Decision support system on IBM PC for design of economic steel structures applied to crane girders PDF

Preview

Summary

Thin-Walled Structures 10 (1990) 143-159 Decision Support System on IBM PC for Design of Economic Steel Structures Applied to Crane Girders K. J~irmai Department of Materials Handling Equipment. Technical University for Heavy Industry. H-3515 Miskolc, Hungary (Received 3 October 1988; revised versio...

Description

Thin-Walled Structures 10 (1990) 143-159

Decision Support System on IBM PC for Design of Economic Steel Structures Applied to Crane Girders

K. J~irmai Department of Materials Handling Equipment. Technical University for Heavy Industry. H-3515 Miskolc, Hungary (Received 3 October 1988; revised version received 28 April 1989: accepted 1 May 1989)

ABSTRACT A decision support system (DSS) was developed on a personal computer for the economic design of steel structures. The DSS contains six various-type single-criterion and seven multicriteria optimization methods. The economic design of the asymmetric main box girders of overhead travelling cranes was realized by considering four objective functions and sixteen nonlinear inequality constraints according to BS 2573 and BS 5400. Constraints on static and fatigue stress, on local buckling offlange and web plates, as well as on static deflection, are considered. Numerical computations show the effects of material, welding, surface preparation and total cost on each other. Use of higher strength steel may result in savings on the cost of materials, depending on the cost factor employed.

MAIN NOTATION ad aw

A Ak

b

Cm, C,,Cw

Distance of diaphragms Effective length of wheel and rail connection Area of cross-section Torsional hole Width of flanges Costs

143 Thin-Walled Structures 0263-8231/90/$03.50© 1990 Elsevier Science Publishers Ltd, England. Printed in Great Britain

144

1(_ Jarmai

E F

Young's modulus of elasticitv Wheel load Wind load Fw g Gravitational acceleration Mass of trolley Gt h Height of webs H Hook load L,I> Moments of inertia of cross-section km, ks, kw Cost factors Kp Spectrum factor Span length L Mx, My, Mw Bending moments N Operation cycles Permissible tensile fatigue stress Pf, Dead loads from rail and sidewalk P,,P w Permissible static stress Ps q Wind pressure Thicknesses of plates twl, tw2, tf w Deflection of the girder Section moduli Y At, Zw, A¢ P (7

~d

Duty factor Safety factor Slendernesses of flange, web and upper part of web, respectively Material density Normal stress Shear stress Impact factor 1 INTRODUCTION

Design engineers are continually making decisions. These decisions occur at all stages and all levels of the design process. Many of these decisions are intuitive, some are qualitatively logical and some are based on the laws of science. To make decisions, the designer must predict the results of more than one possible course of action. The designer cannot predict certain future events. He cannot be certain of the maximum loading, the initial imperfection, the effects of corrosion, or the material properties. To make established decisions, we developed a so called decision support system (DSS). Optimization methods are efficient tools of DSS.

Decision support ~stem on I B M PC applied to crane girders

145

Single-criterion optimization methods can determine the best version without actually testing all possible versions by the use of a modest level of mathematics and by performing iterative numerical calculations using clearly defined logical procedures or algorithms implemented on computing machines. In complex engineering optimization problems several noncommensurable criteria have to be considered. This situation is formulated as a multicriteria optimization problem in which the engineers goal is to minimize and/or maximize not a single objective function but several functions simultaneously. 2 INTERACTIVE DECISION SUPPORT SYSTEM The combination of single-criterion and multicriteria optimization methods gives a large number of results (Pareto optima) from which the designer can choose the best. Optimization methods are good tools for economic design of structures; for finding the best structural sizes using various cost factors and weighting coefficients. The economic structure is characterized by the minimum cost/mass or by other parameters which are important to the designer. An interactive decision support system has been developed on an IBM PC/AT, using the FORTRAN language, which contains six various-type single-criterion and seven various-type multicriteria optimization methods. The single-criterion optimization methods are as follows: the Flexible Tolerance method (FT) worked out by Himmelblau, ~the Direct Random Search method (DRS) of Weisman, 2 the Hillclimb procedure (HI) of Rosenbrock, 3.4 the Complex method (Bo) of Box: .6 the Direct Search Feasible Directions method (DSFD) of Pappas, 7 and the DavidonFletcher-Powell method (DFP). 8 The multicriteria optimization techniques are as follows: the min.-max. method proposed by Jutler, 9 the weighting min.-max, method, ~° two types of global criterion methods, ~°'~l the weighting global criterion method developed by the author, and the widely applied pure weighting and normalized weighting methods. The structure of the computer code can be seen in Fig. 1. All of the algorithms were developed in such a way that they can find both the maximum and the minimum of the objective functions. The singlecriterion methods do not need feasible starting points since they use a procedure for finding them. These algorithms use continuous variables. A secondary search is added to them for finding discrete variables from a previously given range of discrete values.

146

K. Jarmai

-I MULTICRITERIA OPTIMIZATION METHODS MIN

-

]

MAX

CONTROL PROGRAM

OBJECTIVE

SINGLE-CRITERION OPTIMIZATION

FUNCTIONS

METHODS FLEXIBLE TOLERANCE

EQUALITY CONSTRAINTS

~ZT)

GLOBALCRITERIONTYPEi GLOBALCRITERIONTYPE2 I I WEIGHTING MIN MAX

[ INPUT DATA

-

WEIGHTING GLOBAL CRII.

PURE WEIGHTING

[ ]

DIRECT-RANDOM

INEQUALITY CONSTRAINTS

SEARCH

]

DISCRETE VALUES

[PRINTING

ORS)

HILLCLIMB METHOD

DIRECT SEARCH FEASIBLE DIRECTION(OSFD)

]

COMPLEX METHO0

NORMALIZED WEIGHTING

, mJ

J

DAVIDON-FLETCHER POWELL METHOD I S : P )

Fig. 1. Structure of the computer code.

The mathematical programming can be formulated as follows. Find 2" such that f(2*) = opt[(2) and such that &.(~)>0

j = 1,2 . . . . . M

hi(E) = 0

l = 1,2 . . . . , P

where ~ is a vector of decision variables defined in N-dimensional Euclidean space, 7(~) is a vector function defined in K-dimensional Euclidean space, &(~), ht(~) are nonlinear nonequality and equality constraints of variables xi, M i s the number of inequality constraints, and P is the number o f equality constraints.

Decision support system on IBM PC applied to crane girders

147

3 ECONOMIC DESIGN OF BOX GIRDERS OF OVERHEAD TRAVELLING CRANES

The interactive decision support code was connected with the operational structure of economic design of steel structures. ~2 The operational structure of economic design can be seen in Fig. 2.

Formulation of the problem: work out the economic design for asymmetric, stiffened box girders; some main dimensions, loading conditions and material properties are given, see Fig. 3. Determination of purpose: the material, welding, surface preparation and total costs of the main girder must be minimal. These are the objective functions. The cost factors are as follows: Material cost of steel Fe 430: km =

0-54$/kg;Cm = kmpV

(1)

Surface preparation and painting costs: ks = 14-1 $/m2; Cs -- k J 2 . bL + 2. hL)

FORMULATION OF THE PROBLEM I

DETERMINATIONOF PURPOSE CREATIONOF MODEL

I ANA,Ysls

j

SYNTHESIS EVALUATION I

1 GENERALIZATION I I BSTRACTION

I

I

I COMPARISON Fig. 2. The operational structure of economic design.

(2)

K. Jdlrmai

148

b!

tv

tf

Ih

g•lf

r

.2h 7--

i

7

"!

,

C

r

S

0.8h tw2 r

d

Fig. 3.

b

_ll_o

Cross-section of the main girder.

Welding cost: a2 kw = 16.2 $/kg; Cw = kw ---g- Lw "19"kc

,/2

(3)

where kc = 1, 2, 3 is the difficulty factor of welding which depends on the position of welding. In this case using the recommendations of Ref. 13, the cost of welding with weld size aw = 5 m m and unit length Lw = 1 m is 4.51 $ if k¢ = 2. Another possibility for quantification of welding costs is to use welding cost parameters between previously determined limits. Thus one can investigate the effect of welding cost parameters on a wide range of dimensions. The total cost is the sum of the previous ones. Ct = Cm + Cs + Cw

(4)

Creation of the model: The two m a i n girders are simply supported and have a welded longitudinally stiffened box cross-section. The loadings are: uniformly distributed dead load from girder, rail and side walk; concentrated load in the middle from the h o o k load; a n d the mass of the trolley. Horizontal loads arise from the acceleration of the crane and from the breaking of the trolley. In the open air wind load must also be considered. The structure is in the elastic stress state. The warping torsion is neglected.

Decision support system on I B M P C applied to crane girders

149

3.1 Analysis according to BS 2573 and 5400 (Refs 14 and 15) The constraint on the static stress in the lower flange at midspan due to biaxial bending is described by: (5)

Mx + My < a d P s

wy

The approximate formulae for moments of inertia are Ix - h3(t"q + t,.z)

12

+

(h + tr)2

(6)

b3tf bttf ht~l x 2 + htwE(b - xs)2 + --~ + T (b - 2x~)2 •

where bl = b + 2d htw2 + b)trb Xs -

A

(7)

A = h(tw~ + t,.z) + 2bttf

Section moduli are W,, -

;W-v = ( b - x ~b+ d )

Ix

(8)

Bending moments are as follows: Mx = -g(1.05A + p r + p s ) + ~

(9)

L-

G,( zt y ( 1 - 0 5 A + p r + p s ) g + ~ - L L -

My = 0.3. Zb LS

h) 2

+ M,,

(lO)

where thewheel load isF = (~,aH + Gt)/4;p 7850 kg/m3;g --- 9.21 m/s2; the factor of 1.05 expresses the mass of diaphragms; k is the distance between the trolley axes; Zb and zt are the numbers of braked and total wheels of trolley, respectively; the factor of 0-3 represents the effect of inertia forces according to DIN 15018;16M,, is the bending moment of wind load. The wind load is calculated from: =

Fw = ),AqCf

(11)

150

K. Jarmai TABLE 1 The Force Coefficient Ct- due to W i n d Load

Height of webs (I49 (m)

Section ratio (h/b)

0.5 >0.5

-)2 )1

Aerodynamic slenderness L/h 5

10

20

30

40

1,3 1,55 1,4

1.35 !.75 1.55

1.6 1-95 1.75

1.65 2.1 i.85

1-7 2.2 1.9

where for the structural strength calculation ?' = 1.0: the effective frontal area isA(m2); and Cr, the force coefficient, depends on the aerodynamic slenderness L/h and on the section ratio h/b as shown in Table 1. For normal types of crane installed in the open air the in-service design wind pressure is: q = 250(N/m 2) Constraint on fatigue stress is

Mxf

+

My

(12)

where

Mxr = g ( 1 - 0 5 A

+pr+ps,,)g+

L -

(13)

where the live load multiplied by the impact factor u/d, and the spectrum factor Kp is as follows Ff = Kp VtdH + G t 4

(14)

The permissible tensile fatigue stress depends on the class of the crane and on the n u m b e r of operation cycles (N). In the case of a crane of heavy duty the operation cycles are 2 X 106, which means for class A7 Kp--0.8, V/d----"1.3 and the duty, factor ad = 0-95. If the members are fabricated with continuous longitudinal fillet welds (class D) a n d the ratio of m i n i m u m to m a x i m u m stress is about 0-2, the permissible fatigue stress is Prt = 167 MPa This stress is the same for steel grades 43, 50 a n d 55. Local flange buckling constraint is reef + m b f < 1

(15)

! 51

Decision support ~stem on IBM PC applied to crane girders

where mcf-

OIf . ( °bf "~2 PsKif,mbf = \P~b J

(16)

Neglecting the shear mqf = 0

Mx o,f-

My

(17)

Wx;a.r =

The slenderness of the plate is Ar

b //~ = ~f v' 355

If

(18)

A.r< 24

then Kit = 1 = ( 2 4 ~ 0"75

24 < A f < 4 7

KIf

kAfj

47 < A t < 130

Ktf = ~,;trJ

(26 08

130...