Simulative Model and Multicriteria Optimization of Truss Beam

in Super-Large Columns at High Temperature

Yanzhen Liu, Hong Gao and Jinsheng Sun

School of Chemical Engineering and Technology, Tianjin University, No. 92 Wei Jin Road, Tianjin 300072, P.R. China

Keywords: Truss Beam, Multicriteria Optimization, Super-Large Column, Finite Element Analysis, Side Beam.

Abstract: With the increasingly enlarged process scale and the consequent requirement for large equipment, such as

column, trusses ever widely applied in civil and building engineering have been introduced in petroleum

chemical industry these years. Under this circumstance, truss structure optimization emerges as a study

focus to balance safety, durability and economy. In this paper, an optimization example is introduced of a

main truss beam system, namely centre, and its side beams in super-large column at high temperature. The

main truss beam is optimized on three counts, that is, cross-section shape of the chord members, structure

height and the pairs of the web members, while side beams are optimized by compromising among

workability, stress, stiffness and weight.

1 INTRODUCTION

With the rapid development of global petrochemical

industry, super-large column application becomes an

inevitable trend of choices in unites of this area, so

how to improve the performance (mass-transfer

efficiency, stability, operation safety, etc.) of the

super-large column is becoming a hot topic (Wang,

2011).

Supporting beams as one of the important parts

in super-large column have great impacts on mass-

transfer efficiency and operation safety. Trusses ever

widely applied in civil and building engineering are

now tend to be used as supporting beam instead of

traditional beams, such as I beams and channel

beams, in super-large column. Moreover, optimum

truss beam systems are believed to have following

properties (Pascal, 2011): (1) enough strength to

support separation or reaction apparatus, such as

packings and trays, and possible less deformation to

reduce structural deflection which will cause uneven

or unsteady liquid flow within these apparatuses;

(2) optimal shapes to lessen vortexes which

aggravate the harmful gas phase turbulent move; (3)

lower pressure drop; (4) material-saving, and

workability; That is, to further increase the operation

efficiency in large-scale chemical production, a

comprehensive optimization will be inevitable. So

how to optimize truss beam structure applied in

petrochemical industry is an indispensable work that

should be taken into account.

Many investigations about optimization of truss

beams based on mathematics or FEA has been done

to provide the most efficient design of a given

structure that complies with all applicable strength,

stiffness and light weight requirements (William and

Yong, 2004). But most works aim to optimize the

structure size or to adjust the relations between the

design variables and state variables to reduce the

cost in ambient temperature on the basis of ensuring

the enough strength and less deformation.

In this case, the truss operates in super-large

column, with a smaller elastic modulus of the

material at field high temperature, which results in

larger deformation and puts forward higher demands

to optimization methods. So three criteria of

simulative optimization by ANSYS have been

provided to work out the least weight of the truss

beams in the following work, that is, the cross-

section shape combinations of chord members and

web members (Kočvara, 2002), height and the pairs

of the web members, which finally lessen the weight

with better stiffness. Besides, factories normally

tend to apply too safe truss beams as side beams.

However, side beams simplified and simulated in

this paper demonstrates that available I beams

perform well to meet the current field applications.

177

Liu Y., Gao H. and Sun J..

Simulative Model and Multicriteria Optimization of Truss Beam in Super-Large Columns at High Temperature.

DOI: 10.5220/0004016001770181

In Proceedings of the 2nd International Conference on Simulation and Modeling Methodologies, Technologies and Applications (SIMULTECH-2012),

pages 177-181

ISBN: 978-989-8565-20-4

 2012 SCITEPRESS (Science and Technology Publications, Lda.)

2 MODEL AND OPTIMIZATION

2.1 Structure Description

Truss beam in a vacuum column with diameter of

13700mm is called centre beam, and the side beams

are in the both sides of the centre beam with a

distance of 3300mm. The visual position is showed

as figure 1.

Figure 1: Distribution of beams.

The truss beam is made up of three parts, namely

top and bottom chord members as well as web

members (figure 2). The top chord member is fixed

on the inner surface of the column by supporting

brackets at both ends of the beam. This truss uses

double-web member. At both sides of the structure,

web members are weld to the top and bottom of

chord members, by attaching on the joints board.

This structure can improve the integral stability and

stiffness. The initial top and bottom chords consist

of two angle steels that are attached by welding.

Figure 2 structure of the truss.

1-top chord member; 2-stopporting bracket; 3-ten pairs of web

members; 4-bottom chord members

The truss is operated under 400℃ in the strong

corrosive environment. The material selected for it

in this condition is 316L with the prosperities of

strong heat-resistant and corrosion-resistant. Its

mechanical property parameters and initial sizes

under operating conditions are collected in the table

1 (Wang, 2008).

2.2 Finite Element Simulative Model

The universal finite element software ANSYS has a

rich unit library with a powerful function of before

and after processing. According to the prosperities

of each unit, the structure of the truss and the load

on it, when calculated, are simplified as follows:

(1) Unites attributes. Truss is a kind of plane

structure, which is mainly bending deformation

when being loaded. So when modeled, chord

members can be built with the attribute of beam 188,

which is an more appropriate unit in this linear and

large angle rotation or nonlinear big strain project, as

well as web members.

Table 1: Initial parameters.

parameter

value

remarks

dist/mm

670

nodal distance

height/mm

700

height between top and bottom

nodes

h/mm

900

initial whole height of truss beam

/mm

13440

length of truss

top

/N/mm

20.698

top linear load

bottom

/N/mm

1.612

bottom linear load

E/N/mm

1.69e5

elastic modulus



0.31

Poisson's ratio

den/Kg/mm

7.85e-

density

Initial pairs of the web members

bottomw1/m

450

width of chord members

bottomw2/m

200

height of chord members

bottomt1/m

leg thickness of chord members

bottomt2/m

waist thickness of chord members

topw12/mm

164

width of web members

topw22/mm

height of web member

topt12/mm

leg thickness of members

topt22/mm

waist thickness of members

92409

the weight of the packing and the

top chord member

dis

71988

the weight of the distribution and

the bottom chord member

[]

/Mpa

90.9

allowable stress

sigi

allowance displacement

(2) Cross-section showed as figure 2. Initially chord

members and web members are given a cross section

of T steel formed with two welded angle beams.

(3) Pressure on truss. Pressure on axis is called the

linear load. So it is necessary to convert the load on

the top and bottom chord members into linear load q

before calculation (Xu et al., 2003).

top

col g

 

(1)

dis

bottom

col g

 

(2)

where

col

is the area of the column,

is the

equivalent area of the truss beam (see the figure4).

Based on (1), (2) and table 1, the value of

top

20.698N/mm and

bottom

is 1.612N/mm

SIMULTECH 2012 - 2nd International Conference on Simulation and Modeling Methodologies, Technologies and

Applications

178

(4) Constraints on truss. According to trusses

installation and the field operation, the top chord

member is imposed surface constraint that the Y and

Z coordination directions are fixed. It could only

stretch freely in X direction, while the bottom chord

member is confined to rotate in Y-Z plane.

Figure 3: Equivalent

loaded area of beams.

Figure 4: Simulative model.

2.3 Calculation and Result Analysis

Based on the above parameters and former

constraints, simulative model can be built by

ANSYS and the results will be gained after being

defined as a static analysis.

When long thin rod bears uniform load, the

distorting stress is far less than the bending stress,

only the bending stress needs to be checked. The

main evaluated results for chord members are the

bending stress and the deflection. Meanwhile, Von-

Mise stress is regarded as the failure criteria for

material of 316L failing in the plastic state. The

following are the Von-Mise stress and deflection

figures of the truss beam

Figure 5: The von miss

stress nephogram of truss.

Figure 6: The deflection of

the truss.

Shown in the above two figures, the maximum

stress

max

39.97





is much less than the allowable

stress, while the maximum deflection

max

9.64sigi 

approaches the extreme displacement, which guides

the structure to be optimized by improving the

stiffness of the truss. Too safe strength and a little

strict deformation requirement, the design of truss is

judged to be a little conservative.

3 STRUCTURE OPTIMIZATION

3.1 Variables and Optimum Method

The optimization problem is formulated and solved

simultaneously in design and state variables, where

the state variables include both nodal displacements

and element forces. So it is necessary to declare the

variables first.

In this paper, the design variables are height,

topw1, topw2, topt1, topt2, topw11, topw12, topt11

and topt12. And the state variable is sigi. Stress as

the state variable can’t be defined in ANSYS. It is

checked by Von-Mise stress when the iteration is

finished. Volume represented by vtot is regarded as

the objective function to gain the least weight.

To ensure the iteration converge as fast and

accurate as possible, First-Order solution is the

proper method, whose iteration time is defined 60.

3.2 Optimization Criteria

3.2.1 Cross Section Shape Optimization of

Chord Member

Firstly the initial variables are optimized based on

optimum model 3.1 on the condition of

900,h 

800,h 

700h 

by ANSYS. Secondly the

initial cross section of chord members is replaced by

two channel steels with I steel attribute(ITI) welded

with each other based on the former optimization;

thirdly the bottom chord is replaced with two angle

steels of T steel attribute(ITT)welded with each

other based on the former two optimization.

Comparisons of the above three types of the cross

section are showed in the figure 9.

It is obvious that truss beam is more applicable

than I beam in super larger column, and from figure

9, I steel cross section for chord members is the best

choice among the three cross sections. Besides, the

volume of truss with I steel cross section under three

given heights is less than that with T cross section,

which indicates truss stiffness per volume with I

steel cross section is larger than that of T cross

section. So ITI is the best cross section combination

for the truss, and is applied in the optimization of the

pairs of web members

Simulative Model and Multicriteria Optimization of Truss Beam in Super-Large Columns at High Temperature

179

Figure 7: Volume

comparisons of different

cross section types.

Figure 8: Comparisons of

volumes with ITI cross

section under different pairs

of web members.

3.2.2 Optimization of the Pairs of Web

Members

Simulative model will be rebuilt when the pairs of

web members are redefined. The pairs of the web

members n are ranged from 8 to 16 with the

increments of 2. Then optimization proceeds

similarly to 3.2.1. Based on the outputting results,

vtot venues to n is mapped in the figure 10

As shown, under the same pairs of web members,

the higher the height is, the larger the truss volume

will be. That means there must be a compromise

between height and volume. And

14n 

are the best

pairs of web members for

900,h 

800,h 

700h 

Considering there is not so much gap of volume

from

10n 

14n 

when

900,h 

it is more

financial to produce ten pairs of web members.

Finally, the best two optimum results with ITI

cross section are picked out to contrast with initial

result with TTT cross section as follows:

(1)When height is more important than volume

800 900

% 11.11%

900

h 





(3)

7.83 7.41

% 5.67%

7.41

vtot





(4)

The best result is

14,n 

800h 

with ITI cross

section, which lowers the height by 11.11%, but

only increases the volume by 5.67%.

(2)When volume is more emphasized:

6.45 7.41

% 12.96%

7.41

vtot 





(5)

The optimum result is

900,h 

10n 

with ITI cross

section, which can reduce the weight by 12.96% and

decrease the cost by choosing

10n 

instead

14n 

3.2.3 Side Beam Optimization

The simulative model and constraints of the side

beam are the same as that of the centre, while

relevant sizes are replaced by the size given in 2.1.

The linear load is gained from the following

function:

(2 2 )





total circle

tatal c au

S L L

(6)

In equation (6) (Xu et al., 2003),

total

is the total

weights of the packing and distributor which are

loaded on

total

circle

and

circle

showed in figure 4 is

respectively the area and the length of the circle cut

by the two side beams.

From the viewpoint of engineering, it is

preferable for stability to regulate the centre

deformation equal to that of side beam. In this part,

truss beam with I steel cross section as side beam is

compared with I beam under the same beam height.

Table 2: The optimum results of side beam.

type

height/mm

vtot/mm

truss beam

h=800(n=12)

1.38E 08

I-beam

h=800

1.49E+08

From the table 2, the volume of truss beam is

near to that of I beam. It can be concluded that I

beam is more appropriate to side beam not only for

stability but also for lower manufacturing cost.

4 CONCLUSIONS

Multicriteria optimization of truss beam applied in

super-large column at 400℃ is presented in this

study. It demonstrates that chord members with I

steel cross section are superior to that traditional

with T steel cross section, not only in material-

saving, but also in uniformity of liquid distribution.

Influence of pairs of web members on optimization

reflects how big the angle between chord member

and web member is more favourable. As for side

beam, judging from the stability and lower cost, it is

best to choose I beam rather than truss beam on the

foundation of enough strength and stiffness.

By contrasted the influence of different shapes

on truss performance, some other shapes of truss

beam cross section which may be more effective in

material-saving and energy-saving can be

investigated in the future. In addition, the relation of

the angle between chord member and web member

and the distance between web members can be tried

SIMULTECH 2012 - 2nd International Conference on Simulation and Modeling Methodologies, Technologies and

Applications

180

to build in order to reduce variables, which can

somewhat improve the speed of optimization.

REFERENCES

Wang, X, J., 2011. The optimum design of large-scale

inner-tower truss-stopporting structure based on Finite

element analysis.

Pascal, L., 2011. The certain generalized stresses method

for the static finite element analysis of bar and beam

trusses with variability.

W, Y, J., 2008. Manual of steel construction.

William, N., Il Yong, K., 2004. Structural shape

optimization considering both performance and

manufacturing Cost.

X, S, M., J, Q, Y., 2003. Structural analysis of stopporting

beam in rectification tower with large diameter.

M, Kočvara., 2002. On the modelling and solving of the

truss design problem with global stability constraints.

Simulative Model and Multicriteria Optimization of Truss Beam in Super-Large Columns at High Temperature

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