Shape optimisation of steel standard profiles

Shape optimisation of steel standard profiles

A.N. Fontan & S. Hernandez School of Civil Engineering, University of La Corulia, Spain

Abstract

In this paper a specific application of shape optimization related with finding the optimal values of the internal dimensions of wide flange steel profiles. Two different problems have been solved in this piece of research by using a computer code SAFO written by the authors. This software has a user friendly graphic interface which allows the user to be comfortable with the code. According with the results of the research work carried out new series of wide flange profiles more efficient than the current one are included in this paper.

1 Introduction

In the last few decades, the European steel industry has suffered various crises. These were the result of overproduction and the high competitiveness among companies due to the technological changes experienced in the industrial sector.

That is not to say that on a world scale this sector is in decline. This situation is caused by the great inertia demonstrated by some companies when it is time to update their products or elaborate new ones.

Playing an important role in steel production are the laminated steel products used in a wide variety of engineering sectors. Several of these products appear in Figure 1 in their spanish denominations.

I1

h . -. -. -

- - 4 b b

P E HEB HEM HE A Figure 1. Laminated steel shapes.

Transactions on the Built Environment vol 52, © 2001 WIT Press, www.witpress.com, ISSN 1743-3509

The design of structures composed of these shapes must meet with a series of conditions indicated in the technical regulations of each country. These regulations guarantee that the dimensions of the laminated steel shape structures are adequate and that there are no problems with resistance. This set of conditions will be described later. The conditions are very varied, so much so that the shapes currently in industry could easily be considered compatible with some of them. However, the shapes seem too loose, too large in the face of other conditions. This situation means that, in many projects involving metal constructions, shapes of a special size are made up. These are called fabricated sections or. sometimes, plate girders and are produced with several layers of steel joined together with welded chords. An example of this type of shape appears in Figure 2b.

a) Laminated shape b) Fabricated section Figure 2. Types of steel shapes

Alongside laminated shapes, fabricated sections have as a disadvantage the fact that their welding must be strictly controlled. Consequently, it would be ideal to produce laminated shapes not only following the dimensions of what appears in the steel industry's catalogues, but also of any given size, according to customer requirements and avoiding the welding process.

To follow through with this hypothesis, designers could then establish the shape dimensions needed to suit those of the structures they are designing: that is to say, an optimum shape. It would no longer be a question of making due with what is in the catalogue or having to prepare fabricated sections by welding sheets together. Instead, a laminated shape with the specified dimensions would be made. This is not a utopian scenario. It can be achieved in practice because laminated shapes are manufactured by passing steel ingots through a rolling mill. In this device, the position of the vertical and horizontal rollers determines the final geometry of the shape. Consequently, all that is needed to modify the shape's geometry is to change the rollers' position. Figure 3 shows how this is done.

W

a) Rolling mill Figure 3. Laminated shape manufacture


b) Standard shape c) Special shape Figure 3. Laminated shape manufacture (cont'd.)

These profiles are used mainly for bending resistant element and they have to accomplish several conditions imposed by steel code regulations. According with the spanish code of practice [l]. Most important among them are - Local buckling of the compressed flange -

being o,, the maximum design stress of steel.

- Local buckling of web

- Yielding stress condition

being M the bending moment and W the strength modulus of the element. Two different problems can be considered: Problem 1. Let obtain the optimum shape of a HEB made with steel of o, = 2.6

t/cm2 having a value of the strength modulus W of W = 570 cm3. Objective function considered will be the amount of material A

A = 2heI + ( h - 2el)e (4) Table 1 shows actual dimensions of HEB-200 profile, having a value of W = 570 cm3, and the optimum HEB* obtained. Volume material has dicreased by a ratio of 33.7%.

Table 1. Actual and optimum profile dimensions

The new profile needs less material to produce equal performance but the total height is not a round number ( h = 248 mm). This is an inconvenient in order to identify it. This leads to a new problem.

HEB-200 HEB *

(mm) I (mm) I

(,,,m) 15.0 8.7

200 248

9 0 3 5

A

(,,,, 2) 78.1 51 8

S

(cm31 570 570


Problem 2. Let obtain a new series of optimized HEB profiles having optimum value of area A. The aim of this problem is to provide a new series of profiles with a correct sequence of height values, namely 11 = 180, 200,220, ... In order to check the efficiency a parameter C needs to be defined as

where W*, A * are strength modulus and area of the optimized profiles. The cocients W*/A *, W/A meisure the unitary ratio of strength modulus.

Table 2. Current HEB profiles

Table 3. Optimum HEB profiles

A * 7

(cm-) 27.2 33.6 40.3 48.5 56.4 65.2 74.4

2. Shape optimization of open laminated shapes

The approach that will be taken in this book is for carrying out a practical application of optimum design within the steel industry. It uses optimization methods for producing laminated shapes different from the standard ones. In this way, one can make thorough use of the material and thus achieve a higher degree of efficiency.

Just as one has defined the efficiency rate, C, will be for the efficiency modulus for W, and another, C,,, for W,,. That is to say:

These rates C,, C, have a clear physical interpretation. In the expressions, the numerator represents the resistance modulus under unitary bending, that is, by


area unit, of the optimum profile. The denominator expresses the same concept for the original shape. Thus, one expects the numerator to be larger than the denominator for the optimum shape and the results should be:

C, > l C, > 1

As C,, C,, increase, so should the efficiency of the shapes obtained by this method, when compared with the ones currently fabricated. For example, if in one case C, = 1.2, this means that the new shape has improved by 20% over its current counterpart.

3 Description of the SAFO code

The SAFO Programme comes from the Spanish acronym for Steel Sections with an Optimum Shape (Secciones de &er0 de Forrna Gt irna) . It consists of a computerised application that resolves the two types of design problem related to the optimum design of steel cross sections mentioned earlier. The programme attempts to show, in a straightforward fashion, how to formulate the problem and its solution.

OFTIMIZATION

OFTIMIZATION

PROBLEM

Figure 4. SAFO Programme Modules

Each module carries out the following tasks:

-

The Data Input Module: Requests the following information:

PRESEWATION

OFTHE

-The section's original geometry, when a generic geometry is to be optimized

1 RESLITS

-The type of shape, when dealing with a series of standard shapes. -The elastic limit of the steel.

The module concerned with the Preparation of the Optimization Problem: -Defines the problem to be resolved. This could be one of three types:

Optimize a section, maintaining the strength modulus W, as a constant. Optimize a section, maintaining the total depth of the section as a

constant. Optimize a series of shapes.

-Makes the connection with the optimization module. The Optimization Module:

-Requests the algorithms of the optimization that has been chosen. Possible methods include [3-41:

Modified method of feasible directions. Sequence linear programming. Sequence quadratic programming


- Establishes a link with the DOT programme [ S ] , which contains the implementation of these three methods and executes the optimization process.

The module presenting the results allows the optimization solution to be known. It contains the following information: - The new cross-section's geometry and efficiency, in contrast with the

original. - The mechanical characteristics of the initial and final sections. - Numeric values of the constraints to test the accuracy of the numeric

optimization process. - Tables with the new series of standard shapes HEA, HEB, HEM and IPE in

optimized form.

Those using SAFO interact with a series of visual screen displays developed through the language, Visual BASIC 6.0 [6-71. The following are displays that one commonly finds: - This screen, which introduces the programme, comes up when SAFO is

loaded.

SAFO Secclones de Acero do Forma optima

Vers~on 1 0 cm& e ~ s b h i ~ y 13s

Figure 5. Screen introducing the programme

The screen introducing the prograinme has a menu that allows the user to: Start up a new case or recall one that has already been worked on. Conclude the application and, optionally, save the data.

Figure 6. Start-up and closing screen


The geometry selection screen allows one to optimize either a generic geometry or a series of shapes

- The generic geometry screen appears when the user chooses to optimize a generic section on the previous menu. It comes up without data in a new problem.

Figure 8. G e o m e t ~ section screen

- If one chooses to optimize a shape related to a series on the geometry selection screen, then the following screen appears. This is the shape series selection screen.

I Tipy of chap IPE Shape

J Figure 9. Shape serles selectiotl screen


228 ( omptei' 41dcd Optrrrrrm Ucsrerl of Jtr ~ ( C I I I ~ L>\ I 11

- The opt~mizatron mode screen allows the user to define the type of problem that is to be solved.

timization mode---- - - OK I trength modulus constant (along axis X) F] l

1 Help I Flgure 10. Optimization mode screen

- The optimization method preparation screen indicates the value of the steel's elastic limit, which will influence how the web's denting constraint is expressed and define which optimization method to use.

steei S ~ E S S Limit - I ~~~~~~~i lnformat on 4 I Tn~s p r c g r a m m mm8mmr the iecfmn area u t s l r e l

r x n g under r tmpe bendlng m m e l o i c m n g c a n d n o n

eCun1? o f t h e Comonsred flange n p e c e r iubjecled $0 end,ng ecu.tty o f t h e w e b with r e r p e r l o ~ ~ cent 12

1 11

Figure 11. The opt~rnizatlon method prepnratlorz screen

- The section geometry screen compares the geometry and efficiency of the original and final sections.

Mtmrr-br.wblw LTrlu.m).m*.W

Flgltre 12. Screen with the geometric results of the opti,

The mechanical characteristic screen indicates characteristics of initial and final section.

mizatiorz

the mechanical


-

OpUrnized Sectlons Nowon8 h . 7 "D h..dga/n,ghtj

mn s=mblhakna.

e i - /I-) m I I=f lmpeIMnen

r = /D m ,=,ad,". II."Q.*b union

hl. F"" t1.h I l l 2 1 - m i=,,CII.nmnmllW

A. /96(1 Fnt * = i K l , o n a n a

sr = )66.6 L"1 6%- U mam aecbn m+ nl X

11- m4 l? = m@nial m m n h m1o8illo X

Figure 13. Technical characteristic screen

- The optitnization process control screen presents the values of the constraints at the end of the optimization process.

Conslraints values: Corrsbaint 1: Securlty of the v compressed flange in

bending piaces

CnmlraIn12: Sewrdy ofme web s x p w d to dmttng

Cnndraim 3: improveman1 o f Sfrength modulua mmpared v

with original piscs - Figure 14. The optimization process control screen

- The optitnized series of shapes screen presents the data for previously mentioned series, already optimized, along with the coefficients for their comparative efficiency.

Figure 15. The optimized series of shapes IPE


4 Optimization of the series of shapes

By using of the SAFO software a optimized series of wide flange profiles have been obtained. Information of the current and optimized shapes is next presented

perfiles HEA

Sx = Mornenx ertaucode rnadtoperl#l con relacion I X-x

1-1 = Ele de gravrdad do rnedto perill

I , = Moment0 de m e m a d e m e d o pert11 respecto a 1-1


S. @:I O L C C 1 BO'L 106 ' 0CS C1 , L E 2

s r ! @L, 1 0 0 8 1 : 11'1 L 1 8 L t O i l i Z C L

$ 0 I m, " l * ? W' ! Lffi l .T9LI I L , z


PO2 bZ 1. 1s *S1 2188808 190981. P1 10 9 6 P l j 8 6LBLC LE Dl. OSSZ E9S6E3 C O l E l LOC61 PGSL 122 PC/ S L 1 8E. 905. OLC?BLH3H / / 80 L 1 9Z l SE LE1 L9V66LS PSLESI LC EL C 0621 1 l8SOiC 6CEI 0912 l OSElE 6 L S l L S6 P11 LSVZ. 602 PL1 L 9 1 9 E I B I O S Z D 9 Z W 3 H H

58L L81

LLL VC9

,CL C i ' 9

'L8 12'4

' E t P I I

:L 'L

1c ' I* L

is" - I f ' L

'8 L

16' 16'1

10'8 - 8.''

C 9 ,C8 L 5

1 5

' ' V

r* CE

rc " 2 - U,

-

OIL l 51681 9 5 2 0991 IBDLCZ

O I L 1 SS! BLi 9CZ 0 2 6 9 186161


perf iles I P E

S, = Mornenra eiralico de medio o e i f l i con re lacon a ele X -x 1 1 = Ele ae giavedao de m e d c pert11 S = S u p e r f c ~ e de pintura

I , - Moment0 de inercla de medio p c i f l l rcipeclo a 1 - 1


5 Conclusions

The following conclusions can be drawn from the paper: -Geometry of taylor-made profiles can be highly improved by using design optimization methodologies. -Standard profiles can be updated to best accomplish code of practice regulations by using design optimization techniques. -Computer codes having graphical interfaces can help in introducing design optimization in steel and construction industries.

References

EA-95. Norma Oasica de la edificacidn. Estructuras de acero etz edificacidn. Ministerio de Obras Publicas, Transporte y Medio Ambiente, 1995. TRADE ARBED. CD-Rotn for Windows and Macintosh, 1998. EA-95. Norma brisica de la edificacidn. Estructuras de acero en edificacidn. Ministerio de Obras Publicas, Transporte y Medio Ambiente, 1995. VANDERPLAATS, G.N, Numerical optitnization techniques for engineering design: with applications. MC Graw-Hill, 1984. DOT. User's Manual, version 4.20, VR&D, 1995. MICROSOFT VISUAL BASIC, v. 6.0. Manual de Usuario, 1998. SILER, B. & SPOTTS, J.: Visual Basic 6 Edicidtz Especial, Prentice Hall, 1998. HERNANDEZ, S and FONTAN, A. N.. Practical applications it1 design optimization. WIT Press, 2001


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Shape optimisation of steel standard profiles