Optimum Design of Steel Skeleton Structures - Music-Inspired Harmony Search Algorithm: Theory and Applications - page 93

y

x

z

Fig. 2. Steel Grillage system

4.1 Discrete Optimum Design Problem

The optimum design problem of a typical grillage system shown in Figure 2 where
the behavioral and performance limitations are implemented from LRFD-AISC (Load
and Resistance Factor Design - American Institute of Steel Construction) [27] can be
expressed as in the following.

Find a vector of integer values I (Eq. 14) representing the sequence numbers of
W-sections given in W-section list of LRFD-AISC assigned to ng member groups
[ ]

T

I = I , 2 I ,..., I (14)

1 ng

to minimize the weight ( W ) of the grillage system.

ng n

k

Minimize ∑∑
=

W = m l

(15)

k i

k 1 i = 1

subject to

δ / δ ≤ 1 j = 1 2 … , p (16)

j ju

(17)

M /( φ M ) ≤ 1 r = 1 2 … , nm

ur b nr

V /( φ V ) ≤ 1 r = 1 2 , nm (18)

…

ur v nr

where m in Eq. 15 is the unit weight of grillage element belonging to group k to be
selected from W-sections list of LRFD-AISC, n k is the total number of members in
group k , and ng is the total number of groups in the grillage system.

i l is the length

of member i . is its upper bound.

The joint displacements are computed using the matrix displacement method for gril-
lage systems. Eq. 17 represents the strength requirement for laterally supported beam

δ in Eq. 16 is the displacement of joint j and δ

j ju