Optimum Design
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for these are still being studied). The material behavior of the beam and
columns are vital, in bridge construction as older chain link bridge material
has changed with time, causing the bridge to fall into the river sometimes
with people on the span. Structural members are minimized for cross sectional area and weight for the applied loads.
1. Criterion function
Minimize cost
Maximize life of structure
2. Functional constraints
Buckling, tension stresses due to design loads
3. Regional constraints
Size and height
F. Ships or Barges
Ships or barges are buoyed upward by displaced water that provides a uniform elastic support to the structure. The ships and barges roll and pitch
overall as well as elastically deflect along the length. The members must
withstand the fatigue stresses and buckling loads.
1. Criterion function
Maximize cargo
Minimize costs
2. Functional constraints
Buckling and fatigue loads
3. Regional constraints
Size to fit in the canals at Panama and Suez, berths at ports
Draft to fit in most channels and harbors
III. OPTIMIZATION BY DIFFERENTIATION
The optimum design is obtained by several mathematical techniques. When
all functional constraints can be substituted into a criterion function the
derivative with respect to each variable may be set equal to zero. For n
variables this can yield n equations for a solution.
EXAMPLE 3.1 [3.23]. An open top rectangular tank with its base
twice as long as wide is to have a volume of 12 cubic feet. Determine
the most economical dimensions, if the bottom sheet material cost 0.20
dollars per square foot and the sides 0.10 dollars per square foot.
Let:
a - width of base
2a - length of tank
b - height of tank