3.2 Collapse mechanisms of the frame.Mb, moment carrying capacity of beam;Mc,
moment carrying capacity of column [3.9].

of the plastic moment capacities, find the values of the ultimate moment capacities
MbandMcfor minimum weight. Assume that the two columns are identicaland that
P 1 = 3 ,P 2 = 1 ,h=8, andl=10.

SOLUTION The objective function can be expressed as

f (Mb, Mc) =weight of beam+weight of columns

=α( 2 lMb+ 2 hMc)