Optimum Design of Steel Skeleton Structures - Music-Inspired Harmony Search Algorithm: Theory and Applications - page 95

272 W-sections starting from W100×19.3 to W1100×499mm as given in LRFD-AISC
[27]. The sequence number of each section in the set is used as design variable. Hence
the terms of the harmony memory matrix represents the sequence number of W-
sections in the discrete set.
After carrying out a sensitivity analysis with different values of harmony search
parameter, it is noticed that the values of 50 for hms , 0.9 for hmcr and 0.5 for par re-
spectively produces the grillage with the minimum weight. With these parameters the
optimum design obtained for the system is given in Table 2. Harmony search algo-
rithm has selected W200×22.5 section for the first group and W690×217 section for
the second group in the optimum design which has the minimum weight of 14,384kg
[28]. Furthermore it is observed that the vertical displacement constraint is at its upper
bound, the strength ratio is only 0.48 which is much less than 1. This clearly reveals
the fact that the serviceability constraints are dominant in the design problem. The op-
timum result presented in Table 2 is obtained after 10,000 iterations of the harmony
search method. However, it was noticed that the optimum sectional designations
remained the same after 4,000 iterations.

Table 2. Optimum Design for 60-member grillage system

Optimum W-Section Designations

Maximum
Strength
Ratio

Minimum
Weight
(kg)

δ max
(mm)

Group 1 Group 2

W200×22.5 W690×217 25.0 0.48 14,384
The harmony search method based optimum design algorithm presented above is
also used to demonstrate the effect of beam spacing in the optimum design of gril-
lages [29]. For this purpose, it is decided that the square area of 12m×12m is to be
covered with grillage systems each having different beam spacing. The grillage sys-
tem that can be used to cover the area will have 12m long the longitudinal beams and
12m long the transverse beams. For this purpose five different grillage systems are
considered having 3m, 2.4m, 2m, 1.5m and 1m beam spacing. The total external load
of 2,160kN is distributed to joints of the grillage system as a point load value of
which is calculated according to the beam spacing. A36 mild steel is selected for the
design which has the yield stress of 250MPa, the modulus of elasticity of 205kN/mm 2
and shear modulus of 81kN/mm 2 respectively. The members of grillage structures are
collected in two groups. The longitudinal beams are considered to belong to group 1
and transverse beams are taken as group 2. Harmony search parameters; Harmony
memory size ( hms ) is taken as 50, Harmony memory considering rate ( hmcr ) is se-
lected as 0.9 while pitch adjusting rate ( par ) is considered as 0.5 on the basis of sensi-
tivity analysis.
Each grillage system with five different spacing is designed using the design algo-
rithm. It is noticed that the minimum weight of grillage systems changes with the
beam spacing. There is a decrease from 3-m beam spacing to 2-m beam spacing, then
the minimum weight increases. The variation of the minimum weight with the beam
spacing is shown in Figure 4. In this study, the beam spacing is selected as numbers