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W
L
i
i+1
V
i
M
i+
1
x
0
T
i
T
i+1
(H
S
-D
0
)/
2
M
i
V
i+1
A
A
V
h
S-D
0
S
Fig. 10.
Horizontal and vertical shear forces in web post of a cellular beam
6.2 Design Example
Harmony search method based optimum design algorithm presented in the previous
sections is used to design a simply supported cellular beam with a span of 9m. The
beam carries a uniform load of 40kN/m including its own weight and two concen-
trated loads of 50kN as shown in Figure 11. The allowable displacement of the beam
is limited to 25 mm. The modulus of elasticity is taken as 205kN/mm
2
and Grade 50
is selected for the steel of the beam which has the design strength of 355MPa.
Among
the steel sections list of British Standards [25] 64 Universal Beam (UB) sections start-
ing from 254×102×28 UB to 914×419×388 UB are selected to constitute the discrete
set for steel sections from which the design algorithm selects the sectional designa-
tions for the cellular beam. In the design pool of hole diameters 421 values are ar-
ranged which varies between 180 and 600mm with increment of 1mm. The discrete
set for the number of holes starts with 2 and goes up to 40 with increment of 1.
The optimum design of the cellular beam described is carried out by the design al-
gorithm presented. The algorithm necessitates selection of harmony search parameters
50 kN
50 kN
40 kN/m
3 m
3 m
3 m
9 m
Fig. 11.
Simply supported beam
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