Mitsubishi Heavy Industries Technical Review Vol. 52 No. 1 (March 2015)
8Development of Rational Design Technique forFrame Steel Structure Combining Seismic Resistanceand Economic Performance
MOTOKI KATO*1

KUNIHIRO MORISHITA*2

MASAKI SHIMONO*3

YASUHARU CHUMAN*4

TAKASHI OKAFUJI*5TOSHIAKI MONAKA*6

Anti-seismic designs have been applied to plant support steel frames for years. Today, arational structure that further improves seismic resistance and ensures economic performance isrequired in response to an increase of seismic load on the assumption of predicted future massiveearthquakes. For satisfying this requirement, a steel frame design method that combines a steel
frame weight minimizing method, which enables economic design through simultaneous
minimization of multiple steel frame materials, and a seismic response control design technologythat improves seismic resistance has been established. Its application in the design of real
structures has been promoted. This paper gives an overview of this design technology and presents
design examples to which this design technology is applied.

|1. Introduction
Mitsubishi Heavy Industries, Ltd. (MHI) has numerous plant products and there are various
sized steel frames to support them.
The performance of these plant support steel frames is to reliably support plant equipment,
and they are required to withstand natural disturbances such as earthquakes and violent winds while
ensuring safety and reliability. In particular, Japan is an earthquake-prone nation and MHI has beenenhancing the seismic resistance of plant support steel frames while following changes of aseismic
design codes. On the other hand, the level of seismic load considered in the design phase is on theincrease and further enhancement of seismic resistance has been demanded in the wake of the Great
East Japan Earthquake in 2011 and the predicted occurrence of giant earthquakes including theNankai Trough Earthquake. Naturally, economic efficiency is a necessary factor for a product, andtherefore, designers are now proceeding with designs in consideration of both seismic resistanceand economic efficiency through trial and error. However, there is a limit on the manually
performed design of steel frames consisting of thousands of members as described above, so arational design technology that simultaneously realizes the contradicting performance factors ofseismic resistance and economic efficiency is required.

|2. Overview of plant support steel frame design
In Japan, the seismic resistance of plant support steel frames is designed mostly according to
the Building Standards Law, and primary design and secondary design are undertaken inconsideration of a level 1 earthquake, which is assumed to rarely occur, and a level 2 earthquake,
which is assumed to very rarely occur, respectively. Figure 1 shows a schematic diagram of thedesign flow. In the primary design, plant support steel frames are designed so that the seismic force*1

Hiroshima Research & Development Center, Technology & Innovation Headquarters*2

Manager, Hiroshima Research & Development Center, Technology & Innovation Headquarters*3

Hiroshima Research & Development Center, Technology & Innovation Headquarters*4

Chief Staff Manager, Nagasaki Research & Development Center, Technology & Innovation Headquarters*5

Nagasaki Research & Development Center, Technology & Innovation Headquarters*6

Manager, ICT Solution Center, ICT Solution Headquarters

Mitsubishi Heavy Industries Technical Review Vol. 52 No. 1 (March 2015)
9does not exceed the allowable stress for temporary loading of all steel frame members and thestory drift (horizontal relative displacement between the lower floor and the upper floor) does not
fall below the allowable value of 1/200. In the secondary design, on the other hand, seismic control
design using seismic control devices that can efficiently absorb seismic energy and reduce seismic
response has increasingly been applied in recent years because the conventional design method
sometimes results in an irrational design with enlarged steel frame members due to an increased
seismic load.
This paper presents a case example where a rational design with excellent seismic resistanceand economic efficiency is established by applying to the primary design a steel frame weightminimizing method that satisfies design evaluation while meeting various constraint conditions, notby trial and error as shown in Chapter 3, and by applying to the secondary design a seismicresponse control design that effectively utilizes seismic response control devices described inChapter 4.

Figure 1

Plant steel frame design flowPrimary design and secondary design are performed in considerationof earthquakes that occur rarely and very rarely, respectively.

|3. Steel frame weight minimizing method
As described in the preceding chapter, the M-FRAME (Mitsubishi Frame weight Reduction
Algorithm for Multiple Elements) steel frame cross section minimizing method that cansimultaneously minimize the weight of many members forming the plant support steel frame isapplied to the primary design of plant support steel frames. Figure 2 shows the outline flow of thismethod. Each phase of this method is explained as below.

Figure 2

Steel frame weight minimizing design flow

In the steel frame weight minimizing calculation, various design conditions and cross section
conditions can be considered simultaneously in order to deal with all structures. A particle
swarm optimization method is used to efficiently search for a solution.

Mitsubishi Heavy Industries Technical Review Vol. 52 No. 1 (March 2015)
10(1)Calculation conditions
The steel frame weight minimizing method performs calculation so that the evaluation
value of the weight of the entire structure is minimized in order to attain the economic
efficiency of the entire structure. Steel frames need to be designed to enable various allowablevalues such as generated stress and story drift to be satisfied as described above. Therefore, thismethod established a system that can consider these design conditions as constraint conditions,and realized simultaneous minimization of weight of multiple members under multiple designconditions. As a result, the appropriate cross section of multiple members can be selected
automatically; otherwise it is normally selected by trial and error. Figure 3 shows the change ofthe relationship between the stress ratio (ratio of the generated stress to the allowable stress)
and the number of members resulting from application of this method. As shown in the figure,the weight of the entire structure is reduced by making smaller the cross sectional area ofmembers with the lower stress ratio that are relatively strong enough within the constraint
conditions (allowable stress ratio of 1.0 or less, allowable story drift of 1/200 or less, etc.).

Figure 3 Change in relation between stress ratio and number ofmembers
With the steel frame weight minimizing method, the weight of the entire
structure is reduced by making smaller the cross sectional area of memberswith the lower stress ratio that are relatively strong enough within theconstraint conditions. As a result, the number of members with smaller stressratio decreases and the number of members with larger stress ratio increases.

(2)

Setting the conditions of the cross sectional shape
Plant support steel frames of MHI products have various cross section sizes. Forstructures consisting of members with relatively small cross sections such as small andmedium-scale structures, shaped steel members typified by JIS-shaped steels, are used in manycases. On the other hand, for large-scale structures that resist a great load such as large boiler
support steel frames, build-up members (components manufactured in a factory by assembling
steel pieces cut from a steel sheet) and shaped steel members are used in a mix because
necessary performance cannot be attained by shaped steel members in some points. The crosssection minimizing method has the ability to deal with the cross sections of both shaped steel
members and build-up members in order to handle all structures of any scale. Specifically,
discrete values and continuous values can be calculated simultaneously. When shaped steel
members are used, an appropriate cross section is selected from a list prepared in advance (fordealing with discrete values). When build-up members are used, a cross section property thatattains the goal of weight minimization is obtained by continuously changing the cross section
property such as the cross-sectional area and the moment of inertia (for dealing with continuousvalues).

Mitsubishi Heavy Industries Technical Review Vol. 52 No. 1 (March 2015)
11(3)Calculation algorithm
The steel frame minimizing method uses particle swarm optimization (PSO) as acalculation algorithm. Figure 4 shows an image of this algorithm. This method imitates theintelligence of a swarm of insects, fish, or birds that allows all swarm members to exchange
information when one of the swarm members finds a goal, such as food, and to move toward it
no matter where they are. Specifically, the final best solution is obtained as shown in Figure 4
by updating the position of each individual based on three kinds of information: [1] the bestsolution for the swarm, [2] the best solution for each individual, and [3] the current moving
direction (inertia) seen from the previous position of each individual. Because the steel frame
weight minimizing method handles both shaped steel members and build-up members as
described above, the calculation is performed as a mixed integer optimization problem that
deals with discrete variables and continuous variables. This method allows each individual tosearch for a solution while holding the best solution for itself and the best solution for theswarm, and therefore, can obtain a solution that efficiently attains a goal.

Figure 4 Overview of particle swarm optimization

The particle swarm optimization method searches for a solution based on threekinds of information: [1] the best solution for the swarm, [2] the best solution foreach individual, and [3] the current moving direction (inertia) seen from theprevious position of each individual.

|4. Seismic response control device
The adopted seismic response control device is a hysteresis damper that is inserted in thediagonal member part of a truss structure. This hysteresis damper has an energy absorption
mechanism using the elasto-plastic characteristics of a steel material, not using a mechanicalfeature such as friction or oil. The hysteresis damper used here (hereinafter referred to as a damperbrace) is an axial yielding-type buckling-restrained brace that can be used for a long member with alength of 10 meters or more.

Figure 5 Overview of damper brace structure
The damper brace consists of cruciform core, buckling-restrained pipes, anintermediate member, and connection members.

Figure 5 shows an overview of the damper brace structure. The damper brace consists of thecruciform core (having a cross-shaped cross section) that absorb elasto-plastic energy by yielding
axially against an acting axial force, buckling-restrained pipes (rectangular steel pipes) that restrain
the core member from lateral buckling and twist buckling after yielding when a compression force

Mitsubishi Heavy Industries Technical Review Vol. 52 No. 1 (March 2015)12

is applied, and an intermediate member that connects damper components (the cruciform core andthe buckling-restrained pipes) positioned on both ends of the brace. This structure can adjust theyielding axial force and the axial stiffness separately with the cruciform core and the intermediate
member, respectively, and therefore, the optimum characteristics of the brace can be set. When anaxial force acts on the brace, the cruciform core yields against the compression force and thenbegins a buckling deformation, but the buckling-restrained pipe restrains the buckling deformationof the core member.
As a result, elasto-plastic behavior similar to that occurring in the tensile side also occurs
when a compression force is applied.
Figure 6 shows the result of an experiment where load was repeatedly applied to the damper
brace. The vertical axis represents the mean axial stress σd, and the horizontal axis represents themean axial strain εd. This result indicates that a very stable elasto-plastic energy absorption effectwas generated.

Figure 6 Damper brace hysteresis characteristics

The cruciform core yields axially, but the effect of thebuckling-restrained pipe restrains the buckling deformation of the core
member. As a result, elasto-plastic behavior similar to tensile yielding
occurs. This figure shows the result of an experiment where the staticload of compression and tension was applied alternately. This result
indicates that behavior similar to the tensile side was also generated
for the compression force (minus side).

|5. Case example of plant support steel frame anti-seismic design
This chapter presents a case example to which the above described combination of the steel
frame weight minimizing method and the seismic response control design was applied.
(1) Object structure
Figure 7 shows a model diagram of the object structure. The object structure was a boiler
support steel frame, and a large structure consisting of approximately 2,000 members. The redlines in the diagram are the positions where the damper brace was installed.

Figure 7Object structure (model drawing)

The object structure was a boiler support steel frame (consisting ofapproximately 2,000 members). The red lines are the positions wherethe damper brace was installed.

Mitsubishi Heavy Industries Technical Review Vol. 52 No. 1 (March 2015)
13(2)Design method
The structure was designed according to the procedures shown in Figure 1. The primary
design used the steel frame weight minimizing method, and the secondary design used theseismic response control design. The level of the external force of an earthquake for thesecondary design was twice as much as that for the primary design.
(3) Result of design
Figure 8 shows the weight reduction effect obtained by the design. This figure comparesthe designed weight with the weight to which the steel frame weight minimizing method is notapplied (excluding the weight reduction due to seismic control design). As shown in this figure,weight reduction of several percent to more than ten percent could be attained due to theefficient design of the steel frame weight minimizing method.

Figure 8Weight reduction

A weight reduction of several percent to more than ten percent wasattained due to the application of the steel frame weight minimizing
method (excluding the weight reduction due to seismic control design).

Figure 9 shows the change of the number of members with the stress ratio (ratio of thegenerated stress to the allowable stress, which is set at less than 1.0 in the design) of 0.8 to 1.0
in the primary design as a result of the steel frame weight minimizing method. As shown in thisfigure, the application of the steel frame weight minimizing method resulted in a three-foldincrease in the number of members with a stress ratio of 0.8 to 1.0. This verifies the fact that anefficient design was attained due to the steel frame weight minimizing method.

Figure 9

Change of unit stress ratio

This figure shows the change of the number of members having a stressratio (ratio of the generated stress to the allowable stress) of 0.8 to 1.0.
Application of the steel frame weight minimizing method resulted in athree-fold increase in the number of members having a stress ratio of 0.8
to 1.0.

Figure 10 shows a distribution chart of the story shear force in the secondary design(analysis of seismic response). This chart compares cases in which the damper brace wasapplied and not applied and the vertical axis represents the height of the structure and thehorizontal axis represents the story shear force (indicated while using the story shear force atthe base in the case in which the damper brace was not applied as 1). As shown in this figure,Mitsubishi Heavy Industries Technical Review Vol. 52 No. 1 (March 2015)14

the story shear force was reduced throughout the height of the structure when the damper brace
was applied. In particular, a reduction by 20 to 30% was attained at the base. This reduction
was due to the above-mentioned seismic response control effect of the damper brace. In thisway, an efficient anti-seismic design was realized by the installation of the damper brace, whichsignificantly reduced the seismic response. In this result, all the generated stress of steel frame
members excluding damper braces was less than the allowable stress in the secondary design.

Figure 10

Distribution of story shear force in secondary design

This chart represents the distribution of the story shear force of the structure in
analysis of seismic response of the secondary design (indicated while using thestory shear force at the base in the case in which the damper brace was notapplied as 1). The story shear force was reduced all over the height of thestructure due to the seismic response control effect of the damper brace.

|6. Conclusion
For steel structures such as plant support structures, MHI has established a design method
combining a steel frame weight minimizing method that can simultaneously minimize the weightof many steel frame members with a seismic response control design technology that attains asignificant reduction of the seismic response using seismic response control devices having aseismic energy absorption effect. The application of this design method allows rationalization of
the plant support steel frame and also reduction in the scale of the foundation structure that
supports the steel frames due to the seismic response reducing effect. In this way, the rational
design of whole structure including the steel frames and the foundation that simultaneously realizes
both seismic resistance and economic efficiency is attained and an environmentally friendly design
also becomes possible due to the reduction of material usage for the steel frames and foundation.
MHI is willing to extend the application of this design technology to other products in the future.