Optimum Design of Steel Skeleton Structures - Music-Inspired Harmony Search Algorithm: Theory and Applications - page 103

6 Optimum Design of Cellular Beams

Common steel I-beam sections can be modified to intensify their strength by creating
an open-web section from a root beam. This is achieved by cutting the web of the root
beam in a certain pattern and then re-welding the two parts to each other. As a result of
this process the overall beam depth increases that causes increase in the capacity of
section. Cellular beams are steel sections with circular openings that are made by cut-
ting a rolled beams web in a half circular pattern along its centerline and re-welding the
two halves of hot rolled steel sections as shown in Figure 8. This circular opening up of
the original rolled beam increases the overall beam depth, moment of inertia and sec-
tion modulus, while reducing the overall weight of the beam. Cellular beams have been
used in over 3,500 projects in over twenty countries [32]. The most common building
types for the cellular beams are office buildings, parking garages, shopping centers and
any structure with a suspended floor. These beams are approximately 40-60% deeper
and 40-60% stronger than the original member while reducing the overall weight.

Flexible

H s

H

Fig. 8. Cellular beam

6.1 Optimum Design Problem

The design of a cellular beam requires the selection of a rolled beam from which the
cellular beam is to be produced, the selection of circular hole diameter and the selec-
tion of spacing between the centres of these circular holes or total number of holes in
the beam as shown in Figure 9. Hence the sequence number of the rolled beam sec-
tions in the standard steel sections tables, the circular hole diameter and the total
number of holes are taken as design variables in the optimum design problem consid-
ered. For this purpose a design pool is prepared which consists of list of standard
rolled beam sections, a list of various diameter sizes and a list of integer numbers
starting from 2 to 40 for the total number of holes in a cellular beam. The optimum
design problem formulated by considering the design constraints explained in The
Steel Construction Institute Publication titled “Design of Composite and Non-
composite Cellular Beams” [33] which are consistent with BS5950 [25]; part 1 and 3
yields the following mathematical model.
Find a integer design vector

{} { }

T

where I is the sequence number of
the rolled steel profile in the standard steel sections list, I is the sequence number
for the hole diameter in the discrete set which contains various diameter values and
I is the total number of holes for the cellular beam. Once I is selected, then the
rolled steel beam designation becomes known and all cross sectional properties of the

I = I , I , I

1 2 3