PRACTICAL OPTIMIZATION OF STEEL HIGHWAY

BRIDGE BEAMS

MAY 1971 - NUMBER 8

JOINT HIGHWAY RESEARCH PROJECTPURDUE UNIVERSITY ANDINDIANA STATE HIGHWAY COMMISSION

11-8Final Report

PRACTICAL OPTIMIZATION OF STEEL HIGHWAY BRIDGE BEAM3

TO: Jo F. McLaughlin 9 DirectorJoint Highway Research Project

FROM: H. L. Michael, Associate DirectorJoint Highway Research Project

May 11 , 1971

File No,: 7-^-17

Project No, : C-36-56Q

The attached Final Report titled "Practical Optimization of SteelHighway Bridge Beams" is submitted for acceptance as fulfilling theobjectives of the Plan of Study "Optimum Design of Continuous HighwayBridge Girders" approved by the Advisory Board on February 17 » 1970

.

Mr. Robert H, Busek, Graduate Assistant In Research on our staff,authored the report and conducted the research under the direction ofProfessors J. T. Gaunt and A. D. M. Lewis ,

A program for optimization of a rolled section highway bridgegirder is presented with either minimization of weight or cost, Eithercomposite or non-composite design theory can be used. Two publisheddesign examples were solved by the computer and the results orereported and compared to the published results.

The research was financed from JHRP funds and is submitted witha request that comments on the report are encouraged, A report ofapplication of the results by the ISHC would certainly be welcome.

Respectfully submitted,

Harold L, MichaelAssociate lirector

HLMrms

cc: F, L, AshbaucherW. L, DolchW. H. GoetzW. L. GreccoM. J, GutzwillerG, K. Hallock

M. E. HarrR. H. HarrellM. L. HayesE. M. MikhailR. D. MilesJ. W. Miller

C, F. ScholerM, B. ScottW, T. SpencerN, W, Steinicamp

H. R. J, WalshK. Bo WoodsE. J, Yoder

Final Report

PRACTICAL OPTIMIZATION OF STEEL HIGHWAY BRIDGE BEAMS

by

Robert H. BusekGraduate Assistant in Research

Joint Highway Research Project

File; 7-k-VJProject: C-36-56Q,

Purdue UniversityLafayette , Indiana

May 11, 1971

Digitized by the Internet Archive

in 2011 with funding from

LYRASIS members and Sloan Foundation; Indiana Department of Transportation

http://www.archive.org/details/practicaloptimiz7108buse

I ]

ACKNOWLEDGMENTS

The author expresses his appreciation and "thanks to

Professor John T. Gaunt and Professor Albert D. M. Levis,

who were co-chairmen of his advisory committee, for their

help in selecting this topic and for their guidance,

leadership and comments throughout the course of the

research project.

The financial support of the Joint Highway Research

Project is gratefully acknowledged. The guidance and help

of Professor Harold L. Michael, the Associate Director of

the Project, is appreciated.

The confidence, expressed in him by Neil II. Bettigole,

is acknowledged by the author. Many thanks go to Linda

and Frances for their support, help and friendship during

the past two years at Purdue.

To his family, who, although they remained ".any miles

away, always expressed their love and concern, as well as

an interest in the research, the author is eternally

gra tefu 1

.

TABLE OF CONTENTS

1 1 i

LIST OF TABLES

LIST OF FIGURES

LIST OF SYMBOLS

ABSTRACT

CHAPTER I - INTRODUCTION. . .

1.1 Structural Optimization.1.2 Background Revieiv'.

1.3 Scope of the Investigation

CHAPTER II - GIRDER ANALYSIS .

2.1 Design Loads ....2.2 Analysis Theory2.3 Analysis Program .

2.4 Load Subroutine

CHAPTER III - GIRDER DESIGN.

3.1 Girder Design The o ry

.

5.2 Fatigue Design.5.5 Design Details.5.4 Design Program.

CHAPTER PROBLEM TIM j ZATION

4.1 Optimization Theory .

4.2 Ibjective Function4.5 Constraints

CHAPTER V - COMPUTER PRO IRAM

5.1 Description of the MAIN P

5 . 2 Samp 1 e Probl ensrour

Page

v

vi

vii

x

1

1

5rb

7

7

1019?7

5 2

3841

45

im

54

M6 5

6 9

6!

78

i V

age

CHAPTER VI - SUMMARY AND CONCLUSIONS 85

6. 1 Summary 8 5

6.2 Recommendations for Further Research .... 86

BIBLIOGRAPHY 88

APPENDICES

APPENDIX A - SUBROUTINE DESCRIPTIONS 91

APPENDIX B - SELECTED PROGRAM NOMENCLATURE 95

APPENDIX C - PROGRAM DATA 108

READIN Subroutine 108Method of Data Input 113Input Data Samples 123

APPENDIX D - COMPUTER PROGRAM LISTING 127

LIST OF TABLES

Tabic > Page

2.1 AASHO Load Designations and Parameters. ... 8-

•3.1 Values of the Modular Ratio 36

3.2 Fatigue Constants 40

5.1 Composite Section Properties 79

5.2 Unit Costs 79

5.3 Costs and Weights for Problem No . 1 80

5.4 Costs and Weights for Problem No . 2 82

AppendixTable

C-l Input Data for Sample Data Problem No . 1 . . . 124

C-2 Input Data for Sample Data Problem No . 2 . . . 126

LIST OF FIGURES

v I

Figure

2.1 Determination of Compatibility Equations

2.2 Sample Girder for Equation Development

2.3 Analysis Program Flowchart ....5.1 Standard Composite Girder Cross Section

3.2 Facia Cirder Composite Cross Section

3.3 Design Program Flowchart ....5.1 Flowchart for the MAIN Program .

5.2 Optimum Design for Problem No . 1

5.3 Optimum Design for Problem No. 2

Page

15

18

20

3 5

3 5

4 6

70

81

8 3

LIST OF SYMBOLS

v 1 1

a(x)

iJ

A.

A

A

b

c

Ec

Ec

f

f

pi

web

all

£r.

u

Fv

Fy

the influence line function

the influence coefficient at point i

the area of a cover plate

the area of the longitudinal steel reinforcement

the area of the steel section web

the width of the steel section flange

the distance to the extreme steel fiber

the modulus of elasticity of concrete

the modulus of elasticity of steel

the longitudinal flexural stress

the allowable flexural stress

the 28-day concrete strength

the flexibility coefficient

the allowable column stress for the stiffeners

the allowable bending stress

the allowable stress reduced for fatigue

the minimum tensile strength of steel

the allowable weld metal stress

the yield point stress of steel

the distributed load function

the moment of inertia oi' element i

viia

hm<

line

St

I.1

CPmin

w

DL

M

M

M

M

LL

SLL

tot

n

nc

P.J

cpm a x

the moment of inertia of the high modulus

e o n c r e t e section

the moment of inertia of the low modulus

concrete sect ion

the moment of inertia of the steel section

the unsupported length of the compression flange

the length of the subelement i

the minimum cover plate length

the length of a weld

the moment due to the dead load

the moment at section i

the moment due to the live load

the moment due to the superimposed live load

the total moment at a given section

the modular ratio for concrete

the number of shear connectors per section

the concentrated load at point j

the statical moment of the area above or below

a section, taken about the neutral axis

the algebraic ratio of the minimum stress to

the maximum stress

the range of horizontal shear per inch

the ultimate strength of a shear connector

the required weld size

the maximum cover plate thickness

the fiance thickness o^ the rolled section

I X

w

V

V

Vi

w

WPi

lmc

hmc

ySt

the web thickness of the Tolled section

the unit shear stress

the external vertical shear

the range of external vertical shear due to

the live load plus impact

the magnitude of a uniformly distributed load

the width of a cover plate

the extreme fiber distance for the low modulus

composite section

the extreme fiber distance for the high modulus

composite section

the extreme fiber distance for the steel section

the allowable shear per connector

ABSTRACT

Busek, Robert Henry. M.S.C.E., Purdue University,June 1971. PRACTICAL OPTIMIZATION OF STEEL HIGHWAY BRIDGEBEAMS. Major Professors: J. T. Gaunt and A. D. M. Lewis.

A program for the optimization of a rolled section

highway bridge girder is presented. The girder is designed

by minimizing either the weight or the cost. The cost

function used is a representative model of the total cost

of the girder, including both material and fabrication costs

The function presented is a sample and can be altered if a

different cost function is more appropriate.

The program produces the optimum design of a rolled

section girder, using either composite or noncomposite

design theory. • The required cover plates are determined,

using both static and fatigue stress conditions. The

fatigue stresses are based on 500,000 cycles of stress.

If a design is composite, 7/8- in. shear connector studs

are provided in the positive moment region. No connectors

are placed in the negative moment region. Ml design

theory, analysis theory, and optimization constraints are

based on the 1969 AASHO bridge specifications. The method

of influence lines is used in the analysis.

The exhaustive search technique is used as the main

method of optimization. The cover plate thicknesses arc

X 1

determined by using the method of interval halving, and the

locations of the cover plate splices arc determined by using

dynamic programming.

Computer solutions for two published design examples

were obtained and compared to the published results.

CHAPTER I

INTRODUCTION

1 . 1 Structural Optimization

Optimization is the process of obtaining "the best"

solution to a problem based on a given criterion. Struc-

tural optimization, therefore, is the process of obtaining

the "optimum" solution to a structural problem. This

optimum is obtained by using analysis and design theory

and an optimum- seeking method suited to the problem.

Structural optimization has only recently been

approached systematically. One of the reasons for this is

that the computer is a relatively new tool for the engineer.

When doing an optimization, there are a large number of

calculations which must be completed. Performance of these

calculations by hand would be very time consuming. The

computer gives the engineer a quick and fairly inexpensive

method of calculating quantities and making decisions based

on these calculations.

Another reason for the recent prominence of structural

optimization is the rising cost of construction. Since the

costs of material and labor have risen steadily over the

past years, and since the trend for the future seems to be

in the same direction, the engineer mast place mere emphasis

on the economics of design. By using optimization proce-

dures, the designer may actually reduce construction costs

by minimizing the total cost of the structure.

The formulation of the optimization problem depends on

the type of structure being designed. For any problem, the

design variables, the design constraints and the criterion

for the objective function) of the optimization must be

defined. It is the values of the design parameters which

are desired so that the value of the objective function is

a minimum and the constraints arc not violated.

The design parameters required depend on the type of

optimization problem and on the theoretical equations used.

The specification used to control the design specifies the

necessary constraints for the problem. In most problems,

both equality and inequality constraints are used.

The objective function can be any desirable measure of

the effectiveness of the design. Some of the measures which

have been used are weight, cost, cost- benefit ratios and

reliabil i ty . for the highway bridge girder, minimum weight

has been used for many years, because of the relationship

which exists between weight and cost. In this optimization

problem, however, the cost function used is more realistic

because it includes the fabrication costs.

The general optimization problem can he expressed in

the following mathematical form:

Find the variables x. i = 1 , 2 ,• •

• , m

wi

where

ze G fXjl 1 .

1

gCxp

)= P = 1, 2, • •

, n 1.2

h(x k ) > o k = n, • • , m 1 .3

xj

> o j = 1, ? •, m 1 .4

The variable vector, x, must be determined so that the

equality constraints (1-quation 1.2) and the inequality

constraints (Equations 1.5 and 1.4) are satisfied and the

objective function, G (x) , is optimized. The G function can

be either maximized or minimized depending on the type of

problem

.

The optimum- seeking methods which are available to the

structural designer are numerous. Many of the methods are

general in nature and can be used for any type of optimiza-

tion. There are, however, some specific methods which are

best suited for particular types or formulations of problems

1 . 2 Background Review

The methods of optimization can be divided into direct

and indirect methods. The indirect methods are mathematical

methods which can use the gradient of the algebraic form of

the objective function to solve a given problem. Direct

methods are ones which make trial solutions in so: e

organized manner. 1 ach solution is compared to the present

optimum and a decision is then made as to the next design

step. Each of the types has its own advantages and dis-

advantages when used in a particular structural optimization

problem

.

Structural optimization problems have been approached

in the past as minimum weight design problems. Drucker and

Shield [1 and 2] have presented some of the general minimum

weight design theory. Faulkes [3] and Ilcyman [4] have used

this criterion i- n optimizing frames, and Krishman and Shetty

[5 and 6] and Haug [7] have used it in elastic beam design

problems. Ilahn [8] extended the work to include plastic

design of beams and simple structures. The assumption made

in these minimum weight problems is that the cost of the

girder is proportional to its weight.

Computer design methods have been developed for highway

bridge design. Sturman, Albertson, Cornell and Roesset [9]

developed a program called BRIDGE which can be used to make

comparative studies of different types of bridges. The

system can also completely design a particular structure, hut

it makes no attempt to optimize the design. Since the com-

plete optimization of a highway bridge is a long and compli-

cated problem, the approach so far has been to optimize the

individual parts of the bridge system.

The optimization of girders lias also been approached by

using the minimum weight method. bdward [10] and Holt and

Heithecker [11] have attempted to optimize the girder by

minimizing the cross -sectional area. If i s in turn minimizes

the weight of the structure.

The total cost optimization has been developed for both

building and highway girders. Annamalai [12] uses the back-

track programming method for welded plate girders, developed

by Lewis [13], to optimize the design of building plate

girders based on the AISC 1969 specifications. Okuba [14]

solves the girder problem by using a linear programming

method

.

The work by Razani , Coble and DeSantis [15, 16, and 17]

on the optimum design of plate girders has led to the

development of a computer-aided design system. Coble and

DeSantis [IS and 19], with the aid of the Ohio Department

of Transportation, developed a program referred to as Girder

Automated Design - 1 or CAD- I. The program completely

designs the constant depth plate girder and specifies all

of the details of the design, including the flange thick-

nesses, the flange splice locations and the locations of the

transverse and longitudinal stiffeners if they are required.

1 . 5 Scope qj_ the I nves t i gat ion

Since the GAD- I program has been developed, it has been

possible to design the optimum welded plate girder for a

highway bridge. This girder, however, is not necessarily

the actual optimum design for the problem. There is a possi-

bility that cither a composite or noncomposite rolled-section

girder may be more economical than the plate girder. This

is particularly true if the spans of the girder arc rela-

tively short

.

in order to determine the true optimum design, a com-

puter-aided design system for the rolled section bridge

girder has been developed. With this program, a given

problem can be designed with a plate girder and a rolled-

section girder and the true optimum can be chosen directly.

In the present study, the American Association of late

Highway Officials bridge code [20] is used to control the

design of a highway bri'dge girder. The cross section of the

girder is limited to the 36-in. and 33-in. wide- flange

rolled sections. The design can be either composite or

noncomposite and can have cover plates If they are required.

The problem is limited to a maximum of four continuous spans

designed for all types of static and Fatigue highway Loads.

The fatigue conditions arc based on 500,000 cycles of stress

If the design is composite, then 7/8- in. diameter shear

connector studs are provided at the proper spacing. The

method of exhaustive search is used in the program because

of the limited number of rolled sections of proper size.

Each of the eighteen possibilities is designed, using, the

optimum-seeking methods of Interval halving and dynamic

programming to determine the required cover plates.

CHAPTER II

G [RDER ANALYSIS

2 . 1 Pes ign Loads

The first problem that confronts the designer of a

particular structure is to determine the required design-

load conditions for that structure. These conditions usual-

ly vary with the size, purpose and location of the structure

The actual conditions are often designated by design speci-

fications and can be found in design codes.

The design of a highway bridge is controlled by the

American Association of State Highway Officials code [20].

This code, known as the AASIIO code, states that all of the

girders in a bridge structure must be designed for the

largest truck load and the corresponding equivalent lane

load which the bridge must sustain. The code designates

the loads by the size of the truck being considered, i.e.,

IIS20. Once the required designation is chosen, the actual

loading parameters can be determined. These parameters

include the axle loads, the axle spacings, the equivalent

lane loads and t h e corresponding concentrated loads.

Table 2.1 contains a summary of the load parameters for

all of the AASHO truck designations.

Table 2.1: AASHO Load Designations and Parameters

Truck Loadingsi quiva 1 cnt Lane

Load i ng

Axle Loads Axle Spacing

s

llni form Concentrated

Des. 1 7 5 1 - 2Min2 - 3

Max2 - 3

Moment Shear

H10

1115

H20

IIS15

US 2

4k

6k

8k

6k

8k

16k

24k

32k

24k

3 2k

24k

32k

14'

14'

14 '

14 '

14'

14'

14 '

30'

30'

.32k/

'

.4 3k /'

.64k /'

.4 8k/

'

.64k /'

9.0k

15. Sk

18.k

1 .) . 5

18.k

1 5 .

k

19.

5

k

26.k

19. 5k

26.0

If the bridge is being designed as part of the Inter-

state Highway System, the girders must also be designed for

a specified interstate loading condition. This loading

condition is based on the dimensions and weight of the

largest military vehicle which would use the structure

during a national emergency. The loading consists of two,

24 -kip concentrated loads with an axle spacing of 4 ft.

The effect of this loading must he calculated in order to

determine if it g ov e r n s t h e g i r d e r d e s i g n

.

Another possible girder loading condition is produced

by pedestrian pathways. If the bridge is supplied with

sidewalks, then the sidewalk loads must be calculated.

According to the AASHO code, the following set of formulas

is used in calculating the sidewalk load:

p = 8 5 for L s < 25 ft

P = 60 for 25 ft < Ls

< 100 ft

P = 303000

'S

5 5 - IV

50for L

s> 100 ft 2.1

where P = the load in pounds per square foot.

Ls

= the loaded length of sidewalk in feet.

IV = the width of sidewalk in feet.

The total sidewalk load is distributed over all of the

girders in the structure. Although the moments due to this

loading condition are usually small, they are included to

provide a complete analysis.

Besides the above loads, which are considered to be the

live loads for the structure, there are also dead loads which

must be considered. Dead loads include the weight of the

steel girder, the weight of the deck slab and the weight of

the bridge railing, light fixtures, and similar loads placed

on the constructed bridge. If the design of the girder is

noncompos i te , then all of these loads are combined in one

dead load condition. If the design is composite, however,

the loads are placed into two groups because the} - act on

different composite sections. The first group is considered

the dead load and includes the weight of the slab and the

steel girder. The second group is the superimposed dead

load (sometimes referred to as the long-term live load).

This group contains dead loads applied to the composite

girder after the concrete has reached its maxii un strength

1

capacity. An example of a superimposed dead load is the

weight of the bridge railings and the Light fixtures.

2 . 2 Ana Lysis Theo ry

Once the loads which act on the structure have been

defined, the stresses caused by these loads must be deter-

mined. The design loads must be placed on the structure

so that maximum design conditions are developed at the

critical points in the structure. The determination of

these design values constitutes a complete analysis of the

structure being designed.

Since the loading conditions, as shown above, for the

highway bridge girder are complex in nature, the method of

analysis which is most efficient is the method of influence

lines. This method enables the structure to be loaded with

a large number of loading conditions and the controlling

maximum to be chosen from these conditions.

An influence line is a graph showing the variation in

a particular function at a point with respect to the posi-

tion of a unit load. flic ordinates of the influence line

arc referred to as the influence coefficients. The ordinate

at point j for the function I' at point i, usually called the

influence coefficient a. ., is defined as the value F. due tolj i

a unit load at point j [21], With this definition various

theorems can be developed pertaining to the use of influence

lines. Norris and Wilbur [--] describe the following four

basic Influence line theorems:

] ]

Theorem 1 - The maximum value of a function due to

a single concentrated load is found by

placing the load over the maximum

influence coordinate.

Theorem 2 - The value of a function due to a single

concentrated load equals the product of

the load and the influence coefficient

at the load location.

Theorem 2 is stated mathematically as

F . = P .x a .

.

2.2

Prom Theorem 1, the maximum value of P., F-; , is found'

l 'max

'

when the single concentrated load is placed at the point

where a. . is the maximum. By using superposition, the value1J

. t. r t-

of the function F due to a series of concentrated loads can

be found from Equation 2.5.

F . = J P . x a . .

m

I

j=

l

where m is the number of loads.

Theorem 3 - The maximum value due to a distributed

load occurs when the structure is loaded

over those portions which have influence

coefficients with the same sign as the

character ol~ the function desired.

Theorem 4 - The value of the function due to a dis-

tributed load is the product of the load

1 2

magnitude and the net area under the

portion of the influence line loaded.

Theorem 4 is stated mathematically as

g(x) • a(x)dx 2.4

where r and-s are the load limits.

The derivation of Equation 2.4 can he found in the structural

analysis texts by Norris and Wilbur [22] and by Shedd and

Vawter [ 2 3 ]

.

There are two simplifications that can be made to liqua-

tion 2.4 when dealing with highway structures. In all cases,

the distributed load, g(x), can be replaced by a constant

representing the uniformly distributed loading condition.

The uniform load is usually represented by w. The second

simplification deals with the influence line function, a(x).

Since this function is usually fairly complex in nature and

too difficult to obtain, the coefficients are determined at

a number of discrete points and the values in between are

found using linear interpolation. The value of the function

F, due to a uniform loading condition, over a pieccwise

continuous influence line, can be determined by using Equa-

tion 2.5.

Fi

=

J llai,k

+ ai,k +1 jH

K= 1

2.5

where n is the number of elements

13

With the theorems and the equations expressed above,

any effect of a Loading condition can be obtained, provided

the influence coefficients can be calculated. The influence

line is developed by computing the required influence coeffi

cients for each position of a unit concentrated load. The

process is quite simple for statically determinate girders',

but becomes much more complicated for indeterminate or con-

t inuous g irders

.

For the statically determinate problem, all that is

required to solve for any influence coefficient are the

equilibrium equations. The unit load is placed on the

structure and the reactions are determined using the equa-

tions shown as liquation 2.6:

Fm, r+ , = o- left end

2.6

L vertical

Once the reactions are found, the influence coefficient for

any function can be determined.

If the girder being designed is statically indetermi-

nate, then equations of compatibility arc required. One

compatibility equation is needed for each redundant reaction.

These equations refer to the requirement that all the dis-

placements throughout the structure are consistent. Killems

and Lucas [211 note that the compatibility conditions

require that the displacements at supports must be externally

II

satisfied. In the particular case of unyielding supports,

the total displacement must be equa] to zero.

The compatibility equations can be developed with

reference to figure 2.1. The structure is made statically

determinate by removing the interior supports (Figure 2.1b)

With the determinate structure defined, the deflections at

the interior support points, due to the external loads on

the simple girder, can be determined. Next the flexibility

coefficients are determined (Figure 2.1c and d) and the

equations can be formed:

R2f 22 + R

3f 32 - n

2= n

Mn + R3f33 - D

3- °

2.7a

In matrix form, these equations may be written

f f12 2

x3 2

f f2 3 13 J

Ft.,

3J

2. 7b

orf

F ] [ R ] =[ D 2.8

The F matrix is called the flexibility matrix and is inde-

pendent of the external loads on the structure. The coeffi-

cients of this matrix represent the deflections at the

interior support locations due to unit loads at the interior

support locations. These deflections can be found by using

the moment -area theorems.

1 5

2.1 a: Indeterminate Structure

2.1 b: Determinate Structure

2.1 d : Unit Load at Point 3

Figure 2.1: Determination of Compatibility Equations

16

The moment-area theorem used to deteri Lne the del lec-

tion is called the second moment-area theorem. The theorem

states that the deflection at point 1, relative to a tangent

at point 2, is equal to the moment of the area under the

bending moment diagram, between points 1 and 2, about point

1 divided by the flexural rigidity oi' the girder. l'ippard

and Baker [25]* give the following mathematical form of the

theorem:

DEI

Mxdx 2.9

If the moment of inertia varies along the girder and the

moment diagram is given as a piecewisc continuous curve,

varying linearly between the analysis points, then Equation

2.9 takes the following form:

1_ y1/ ^

l

DE i-i 2

M.+M. x.i i +

i I I . i2.10

where x. is the distance from the center of thei

element to the center of moments.

Once the required deflections are determined and the

compatibility equations, 2. "a, are defined, the values of

the redundant reactions can be determined. With these

reactions and the equilibrium equations, 2.0, the remaining

reactions can he calculated.

In order to develop the influence line, the unit load

must he located at each point along the structure. This

means that there would he NA different matrix equations oC

1 7

the type shown in Equation 2.S, where NA is the number of

analysis points. Since the flexibility matrix, however,

docs not change with the location of the external load, the

only part of the equation that wil] vary is the D matrix.

For this reason it is possible to set up one matrix of NA

columns for all the positions of the unit load. Also by

adding two more rows, which represent the equilibrium equa-

tions, all of the reaction influence coefficients can be

determined at the same time. Shown in Figure 2.2 is a

three -span girder with seven analysis points. The matrix

equation required to solve for the reaction influence

coefficients is

[ CC] [ R ]

where

[ CC ]

[ RIL ]

11 1 1

Lj L 2 L 3

d 3 3 d 5 3

d 35 d 55

.11

an.

[ Rib ]

1 1 1 1 1 1 1

Xi x 2 x 3 X,, X 5 x 6

x 7

d 31 d 32 d 33 d 3. d 35 d 36 d3

5 1 5 2 5 3 5 5 5 6

3 7

5 7-1

This equation is the same as the one which appears in the

analysis development by Goble and DeSantis [18].

The solution to this matrix equation can be approached

in a number of ways. The most efficient method is one in

which the final solution for the reaction influence lines

18

Figure 2.2: Sample Girder for Equation .Pevel opment

is found in the RIL matrix. By using a Gaussian search

technique, the CC matrix is reduced to an identity matrix

by simple row and column operations common to matrix

algebra. By repeating the same operations on the RIL

matrix, the reaction influence coefficients are determined

and stored in the RIL matrix. A complete description of

the Gaussian search technique employed in the solution is

given by Coble and DeSantis [19].

With the solution for the reaction influence coeffici-

ent complete, all of the remaining influence lines for the

complete analysis can be calculated by simple statics.

The influence lines can then be loaded and all the design

conditions for the problem can be determined. With these

conditions, the girder can be designed and optimized.

All of the theorems and equations discussed above arc

used to determine the design reactions, moments and shears

1 9

After a fiiKil design has been chosen, the \ASHO code

requires that the deflections be calculated and compared

to certain allowable live-load deflections. In order to

calculate the maximum deflections, the deflection influence

coefficients must be determined. The amount of calcula-

tions, however, can be reduced by employing Maxwell's law

of reciprocal deflections. The law says that, on a girder,

the deflection at point 1 due to a unit load at point 2 is

equal to the deflection at point 2 due to a unit load at

point 1. This enables the deflection influence coefficients

for a point j to be determined by calculating all of the

deflections along the girder due to a unit load at point j.

The maximum deflections can then be calculated by using the

influence coefficients and the design loads. These maximums

can then be compared to the allowable deflections specified

by the AASHO code.

2 . 3 Analysis Program

The analysis portion of the computer program uses the

theory described in Section 2.2 to develop the values

required by the design portion of the program. A basic

flowchart for the analysis program is shown in Figure 2.5.

The step numbers, used in the following program description,

refer to the numbers in parentheses on the flowchart.

ViDEnter the ANAL

Subroutine

I (2)

Enter the REACSubroutine

I = 1

I > NA

I = 1 + 1

True -M a

F a 1 s e

Determine the simplespan bending moments

I (3)

Enter the EQSFT subroutine anddetermine the simple span deflections

I (4)

Set up the cut i reK 1 L matrix

Figure 2.5: Analysis Program Flowchart

21

Set up theCC matrix

I {6}

Use the SOLVE routine to determinethe reaction influence coefficients

Load the reactioninfluence line

I (9)

Determine thedesign reactions

Xo Yes -©

Fi eure 2.3: ("Cont ' d .

©{(13 )

Determine the moment influencelines and load the lines

IDetermine thedesign moments

No

Determine and load theshear influence lines

IDetermine thedesign shears

No Yes

Figure 2.5: (Cont'd.)

23

Step 1

The analysis program is started by calling the ANAL

subroutine. This subroutine calls on the other subroutines

in the proper order required to produce a set of usable

design conditions.

Step 2

The REAC subroutine is called on to solve for the

reaction influence lines. The simple-span girder, defined

as the problem girder with the interior supports removed,

is loaded with a unit load at each analysis point, and the

bending moments are determined. These simple-span bending

moments are transferred to the EQSET subroutine.

Step 3

The EQSET subroutine is used to calculate the simple-

span deflections at the interior support points. The value

of the tangent at the left end (TALE) is determined by using

Equation 2.10 and is then used in the following equation to

determine the required deflections:

d. = TALI', x COOR(I) - WA(I) 2.12

Step 4

The RIL matrix is prepared by using the deflections

obtained in step 3 and the equilibrium equations. The RIL

matrix is the right-hand-side matrix of liquation 2.11.

Step 5

The coefficient matrix (CC) is prepared by using the

appropriate values of the deflections found in step 3 and

the coefficients of the equilibrium equations. This CC

matrix corresponds to the matrix CC in Equation 2.11.

Step 6

The SOLVE subroutine is called to determine the solu-

tion to Equation 2.11. By using a Gaussian search technique,

the CC matrix is reduced to an identity matrix and the reac-

tion influence coefficients are determined and stored in

the RIL matrix.

Step 7

Steps 2 thru 6 are repeated using a different moment

of inertia for each subelement. By doing this, the differ-

ent influence coefficients for the steel section, the low

modulus concrete section, and the high modulus concrete

section are determined. Bach set of coefficients is stored

in its proper location in the RIL matrix. Control is now

passed back to the ANAL subroutine where the reaction

influence coefficients are printed if IPT10 is greater

than 2.

Step 8

The reaction influence line is Loaded by calling on

the LOAD subroutine and the values of the ten [10] loading

conditions are returned from this subroutine. Since the

LOAD subroutine is used extensively in the analysis, it

is described in Section 2.4.

Step 9

The design reactions (DESREA) are now determined. The

dead-load reaction is set equal to ST0REC1) and the super- '

imposed dead-load reaction is set equal to STORE(IO). The

positive and negative live- load design reactions are equal

to the maximum live- load reactions possible. These maximums

are obtained by combining the sidewalk live load with the

other individual live loads of the same sign until the

largest value of the sums is found. If the sidewalk live

load is zero, then the positive and negative design reactions

are respectively equal to the largest positive and negative

truck load, lane load or interstate load.

Step 10

Steps 8 and 9 arc repeated for each support along the

girder. The maximum number of repetitions is NS. The

DESREA array is now printed out if the 1PT10 parameter is

greater tha n zero

.

Step 1

1

The reaction influence coefficients are used to deter-

mine the moment influence line at a particular point. This

influence Line is then loaded by the LOAD subroutine and the

ten loading conditions arc determined. The design moments

moments (DESMOM) are determined in the same manner as the"

design reactions in step 9.

Step 12

Step 11 is repeated for each analysis point along the

structure and the DESMOM array is printed if N'TIO is

greater than 0. The maximum number of repetitions is NA

.

Step 15

The reaction influence coefficients are used to deter-

mine the shear influence line and this line is loaded by

the LOAD subroutine to calculate the values of the ten

loading conditions. These conditions are used to calculate

the design shears (DESSI1) in the same manner as described

in step 9.

Step 14

Step 13 is repeated for the locations immediately to

the left and to the right of each analysis point. The maxi-

mum number of repetitions is 2NA-2. (The minus 2 is neces-

sary because there is only one repetition made for the

first and the last analysis points.) The DESSI1 array is

printed if tPTIO is greater than 0.

Step 15

The analysis of the girder is complete and the control

is returned to the main program for design.

2 . 4 Load Subrouti nc

The load subroutine is used to load any given influence

line with the complex loadings required in a highway girder

analysis. It should be noted that a given influence line

actually consists of three different influence lines, if

the design is composite. There is one line for the steel

section, one for the low modulus concrete section, and one

for the high modulus concrete section. All three lines are

calculated in the ANAL subroutine and are transferred to the

LOAD subroutine at the same time.

Step 1

The steel section influence line is set into the RO

array and the properties of this line are determined by the

ILPROP subroutine. The properties which are required by

the LOAD routine are the positive and negative areas and

the locations of the maximum and minimum ordinates.

Step 2

The unit dead load is calculated. Using the area

properties of the influence line, the dead- load loading is

found by using Equation 2.5 with the load extending over

the entire girder. The dead -load loading is then stored

in STORE! 1 )

.

S t ep 3

If the girder is noncompositc, then the .superimposed

dead-load loading (STORE(IO)) is set equal to zero. If the

design is composite, then the low modulus concrete section

influence line is set into the RO array and the properties

are found. The superimposed dead load is determined and

the values of STORE(10)-is calculated using%Equation 2.5

with the load extending over the entire girder.

Step 4

If the design is noncompositc, then the live-load

determination can be started immediately. If the design

is composite, however, the high modulus concrete section

influence line is set into the RO matrix and the properties

are determined by the ILPROP subroutine.

Step 5

The IMPACT subroutine is called on to determine the

impact factor required by the AASHO code. This factor (HT)

is determined from the following formula:

HT = 1.0 +,

S01 „ r 2.13

D I NG - 1 2

5

The code places an upper limit of 1.5 on the impact factor.

Step 6

The positive lane load is found by loading the positive

area with the equivalent lane load and by placing the

required concentrated load over the maximum ordinate. The

load is Increased by the Impact factor and stored in

ST0RE(2). The negative lane load is obtained by loading

the negative area with the equivalent lane load and by

placing the required concentrated load over the minimum

ordinate. The AASHO code also requires a second concen-

trated load placed in one other span as to produce the

maximum negative moment. The negative lane load is then

increased by the impact factor and stored in ST0RE(3).

Step 7

The sidewalk live load is found by multiplying the

uniform sidewalk load by the positive and negative areas

respectively. The positive sidewalk load is placed in

STORE (8) and the negative sidewalk load is placed in STORE (9 J

Step 8

If the interstate loading is desired, the influence

line is loaded with the two interstate concentrated loads

which are spaced 4 ft apart. There arc three loading con-

ditions considered in the interstate loading. The first

two have one load on the maximum ordinate and the second

4 ft to the right or 4 ft to the left. The third condition

has the two loads centered about the maximum ordinate. The

total maximum condition is increased by the if. pact factor

and stored in ST0RE(4). To find the negative interstate

load, the sane three conditions are repeated using the

minimum ordinate as the reference. The negative interstate

load is stored in ST0RE(5).

Step 9

The truck load analysis begins by moving the truck

from left to right. A complete analysis consists of placing

each of the truck's axles over the point in question and

calculating the loads due to the combinations of the

remaining axles.

Step 10

The first step is to place the rear axle on the

analysis point and to use the maximum spacing for the front

axles. The values of the influence line are determined by

using the interpolation subroutine (ILINT). The resultant

load is found by using Equation 2.5. This load is compared

to the current maximums. (The positive maximum is found

in POS and the negative maximum is found in SEG. ) The

calculation is repeated using the minimum spac.ings for the

front axles.

Step 11

Next the front axle is placed on the point in question

and the second axle is located the specified fixed distance

away. The effect of these two axles is calculated and com-

pared with 40 percent of the current maximums. It is

assumed that if the effect of the front axles is less than

40 percent of the maximums, then the effect o 1

'

the rear

31

axle can be neglected. If the effect of the rear axle must

be calculated, the rear axle is placed at the minimum

distance, at the maximum distance, and at each analysis

point in between. Goble and DeSantis [18 and 19] refer to

this as "wiggling the rear axles." Each total effect is

compared to the current maximums and stored in POS and SEG

if required.

Step 12

The final loading for a particular point is to place

the second axle on the point and the first axle the speci-

fied fixed distance ahead. The effect of these two loads

is calculated and compared in the same manner as in step 11.

If necessary, the rear axle is wiggled and the total effects

are compared to the current maximums

.

Step 15

The truck load is repeated for the truck moving from

right to left. The final maximums are increased by the

impact factor and the positive load is stored in ST0RE(6)

and the negative load is' stored in STORE [7).

Step 14

The STORE array is now returned to the ANAL subroutine

where it is used to determine the design loading conditions.

32

CHAPTER J 1 I

GIRDER DESIGN

3.1 Girder Design Theorv

With the design conditions defined at each analysis

point, the cross section can now be proportioned to carry

the necessary design stresses. If the design is noncompos i te

,

then the simple, pure bending theory can be used to determine

the stresses. The equation which expresses this pure bending

theory is known as the flexure formula and is shown as Equa-

tion 3.1:

f = M. . x - 3.1tot i

or

f = Mtot

/S

where S = the section modulus of the section and

is equal to I/c

.

A derivation of this formula is presented by Byars and

Snyder [26] and many other mechanics textbooks.

The section used in a noncompos i te design is symmetrical

about the horizontal axis. This al loves the top and bottom

fiber stresses of the steel section to be equal. The con-

crete in a noncomposite design is assumed to carry no longi-

tudinal stresses because there is no provision for the

3 3

transfer of shear between the slab and t lie beam. If pro-

vision is made for this transfer, then the design becomes

compos i tc

.

The design of a composite bridge girder takes advantage

of the high compressive strength available in the concrete

slab. Some of the advantages of composite action expressed

by Viest, Fountain, and Singleton [27] and by McCormac [28]

are

:

1. A savings in steel costs is realized,

2. The beam depth can be reduced,

3. A larger percentage of steel is in tension,

4. The deflections are reduced due to the increase

in the beam stiffness,

5. A composite section can withstand a greater

overload than a noncomposite design.

The one disadvantage of the composite action is the cost of

providing the shear connectors. This disadvantage, however,

only takes precedence over the advantages in short, lightly

loaded structures.

In designing a composite girder by the AASHO code, the

properties of the steel beam and slab are established on the

basis of the moment of inertia of the composite section.

Bresler, Lin and Scalzi [29] give the following two basic

assumptions used in the analysis and design of composite

beam s £ o r h i g hw ay g i r d e r s

:

1. The slab is connected throughout the length

o f tli e g i r d e r,

34

2. The stress and the strain are linear across

the depth of the member.

The AASHO code, unlike the American Institute of Steel

Construction specification [30], docs not allow any slippage

for the shear connectors.

The composite design section shown in Figure 3.1 is

composed of a rolled section, an effective slab section,

a bottom cover plate, and a haunch. The section could also

be designed without the bottom plate. It is also possible

for the slab to be on one side of the girder. This type of

section would be used for a facia girder and is shown in

Figure 3.2.

The effective slab section is defined as a section of

the bridge deck having an effective slab width and a thick-

ness equal to the structural depth of the slab. The AASHO

code defines the effective slab width of the section in

Figure 3.1 as not exceeding any of the following:

1. One- fourth of the girder span,

2. The distance center- to- center of girders,

3. Twelve times the slab thickness.

If the composite section is similar to the facia girder

shown in Figure 3.2, then the effective slab width should

not exceed any of the following:

1. One- twelfth of the span length,

2. One-half the center- to-center distance to

the adj acent gi rder

,

3. Six times the slab thickness.

35

£

SLABWD

}. " « <i

HAUNCH i

' '

.

.

' V

JV-SLABTH

Rolled Section

D

/ \Cover Plate / N— Seal Welds

Figure 3.1: Standard Composite Girder Cross Section

SLABIVD

SLABT1

Rolled Section

Cover Plate Seal V.elds

Figure 5.2: Facia Girder Composite Cross Section

36

The section properties of the composite section are

determined by the transformed area method. This method

assumes that the bond between the concrete and steel is

strong enough so that the strains in the concrete and steel

at the junction are equal. Due to this assumption, the

relationship between the stresses at a given distance from

the neutral axis is

where

-1

f = - fc n s

n = E /Es c

3.2

The factor n is called the modular ratio. The area of the

concrete slab is transformed into an equivalent area of

steel by dividing the effective slab width by the modular

ratio. The values of the modular ratio specified by the

AASHO code are shown in Table 3.1.

Table 5.1: Values of the Modular Ratio

ConcreteStrong tli

n

2000 - 2400

2500 - 2900

3000 - 5900

40 - 4900

5 00 or more

15

12

10

8

6

37

The actual form of the flexure formula used in a com

positc design contains- three terms instead of just one as

i n Equat ion 3.1:

Mn . y M . y, M \-

,- DL 's SLL 'hnc LL - hmcI

stIlmc

T3.3

hmc

The first term in Equation 3.3 represents the stress at a

point due to the dead load of the structure. This dead load

is carried by the steel section alone. The properties of

the steel section are independent of the slab dimensions.

The second term in the equation represents the stress

due to the superimposed dead load. This load must, accord-

ing to the AASHO code, be carried by the low modulus com-

posite section. The properties of this section are calcu-

lated by using a concrete area transformed by a modular

ratio equal to 5n. The increased ratio is used to account

for creep effects.

The third term in the equation represents the stress

due to the live load on the structure. The live load, since

it is placed on the structure after the concrete has reached

its maximum strength, acts on the high modulus composite

section. The properties of this section are based on a

concrete area transformed with a modular ratio of n.

By using Equation 3.1 for a noncomposite design and

Equation 5.3 for a composite design, the steel girder cross

section can he proportioned so that the resulting flexural

stresses are within the allowables required bv the design

38

code. [f the design is composite, then the compressive

stress in the extreme concrete fiber must also be within

the accepted code allowable.

With the girder designed for flexural stresses, the

shear stresses must be determined. The horizontal and

vertical shear stresses at any point in the cross section

can be found from Equation 3.4:

v = VQbl

3.4

where b = the width of the section where the

shear stress is desired.

Byars and Snyder [26] derive this formula and also demon-

strate that, for an I-shapcd section, the shear stress

across the web can be assumed to be uniform. Since the

stress is uniform, the AASHO code states that all of the

external vertical shear is carried by the steel girder web

and can be calculated using Equation 3.5:

v = V. ./A ,tot web3.5

For this calculation, the area of the web is equal to the

product of the overall depth of the rolled section and the

web t h ickness

.

5 . 2 Fatigue P> e s i g

n

In a highway bridge girder there is a fluctuating

stress level at every point because of the alternating

loading and unloading of the structure due to the live

39

loads. This continuous fluctuation causes dislocations in

the crystalline structure of the steel, and eventually

causes cracks and other localized failures. This type of

failure is referred to as a fatigue failure.

The fatigue failures in a structure nay occur at loads

which are well below the allowable static loading conditions,

because the stress is continually fluctuating over a particu-

lar range. The larger the fluctuation, the worse the condi-

tion. The fatigue condition becomes extremely critical

when the stress alternates between tension and compression.

The number of fluctuations, or cycles, for which a

girder can be designed varies from 100,000 cycles to

2,000,000 cycles. The exact number of cycles used depends

on the use and location of the bridge.

The method used in fatigue design is to reduce the

allowable stresses at critical points. The AASHO code

provides the following formulas for this fatigue reduction:

k,

f

r 1 - k ? R

and

where

. S 5 F

r .55 1-

*- l ro

F

and R = the algebraic ratio of the minimum stress

to the maximum stress.

The k. , f , and a are the fatigue constants. These fatigue• ro °

constants have been determined primarily from fatigue tests.

A description of some of the tests and the results are given

in the II. S. Steel bridge manual [51].

The values of the fatigue constants depend on the num-

ber of cycles of stress, the category, type and location of

material and the yield point of the base metal. The values

required for a particular fatigue calculation can be found

in the AASHO code. The constants for 500,000 cycles of

stress are given in Table 5.2. These are the values which

are used in the design program.

Table 5.2: Fatigue Constants

AASHOCate-gory

Type andLocationof Metal

Type ofMaximumStress

Equation500,000 cycles

fro

a k2

A

D

F

C

BaseMetal

MetalAdj acentto ButtWeld

MetalAdj acentto FilletWeld

WeldMetal

TensionCompr

.

Tens ionCompr

.

Tens ionCompr

.

Shear

5.65.7

5.65.7

5. 6

5.6

3 . 6

2050013500

17200106 00

1200012000

108 00

.78

.78

. 2 5

. 25

0.00.0

. 3 6

'. 5 5

.62

1 .0

1 .0

.55

11

hi the design of a rolled section, fatigue is ;i major

factor in the cover plate design. The ends of the cover

plates are determined by using fatigue calculations for the

base metal adjacent to a fillet weld [Category 1 J. The

allowable stresses in this case are greatly reduced, thus

requiring that the plates be cut off in regions of low

moments. The remaining categories are checked in the design,

but they usually do not govern the design of the girder.

5.3 Design Details

After the cover plates required for a particular rolled

section are determined, the details of the design must be

calculated. These design details include the determination

of the weld sizes for the cover plates, the design of the

required bearing stiffeners and the calculation of the shear

connector spacing for a composite girder. In the optimiza-

tion problem, each of these details must be completed for

each design because they add a substantial cost to the

girder.

The welds which must be determined for each cover plate

include the end welds and the seal welds. The end welds arc

designed to carry the maximum flexural stress developed at

a fixed distance from the ends of the plate. The code sets

this distance as 1.5 times the width of the cover plate.

The required stress is determined using either Equation 3.1

or 5.5. V.'hcn the stress in the plate is known, Equation 5.8

is used to determine the force in the plate:

ILL tot pi

When the Force in the plate is known, Blodgett [31J

shows that the size of the required fillet weld is

3.8

t = Force707 L £ ,,

w all3.9

In the ahove equation the L is the total length of the weld1 w

which, according to the AASIIO code, is four tines the plate

width. The allowable weld metal stress (f ,,) is the lesserall

value of the allowable static shear stress and the allowable

fatigue stress, calculated using Equation 3.6 and the

constants listed under category G from Table 3.2. The

fillet weld equation then becomes

Force2.8 28 W , f .

.

pi all5.10

The required weld size is usually given in sixteenths of an

inch. The code requires that a minimum size be used depend-

ing on the thicknesses of the plates being joined.

The design of the seal weld for a cover plate is

basically similar to that of the end weld except that shear

stress is used instead of flexural stress. Equation 3.4 is

used to determine the maximum shear stress developed along

the cover plate and then liquation 3.11 is used to determine

the size of the seal weld:

1 v_2 ( . 7 7 ) f

al 1

1.414 f5.11

all

13

The 2 in the denominator is present because there is a seal

weld on each side of the cover plate. The code specifies

that the seal weld must extend over the entire length of

the plate in order to prevent corrosion and must have a

minimum thickness of 5/16 in.

The bearing stiffeners are required to transfer the

large web shear stresses, at the reactions, to prevent web

crippling. In most of the wide-flange rolled sections,

bearing stiffeners arc not required. AASHO requires bearing

stiffeners in those girders which have shear stresses in

excess of 75 percent of the allowable shear stress. If

stiffeners are required, they are designed as columns. The

column section used is composed of the two stiffener plates

and a portion of the web which is 18 times the web thickness

in length. The fillet welds which connect the stiffener to

the girder web are designed similar to the seal welds for

the cover plates.

The shear connectors for a composite girder arc designed

to transfer the horizontal shear from the slab to the steel

section. These shear connectors are placed transversely

across the flange at either regular or variable spacings.

The connectors are designed for fatigue as presented by

Slutter and Fisher [35] and checked for ultimate strength.

The spacing at any location can be found as follows:

Spac Lng =

nr c 3.12

1

1

where S = the range of horizontal shear per inch.

The allowable shear per connector depends on the number of

fatigue cycles and the type and the size of the connector

used. The horizontal shear per inch is found by using an

equation similar to 3.4:

S = V Q/I 3.13r r K

where V = the range of vertical shear due to

live load plus impact.

The moment of inertia used in Equation 3.13 is the trans-

formed moment of inertia in the positive region. If shear

connectors are placed in the negative moment region, then

the moment of inertia, for the negative region, is that of

the steel girder and the longitudinal slab reinforcement.

In order to satisfy the ultimate strength requirements

for the connectors, a specified number of connectors must

be placed between the points of maximum moment and the points

of zero dead-load moment. Equation 3.14 is used to determine

the number of connectors required for the ultimate strength:

N =8 5 S

3 . 1 4

u

where I

1 = the lesser value of the force in the

steel girder and the concrete slab.

The ultimate strength of a shear connector depends on the

size and the tvpe of connector.

45

The final shear connecter requirement which must be

satisfied is an additional number of connectors to develop

the slab stress around the points of contraflexure. The

number of connectors required is

A f

Nc

= .

r2

r3.15

r

where A = the area of the steel reinforcement,

and f = the range of live load stress in the

reinforcement (may be taken as 10,000 psi).

These additional connectors are needed only if the negative

moment region is noncompos i te

.

3 . 4 Design Program

The design portion of the computer program operates on

each wide-flange rolled section and completely designs the

girder for the given problem. A complete design consists

of the determination of the cover plates and their required

welds, the design of the bearing stiffeners and the calcula-

tion of the shear connector spacing.

The design program is started by determining the lightest

section which will carry the loads without cover plates. This

section is completely determined and its cost becomes the base

cost for the optimization problem. The urogram now enters a

loop which designs all of the remaining rolled sections. A

flowchart for this loop is shown in Figure 3.3.

n

£> Enter THDES for a

given rolled section

Hi*

rue -0a 1 s e

Determine themaximum moment

Yes

letermine the plate thicknessesbv interval halving

Lgure 5.5: Design Program Flowchart

\1

Calculate the propertiesof the subelements

(8)No . of

latesI = I+l~""

True

False

(6)

Set up the conditionsfor the plate cutoff

IillDetermine the cutoff distance

using the TERMIN routine

121

Optimize the platesplice locations

IULLDesign the plate

welds with CPWDES

Jillf s e STIFF' to design

the stiff eners ©i' i gurc 3.3: ( Cont ' d . )

1-.

No

iHDesign connector

spacing with CONDES

I (13)

Find the cost andweight with OBJECT

Store the design asthe current optimum

Continue on inthe program

No ~©

F igure 5.3: (Cont ' d.

)

19

Step 1

The rolled section being designed is transferred to

the THDES subroutine where the thicknesses of the cover

plates required for each subelcment are determined.

Step 2

The THDHS subroutine first determines the maximum

moment in the subelement. . With this moment determined,

the rolled section is tried without plates. The individual

stresses are determined and checked against the allowable

static and fatigue base metal stresses. If these stresses

are not violated, then no cover plates are required for the

element

.

Step 5

If a cover plate is required at a particular subelement,

the width of the plate is determined based on the flange

width of the rolled section. The thickness of the plate is

determined by using interval halving. The interval halving

technique uses only thicknesses of sixteenths of an inch.

The thickness is varied until the allowable stress condition

is satisfied. The thickness and width of the required plate

are stored in the proper array.

Step 4

Steps 2 and 3 are repeated for each of the subelements

along the girder. With all the plate sizes determined, the

c;ontrol is passed back to the main program

50

Step 5

The properties of each subelement are calculated by

using the SFMIC subroutine and these properties are trans-

ferred to the CPDES routine.

Step 6

The CPDES subroutine uses the fatigue theory discussed

in Section 3.2 to determine the actual location of the ends

of the required cover plates. The routine is used to deter-

mine all of the necessary conditions required to determine

the cutoff point for each plate. The actual point is

located by the TERMIN subroutine.

Step 7

The TERMIN subroutine uses an increasing step size

optimization technique to determine the ends of the plates

in the most efficient manner. The end of the plate is

defined as the point along the girder where the stress docs

not violate the fatigue allowable stress. >nce this point

is determined, control is passed back to the CPDES routine.

Step 8

Steps 6 and 7 are repeated until the fatigue limits oi~

each cover plate on the top and bottom of the girder arc

determined. With the limits found, the final cover plates

for the top and bottom of the girder are determined in the

FLOPT subroutine.

51

Step 9

The FLOPT routine uses the cost array and the cover

plate arrangement to determine the optimum location of the

cover plate splices. A dynamic programming method is used

to accomplish this optimization. Upon completion of this

optimization, the COVPL array is determined in its final

form and control is returned to the main program.

Step 10

The CPWDES subroutine is now used to design all of the

cover plate welds. The end welds for a particular plate are

designed for both ends and the larger thickness is retained

as the design. If the plate is butt welded to other plates

at both ends, then the end weld thickness is set to zero.

The seal welds are designed by the subroutine using Equation

3.11. After these calculations for each cover plate aloni*

the girder are completed, the control is returned to the

main program.

Step 11

The STIFF routine is called to design the bearing

stiffeners for each support. If the support does not

require a stiffener, then the values of the BEAR array are

set equal to zero. if a stiffener is required, the width

and thickness are calculated such that the allowable bearing

and the allowable compressive stresses arc not violated.

The welds which hold the stiffeners in place are calculated

and the control is returned to the main program.

52

Step 12

The CONDES routine is used to determine the spacing of

the shear connectors. The shear connector design is based

on the use of 7/8- in. shear connector studs. The required

spacing at each analysis point is determined and rounded

off to the nearest lower multiple of three inches. The

spacing is corrected for the ultimate strength discussed in

Section 3.3 and the CONSP array is filled with the required

spacing information. The routine sets the least number of

spaces at a particular value at three. Upon completion of

the spacing design, the control is returned to the main

program

.

Step 15

Once the spacing for the connectors is determined, the

design of a rolled section is complete. The OBJECT sub-

routine is now called on to determine the weight and, if

necessary, the cost of the given design.

Step 14

The cost or weight of the design is compared to the

current optimum by the KEEP routine. If the girder is an

improved design, the elements are stored in the proper arrays

If the girder is not an improved design, then the old optimum

is retained.

53

Step 15

Steps 1 to ] 4 arc repeated for each of the remaining

rolled sections. After the last section is designed, the

program takes the current optimum and continues into the

remaining optimization phases of the program.

5 4

CHAPTER [V

PROBLEM OPTIMIZATION

4 . 1 Optimi zation Theory

Optimization, as stated by Beveridge and Schechter [34],

"is the collective' process of finding a set of conditions

required to achieve the best result for a given situation."

In other words, optimization is the process of obtaining a

set of design parameters which either maximizes or minimizes

a particular function. The function being optimized is

referred to as the objective function. This function may

be either mathematically simple or complex, depending on

the nature of the problem. The actual form of this objective

function usually determines the most appropriate method of

optimi zation

.

The design of a physical system ideally contains three

steps. These steps, according to Wilde and Beightler [35],

are

Determination of the interaction of the

system variables,

Development oi' a simple measure of

e f fee t

i

vencss,

Determination, development, and solution o

the most effective optimum-seeking method.

55

The first step is handled by developing a set of constraints

for the particular problem being solved. These constraints

can be imposed by design codes, tradition, or the designer.

This step usually requires the greatest amount of effort.

The second step is the actual development of the

objective function. The formulation of the function can

range from being simple to being so complex it is almost

impossible. The degree of difficulty in describing the

function depends on the type of problem, the type of

effectiveness being measured, and the degree of accuracy

desired. The less the degree of accuracy of the objective

function, the less accurate will be the developed optimum

solution.

The third step leads the designer to many different

types of optimization procedures. The advantages of each

method vary with the problem being solved. It is the

designer's responsibility to know the limitations, the

advantages and the disadvantages of each -method as they

relate to the particular problem being solved.

In the design program for the optimization of a rolled-

section highway bridge girder, there are actually two differ-

ent opt i mum- seeking methods employed. I'he method of

exhaustive search is used as the basic design method and

dynamic programming is used to determine the locations of

the cover plate splices. The thicknesses of the cover plates

are determined by using interval halving to solve the govern-

ing equa.t i on .

56

The exhaustive search technique, sometimes called

exhaustive enumeration or brute force method, simply

evaluates the objective function for each of the problem

possibilities and picks the optimum solution directly.

This method can be very tedious if the number of design

possibilities is large. It is therefore used only when the

overall design space for the problem is fairly limited in

size.

Since the wide-flange sections used for highway girders

include only the 36- and 33-in. sections, there are only

IS sections to be considered. The value of the objective

function is determined for each wide-flange section after

it has been completely designed, including the cover plates,

the bearing stiffeners and the shear connectors. The

design With the minimum value of the objective function is

then chosen as the optimum design.

By setting up the wide-flange sections in descending

weight order, the number of executions in the exhaustive

search can be reduced. Starting with the heaviest, and

proceeding in the descending weight order, each section is

tried without cover plates at the critical moment location,

until the lightest girder which is acceptable is determined.

By assuming that the cost of the shear connectors and

stiffeners for a uniform section are independent of the

section used, all of the sections heavier than the one which

has been determined can be eliminated from the search. This

57

means thai a number of the rolled sections need not be

designed completely and a resulting savings in computation

costs i s real i zed

.

Interval halving is a technique which can be used to

solve equations when the simple, direct methods are

inappropriate. The method uses a bounded interval which

is continuously reduced in size until a certain tolerance

is obtained. By reducing the interval size by a factor of

one-half with each calculation, the total number of neces-

sary calculations is greatly reduced and there is a result-

ing savings in calculating costs. The two necessary condi-

tions for the interval halving technique are:

1. The function must be continuously increasing

or decreasing.

2. The initial boundaries must be specified.

The first condition enables the method to completely elimi-

nate one half of the interval with each calculation, and

the second condition enables the first calculation value to

be specified.

The method begins with the specified interval and

calculates all the necessary information for the interval

midpoint. If all of the constraints are satisfied for this

midpoint value, then the value becomes the new upper bound-

ary. This is possible because the function is continuously

increasing or decreasing and the higher values of the vari-

ables w i 1 1 also satisfy the constraints, but will cause a

58

larger cast. If the constraints are not satisfied, then the

midpoint value becomes the lower boundary. The new interval

is used in the sane manner as the initial interval. The

entire procedure is repeated until the remaining interval

is less than the tolerance desired. Either the upper or

the lower bound can then be used as the optimum solution.

In most problems the average of the two bounds is considered

as the solution., provided that the final interval is small

enough

.

In determining the cover plate thicknesses for each

subelement, there are many calculations required, including

the section properties for each plate size, the bending

stress at the point in question and the allowable stresses

for the fatigue and static conditions. Since, for each

moment condition and rolled section there is only one plate

size which will give a stress equal to the allowable stress,

the function for the thickness can be considered to be con-

tinuously decreasing. The initial boundary conditions can

be specified by using the requirements of the AASHO code.

With the two conditions for interval halving satisfied, the'

method can be used for the determination of the cover plate

thi cknesses

.

In order to use interval halving, however, the method

must be adjusted so that the thicknesses wi 1 1 he determined

in values of sixteenth-inch increments. This is accomplished

bv adjusting the initial interval size and by making the

59

boundaries Integers. Each halving process then produces an

integer which corresponds to the number of sixteenths of an

inch in the plate thickness. The calculations are completed

for the thickness and the interval is reduced. The process

is continued until the final interval size is 1.0. The

optimum plate size is then stored in the proper array loca-

tion.

Dynamic programming is a method used in sequential

system optimization problems. It can be applied to situa-

tions in which many decisions arc required, as long as the

decisions made at later stages do not affect the performance

of earlier stages. A mathematical formulation of the dynamic

programming method can be found in the optimization texts by

Wilde and Beightler [35], Pierre [36] or Penn [37]. All of

the mathematical formulations arc based on Bellman's [38]

principle of optimal ity.

Dynamic programming is a method of decomposition which

divides the Riven problem into a set number of individual

problems. In determining the optimum condition for section

i, the onlv quantities which are used are the values of the

variables in sections i+1 and i, and the value of the

objective function for the system up to and Including

section i-1. The objective function is determined for all

of the possible combinations of the variables in section

i and i+1. The values of the objective ''unction arc then

added to the value of the function for the problem through

1,(1

section i-1. The optimum variable can then be directly

chosen and placed in an appropriate array location defined

by the section number i and the variable value in section

i + 1.

The method begins by calculating the variable combina-

tions for all of the sections and their adjacent sections

in the problem sequence. When the last section is reached,

the final values of the objective function are calculated.

By comparing these values, the optimum for the last section

is determined. Then, by working backwards, all of the

variables in each section can be determined. This process

leads to an optimization of the entire problem.

The dynamic programming method is used to determine

the final cover plate combination for a given rolled section

The actual problem is decomposed into sections corresponding

to the cover plates which have been tie fined by the fatigue

stress conditions. The variable of each section is the

plate thickness, and the function being minimized is the

total cost of the cover plate. By varying the thickness

o l~ each section and determining the total cost of the plate

by the procedure described above, the optimum location of

the cover plate splices can be located. This method is

similar to the flange smoothing method used by Goble and

Razanj [17]. DeSantis and Goble [18] illustrate this

method for the optimization ol~ the Flanges for a welded

p late g i rder

.

M

4 . 2 Ob j ect ive Function

The term objective function refers to the means by

which the program evaluates the merit of a particular design

For the rolled -sect ion highway girder design, the function

can be either the total weight or the total cost of the

girder. The designer specifies which method of optimization

is desired by the value used for IPT6. If IPT6 has a value

of 0, then the optimization is based on cost. The equation

for the total girder cost is

Total Cost Cost of the rolled section +

Cost of the cover plates +

Cost of the shear connectors +

Cost of the bearing stiffeners +

Cost of the welding.

4.1

If the value of IPTb is 1, then the optimization is based on

the weight of the girder. The equation for the total girder

weight is

Total Weight = Weight of the rolled section +

Weight of the cover plates +

Weight of the bearing stiffeners +

Weight of the shear connectors.

4.2

The weight function first determines the volume of steel

used in each of the individual portions of Equation 4.2. A

unit weight of 490 pounds per cubic foot is used to convert

62

the volumes into weights. These weights are added together

to get the total weight.

If the cost of a girder is desired, then the weights

are calculated as above and then converted into costs. The

costs of the rolled section, the cover plates, and the

bearing stiffeners are determined by multiplying each of

the weights by their respective unit costs. These unit

costs are expressed in dollars per pound.

The cost of the shear connectors consists of two

separate elements. The first element is the material cost

of the connectors and is based on the total weight of the

connectors. The cost is calculated by multiplying the total

connector weight by the unit cost. This unit cost is also

expressed in dollars per pound. The second element is the

installation cost and is based on the total number of

connectors. This cost is calculated by multiplying the

total number of connectors by the installation cost per

connector

.

The welding costs are determined for all the welds on

the girder. The welds which are considered are the cover

plate butt welds, the cover plate seal welds, and the welds

used to connect the stiffeners to the girder. The weld cost

can be found for any weld using the following equation:

Cweld= C

>

+ C 2 (L) + C 3^V ) 4 - 5

63

where C] is the fixed cost of the weld, C 2 (L) is the vari-

able cost which is a function of the weld length and C3(V)

is the variable cost which is a function of the weld volume.

The fixed cost of a weld accounts for all of the costs

involved in the set-up time, the inspection, and the other

fixed items of cost. 'Die variable cost, based on the weld

length, reflects the costs of x-ray inspection and joint

preparation

.

The variable cost, based on volume, reflects the. actual

cost of the weld material. The volume of a weld depends on

the size and shape of the weld. For a fillet weld, the

volume is based on a weld cross section which is triangular.

For a butt weld, the volume is based on the cross section

of a double vee butt weld. F.ach of these welds is the

standard weld used in highway girder design.

The objective function for this problem is similar to

the one found in the CAD- I program developed by Goble and

DeSantis [19]. This is done so that final comparisons

between rol led -sect ion girders and welded plate girders can

be made. These comparisons can only be accurate if the

objective functions for both types of design arc similar in

form and content.

\ . 7> Constraints

The problem constraints are the limitations placed on

various parts of the design in order to limit the total

design space. There are two types of constraints in an

64

optimization problem. One type of constraint, referred to

as a side constraint, is imposed on the design by functional

limitations. The second type, called a behavioral constraint,

is imparted to the design by a specific specification.

A functional, or side, constraint used in the girder

design problem is the total number of rolled sections

designed. Since the design of a highway bridge girder is

usually limited to the 36- and 33-in. wide-flange sections,

the limited number of design possibilities actually becomes

a side constraint for the problem.

The allowable width of the cover plates is also con-

trolled by a functional constraint. The plates are limited

to sizes of whole inches and must be smaller than the width

of the rol led -section flange. The reason for this is to

make the welding process more efficient. With this con-

straint, the widths of the cover plates are limited to

10, 14, or 15 in.

The behavioral constraints for the highway girder

design are specified in the American Association of State

Highway Officials bridge design code [20]. The AASHO code

specifies all of the design criteria, which must be converted

into the problem constraints, for the design of a rolled-

section girder. These behavioral constraints are divided

into the following four groups:

1 . Static stress constraints,

2 . Fatigue stress constraints,

65

3. Cover plate size constraints,

4. Secondary design constraints.

The static stress constraints arc based on the required

allowable stresses with no regard to fatigue considerations.

There are actually five different static stress conditions

which must be satisfied before a design can be considered

acceptable. Four of the conditions consider the bending

stresses in the girder and the fifth considers the shear

stress in the girder web. The five constraints are:

1. The allowable flexural tension stress in

the extreme fibers of rolled shapes or built-

up sections is 0.55 F where F is the yieldv v -

point stress

.

2. The allowable flexural compression stress

in the extreme fibers of rolled shapes and

built-up sections is 0.55 F when the com-1

y

pression flange is continuously supported

by being embedded in concrete.

3. The allowable flexural compression stress in

the extreme fibers of rolled shapes or built-

up sections is determined by Equation 4.4:

3F0.55 F 1.0 via) 21

TT2

F.{b

4.4

This constraint reduces the allowable com-

pressive stress in order to prevent the

buckling of the compressive flange.

66

4. The allowable compression stress in the

extreme fiber-s of the concrete slab is

0.4 f' where f ' is the 28-day concretec c

strength

.

5. The allowable shear stress in the girder

web is 0.35 F .

y

.

The fatigue stress constraints reduce the allowable

stresses because of the fluctuations in stress caused by the

repeated applications of the liv.e load. The fatigue stress

conditions are governed by Equations 3.6 and 3.7. The

fatigue theory used in the design program is described in

Section 3.2.

The maximum permissible thickness of a cover plate is

governed by Equation 4.5:

t = 1.5 tr 4.5cp f*max

Equation 4.6 governs the length of the cover plate:

L = 2 D + 3 4.6cp •

1 mm

where D is the depth of the rolled section

i n feet

.

Equations 4.5 and 4.6 set the requirements for a cover plate

on a given rolled section and make up the cover plate size

constraints .

The final group of design constraints control the

secondary details of the girder design. The details which

67

are controlled by this group arc the shear connector spacings,

the bearing stiffener design, and the weld design.

If the design is composite, then the following four

constraints control the spacing of the shear connectors:

1. The shear connectors are spaced so that the

horizontal shear is transferred from the slab

to the steel girder. This spacing is designed

according to fatigue stress conditions.

2. The design of the shear connector spacing is

checked for ultimate strength.

3. Extra connectors must be provided at the

points of contraf lexure

.

4. The maximum permissible spacing is 24 in.

The equations and the theory used in the design of these

shear connector constraints can be found in Section 5.3.

The design of the bearing stiffeners is controlled by

the following constraints:

1. Stiffeners are required at a support if the

shear stress in the web at that support is

greater than 75 percent of the allowable shear

for gi rder webs

.

2. The minimum thickness for a stiffener is

given by

m mbi 1 / ^__12 V 53(100

I.~

where b' is the width of the stiffener.

6 8

The bearing stress between the stiffener

and the rolled-section flanges must be less

than 0.8 F .

y

The compressive stress in the stiffener must

be less than the allowable column stress

determined from Equation 4.8:

'0.75L'

1

2

0.55Fy

1. 251.0

F

4tt2E

4.8

where L'/r is the slenderness ratio of

the stiffener and a section of the

web which is 18tw inches wide.

The final secondary design constraint is used to con-

trol the weld design. The allowable static shear stress in

the weld material (Fv ) is specified by Equation 4.9:

If F < 36 ksi, F = 12.4 ksiy — ' v

If F > 56 ksi, F = 14.7 ksiy v

4.9

The allowable shear stress for the weld material must be

reduced for fatigue by using Equation 3.6 and the constants

under category G in Table 3.2.

69

CHAPTER V

COMPUTER PROGRAM

5 . 1 Description of the MA I N Program

The computer program for the design of rol led- section

girders consists of two parts. The analysis portion is

used to determine the design conditions for the problem and

the design portion is used to determine the optimum combina-

tion of rolled section and cover plates. The entire program

is composed of a MAIN program and thirty- four subroutines.

The purpose of the MAIN program is to call on the

subroutines in the correct sequence to produce the optimum

design for the particular girder. The following description

is a step-by-step summary of the MAIN program. A flowchart

for this program is presented in Figure 5.1.

Step 1

The rolled section information required for the design

program is read from data cards. All the information for

the eighteen 56- and 55- in. wide- flange sections is already

on cards supplied with the program.

Step 2

The READIN subroutine is called to read all of the data

for the design problem. A detailed description of READIN is

presented in \ppcndix C.

70

G>

0-

Read the rolled section information

I (2)

Read all the problemdata using READIN

f (5)

Determine F

j (4)

Analyze the structureusing ANAL

I (5)

CMIN = 999999WMIN = 999 999

I (6)

Design the uniform section grrder,I, with the UNIFST subroutine.

6Figure 5.1: Flowchart for the MAIN Program

"1

True

False

Design the rolled section J, usingthe sequence of steps described in

Section 3 .

4

(8)

Place the optimum designworking arrays

in the

IUse SFMIC to determine the section

properties

t C£j

Determine the new girder weight

Reanalyze the structure

i

; igure 5.1: (Cont ' d

72

No

Print new designconditions

t (11)

Recalculate the stiffeners and theshear connector spacing

ICheck all the stresses using STRCHK

Y e s No

Print the optimumdesign information

<D

igure 5.1: (Cont ' d.

)

73

Figure 5.1: (Cont'd. J

74

Determine the total moment at thecritical section

Calculate the percentage, PI

o No

Yes

Yes <5

i ULLL

Completely redesign the rolledsection used in the optimum design

I (16'

Calculate the deflections usingthe DEFLEC subroutine

o w (17;

Print the finaldesign information

figure 5.1: (Cont'd.

)

75

Step 3

The minimum tensile strength used in the fatigue calcu-

lations is determined from the yield point stress of the

material used in the problem. This tensile strength is a

measure of the minimum ultimate strength of the steel.

Step 4

The ANAL subroutine is called to analyze the given

problem and to determine all of the design reactions, the

design moments, and the design shears. These conditions

are used to determine the optimum girder for the problem.

Step 5

The minimum weight and the minimum cost variables are

initialized at very high values.

Step 6

The UNIFST subroutine is used to design the uniform

section girder. This girder is the lightest rolled section

which satisfies all of the design constraints without the

use of cover plates. This section then becomes the initial

design.

: tep 7

A design loop, which completely determines the girders

composed of the sections lighter than the one used as a

uniform section, is begun. This loop is described in

Section 3.4 and a flowchart is presented in Figure 3.3.

76

Step 8

After the design loop is completed, the optimum design

for the cycle is stored in the optimum storage arrays. This

design is then placed into the working arrays of the program

and all of the section properties are computed using the

SFMIC subroutine.

Step 9

The new unit dead weight of the girder is determined

and the problem is analyzed again, using the new distribu-

tion of the moments of inertia. If the problem is a con-

tinuous girder, then the ANAL subroutine is called to do the

complete reanalysis. If the problem is a simple- span

girder, the dead-load design conditions are changed directly

in the MAIN program. This is the only change required

because the moments in a simple-span girder are independent

of the cross - section properties.

Step 10

If IPT10 is greater than 0, all of the design conditions

are printed out

.

Step 11

Using the new, design conditions, the stiffeners and

connector spacing for the optimum design are recalculated.

All of the stresses in the girder arc determined bv the

STRCliK subroutine and a new value of the objective function

77

is determined. All of the information regarding this design

is then printed if IPT10 is greater than 0.

Step 12

If the design cycle parameter, IPT7, equals 2 and the

maximum number of cycles has not been readied, the counter

is increased by one and control is returned to step 5.

Steps 5 thru 11 are repeated until the specified maximum

number of cycles is reached. Control is now passed to

step 15.

Step 13

If IPT7 equals 1, the total moment at the critical

section is determined and the percent change from the

previous analysis is computed. If this percentage is less

than the specified percentage, control is passed to step 15.

Otherwise, control is returned to step 5, where steps 5 thru

11 are repeated until the percentage is less than that

specified

.

Step 14

If IPT7 equals 0, no redesign cycles are required and

control is passed to step 15.

Step 15

Using the final conditions, the rolled section used in

the optimum design is completely recalculated using the

sequence of steps described in Section 3.4.

78

Step 16

The required deflections are calculated, using,the

moment of inertia distribution of the final design. These

deflections are calculated by the DEFLEC subroutine.

Step 17

All of the information pertaining to the final design

is printed in the output. This includes the section proper-

ties, the required cover plates, the required stiffeners

,

the shear connector spacing and all of the deflections. The

cost or weight of the design is also presented, depending on

the value of 1PT6.

Step 18

Control is returned to Step 2 where the program is

either terminated or the data for a new design problem are

read

.

5 . 2 Sample Problems

In order to show the usefulness of the computer program,

two sample girders have been designed. Both problems are

presented in the U. S. Steel Manual [31]. The costs of the

manual design and program design are compared below.

The first problem is a two-span girder having equal

span lengths of 70 ft. The design is based on a composite

section having the properties shown in Table 5.1. The design

loading is the AASHO HS20 loading.

7 9

Tabic 5.1 Composite Section Properties

Property Value

SLABWD 84. 00 in

SLABTI1 7.00 in

FPC 300 0.00 psi

MR 8.0

AS 4.34 sq in

HAUNCH 1.87 5 in

Table 5.2 Unit Costs

Item unitCost inDollars

Rolled Section

Cover Plates

Sti f f eners

Connectors

Connector Installation

Fixed Weld Cost

Weld Material Cost

Weld Length Cost

lb

lb

lb

lb

ea

ea

cu in

i n

0.15

0.12

0.12

0.00

0.75

20.00

2.00

0.0

80

The optimization of the girder is based on the total

cost. The unit costs used in the optimization procedure

are shown in Table 5.2

The final design produced by the computer program is

shown in Figure 5.2. The itemized costs and weights of

both the computer design and the manual design are given

i n Table 5.3.

Table 5.5: Costs and Weights for Problem No. 1

ItemU. S. Steel Manual Computer Program

Weight Cost Weight Cost

Rolled Section

Cover Plates

St if feners

Connectors

Welds

Totals

18900.

2361.6

202.2

21465.8

$2855. 00

$283.40

$193. 50

$628.29

$3940. 19

22400.0

243.1

181.

22824.1

$3560.00

$28.16

$174.00

$206.90

$3769.06

Table 5.5 shows that the optimization program produced

a girder which is approximately 6.0 percent heavier than the

girder found in the manual. The optimum design, however,

costs 5.0 percent less than the manual design. Most of the

cost reduction can be found in the cover plate cost. The

total cost of the plates, including both material and

fabrication costs, for the optimum girder is $255.06. The

r\ A^ V

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<* i—

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X 1

<SJ

vO ^

i—

t

to oCM f-

: [_

wr- ]

P (SJ

3 *to<|

-

bO 3CS-.

.—

1

-1- C2;

touH

ofH

X ;

u vOr-» i—i

o s.> LO

C co

•H T3 CD

rH S-

tA CD rt

S-< 5o to i—l

+-> 13 T3O C i—i •

cd o CD Oc > 2c -

o ^c i—l £3

(J r-H rt 03

--^. o r-H

•St- LO in

oCD O r-H £-<

C/l 1/1 i—

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oc+j

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CD c4-> GOO H2

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r J

uo

O

82

same costs for the manual design give a total of $911.69 or

approximately four times as much as the program solution.

This cost difference offsets the increased cost of the

rolled section used in the optimum design.

The second example is a four-span composite girder.

The outer spans arc 70 ft and the interior spans are 90 ft.

The composite section properties, the loading conditions and

the cost parameters are the same as for the first problem.

The program design and the itemized costs and weights are

shown in Figure 5.3 and Table 5.4 respectively.

Table 5.4: Costs and Weights for Problem No. 2

ItemU. S. Steel Manual Computer Program

Weight Cost Weight Cost

Rolled Section

Cover Plate

Stiffeners

Connectors

Welds

Totals

43200.0

9855.0

4 7 5.0

53520.0

$6480.00

$1182.60

$458.00

$1598.44

$9719.04

51200.0

3509.6

548.0

5 5 5 7.6

$7670.00

$420.93

$536.50

$1251.68

$9679.11

Table 5.4 shows that the computer solution is approxi-

mately 2.9 percent heavier and onlv 0.5 percent cheaper than

the manual design. These figures show that there is a

slight saving in the computer solution. The small amount

.

c^,

i

•H c bo -

CO

c c -ro

o CD u (J r

J=> CQ TO oTO • a,

fH tO to -. a) \DF 4-1

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to u

(H

O•Hh(D+J

G bfi

I—

i

G•i-i

4-> uCO TO

^ a>•H OQUh

c^>

bQg

•H

TO

apq

GW

CMC2J

CM

CO

o4->

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GGoC_}

o2

en

CM

Ocm

CM

u-.

to

83

5 CO

o T3!- i—

i

<Dr-* - *>

O \DTO r—

<

13a) \ C

LO CD

CH <D~

s-l <st

CO TO \?H i—

1

O CO CM4-> T3 T3U <-n C •

<d a) TO oG.> 2C n

O i-H vO eU TO i—

1

CD

<U *»s. T—

(

•=t CO LO ^3o

<D i—

1

CD (h

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3 <O

<4H

CO

CD GP fcC

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CD

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&o

to

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bo

84

indicates that the manual solution approaches, for these

cost figures, the optimum design. The similar costs show

that the computer not only approaches the optimum solution,

but also produces a practical design.

The computer program is approximately 4000 cards in

length and was developed using the CDC 6500 computer. The

compilation time for the program is about 48 seconds. The

execution times for the two sample problems were 60 and 40

seconds respectively.

The 10 x 1/4 plates, shown in Figure 5.3, violate

width-to-thickness ratios of the AASHO code. The program

is being modified such that the cover plates conform to the

code requirements

.

85

CHAPTER VI

SUMMARY AND CONCLUSIONS

6 . 1 Summary

The cost optimization of a highway bridge girder,

composed of a rolled section acting compos itely with the

bridge deck, has been formulated and programmed. An

objective function, based on the material and the fabrica-

tion costs, has been developed and used in the examples.

The design of the girder is controlled by the 1969 AASHO

code

.

Due to the complex loadings required on a highway

bridge, the method of influence lines is used in the

analysis. The analysis portion of the program produces

the design conditions for the problem, which are used to

design and optimize the required girder.

Since the number of possible designs is fairly limited,

the program uses the exhaustive search technique. The

techniques of interval halving and dvnamic programming are

also used within the design program. Interval halving is

used to determine the thicknesses of the cover plates for

the subelements and dynamic programming is used to determine

the optimum location of the cover plate splices.

86

The computer program developed will solve a simple-span

problem as well as a continuous problem of up to four spans.

The girder can be either composite or noncompositc and is

designed for static and fatigue loads. All the design

details are developed and then listed in the output. No

attempt is made to design the girder for deflection, but the

total deflections for the final design are tabulated. The

engineer has the option to optimize the design based on

either the total weight or the total cost.

6 . 2 Recommendations for Further Research

1. Beams with different steel strengths may be

cons idered.

2. Varying the rolled section at points of zero

dead- load moment may be considered.

3. The effect of field splices on the optimiza-

tion problem could be established.

4. A more accurate objective function could be

developed, provided that cost information

could be obtained from steel fabricators.

5. A complete optimization study of rolled-

section girders and plate girders could be

made using the program in conjunction with

G ,D-I .

6. The effect of the girder spacing on the

optimum solution could be determined.

87

10

The effect of composite action in the negative

moment region on the optimum solution could be

studied

.

The effect of a variable slab thickness on the

problem optimization could be determined.

An optimization of the bridge deck and stringer

portion of a highway bridge could be developed.

An optimization study of the various types of

highway overpass structures, such as plate

girders, rolled- sec tion girders, reinforced

and prestressed concrete girders and concrete

slab bridges, could be made with the ultimate

outlook on optimizing the entire bridge

design pro j ect

.

BIBLIOGRAPHY

8 8

BIBLIOGRAPHY

1. Druckcr, D. C. and R. T. Shield: "Bounds in MinimumWeight Design," Quarterly of Applied Mathemat ics , 1957.

2. Drucker, D. C. and R. T. Shield: "Design for MinimumWeight," Proceedings on the 9th International Congressof Applied Mechanics , Brussels, 1956

.

3. Faulkes, J.: "The Minimum Weight Design of StructuralFrames," Proceedings of the Royal Society , London, 1954.

4. Heyman, ,T . : "On the Absolute Minimum Weight Design ofFramed Structures," Quarterly Journal of Mechanics andApplied Mathematics , No. 12, 1959

.

5. Krishman, S. and K. V. Shetty: "On the Optimum Designof an I -Section Beam," Journal of Aerospace Science

,

No. 26, 1959.

6. Krishman, S. and K. V. Shetty: "A Method of MinimumWeight Design for Thin-Walled Beams," StructuralEngineer , No. 5, 1961.

7

.

Haug , E . : Minimum Weight Pes ign of Beams wi th Inequal -

ity Constraints oT Stress and Deflection,

Ph.D. Thesis,19 66,. Kansas State" University.

8. Ilahn, P.. W. : Minimum Weight Elastic and Plastic Designof Beams and S i mp 1 e Structures , Ph.D. Thesis, June 1969,Purdue University

.

9. Sturman, G., Albertson, L., Cornell, C. and J. Roessct:"Computer-Aided Bridge Design," ASCE Journal of theStructural Division , Vol. 92, No. 6, Dec. 19 66.

10. Edward, C. H. and L. II. Gary: "Minimum Weight Propor-tions for Steel Girders," ASCE Journal of the StructuralDivision

,Vol. 95, Oct. 1969.

11. liolt, E. C. and G. L. Heithecker: "Minimum WeightProperties for Steel Girders," VSC E J ournal of theS t ructur a 1 Division, Vol. 95, No . 1 , Oct. 1 9 69

.

89

12. Annamalai, N. : Cost Optimization of Welded PlateGirders , Ph.D. Thesis , Purdue University, 1970.

15. Lewis, A. D. M. : "Backtrack Programming in WeldedGirder Design," Proceedings o t" the Share - ACM - I ELLDesign Automation Workshop 7 July 15-18, 1968

,

—

Washington , D. C.

14

.

Okuba , S . : Optimum Design of Compos i te Plate GirderSuperstructures , C E Thesis , 1965, M . I . T.

15. Razani , R. : The Iterative Smoothing Method and It s

Appl icat ion to Minimum Cost Pes ign of Highway BridgeGirders , • Ph . D . Thesis, 1965, Case Institute of Tech-nology .

16. Razani, R. and G. Goble: "Optimum Design of ConstantDepth Plate Girders," ASCE Journal of the StructuralDivision , Vol. 92, April 1966.

17. Goble, G. and P. V. DeSantis: "Optimum Design ofMixed Steel Composite Girders," ASCE Journal of theStructural Division , Vol. 92, Dec. 1966

.

18. Goble, G. and P. V. DeSantis: Girder AutomatedDesign - I , Vol . 1 - User's Manual , Oct. 1968.

19. Goble, G. and P. V. DeSantis: Girder AutomatedDesign - 1 , Vol . 2_

- Maintenance Manual , Oct. 1968.

20. American Association of State Highway Officials,Standard Spec ificat ions for Highway Bridges , TenthEdition, 1969.

21. Gaylord, E. II. and C. N . Gaylord: Structural Engineering Handbook , McGraw-Hill Book Company, New York, 1968

22. Norris, C. II. and J. B. Wilbur: Elementary StructuralAnalys is , Second Edition, McGraw-Hill Book Company,New York, 1960.

25. Shedd , T. C. and J. K. Vawter: Theory of SimpleStructures , J. Wiley and Sons, Inc., N'e/v York, 1941.

24. Will ems, X. and W. M. Lucas: Matrix Analys i s forStructural Engineers , Prent ice- Hal 1 , Inc., .Yew Jersey,1968.

25. Pippard, \. .J. S. and J. Baker: The A n a lysis o_f

Engineering Structures , Eourth Edition, AmericanElsevier Publishing Co., New York, 1968.

26. Byars , E. F . and R. D. Snyder: Engineering Mechanicsof Dcformable Bodies , International Textbook Co.,Pennsylvania, 1963.

27. Viest, I. M. , Fountain, R. S. and R. C. Singleton:Composite Cons truct ion in Steel and Concrete , McGraw-Hill Book Co. , New York, 1958.

28. McCormac, J. C: Structural Steel Design , InternationalTextbook Co., Pennsylvania, 1965.

29. Bresler, B., Lin, T. Y. and J. B. Scalzi: Pes ign ofSteel Structures , Second Edition, John Wi lev and Sons

,

New York, 1968.

30. American Institute of Steel Construction: Manual ofSteel Construction , Seventh Edition, 1970.

31. United States Steel Company: Highway Structures DesignHandbook , Volumes 1 and 2, 1965.

32. Blodgett, 0. W. : Design of Welded Structures, TheJames F. Lincoln Arc Welding Foundation, Ohio , 1966.

33. Slutter, R. G. and J. IV. Fisher: "Fatigue Strength ofShear Connectors," Highway Research Record , No. 147,Highway Research Board , Washington , D. C., 1966.

34. Beveridge, G. S. G. and R. S. Schechter: Optimi zation :

Theory and Pract ice , McGraw-Hill Book Company, Neiv York,1970.'

35. Wilde, D. J. and C. S. Beighlter: Foundations ofOptimization

,Prentice-Hall, Inc., New York, T967.

56. Pierre, D. A. : Opt imi zation Theor y wi th Appl icat ion s

,

J. Wiley and Sons, Inc., New York, 1969.

37. Denn , M. M.: Optimi zatio n by Variational Methods,

McGraw-Hill Book Company , New York, 1969.

3 8 Bell m a n Dynamic Programming , Princeton UniversityPress, New Jersey, 195'

APPENDICES

APPENDIX A

91

APPENDIX A

SUBROUTINE DESCRIPTIONS

The subroutines used in the program are listed and

described in the following list. The listing is presented

in alphabetical order.

ALLOW - returns the allowable bending stress

for any location along the top and the

bottom of the girder, disregarding all

fatigue conditions.

ANAL - determines the design conditions

(reactions, moments and shears) for

a particular problem.

BASFAT - returns the allowable base metal fatigue

'stress at a given point on the girder.

CONDES - designs the shear connectors for a given

girder

.

CPDES - designs the cover plates for a given

rolled section.

CPWDES - designs the required end and seal welds

for each cover plate required on the

girder

.

DEFLEC - determines the required deflections for

the final girder design.

92

EQSET - calculates the simple beam deflections,

at the interior support points, which

are used in calculating the influence

lines for the reactions.

FLOPT - uses the optimization method of dynamic

programming to determine the final cover

plate arrangement along a girder.

ICALC - determines the moments of inertia and

the distances to the lower extreme fibers

for any rolled section and cover plate

combination. It is also used to find the

similar properties for the composite

sections by treating the slab as a top

cover plate.

ILINT - returns the interpolated value of any

point along an influence line using

straight line interpolation.

ILPROP - determines the various required proper-

ties of a given influence line including

the crossover points, the positive and

negative areas and the locations of the

maximum and minimum ordinates.

IMPACT - determines the impact factor for any

particular analysis function.

KEEP - decides whether or not to retain the

given design as the present optimum.

9 3

LOAD - places all the required loads on the

influence line in such a manner as to

return the maximum loading conditions

required.

MAIN - calls on the remaining subroutines in

the correct order to produce the optimum

design.

OBJECT - contains the function being minimized

during the optimization of the design

problem

.

PRCON - prints the connector design for a given

girder

.

PRCOV - prints the cover plate information for a

girder .

PRDEF - prints the deflections for the final

girder design .

PRSEC - prints the section table for a given

girder .

PRSTIF - prints the bearing stiffener information

for a given girder design.

PRSTR - prints the stress table for a given

g i rder des i gn

.

REAC - determines the reaction influence lines

for a continuous girder using the moment-

area theorems

.

READIN - reads in all the pertinent data required

for a particular design problem.

SFMIC - calculates the properties for each sub-

element along the girder.

SORT - places the required cover plate thick-

nesses in ascending order so they can

be used in the FLOPT subroutine.

STIFF - completely designs the bearing stiffeners

for a given girder if they are required.

STRCHK - determines the stresses on a given girder

and checks them against the allowable

stresses .

STRMAX - determines the maximum design stress

conditions

.

TERMIN - determines the locations of the ends of

the required cover plates based on the

fatigue stress conditions.

'HIDES - calculates the required cover plate

thicknesses for each subelement along

the g i rder

.

TOPT - determines the required minimum weld

thickness Lor a fillet we 1 d

.

UNIFST - designs the girder which has a uniform

steel section composed of a rolled, ki de-

fiance section without cover plates.

APPENDIX B

95

APPENDIX B

SELECTED PROGRAM NOMENCLATURE

The following alphabetic list contains some of the

more pertinent variables used in the program. The list

basically contains all the variables which are interchanged

between the program subroutines. The numbers in the paren-

theses immediately following the \rariable name give the

maximum dimensions of that array within the program.

ANEG - the negative area under a given

influence line.

APOS - the positive area under a given

influence line.

BEAR (5, 3 J- the bearing stiffener array.

(1.1) - width of stiffener at support I.

(1.2) - thickness of stiffener at support I

(1.3) - size of connecting weld for

stiffener at su^ort I.

CC (5,5) - the coefficient array for the reac-

tion influence line calculations.

CH (80) - the distance from the neutral axis

to the lower extreme fiber within

a sub el orient for the high modulus

composite section.

96

CL (80) - the distance from the neutral axis

to the lower extreme fiber within

a subelement for the low modulus

composite section.

CMIN - the cost of the present optimum

design.

CONSP (1 6 , 3 , 4 ) - the shear connector design array.

(J, 1,1) - spacing of the J group of connectors

in span 1

.

(J,2,I) - the starting coordinate of the J

group of connectors in span I

.

(J, 3, I) - the final coordinate of the J group

of connectors in span I

.

COOR (81) - the coordinates of the analysis

points

.

COST (9) - the unit cost array.

(1) - cost of the rolled sections.

(2) - cost of the cover plates.

(3) - cost of the bearing stiffeners.

(4) - cost of the shear connectors.

(5) - cost of the connector installation.

( 6

)

- fixed cost of a weld.

( 7 J- cost of the weld material.

(8) cost of the weld Length.

COVPL (12 , 6 , 2) - the cover plate design array.

(J, 1,1) - the starting coordinate of Jth plate

97

(J ,2,1)

(J , 3 , I )

(J ,4,D

(J, 5, I)

CS (80)

DAF (18)

the final coordinate of Jth plate.

the thickness of Jth plate.

the width of the Jth plate.

the size of the end welds for the

Jth plate.

(J , 6 , I ) - the size of the seal weld for the

Jth plate.

Note: For the COVPL array, I equals 1 for the

cover plates on the top of the girder

and I equals 2 for the cover plates on

the bottom of the girder.

the distance from the neutral axis

to the lower extreme fiber within

a subelement for the steel section

alone .

the depth divided by the flange

area for the rolled sections used

in the design program.

the depth of the rolled sections

u s e d i n t h e d e s i g n p r o g ram .

the design girder deflections.

the deflection at I OFF ( I ) due to

the dead load .

the deflection at mEF(I) due to

the positive live load.

DEPTH (1 S)

DESDEF (2 0,4)

(1,1)

(1,2)

9 8

(1.3) - the deflection at IDEF(I) due to

the superimposed dead load.

(1.4) the deflection at IDEF(I) due to

the negative live load.

DESMOM (81 , 4 ) - the design moment array.

(1.1) - the moment at I due to the dead

load .

(1.2) - the moment at f due to the positive

live load .

(1.3) - the moment at I due to the super-

imposed dead load.

(1.4) - the moment at I due to the negative

1 ive load

.

DESREA(5,4) - the design reaction array.

(1.1) - the reaction at support t due to

the dead load.

(1.2) - the reaction at support I due to

the positive live load.

(1.3) - the reaction at support 1 due to

the superimposed dead load.

(1.4) - the reaction at support I due to

the negative live load.

DESSH (162,4) - the design shear array.

(1,1) - the shear at point I due to the

d c a d 1 o a d .

99

(1,2 J - the shear at point I clue to the

positive live load.

(1,3) - the shear at point I due to the

superimposed dead load.

(I,4J - the shear at point I due to the

negative live load.

Note: For analysis point I, J. equals 21-1

just to the right of I and J equals

21 - 2 just to the left of I.

DIA - the diameter of the shear connector

used in the program.

DING - the impact length for a given

influence line

.

DIST - the distance a cover plate is cut

off based on fatigue stress con-

siderations .

EM - the modulus of elasticity which is

set at 29,000 ksi in the program.

EPS (4) - the number of elements per span.

FC - the allowable concrete compressive

stress .

FLTH (IS) - the thickness of the flange for

the rolled sections used in the

i i w in (is

d e s l g n p r o g r a n .

the width of the flange for the

rolled sections used in the design

pre rar

LOO

FPC - the 28-day strength of the concrete

I-'U - the minimum tensile strength of

the steel

.

FV - the allowable weld metal stress.

GDL - the weight of 'the steel girder.

11AUNCH - the value of the concrete haunch

for the composite design.

1IT - the calculated impact factor.

IDEF (30) - the analysis points at which the

deflections are calculated.

IHCON (80) - the moment of inertia of a sub-

element for the high modulus

composite section.

ILCON (80) - the moment of inertia of a sub-

element for the low modulus

composite section.

IOSP (5) - the index of the support points.

IPT1 - the subelement input option.

IPT2 - the loading type input option.

IPT3 - the initial cross section input

opt ion

.

IPT4 - the units input option.

IPT5 - the loading components or designa-

tion input option.

IPT6 - the optimization input option.

[PT7 - the design cycle input option.

10]

I P'1'8 the materia] input option.

[PT9 - the deflection input option.

1IT10 - the output option.

[SAVE (80) - the rolled section number for each

sub clement of the present optimum

des ign g i rder

.

1ST - the identification number of the

rolled section being designed.

ISTEEL(80) - the moment of inertia of a sub-

element for the steel section.

IX (18) the moment of inertia about the

x-x axis for the rolled sections

used in the design program.

IV (18) - the moment of inertia about the

y-y axis for the rolled sections

used in the program.

JPT3 - the composite section variable.

Note: If the design is composite then JPT3

is less than 9 and if the design is

noncomposite then JPT3 is greater

than 9.

KOP fin) - the location oi' the crossover

points for a given influence line.

Li) IS - the live load designation.

LENGTH the total length of the girder.

102

LPCM (10)

MAXOL

M I NOL

MN

MR

NA

NAME (18)

NCS

NCY

NCYC

NDEF

NE

NOS (8 0)

N.S

NSECT (18)

the boundary points of the negative

moment regions along the girder.

the point which is the maximum

ordinate of a given influence line.

the point which is the minimum

ordinate of a given influence line.

the number of spans along the

design problem girder.

the modular ratio.

the total number of analysis

points along the girder.

the AiSC name of the rolled sections

used in the design program.

the number of shear connectors per

row.

the design cycle counter.

the maximum number of design

cycles required.

the total number of points at

which the deflections are required.

the total number of subclements

.

the NSECT number of the rolled

section in each subelement.

the total number of supports.

the identification number of the

rolled sections used in the design

program

.

lo:

01

I L

PERCEN

PLATH (80,2)

(I,D- •

(1,2)

PLL

PLTSAV(80,2)

PLWID (80,2)

(1,1)

(1,2)

PL WSAY (8 0,2)

PRO] 1( 5 )

I 1 )

(2)

(3 l

RIL I 5 ,S] ,3)

the Impact option.

the interstate loading option.

the allowable percentage change

in the critical design moment.

the. plate thicknesses for each

subelement

.

the thickness of the top cover

plate in subelement I

.

the thickness of the bottom plate

in subelement I

.

the live load factor.

the PLATH array for the current

optimum design.

the plate width for each subelement

the width of the top cover plate

in subelement I

.

the width of the bottom cover

plate in subelement 1.

the PLWID array for the current

optimum design.

t h e steel properties u s e d in the

d e s i g n .

the allowable bending stress.

the allowable shear stress.

the steel yield point stress.

the reaction influence line array.

104

(I,J,1) - the reaction at support 1, with

the unit load at point .1, for the

steel section.

(I, J, 2) - the reaction at support T, with

the unit load at point J, for the

low modulus composite section.

(I, J, 5) - the reaction at support I, with

the unit load at point .T , for the

high modulus composite section.

RATIO - the ratio of the minimum stress

to the maximum stress used in the

fatigue calculations.

SAREA (18) - the area of the rolled sections

used in the design program.

SAVE (12,6,2)- the cover plate array (COVPL) for

the current optimum design.

SDL - the superimposed dead load.

SLABA - the area of the concrete slab

which acts compositely with the

steel section.

SLABTH - the thickness o\~ the concrete slab.

SLABWD - the effective width of the concrete

slab.

SLABWT - the weight of the concrete deck

which is carried by the g i r d e r

.

SLL - the sidewalk live load.

105

SMAX - the maximum stress at a point used

to determine RATIO.

SMIN - the minimum stress at a point used

to determine RATIO.

STORE (10) - the loadings for a given influence

line.

STRESS (81 ,4,2)- the stress array.

(1,1,1) - the bottom steel stress at point I.

(1,2,1) - the top steel stress at point I.

(1,3,1) - the concrete stress at point I.

(1.4.1) - the shear stress at point I.

(1.1.2) - the bottom stress indicator.

(1,2,2) - the top stress indicator.

(1,5,2) - the concrete stress indicator.

(1,4,2) - the shear stress indicator.

Note: If the indicator is 1.0, the stress

is greater than the allowable and

if the indicator is 0.0, the stress

is less than the allowable.

SUBLEN(80) - the subelement length array.

TCOST - the total cost of a girder design.

TDS - the total design stress at a point.

TITLE (36) - the problem title array.

TRLO (10) - the truck load components.

(1) - the first axle load.

( 2

)

- the second axle load.

1 Ob

(5) - the third axle load.

(4) - the spacing between the first and

second axles .

(5) - the minimum spacing between the

second and the third axles.

(6) - the maximum spacing between the

second and third axles.

(7) - the superimposed dead load.

(8) - the weight of the steel girder.

(9) - the impact option.

(10) - the weight of the slab carried by

the steel girder.

TSWID1 - the transformed slab width for the

low modulus composite section.

TSWID2 - the transformed slab width for the

high modulus composite section.

UNLO (9) - the uniform load components.

(1) - the equivalent uniform live load.

(2) - the concentrated load for moment.

(3) - the concentrated load for shear.

(4) - the superimposed dead load.

(5) - the weight of the steel girder.

( 6

)

- the interstate concentrated load.

(7) - the sidewalk live load.

(X) - the impact option.

(9) - the weight of the slab carried by

the steel gird c r

.

107

IVEBTH (18) - the thickness of the webs for the

rolled sections used in the design

program

.

IVMIN - the weight of the present optimum

design .

WTOT - the total weight of a given girder

design

.

APPENDIX C

108

APPENDIX C

PROGRAM DATA

READ IN Subroutine

The READIN subroutine is used to provide the program

with all of the necessary data to solve a given problem.

The routine docs not, however, read the data cards which

pertain to the section properties of the wide-flange rolled

sections. These cards are read by the main program so that,

if multiple problems are being solved with one run of the

program, the section properties are read only once. The

order of operations used in the READIN subroutine are

described below. After the description, the method of data

input is explained and a few samples of input data are

presented

.

Step 1

All of the arrays involved in the subroutine arc

zeroed and prepared for the given problem.

Step 2

The title cards are read and placed in the TITLE array.

Two cards must be present for the title description. If a

title is not desired or if the title is only on one card,

then blank cards must appear in this position.

1 9

Step 3

The input parameter card, containing the input param-

eters IPT1 to IPT10, is read. These parameters are defined

in Appendix B.

Step 4

The subroutine prints out some specified heading

information if the output parameter, IPT10, dictates this

operation

.

Step 5

The lengths of the individual spans are read and used

to determine the total length of the girder and the number

of supports

.

Step 6

Depending on the value of the subelement input option,

IPT1, the subelement information is either read from cards

or determined by the program. The quantities included in

the subelement information are the number of elements per

span, the analysis point coordinates, the support point

indices, and the lengths of the subelcments. If the design

is continuous and composite, the limits of the negative

moment regions arc tentatively defined as the two elements

on either side of the interior supports. These limits are

then stored in the LPCM array.

1 ]

Step 7

The data determined in steps 5 and 6 are printed out

and converted to inches if required. This conversion is

necessary because the program operates in the units of kips

and inches

.

Step 8

The steel table information for the wide-flange rolled

sections used in the program is printed if the output param-

eter, IPT10, indicates that this 'information is desired.

Step 9

If the design is composite, then the composite section

data are read and printed. The composite action parameter,

JPT3 , is calculated. If the design is noncomposi te , step 9

is omitted.

Step 10

Depending on the value of IPT3, the initial cross

section for each subelemcnt along the girder is either read

from cards or determined by the subroutine. With the

sections specified for each subelemcnt, SFMIC is called to

evaluate the properties for each clement. These properties

are then printed in tabular form if required by the output

parameter

.

Step 11

The required loading conditions desired in the problem

are read from cards. The form of the input depends on the

1 1 ]

value of the loading parameter, IPT2, and the value of the

loading components parameter, JPT5. The TRLO and the II.M

arrays are converted to the units of inches, if necessary,

and are then printed in the output.

Step 12

The properties of the steel used in the problem are

either read or determined by the routine. If the steel

used has the ASTM designation of A36, then the PROP array

is completely prepared by the subroutine. For all other

steels, the yield point stress is read from a data card and

the properties are calculated. The value of the modulus of

elasticity for the steel is set at 29,000 ksi.

Step 13

The allowable compression stress for the concrete is

computed using the 28-day concrete strength read in with

the composite section data. All of the steel and concrete

allowable stress properties are then listed in the output.

Step 14

If the optimization is based 'on cost, the unit cost

data card is read. This card is not read if the optimization

is based on weight. The COST array is then added to the

output

.

Step 15

The method of terminating the design program is either

read or determined by the routine. The method which is

I ]

.

employed depends on the value of the design cycle parameter,

[PT7. This termination method is then described in the

output.

Step 16

The points at which the deflections are required are

either read or determined by the subroutine. The form of

this input depends on the value of the deflection parameter,

IPT9. The points at which the deflections will be calculated

are then listed in the output.

This completes the READ IN subroutine. Once the data

have been completely determined, the control of the program

is returned to the main program and the design and optimiza-

tion of the desired problem is started.

L13

Method of Data Input

The method of data input for this program resembles

the method used in the plate girder design program, GAD-I.

It should be noted, however, that although the methods are

similar, the data cards cannot be interchanged. The reason

is that some of the data have a different meaning and

purpose in this program. The designer should note these

differences and take the appropriate precautions when work-

ing with both programs. The following is a description of

the method of data input.

I. Card Set 1 - Title Cards

A. The card set consists of two cards with

the first 72 columns used on each card.

Format (18A4/18A4)

II. Card Set 2 - Input Parameter Card

A. The card set consists of one card with

the following integer information:

1 . IPT1 - Subelement Information

- 10 elements per span.

1 - Head in the coordinates.

2 - Read in the number of elements

per span.

1 1'T 2 - Type of Loading Required

- Lane, Interstate, Sidewalk and

Truck L oad ins

.

1 14

1 - Lane, Interstate and Sidewalk

Loading

.

2 - Truck Loading.

IPT3 - Initial Girder Section

- W53xll8 used with composite

des ign

.

1 - Read the uniform section with

composite design.

2 - Read the section for each sub-

element with composite design.

10 - W35*118 used with noncomposite

des ign

.

11 - Read the uniform section with

noncomposite design.

12 - Read the section for each sub-

element with noncomposite design

IPT4 - Units of Data

- Units of inches.

1 - Units of feet.

IPT5 - Loading Components/Designation

- Read in the load factor and

the truck designation.

1 - Read in all the load components.

IPT6 - Type of Optimization

- Optimize based on cost.

1 - Optimize based on weight.

1 1 ;

10

[PT7 - Design Cycles

- Use only one cycle of design.

1 - Base the design on the percentage

change in the critical moment.

2 - Read in the maximum number of

des i gn cycles .

IPT8 - Steel Used in the Design

- Use A56 steel .

1 - Read the required yield point

stress

.

1PT9 - Deflections Required

- Determine the deflections at

the span centerlines.

1 - Determine the deflections at

the 0.2, 0.5, and 0.8 points in

each span.

2 - Read in the analysis points at

which the deflections are

requi red

.

1PT10 - Output Parameter

- Data and the final solution.

1 - Level plus each cycle solution.

2 - Level 1 plus each girder design.

5 - Level 2 plus additional output.

4 - Debugging output.

ormat (1015)

! K,

III. Card Set 3 - Span Length Card

A. The card set consists of one card which

contains the lengths of the spans.

Format (4F10.4)

IV. Card Set 4 - Subelement Information

A. If IPT1 = 0, card set 4 is not required.

B. If IPT1 = 1, the card set consists of the

following cards:

1

.

One card containing the total number

of analysis points.

Format (110)

2. The necessary number of cards, each

containing seven coordinates, to com-

pletely define the total number of

analysis points.

Format (7F10.2)

C. If IPT1 = 2, read the number of elements

for each span.

Format (4110)

V. Card Set 5 - Composite Section Requirements

A. If IPT3 = 10, 11, or 12, card set 5 is

not required.

B. If IPT3 = 0, 1, or 3, read the following

composite section requirements from one

card :

1. Effective width o^ the slab, in.

i i;

2. Thickness of si ah, in.

5. Modular Ratio as a floating point

number

.

4. 28 -day concrete strength, psi.

5. Slab steel area, sq . in.

6. Value of the haunch, in.

Format (5F1 . 2 , Fl . 4 J

VI. Card Set 6 - Initial Cross Sections

A. If IPT3 = or 10, card set 6 is not

requi red

.

B. If IPT5 = 1 or 11, the card set consists

of one card containing the following values

1. ID number of the rolled section.

2. Width of top cover plate, in.

3. Thickness of top cover plate, in.

4. Width of the bottom cover plate, in.

5. Thickness of the bottom cover plate, in

Format (I10,4F10.4)

C. If IPT5 = 2 or 12, the card sets consist

of one card for each subelement. The

following values are contained on each

card :

1. IP number of the rolled section.

2

.

W i d th of to p cover plate, in.

3. Thickness of top cover plate, in.

4. Width oi~ the bottom plate, in.

1 IS

5. Thickness of the bottom plate, in.

Format ( 1 10 ,4F 10 . 4

)

VII. Card Set 7 - Load Information

A. If IPT5 = 0, the card set consists of one

card containing the following values:

1. Load designation-

a. Use one of the five (5) standard

AASHO -designations , i.e., 1110,

HIS, JI20, HS15 or IIS20.

b. This input must be right

justified in the first 4 columns.

2. Load factor in decimal form.

3. Weight of the slab carried by the

girder

.

4. The superimposed dead load acting on

the low modulus concrete section.

5. Dead weight of the girder.

6. Sidewalk live load.

7 . Impact option .

a. Use 0.0 if impact is included.

b. Use 1.0 if impact is to be

excluded from the design.

S. Interstate , loading option.

a. Use 0.0 if loading is to he

cons i do red .

1 1 9

b. Use 1.0 if loading is excluded.

Format (A4 , F6 . 3 , 6F1 . 4 J

If [PT5 = 1 and IPT2 = 0, the card set

consists of two cards. The first card

contains the truck loading components

(TRLO) and the second card contains the

uniform load components (UNLO)

.

1

.

Truck load components

.

a. First axle load in kips.

b. Second axle load in kips.

c. Third axle load in kips.

d. Spacing of the first two axles.

e. Minimum spacing between the

rear axles.

f. Maximum spacing between the

rear axles.

g. Superimposed dead load.

h. Girder dead weight.

i . Impact opt ion

.

i . Weight of slab

.

Format (10F7.3)

2. Uniform load components.

a. Uniform lane load.

b. Concentrated load for moment.

c. Concentrated load for shear.

d. Superimposed dead load.

120

c. Girder dead weight.

f. Interstate concentrated load.

g. Sidewalk live load,

h . Impact opt i on

.

i. Weight of slab.

Format (9F8.4)

C. If IPTS = 1 and IPT2 = 1, the card set

consists of one card containing the lane

loading components shown above.

D. If IPT5 = 1 and IPT2 = 2, the card set

consists of one card containing the truck

loading components shown above.

VIII. Card Set S - Material Properties

A. If IPTS = 0, card set 8 is not required.

B. If IPTS = 1, the card set consists of one

card containing the yield point stress of

the steel used in the problem. Up to

4 percent over stress can be programmed by

increasing the yield point stress by the

desired overstress percentage.

IX. Card Set 9 - Optimization Information

A. If IPT6 = 0, the card set consists of one

card containing the following values:

1. Rolled section cost, S/lb.

2 . Cover plate cost, $ / 1 b

.

5. lie;) ring stiffener cost, $/lb.

1 2]

4. Shear connector cost, $/lb.

5. Connector installation cost, $/ea.

6. Fixed weld cost, $/weld.

7. Weld material cost, $/cu. in.

8. Yield length cost, S/in.

Format (9F8.2)

B. If IPT6 = 1, card set 9 is not required.

X. Card Set 10 - Design Cycle Information

A. If IPT7 = 0, card set 10 is not required.

B. If IPT7 = 1, the card set consists of one

card containing the following values:

1. Maximum number of cycles.

2. Allowable percentage change in the

critical moment.

Format (I10,F10.2)

C. If IPT7 = 2, the card set consists of one

card containing the number of design

cycles desired.

Format (HO) -

XI. Card Set 11 - Deflection Information

A. If [PT9 = 0, card set 11 is not required.

B.. If IPT9 = 1, card set 11 is not required.

C. If 1PT9 = 2, the card set consists of one

card containing the following:

1. Number of points at which the deflec-

tions are required. (Max. = 20)

122

2. Analysis point numbers of the

deflection points.

Format (.110,20131

Note: When preparing the data, all integer

values should be right justified and all

floating point numbers should be typed

according to their respective formats.

All floating point fields are large

enough to include a punched decimal

point and this is recommended to avoid

confus ion

.

123

Input Data Samples

Problem No . 1

Design a girder with three spans, each having a length

of 70 ft. Design the girder for HS20 loading with a load

factor of one axle per girder. Also design for impact

loading and interstate loading. Use A36 steel in the design,

and base the design on ten elements per span.

Design the girder compositely with the deck slab. Use

concrete with a 28-day strength of 5,000 psi and a modular

ratio of 8 for the bridge deck. The composite section

properties include an effective slab width of 84 in., a

slab thickness of 7 in., a slab steel area of 1.94 sq. in.,

and a haunch depth of 1.5 in.

The optimization is based on cost. The unit cost per

pound of steel for all steel elements is 10 cents. The

fixed weld cost is $30.00. The weld material costs $5.00

per cubic inch of material and there is no charge per length

of weld. The installation cost for the shear connectors is

50 cents .

Design the girder until the change in the critical

moment is less than one-half percent. Determine the deflec-

tions at the centerline of each span and use the debugging

output option.

The input data for this problem are shown in Table C-l.

24

osz;

Eot—

i

fto

ft

O<D

i—

I

ft£03

CO

(h

Oft

03

+->

03

Q

3ft

uo1—1

03

H

oo

oo

i—

1

t~- LO oCT> . .

r-\ r—

1

CD

n CDto CDrj

tO

Uft >=* •* o< Ol .

oI—

1

o CD'

OO

K"\ O o LO CDft o H LOft . • .

W oO oft H o

CO ft r-o

ftft H CD'

<f 00 i—

1

U ft o CDO oo

CD •

<C . • «

H Z CD CO< < f-.

Q ftCO

ftft

oO

ft I—

1

CD o tn LO[Tj O o t~~- *

H i—

I

o

ft

oor--

r-~

oI—

1

ft o O o CD LOi—

i

CD f—

,

•

ft • *i—

1

CDcc

oor - co

CDCN1

CO

i—

(

T3

Id ° ^H cnj ro «d- LO \0 r-. cc'J *-

T3(h -P

03 Q I—

1

r ) to LO i - o CDU CO ^H

1 25

Problem No . 2

Design a noncomposite girder for a 70 ft simple-span

bridge. Design the girder in A36 steel and for an 1120 AASHO

loading. Use a load factor of 75 percent and do not include

impact in the design. Read in the coordinates of fifteen

analysis points.

Optimize the girder design based on weight and use a

total of three design cycles. Determine the deflections at

all points and print the solution.

The input data for this problem are shown in Table C-2.

! 26

o

<L>

i—

I

Xo

03

•M03

aoiH

E03

in

uoMh

03

M03

a

ft

u

o CD CD

o LO Oto \o

t—

1

f» o CD OCT> • • .

i—

1

LO CD*JD

i—

I

to LOOsl tH

in H"U •—

i

C^ o o CD O<tj • • to

IS

CM

oCM

LOLO

o t—l

cmi—i

r—i

rH<£.

W o o CD LO CDJ • 1—

t

i—

I

PQ LO O •

O r—

I

LO CT.

fVc_ CN

CO COa Hen CO

< W r^

u H i—

1

O o oCM

< 2 CD LO • v£>

h < r—

1

«*

< a,G CO

pqxi

O LO

S ^H CD CD toi—

i

r~- toCO

o

pq

CDrH

LO CD

r—i

t_3 O cd lo cd CD O LO tO LO

c O i—

l

r>. rH1—

1

O LO CDrv- o to r^CC

i—

1

r-.

or )

T3i-H _5S H o-o to Tt LO O r~- co cr. o i—i

—i —j

T3f-i +->

o3 d) i—

1

CnJ ro -r t-- OC_) co i—l i—

i

APPENDIX D

APPENDIX D

COMPUTER PROGRAM LISTING

127

000003

000003000003000003000003000003000003O00003000003000003000003000003000003000003000003000003000003000003000003000003

00000300000500000*

00003*

00003*000037

0000*000004600005400006?000070000076

POO 1 Oft

000106000107

oooi l n

OOOl 1?OOOl 1 3

000123

0001?3

PRO

COM1DAF?1LC3SLA*TM()5FC.6C0SCOlCOMCOMCOMCOMCO*COMCO"i

COMCOMCOMCOMCOMCOMRE*OHDIMINTINT

DONSF

1000 RE«1DAF

1 001 FO*

900 CAlSMF

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HO WMICMIIF

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iMN DES]ION NAME (

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10N/ONF /JlON/IWO/L10N/ IMHtElON/FOWH/iGN/MX/FM&N/SFVEN•IbN/K I I'M r

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iLN/TEN/H40N/0/IOEM(jN/A/li>A

lON/H/SMF•1LN/F /IP f

1LN/F/IP1L IX.IY.TKNS10N Tl

>: NSION Im

rGFK TYPEeGen eps,-It AD IM I

ICOO I =

CI (I) = I

•J (5.1P01(I) t IX ( I

)

1AT (3X,ACALL ON H

)UT THF w

RFADINfC = 0.0>F TEHMINE(ABSIPKOPlARSIPROPIABS (PROP(AHSIPHOP(AHSlPWOf(ABS(PRUPCALL ON A

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= l

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"^ dhi,lit TFUMINf.L UNIFST

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T T TL F

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P.')TINF TO RFAn ANO Thf^K nATA AFTEt ZEROINGICES FOR A MFW P"i'Bi prt

FU FOR FATim/F TALCM ATTOMSI3)-36i) .LT. ) .45 ) Fll = so.(3) -«»0.) .LT. ?.4l ) Fll 6=,(3) -4?. ) .IT. 1 ,7(1 I FU = 60,(3) -45. ) .L T. 1 .M.5 ) FU = 6n

.

(31-60.) .LT. ? . ^ ) fll = 7S

,

( 1) -^5. ) .LT. ?.?1 ) Fll = 7P

.

NAL TO AMALYS17E THE fiT»r>FR

PFSIliN rrCl4QR,QQR.F. 2) wsiTF?PX . 1 Q-HFGI'iTHF UNIFORM

(6.R1) NCYTMF .1^.16" CYCI F

SECTION nFMf.Mr r OF SIG'V/)

MA N I

MA N 2MA n 3

MA N 4

MA N 5Ml N 6

.MA N 7

.Ml <t fl

M\ N 9MA N 10MA N 11MA N 1?MA N 13MA N 14MA N 15MA N 16MA N 17MA N 1«MO N 19MA N 20MA N 21MA N 22MA H 23MA N 24MA N 25MA IN 26MA N 27MA N ?BMA N 29MA N 30MA N 31

1 MA N 32MA N 33MA N 3*MA N 35MA N 36MA N 37MA N 3BMl N 39MA N 40MA N 41MA N 42MA N 43MA N 44MA N 45MA N 46MA N 47MA N 4RMA IM Z<J

MA (J 50MA N 51MA N 52MA fv 53MA N 54MA N 55MA [N 56

128

00013a IB •

0001?* IF UC it

000130 00 10

"00131 isr «

00013? DO 10

C • It

000134 1030 NOSIK0001*0 CALL0001*1 IF U0001*3 CALL0001*4 IF I I

1ILC )N

c l)fc

00016S CALL000166 CALL

c • It

000167 CALLc Of

000170 CALL1BEAH)

r of

000203 CALLr of

000?0* CALLr >,1

000?OS CALL000?1S IF ( 1

000??n CALLICO'M,

000?3h CALL000?4|) rt«I It

000?** 7 10 FO**Anoo?*» CALLooo?*^ CALLnoo?si *H| If

000?61 1518 FCH'iA1F1S.2

O00?61 IF ( 1

non?6S *R] ff

00"?''? 1S»? FO-*^A

P0n?7? GO 10

000?73 60 50 wMI Ik

000301 15 '? f r)4 aA

000301 1'0 C '"> * M

000301 10 <0 CO Ml I

r HL

000303 00 I

00030S 1 NOS< 1

O0O311 IS'I =

000313 DO '

OOO^l 4 DO -»

00 13 i s PL* l >

noo3?? ? PL* II'

000311 00 1

3 11 DO <

0001 14 DO 4

OOf'33- 3 COV-I

1ST • 1

« .Eo. 10) RO Tn lnnoGIN THE DESIGN |

OOP fon THE LIGHT" SFrTlOwS?0 JJ = IB. IBJJ

30 K =1 . NF

TEBMINE ThF S'RfLFmFnT PLATF Tm TC*NFSSe «

) * I STTHOESSwlT ,EO. 11 GO to m?nSFMKp Tlo .GT. ?) CALL PPSEr (NE,N0«;,M4MF. M

I'TH.-'laTm, ISTcFL.CS,

»CLt IMCON.rH.nnH.SllBLENtO.NCY)SIGN THF CnuE» PI ATFSCPOFSSFMICSIGN THF wFl DSCP*DtSSIGN THF STTEFFMEWSSTIFF(loSP,MS.OFS«FA.MOS»FLTH,F|.WTn.".FDTH,r\FPTH,Pi,'On.EM f

SIGN THF ShfaO rONNFCTOB SParT»>r-,

COCOESTF.MMINE THF WFICHT AN" COSTOHJFCTOKI The OfSTGM TF TT IS THE PRFSFMT OPTtMIIMKEtP(NE.N'OS,PLATHtP|.»/Tn,C0\/Pl , tmim.wmt' . TPT6)PT10 .Lt . II GO to io?nPRSFC(NF ,no«;,nia'-iE.pi wID.PLaTh, i^TfFi .re. TITON.CI t IH'-on.CH.SDHLf N.n.NCYIphcov icovpi )

(h.700)T (1H1)PHSTTF (NS.RFAP)PHCQN (NS.CDNSP»NCS1<h.lSia> UTOT, TCOST

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)

PT6 .GT. .SI r-o TO fcnOn

(6t 1 bH?| TMlNI (

1 «0. 30

X

,7hCwtn = ."M?.?!10?P(6.3SB?) WMIN

T I 1 ho. in x , 7h*«in = .M?.?)nufNIlF

AC' 1 HE OPTIMUM DFSTGN IN THF •lOHKI-ir. ,-ppj.';

I = 1 • N«I = ! SAv/M T I

N >s ( 1 TT >

I = 1 . NF

J = 1 . ->

( I »-)) = PLTSAW ( T • Jl

( I . J I = PLK«A|/ ( I , J|

I = I . 1?

1=1.6« = i . :•>

I I , l, i\ I = IjVFIIi.IiK)

MA t'l S7MA :n SBMA N s<»

MA N 60MA N 61MA ii 6?MA N 6*MA N 63M) N 6SMA '1 66MA N 67MA N *HM4 N 6»MA N 70MA N 71MA N 7?MA N 73MA N 74M A N 7SM4 N 76MA N 77Ma IN 7fl

MA N 70MA N BOMA [N BlMA [N B?MA N B3MA N B4MA M mMA N B6MA N B7MA , BBMA N fl<?

Ma N onNA N 01M;l N ov>

MA N 03MA

1 04MA N OSMA N OAMA •'* 07MA N OBHA 'Y 00Ml N ionMA N miM A r. l n?M \ \ l niM 1 N i n**

. N ins^ N 1 Oft

MA h 107M "• N 1 OBMA N I noM A 'j

I 1

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MA J l 1 l

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129

C003S^ COLL S K m I

C

00035*. IF (MN .EU. |)

C ifTF^wlNE 1

000360 IF HPT? .LT.000366 IF (IPT? .Nt.

C wEANALT^E T

000373 CALL ANAL000374 GO ro ?no000375 100 CONI INIJK

c *EanaltZE t

00037S IF UPT3 .LT."00*00 OL') = T«L<1(7)000*03 IF HPT? .EO.

000*05 IF (ULU.I T.HNL000*1* GO 10 41

000*1

5

40 OLU * I 'LO (Hi

000*17 If (IPT? ,EO.001*2) IF (010 .LT. U

ooo*?* 41 IF (IPT? .LT.000*3* IF (IPT? .NE.001**1 IF (JPT3 .LT.ooo*** DLN = T«LO<7)000**7 IF (IPT? .EQ.001*51 IF (DLN.LT.UNl000460 GO IL' 4 3

O00»f>l 4? OLn - THL01H)000*63 IF (IPT? .EU.100*65 IF (UN .LT. 1

000*7? 43 Fl = OLN / mr000*7* DO »* I r 1 , '

000*7* 44 OE*><< "( I . 1 ) =

001503 DEs«t » ( 1 .1 ) =

000^0* 0E>>Ht*(?tH -

000505 [fl a ? o NA -

000507 DO »i- I = 1. I

00051) 45 de>.3M( i,i) = n

O00516 IF (IPTIO .E(v.

ooo51 7 w«l ft (h,70>0005?3 7C FO-'AT (1*1,1°0005?3 DO n I = 1.

1005?S 71 «R| It (6.7?) I

00054S 7? F(H«*T (I^.4((-0005*5 wRflt (6,73)00055n 73 FO««AT (1M0,17000550 00 '* I = 1 1 N00055? 74 *R| It (6,7?) I

000*7? Rl 1 t (6. 7M00057s 75 F")« <AT ( l»t. 1 *

000575 U -- ? • NA -

000577 DO #6 I = 1 • i"

c it TFpmTN- A

000601 76 *SHt (*,7?) 1

O0O6?i ?oO CA L . 5TRCHKr lESIGN 1»IF

"0o*?? Ctl. STIFFIIOtIHEA-I)

r ntSlKN ^r^^

I0 nh 35 CAl . Cu'. r't S

go TO ioomf nf< STFFL nFAO «F1'.hT?) UNLn(S) = WIN / [| FNGTh • .no^.t1) T3 L n(«i « mmIn / hfwgTw • 'OO".)nf 5TRnCT.iRE IF IT 15 rOwTt-ii«.iS

HF SMPLF 5PAN PfrlPLFM9> GO TO al

TH11(8| . TH L O(l0)?) G" TO 4 1

0(4) JNLO(S) »UNLO(9l ) ni le |4I| -.4l»iiNL (5)* iHLO(<*(

T«LO(10)?) GO TO 4 1

NLO (51 .UNI 1 (9) ) DLO = UNLOI^l . II' I 0(9)?) UNLH(5> = MM IN / IiFNGTh • iO0«.l1) T,RLO< B ) « u lN / (I FNGTH • .OO'-.I

9) GT TO 4?TflLTlR) TP| 0( 101

?) GO TO 430(4)* JNLOI5) »DNL 0(9)1 m_*s'lMl "> 1*1 »HNLO(5) »"NL0<9)

TKLO(IO)?) GO TO 4 3

Ntn(5) • iiNLO(Ql) DIN a ,IU(0 ( r, . iiN|Oi9)

PFS*n*, j,, ) o fi

PF5P.FA (1,1) •> FlDFSRFA (?,) I • Fl

?

P

f SSm( 1,1) • F]

0) GO TO ?0O

hfiF5I3N PFACTinNS. .. //)S

tOFSPEA ( I . 1 ) ,r>F5PFA l I ,?) ,nrSPF f I I . 3) .HFSOF r ( I .4)

I*. 4,3,)

)

hinF5I^»i MOMfNTS ...//!A

,nF5«OM ( r , i i ,r)F5M()H| T.?) ,nr = M-.. ( j , 31 ,tfSmiv«( I ,»)

hriFSTV <;-fa-s. . .//I?

J

IL OF thF STPFSSES,(1FSSH( I,] ) , IFsSm ( I ,?| , nrssn , , , n . tESSmi | ,a)

STTFFFmcHSp ,' S.^fSRF/i.NOS* FLTh.FI *Tr, , . r r„, FPT-l.PnOo.FH,

C -F.v MNTrfl" SPACING

MA N 15M» N 16N« N 17MJ N 1»MA N 1<»

Ma N ?0MA N ?1MA N ??MA N ?3Ma N ?*M4 . ?5MA N ?6MA N ?7Ml N ?«MA N ?9MA N 30M.-. N 31M/ N 3?MJ N 33«J N 3*MA N 35MA N 36MA N 37M4 N 3RMA N 39M/l N *0MA '. *1MA [N ft?

MA N *3MA \ *4MA N 45Ml ri 46MA N 7

MA N 4Hhd IN. 49MA N- 50MA N 51MA *?•„ N 53MA • 4 5»n\ t: 5S

u 56MA . 57M> ' SSH 1 .

SQ"•. M 60v a 61HA 6?MA . 63rl. *4

• 66m; 6SM *

. 67M I 6»HA > -

• 70

71

. 77

! !

00 0IS3 A

000637000640

00065700066100066100066500067000067400070100070100070?000710000710000710

00071000071?00071400071500071*0007170007?30007?700074)O0074=i00075000075?000753000754

000756000757

000760000761

00076?

000763

000776

000777

001000

00100100100?

00 10?10010?!ooio?=>0010P7001035

1

1

1015

16601

?0

?5

CAIF

CAICOCAC*CACAIFWRFO60MRFOCOCO

IF

IF

NC<GOIF

01IFIF

PIIF

IF

NClGOI S 1

CAlCAL

CALCAL

CAL'.

CA1BE

IXA-<

i)

CALI

CA

CA

CACA

ICOCACACACAIF

ETF.HMOHJFIPT10PRSF

iSUfll

PRCt)PHSTPRSTPRCC)

IPT6t (6.

AT ( 1

C 16E (h.AT II

1NUF1NUFETERMIPT7NCY= NCY

BOIPT7OESMm .rMil .F

AHS(•-1 .L

ncy= NCYU Bu= NOSF TEHMTHI>F

SFMI{ SIGNCPHESFMI

ESIGNCPwi

ESICSNSTIF

)

ESIGNco^n

t termOHJF

ALCULSTkC

ALCULOFFLPR->E

,SlHLPRCOPRSTPwSTPRr.'O

IPT6

1 Nt IMF «FCT

F'J, 1 GOC (NF.NOStNFN, 1 .NfY

I

V (COVPl )

H <strf<;s.

IF (NS«PE«'i (N^.rnNS. G 1 . .*.) G

11) 1 coslho, 1 o> , ?S'(

15) MruHO. 1 OX ,7?H

Irv-ir an > ens r

TO Ml 1

AMFtPLWin.PLATH.mTFFi .r^. li ton, ci . Im'on.ch,

Ma

)

1 TO 10

ThE cost of tmf '.iKnfr. s Fi?.?i

The «fight OF Thf muoFo . ,d?,;i

INE THF NF.NE. ?) GnFQ. NCYD

1

,Eu. ni go)M| 1 TT . 1 )

I. 1 ) HI a

(J.l . ano.(SMFFC - n

T, PFRCFN/EQ. UCT)

1

(ITT)INE THF SU5

C

ThF f tnals

C

Thf FINALI s

ThF F1MAIf ( IOSP.kjS.

XT OFSTGn. CYCLFTO 511

Gn To ?5

TO ?c,

OF 5mOM( t TT,3) . 0F9'<om , i TT .4 )

OFSmOMI I Tl , 1)

JPT3.GT.9t Dl = DFSMOMI TTT»1 > ofSmO"(|TT.?1 1 / oil

100.) GO TO ?SGn To ?s

ThfFSINt

CTATE

F THAI

THF FT

ThF F I

THF RFATEFCC (NF , NO<: , "I

FN.?, NCY I

V IC0VP| I

R I5TRF5S.IF [AiS.fiFA

N ( N 1- , ("ON 1;

GT. ,m

•IFLFTNT PLATE TH 1 r«NrS<;r<; FOR Tmf FIiaL DES

rnvFB pl aTes

wFl OS

STIFFFNFwSnFS UFA , N05, FLTH.FI WTO. 'r..TH,rFPTH. POO ", EM,

SHFaR CONNECTOR qpAFT'o

maL JFIGHT a-io rrsT

MAL STRFSSFS

lnIREO OFFLECT 10»'<:

amf,RL*IO,PlaTh, TSTFFi .re. li ton, ri .[HrON.CH,

MAI

P,NCSl-) TO ?a

Plj N 173MA N 1 74ma '. 17SMA M 1 7*Ml. N 177Mi N 17HMA N 179MA N 1 «0MA N 1 siMA N 1»?M0 N 1*3M4 N 1 R4MA N IBSMA N 1H6MA N 1R7MA N 1B8MA N 1P.9

MA N 190MA N 191MA M 19?MA N 19.3

MA N 194MA N 195MA N 19AMA N 197

) MA N 19S.

MA N 199MA N ?00MA N ?01MA N ?0?MA N ?03MA N ?04

IUNMA N ?nsMA N ?06MA N ?07MA N ?0flMA N ?09MA N ?10MA N ?11MA N ?1?M \ N ?13MA N ?14MA N ?15MA N ?16MA N '17MA ^. ?1RMA N ?19m N ??0MA N ??1MA N ???MA N ??3MA N ??4AH h ??5MA N ??6MA N ??7MA N ??HMA N jpoMA N 510

1 31

00103* URIll (6(111 TCOSl Mljrj :>31

O01043 GO lO ?q main ?3?(101044 ?H WRIIL <*.15> WlOT main 7-K\

00)05? ?q CO'JIINUF »«!'. i>3«

00105? WH [ I t (*,?1> Hijw ?35001O5* ?1 F0H4AT (1H1) MAIN ,>3is

O010SIS CALL PROEI- (NPEF.nFSnFF,i.i5.SPAN, IOFF , IPT"",".,, r>(7> > MAp. ^37

C -it TOKtj To Imp PFAnln 5TFP FOP a nrJ pnopi r M MAIN ?3«001066 GO 10 S> ;, maji., .>3q

001067 EN" »i\u P40

PROGRA'" LENGTH INCLUDING I/O BUFFFS500400*

UNUSFO rOwPIl FR SHuCF036500

FUNr I Il'p-i ALLOW <nu,rL«NGF .L p C M «I05P,|n , k|5 , PPid ,rOOW .ofSmO <,S"HLEN,IF *t U T)

C iflE'-HINFS THF »L| OwnRLF 5TRFSS AT A S"QFiFMf«'T000017 D

I

»fj 51 IN Li"

r

u( 1 o) 1 1 iSP i 5) .PROP ( 3) , ronoi ol > , shri FN i«i| ,

IDFs 11 'MM ,4 i

000017 IF IM .1.1, -.on GO TO *170000?1 ALL » = PHOPU )

0000?3 RE I i»- NO0 0?4 617 DO -,} i) 1 = l, in, ?

0000?* II « I

oooo?t if mi ,r,F« i.pcm(I) ,ano. ia ,lf. i.TMn.in fin to <-3i

000040 *?0 CONI INUF00004? 6?1 I * = L^CM (II)000045 I C = i t-C'M I I »1 )

00 004* DO >>30 I = it N5000050 IF IIOSP(T) ,fiF. in ,/inn. tOSP(I) .if. m r,« TO 6310000*? GO r(J 6 30

00006? *31 II) s IOSP (I)

000065 GO in 6 15

0000*5 *30 CON I I NUI

000070 *35 IF i I a .11. |M r." ro *4000007? D"i = C'lO'i t in -roo« i ioi - (0F5mum i ir , n 05MHI F' .in)/

1 (OF if on ( IC« I , 1 ) -nFsn v-i ( re, 1 ) )

00010* GO Id 6.1000107 *<.n D"-> - COOR ( I o) .(-(ins

( |k) - (iifumOmi | ti, , ) ocuui c- ,|n_i)|/I (Of ->f om ( I H- | ,1 )_nF5MOM( is, 1 1 1

0001?5 *4l IF (lillS/FLAMGf .fif. ?1 *. /SORT (PROP ( i) ) ) ;<< n ft/.?

000141 RAflO = DUS/Fl ANfiE

000 14? GO ro 643000 1 4?000150 *..3 PA-> = Pl'OHtl) - .I'-M'-H'l I • RAljo o »«T|n .. P >nP ( 3 ) ••? > c m

000157000165000 lh*O0''l*7 * c (' if ij.?»Pi5 ,(.f. p»np(iii in 10 *<.<,

1 7 3

*',? RA 1 H 1 = ? 1 *, /50BT (P-*nP (3)1ft,, 3 PAl = Pl.OPI) ) - . 1 6 7 1 7 <i 1 7 1 1

IF I r FT . E Q

.

l ) (Uj In * 5

n

ALL i* = PASRF f II N

ftcp IF '1 .?».'' .5 , (. F . p ~> '• p ; i i i •

AIL" = 1

.'<• » I- A «.

ali n 1

ALL" ?

ALLO 3

ALL" 4

ALL" 5

ALL" *

ALL i 7

ALL" rt

ALl O q

ALL " IdALL" l \

ALL" 1?

ALl." I 3

ALLC 14ALL" 15ALL " 1*ALL" 17Al.L" 1«ALL'i 10at i

n ?0ALU' ?l

»LL'i ??ALLo ?3ALLO ?4ALL" ?5A|

I1' ?*

ALL" ?7ALL" ?«AIL" ?q

ALL" 30ali n 11

Al.L" 1?

ALL'I 33

ALL 1 34

Al L" 35ALL" 3*

132

00017=. (iO Id 64Snool 7s bfi all >» = PHOH ( 1 )

000177 6^5 roMi iniii

000177 PFf ""'

000?01 EM)

ALLO 17ALLO 3«ALLO 3R

All II 40ALLO 41

SUHPRO'.OAm LFNLTHooo?3s

UNoSFri tUmpii fc S'HF042300

su

00000?

OOOOd?oooon?00000?00000?n o o ?

noooo?00000?ooooo?

noooo?nooooiooooosO0001

3

000014oooo?i0000??O0O03O00003?000034

O0003S00003*000043noons?nooc-nnoons400006?00007300007S

000076

SP1

=.'' 3

SCO

30M

enipa

I'll

tSL'.^ -1

'•FC

enCOCOCORED!

ININ

00(10

OFDODEnot >F

enM*l

IF

DOPIRlnonoR]

RIIF

60

r'OH<(iN

F ( ) H

C n I

I- ] (

ll]N"HON1 •*( i rl

* 41IN

<l 1(>N

AL I

<1r LSIK-

1

Irl.H

/f H

T( I!

V 1

•5 1CM

11. ?

-Hi A

">l 1

->-.M(

U I ] N= N(MMIt 1

1li0

I- c 1 ,

Llr'

.

Id (I

<<I0

I

J

•<F amai ft TESliIVFO'

AME I 1 |.

1 " I ] «)

) .CI («

L'nlH,) iNAtlMH1.4.IF /OPTwo/| Pf

1/HAIJ

/icy?ir.isiN 1)11I rPF

t PS,T1OUT TP

= I

.

= 1

1WFr-T

I .S

. 1 Y

01 .

MRF-ir,

. ?)

3, I

M

MCH

OESIflw REACTIONS! homf'Hs. AN" ShfaRsHOFpA :, FA(l t*),OFpTH(lH).FI.Hln(lL. 1 ,FirH(lH),w='HTH(\«).(I«).NSFC7(1H) ,NOS luni.l^lcrl | on

) , CS< HO 1 «

IHCOM(Bn) •CH(flO) tP| ATH(PO,-m ,P| » II) ( « . ? I . NF i

cooo(mi i

,

h ti is, pi ,i) , cr rs,B ( iFm.SpanU) , iosr isi .

|H,UU(«1 ) .SunLK'URrM i MS .UNI n|0| ,TRt 0< ] 0\ .RPOP(3),nFsMOM <«1 .4) pOFSRFA (Si*) .ncSS'idft?,*]pi ) n

F fi . lurON. THCOoI nM, Fi'M'iii

.Hrt.LFK.r.TH

Ml («i .3) . sTn< ( I ->) i I PCM iml

I IFF nt-SIr.N n q n A v c;

.1)

«1

,i

I = 1

I IPI

CMi.i. »

I)

1"

- 1

MF. 1 ) on io 3ir n

MINE lHF WFArTION INFLUFNCF IImF<; F..r TwF SMP|F sp 4NI =

I . NAl) = uF'"'.H - rTiiiii I /

ifMrsTM

) ) = l . n - «Tl. (1 , r « 1 1

[ = ?, 1

I = 1 . M'

II - HI I

I 1 . I. 1 I

1 ) = PI I. (?, J.l

)

• .ii. > > •; o to inn?I) 3

'i i<FAT ni 1FTFRMIMF THf r'V'TIwil'V'q iFArTION LINrSr

Oil I Ti-f DF \?TI<>»' I "IF IUF-ICF I IMF IF r llliPEn

ANAL 1

ANAL ?

ANAL 3

ANAL 4

ANAL s

ANAL 6

A 'HI. 7

AMAL A

ANAL 9

A'' AL 10ANAL 1

1

anal 1?AiV At 1 3

ANAL 1*ANAL ISANAI. 16ANAL 1 7

ANAL t«ANAL 1RANAL ?nANAL ?lANAL ??ANAI ?3Ar-lAL ?4ANAL ?=.

ANAI ?6AN«L ?7ANA| ?HAhjAt ?•)

ANAI 30A N H

1 31

ANA| 3?A JAl 3 !

ANA( 34

ANAI. 3SANAI 36ANAI 37ANAI 3MANAI 39ANAI 40ANAI. 4 1

L33

IF iIpII'i .LT.31 RO TO 110? a-.al 4?IF I JPT ) .(jr. 9) f,T TO 1003 ANAL 43WR I lb (f.. I 0) o) ANAL 44FO^iAT ( IHl ,4FX , ? MJracrilN INFL'>fMrP Ll* l(-//i AMftu 4500 I l 4 K = 1 . 1 AK'AL 46IF (K ,FU. I) hRTlF (6. 10501 ANAI 47IF If ,E0. S) »H?TF [fi.lnS]) ANAL 45

IF (iv ,60. U *R|IF (6,105?> ANAL 49F0-<1«T ( I .10, If > t ?'>-tJFACTnN I IMF FOB STFFl llfllic//] - ANAI SOFO-hat I 1 Ml i 30* ,4*-H-(r4rTinM I

Inf fo.j inw MnntiLUS COMPOsItF eCTION/ANAi. si

1/1 ANAL 52FOh i<i T ( ] m • jn» ,4""I9EaCT ION I I 'it FOB HIBH MOnnl.lJS CO-IPOSItF ACTION/ANAL 53

I/) ANAL 5400 I 1,41 J = 1 , >U ANAI ssWW I I F (~.|0\>3> Ci'lL ( T , J.KI . I = 1, -IS) • ANAL 56FOx«*T ( 3JX.5 (F 1 ?. w, ?A ) ) ANAL 57CO .1 1NIH . A'-AL 5«RO fO I I I.' ANAL 59WHI Ir (-,,1010) ANAL 60W>^ I I F ('• i 1 O')0) ANAL 61DO ^Uhd 1 = 1 , NS ANAL 6?RlLUtJt?) = RIL(I.J,1) ANAI 611) 1 1 I 1 , J . 3 1 = U 1 I I I , J , 1 ) ANAL 6400 I »»>0 J = 1 . 'I« ANAL 65dHjIt l'.ilO u>3> IP I I I T . I. 1 ) . I = 1, MSI AMAL 66.VH I II I

' . 1 Ot4 ) ANAL 67FO-MA! I lr(0,?OX ,43HThFHF IS NO COMPiSTTF Ar'tON IN ThE O^SIon.) ANAL 6fl

(iO l( |(I0P ANAL 69W»I It I 6, 1004 ) ANAL 70FOrflAI ( 1 ill .->•* ,T-*H-)FAC r ION INFLOEWF i.I'F Fn« 5 1 MP|. F RF*M//) ANAL 71

RO 4005. 1=1, MA ANAL 7?h^Ilf l'.,IO->3) (till I I.I.I). ) = 1. MSI ANAL 73IF | .ip f 1 .(,{. 91 H"»lTt (6,1(1^4) ANAI. 74

^I'lMl rjUI Thf LOAnlNR nFSr H IPlI0f. ANAL 75IF llPH.l .LT. 31 I31TF (6.hP00) ANAL 76FOrf<lAT I 1 Ml 1 ANAL 77IF (IPT|1 ..JF. 3) J3jTF (6.1(lHpt ANAL 7fl

FO11AT ( 1 hi , j nx ,T4-nisrf)IPTlON OF ANALYSTS i rSui TS,. ,/l 1 '. 39HCOI H^A'iAl 791

'I I - nt-AU I O/iI) ON sTFFl. SFfTION/n *,!flH<"ni "MN ? - POSITIVE lAnFANAi. "0-> L'i«!>/1 1 » , 3.)HC0l iim-i 1 . NFRftTlVF L.ANF I "AD/i 1 X , 39HC0LllM'i 4 - POSAN4L HI

3 I T I vf Ii.TMISTATF LOAnlNO/l 1 X,39HCOl'IMN c - kiFRATIVF ]"TrwSTATF LOA'.AI H24. Ai") ( <!/ 1 I * , 3 IhTUI UMN b . POsiTWF T-vur<

I OAn / ] | X , 31 MfOl MmN 7 - NFAnAl «3SGAUVf I "IC< [ OAO/1 1 Xi34rlC0(.UHN S - POMTr SrnEWAI K |.iin/n» ( ANAL 54bKHCOLLMN ) - IMFRATIVF SIOEhALK l.OAO/1 1 v , 66WC0I i imn 10 - supf>MMPi> Viai f>5

fSE'l" Ofc'AO LOAI1 ON LOW mho !(. JS CllrifkFTF up r r j -,..// , ANAi H6000?74 IF lIHlln ,NF. 11 I31TF (6.6001) A'.Al H7000301 ftOM FO-iinl ( 1 MO . 1 I X, JwOTSr-'TPf ION OF OFSIRN I o • r s , , . / / 1 1 X , AMI RH

I35HCU1.U'1N 1 - L1ADIMR n IF To Of nn | Onfl/1 1 *,' I HCOI H«M ? - lOAOINi, K4N*i H9d'Or' "iSlU'/t" itvr i 1A')/1 1 XiABhCOi.UM'1 3 • i lAritNq T'UF TO S '^FHl MPi'SF A MAi 9030 IFAII I OAD/

1 1 > . , I " i| ) in <. - LOAOTM'? FO" 'TrflT'vF I 1 VF i mn//| ...Al 91r 1.040 THE nunUi I ifi iFrtrF

iInn; anal 9?

0003(11 IF (IPT10 .jF. 3) «1PITF (6.1O901 anai 93000310 inwo Fim^l ( 1 N0i??H9FArT ION I

OAOINGS ///1 anai 9400031 n 00 I 100 I = 1 1 'i

c ','iAi 9S000 31? NP = I h xai. 9600O31 3 00 llnl K = 1 , NA 4NAI 97000^1 5 no I 101 J = 1 , 3 ANA| 9»00 31-, 1 1 1 1 I' l*,J) = 3[| ( t ,K , J, ANAL 99

0000770001 0?000105000110 101000011000011?000117noni?5000133 1 0^0000133 10^1

000133 105?

000133000135 1 041O00155 10^3000155 1 040000157000157 1003P00163000167000171000176 ?O'-000O?0?000?03 1 0^0000??1000??^ 1 0S4000??4000??S 3013000?3l 3 0" 4

000?3l000?33 30^5000?5i

l~

000?57 lo^?000?6S 6noo000?65000?74 1 nso

] 34

r call f'lt L nan s HUO'IT IMF anal 00000333 CALL LOAlM Til , 1R| 0, Mi n.SU-M "-J, IA, TPT?.t.F'"fiT i ,rnn«,-jp,4H-'FAC.NS. ANAL 01

i lo-a*. spun .store \ ANAL 02r -<r<IMl fH£ WFApnON LOADINGS \f Pol'UBr ANAL 03

000351 IF lIPTl" .SF. -\\ JRITF(6,1 H'J) IitSTOHFUJl JJ^l .|0| ANAI. 04000370 1103 FOR iAT 1 1 ii KH?.H ANAL 05

r »tT£l<MINE TMF DFSffiN REACTIONS ANAL 06000370 DFl-<l A ( I . 1 ) = STnHF ( l ] ANAL 0700037? 0F-.RI 0(1.3) = STPR^ (10| ANAL on000374 P^ « O.n ANAL 09OO0375 TR a 0,0 ANAL 1000037* DO 1100 M\ = ?, 7 ANAL 11

000377 IF |ST0><F(KK) ,r,r. 0.0) GO T(l Mino ANAL 13000401 RR s STOKE (VI sT'Hr (K-o ANAL 1 3

000403 IF iARS(WW) .11. Ill (50 TO 1 1 rt ANAL 1*00040* TR = AHMWK) ANAL 15000407 DFS <t A ( 1 .4) = PR ANAL 16

000410 GO 10 1100 ANAL 1100041

1

B1P0 RR 1 S TUrlF (rt > S P1RC (<K ) ANAL lfl

000*14 IF lAMStkRI ,| T. PR) 50 TO 1100 ANAL 19000417 PR - ArtMRK) ANAL 20000*20 DES-lt A ( I .2) » RR ANAL ?1

noo*?i 11^0 CO -J 1 INUF ANAL 22c PHlNl TriF DEStG'l RFArTt">MS IF RfriHTOFn ANAL 23

0004?*, if i iR

r

i u .fij. ni m to i oo ANAL 2*000427 wRl if (i-m 1 1 1 =>

)

ANAL 2500043? 1115 FOR-lAT I IMOilOHnFSlSN WF4CT IONS. .. //, ANAL 2600043? DO 1 1 1H I = 1 , MS ANAL 27000434 1 11H WH(fl (6,11201 T .OESnEA ( T , 1 ) .DFSRfA ( T .?) .OFs ,fa <l,i) .OFS'FAU ,4) ANAL 2*000454 1 1?0 F0(<AT ( I5t* (F ) 5,4 , 3X) ) ANAL 29000454 IF (JPT1 . GT. R) 4BITF(6 ( 601O) ANAL 3000046? 6010 FORiAT (lflX»S7MTHF ThIRO COLUMN IS 7FR1 p.Ff"> iSF DESIGN IS NON-COMPANAL 31

10SI IF .) ANAL 32r CUNSHMCT THF MOMFNT InFiiiENCF 1 TNFS ANAL 33

00046? 1 IF (IPTld ,GF. 11 wRiTF (6.1143) ANAL 34

000*7) 1 1*3 FOriAT ( 1h0» I^hmomc^t LOADINGS.,.//) ANAL 3S

O00471 DO 1130 1 *1 . 1 ANAL 36

000473 T 1 1_ ( 1 . I ) = 0.0 ANAL 37000476 1 130 T It. INA . 1 ) = 0.0 ANA|. 3«00050? DO 1140 1 = ?• NF ANAL 39000504 DO 1150 K = 1 . 3 ANAL 40000505 DO I 135 J = ?, nf ANAL *100050* WP s o.u ANAL 42000507 SP = 0.0 ANAL 43000510 IF (J .LT. II so " COOR(T) - COOR(J) ANAL 4400051* JJ ' 1 ANAL 45000515 11*! KK 3 tOSP(JJ) A ; 'AL 4600051 7 IF 11 ,CiT. *.K) wp = wP RILtJJiJiK] • (rOOD ,11 . cnofl IKifl 1 ANAL 4700053? IF (KK .67. 1) on TO 11*? ANAL 4B00053* JJ a JJ « 1 ANAL 49000537 GO (U 1

1

mI ANAL 50000540 114? TII.(J.K) = wp - SP ANAL 51000545 11 " CO j I INUF anal 5?000547 1150 CO j i luiJF ANAL 53

c CALL ON rMF I.OAO S'JMRTjTInE ANAL 54000551 CAi.i LOAD I T H , TOLO.H'JI.'I.S IRI EN.NA . 1PT?,I FM'. rH.rOOR, T ,4H WlMT.NSi ANAL 55

1 10 iP.SPAti.blORt 1 ANAL c h

c PHlNl fnF cCwcmT LOADINGS IF RFOMRFn ANAL 57

1 3 5

ooo566

I) 6 0=.

6070006]

1

noiM 7

0006I

i

00061*.

0006 l «.

n o 6 3 ?

0006*7000653ooohsr00066100066*noo66=;000666000667000671000674000675000677

00070?000701000^06000706000710000730

0007360007360007400007410007430007450007=i000075100075?00076100077000077000077?000774000774000776001000001003001006001007

00100.70010160010160010?o0010??0010?3

IFIF

IF

TR

S?oO

51401 140

1156

1 157

101

1161

1 16?

1 1601 170

1 173

13no

IF 1 1 P r

I

it ft ><

DE i«f>M I I

OF > lOM ( I

Ph * O.i

T« » o.uDO -iUoKB u ? •

IF l «hS ( s

IF ( .US (S

IF tSTOI(STOm

(ABSIa AHS

DFSiumi I

GO Hi 51IF t«nS(PR a ArtS

DEtium ( |

CO •>< INtJE

CO 1( INUF-t-INl

IF (IPTlWRI (E (6FO^iAT (

00 Il57MR I 1 1 ( h

IF (JPT3it" TEH

CO >l I INUEIF (MN .

J ' l

DO I I 60NJ > I

IF (Nj .

SCMl = |'J

SIM? = ri

IF (SUMlIF (Sum?GO TO II

LPC<( J)

J a J

GO IO ll

l_PCi< J)

J s J

CO«l INUtIF (JPT3CALL SFMCO i I INUE

CONSTLEFT

IF (IPTlFO-HA1 (

MN » NSDO l?01XL •

IF (I ,i.

• llF . II -i

'I MF THF hi

, I ) = STOHF, (I si nfif

i r I f I * 1 I 3)

SI i)', >4n-"K'ilS

i i i

(10)

I STOHF (Mil. JJ J 1 . 10)

KK a ?, 7

(l\K / ? )

TOHE (kk n .1

TOHF (hk I i .1

E (KM ,GT.K IKK) .IT.I5E. (i. oi r,n

I'K) .IT. ls>

(I'M)

,H) I PR40PR) .Ll . P») CO TO 5140( -IH)

.?) a PR

T,,00O0t.ANO.KR.FO.KKI Rn,ST^»E(5)«STnBF(KMT. .00001 . ANO.KM.MF ,KK) Rn-STORE (91 STORE (KK)0.0) RR STORE (o | « sTnnr(KK)0.0) RR * STORfiqi . sronclKK)T ' 5?l.0

) GO TO 514

THE OF 5 TOM.EO. 0)

. 1 156)lHOt 1 THOFSIGn MOMENTS...//I1 I > NA. 11?0) I, OF.GT. R| wp

MINE THE NE

MOMFNTS |F ilFOiliRFO

o ro ioi

SMOM( 1,1) ,OESMOM( I ,?)

,

OFcmOMi 1,11 ,DESmOM(I,4)ITE (6,6010)1 LPTM VECTOR ANO CORPFCT THF I V«LuE5

EQ. 1 ) GO TO 1173

I - 1 , N«

1

GT. no) r.o To 1170ESrfOMl I,i)ESMOMINJ, 1

)

•Lr.O.C .AN. l r . o . o .am60= I

1

60= NJ1

0. SUM?. GT. 0.0) r.o TO 11M0, SUM) ,G1 .0.0) GO To Ui,^

, 3E. 10) GO TO 11731C

PuCT ano lOA\0 RIGHT n

,GF. 3 1 *

1 HO, 1 RH^wFA- 1

I * 1 , NA

AO TMF SHFAR INFI'IFNTFF TMF AN/ll YSI S POINTS3 1TF I6.13U0)R L OAOI \G5 //I

I !• FS TO THE

F. 1) GO TO |?06

4li|_ 155ANAL 159ANAI. 160AN«L 161ANAL 16?ANAL 163ANAL 164ANAL 165ANAL 166ANAL 167ANAL I6fl

ANAL 169ANAL 170ANAL 171ANAL 17?ANAL 173ANAL 174A\AL 175ANAL 176ANJL 177ANAL 17fl

ANAL 179ANAL moANAL 1H1ANAL Ifl?

ANAL 1A3ANAL 1R4ANAL 1«5ANAL 1R6ANAL 1B7ANAL IBSANAL 1A9anal 190ANAL 191ANAL 19?ANAL 193ANAL 194ANAL 195ANAL 196ANAL 197ANAL 19HANAL 199ANAt ?00ANAL >01

ANAL ?0?ANAL '03ANAL ?A4ANAL ?05ANAL 706ANAL ?07ANAL ?0fl

ANAL ?09ANAL ?10ANAL ?nANAL ?i?ANAL ?13ANAL ?i*ANAL ?15

136

c CO1 o?s K 1 =.

ooi o?h oo n0010?7 Til. (1

00103? 00 \c

001034 1?03 T 1 L IJ

00104ft 1?^? CONI 1

C lO001050 CALL

1 IOi-iC ->h

OOlOftft If 1

1

00110* GO 1

00110* l?rs If II

c r.v

0011 10 s? =

oolli? K 1 3

001114 DC 1?

001115 T ) L ( (•

001 t ?

1

no i?

0011?? Wl M

O0U?3 DO 1?

0011?S 1?1 4 WP =

001135 l?r« T 1 L IJ

001144 l?t 7 CO-II 1

r LO00114ft C'LI-

110s".r ^H

001164 If 1

1

001J03 GO 1

O01?04 1?1 KL =

001?05 K.I *

r CO001?07 DO 1?

ooi?n OH 1?

00121' WP =

001?13 SK =

ooi?n IF (J

ooi??o JJ =

001??1 1?) 7 K» =

001??3 If ' 1

001?3' IF U00124? IF ir

O0l?4ft JJ =

001?47 go 11

001?50 l?lft TIL 1 J

001?55 GO I (J

001?5ft ??! 7 TIl IJ

00l?f>? 1?15 C P M 1 )

001?fts 1?' 4

c

COM 1 |

001?h7I 1

'

C"Li1 [OlH,

r -Jl.

001 304 If ll

001 3?T GC ll'

C ilf UK

MSIK'JCT THf Ll^Jf FOB BOI NT 1

1

0? K = 1 , T

.*) = -I .0

C 3 J s ? i N». K) = -MIL ( I . UK )

NUEAD ThE PJGhT POINT wITh ThF

i mn SHHBniiTT'lFI OAIM T Il_i 1 "I 0, IM| 0,51.1*1 FN i NA, IPT?,l f'l^M.rnOH, 1 , 4hS'<F",NS.SPAN.SIOF-f I

INI Thf. ShFaH LOADINGS IF ^FO'lTPFflPTin ,GF. T) wPjTF (ft. 1103) I, iSTmfill.n. JJ ) e 1. 10)l??r, »

.i-.F, na) no to i?mUS I '< )C r Thf LTNF FOR ?OlNT NA1 .'I

? « IA . ?

r. 7 k =i , i

am) = i , r>

(;H j = 1 , Mr0.1)

01 J J = 1 I «N-P HIl I JJ, J.<).k) = SP - wPMill-

Oi) IhE LINF "TTh ThF LOAD Siimsoi 1 1 T MPI 0.' [i ( 1 II , 1 U( 0. IkiLO.SIJHl FN.NA . T P T ? , I

r'lr.Tii, rnOR, NA i 4H5NF », NS i

Span, SI OPE )

(nil IhE 5hF^w LOADINGS iF MEOiftRFOPTK .GF. 3) w^xTF (ft. 1103) I, ( STOOP I IJJ) , JJ J » I. 10)l??n

1

? * I - ?

NSK'UCr THF IJVF TO THF LEFT OF THF Pn i • T

1 4 h.

= 1 , 3

1 S J = 1 . NA0."0. I

.11. I ) SP = 1,01

I0SP( JJ),KJ, RK .AMD, T ,fo. J) GO Tn ??17. .T. «K) «o a „p . P!l(JJ,J,M

* .01 . l | r.o ttl ?i ft

IJ 1

1?17,KI - SP - *P1?15

|K) = 1 .00Ml)

NUfAt) THE |!([ vIIh Thf LOAD SURPOIITTN*LOAD (Til . TPLO»||NLO,SUHI Fn,Na,tpt?,i Ftor. TH.rOOQ, I , /, HSHFP.NS.SPH .STOPS )

INl IMF l i-M« LOADINGS JF RFMIIT^FnPT 1 n .(if , t> -J -*

T T F (ft . 1 1 I' 3) I , (Sinci Min , j.| i » l . If)1??"

Mil | Oil I F SI I3\] SHF ftKS

ANSI. ?tft

ANAL ?17ANAL ?lfl

ANAL ?1<)

ANAl. ?20ANAL ??1ANAL ???A'lAL ??3ANAL ??4ANAL ??5ANAL ??ft

ANAL ??7ANAL ??*ANAl. ??v)

ANAL ?30ANAL ?31ANAL ?32ANAL ?33ANAL ?34AN»L ?35ANAL ?3*ANAL ?3TANAL ?3«ANAL ?3<J

ANAl ?40ANAL ?41ANAL ?4?ANAL ?4 3

ANAL ?44ANAl ?45ANAl. >4ft

ANAl ?47ANAL ?4f<

ANAl ?4<J

ANAL ?50ANAl ?51ANA| ?szANAL ?53ANAl. ?54ANAl ?55ANAL ?56ANAL ^=.7

ANA| ?5RANAl ?sgAC Al ?ftO

ANAL •ftl

ANAl vft?

ANAL ?ft3

ANAL 'ft4

ANAL ?ft5

ANA| ^>fth

ANAl ?ft7

ANAl 'ftH

ANAl Jft<S

A" A| ?70A N A 1 ?71ANAl = 7?ANAl ?73

00 1 3?4ooi3?fto o 1 3 3 n

«onn00133?00133300133Soonsi00) 3ftft

00137?001 37ft

nouoo1 * 3

001 40400 1 40S00140ftnoui?001*130014)4ooi <>i ft

00141

7

eoi"?i001 4??0014?1001*?*0014?ft(1014 10

00143?001434

001441

001 4h0001477

00I50O01*0?

001 SOTP01S07ooi^n001S\?ooisi*P0lS?4001S3O001*17

001*41

O01SS?001S7ft

001577

ooi fto?

Opl ftl!3

oo 1 ftn«,

1??0 UFftPfc

ft??<l

1??0

1?<31'

1?'

l? r s

1?' ?

1?» 1

1 ?<

K I

Kl.

if

DOI*.

TF

I COi do

ri

o1 10

If

GO

n:

SPIF0'.)

WPDOw p

nTl

rr

c.1 II

S-.H (

= n

= II

IP1« ?

1 <n s

( jl-^

(SI(S7inI At:

= A

sin i

II

I Mli A

J-lh (

Nl INIfl

CON= ?= o

(NNIPS

I

I

X I 1 NI (

s

L I 1

L V A

I i L

P, s-I-

1

I IP

I

CONl?ft

K.I. )

KJ.3) = STi-iWF I 1 )

I z M"PF (10)

KC» (

,5,1(1

(Ml.Oi'Ft

0''F '

.(,F

SIM'hMI-K 1,4

SU'P4MPK.lt'r1

III

.f u

SUM)« I

.1

J

= ?, 7

KK / ? )

RE(KK)),I I . .nnoOl

.

aND.Kh.fo.kk 1P» r ST/-,HE ( ft ) .SToPf ( KK )

KE(I>K)).L1..0P001.AND.K«,»F,KKI PrJ-STnPE (9) STlHF (KK )

KK) ,GT. 0.01 PR = STOHFC) STO'C(kk)KM .IT. o.u) pw = SlOHf(p) « ";lnviK«i. 0.0) GO TO ft?10

) ,LT, !•') SO TO 1?30H)

) = I'P

) .1 I . PB) GO TO 1?30Fl)

) = HP

. 0) fiO T1 l?n)CT IMF L 1 mf TO T'lF WIGHT or thf pniNT- 1

.10.Ill

1 K

K) r

I) Tt.

OAI1 I

P A t . ,

N I I

TIGl??rSim

J

'• II GO Tl )) ,io

in^i- i i) ) go to l ?=;S

) , 1

1 11 I I ,K) . 1.0E IRF >i?Th Tup I OaD SUpumiT tmtIIL.Ti'l Oi |MLD.SU*3LFN|NA,TPT?,I FM(?Tu,fOOR, T »*H5nFW.NSisrcihl )

HE 'iifAH LOADINGS IF -IFODTOFO..IF. 1) "9TTF ( b . 1 10 3) I, (STO»F( |jj) , JJ I = 1. 10)

Cl ThF i.lMF F13 Thf Wight nF TwF j.tf'MOP sOPPiPTS= 1 . MA

0.0

)?'! CO

If

]?'] F"

IJ

I 2ft

= r

I e'b

I J

L I J

Mi If.

I.OA

LI I

>P,SKF-1

I IPI (>

Ml I

PKTi IP

I If

-(KI

IF. I) S3= 1 . 3

1 .0

7 Kr

P «

.fiO.

K I =

HI

I) TmOADIPAN,III T

T) .i

l??rin

ii i

tI n

('•,

'

(i"

= l . 14HII IKK, J,K)

I ) *P a ?.005P - WP

E ltm *1Th T"F load SUBRnliriNFMl , 1P| (I, l'iLO.Ti)| FN,NA,TPT?.I r»,RTH,(-riOH,T,*HS.JFP,NS,STnr'F i

HF <hFfH tnAOT-gnS \f pfoiitdfo.(iF, Tl "5TTF (ft. 11031 I. (STOPFI i.l.l). JJ I » ]. 10)

"F nFMiiM shfaps IF WFOHT^FnFO. 01 "0 TO lo?

?31l

O.HHTSlfi'i SHF»»S...//1

ANAL ?7*ANAL >7SANAL ?76ANAl ?77ANAL ?7HANAL ?79A'lAL ?B0ANAL ?fl1

ANAl ?R?ANAL ?R3ANAl. ?H4ANAL ?RSANAL ?RAANAL ?R7ANAl ?Rfl

ANAL ?HQANAL ?<J0

ANAl. ?91ANAL ?9?.

ANAL ?93ANAl. ?P4ANAl ?Q5ANAl. ?<Jft

A.nAI. ?97ANAL ?<JR

ANA| ?99ANAL 300ANAL 301ANAL 30?ANAl 103ANAl 104ANAL 10SANAL 10^ANAl 107ANAL 10ft

ANAl 109MNAl. 110ANAl. 111ANAL 11?ANAl 11

1

ANAl •

ANAl *-

ANA[ , 1 f,

ANAL 1|7ANAl. IIPANAl 119ANAL 3?0ANAl 1?lANAl 1??ANAl 1?3A . A

1

1?4A Al 3?SANAl 3?ft

A'lAL 1?7ANAL 1?«A'JAL 1?9ANAl noA'lAL 131

138

00160ft m >?»»»-?O01MO DO 1^3? I =

I . K,

00 161? I?-

"? iPl n (> . 1 1?") T

0016 3? IF(JPT3.6T. 9)

0016*1 102 COvl If J£

O0164O PF r ihN

0016*1 EN)

I'f^Hi I ,) ) , DESShi ! ,3) , TttHI I ,3) . DFSSH(I«4)white ( ft.M i u )

ANAL 33?ANAL 333ANAL 33*ANAL 33SANAL 33ft

ANAL 337ANAL 33H

SUHPRInPAi LFNbTn00P66S

UNUSEn rOMPji EP S">.»CF

03440O

000007

00000700001?00001Snoooi 7

0000?*OOO03?

000034nooo<>o

000041OOOOSnoooos?oooos?

Sl3lso> s (4>

STRESS RATIO

/ Si

FUNCTION tASFAT (S.Fii.Y.YP)

C )t1E"^lNES Thf -*ASE HFTAl FATIftHF STOrSSDM'.NSJUN SU)

C ifcTEHKiINt Thf5L » SI 1 ) S(?)SN * SU)R x i>L / SP.

IF (AHS I Si ) ,f-T . ARS(SR) )

S* • 1.0 ,7ft . IFll/Sfl. •

IF i y ,LT. o.r> r,n in 7nnC HTFKMINE THF FATIGUE STRESS

SFA x si « ?P,s / il

60 10 7 HntTE M MINE THF HaSf MFTA,. FAIIGIIF STRESS f

SFA = (.55«rP)/(1.0-( (.S5*YP/«SK»n.3) »-i.01BASrAT = Sf'A

Pf riJHN

EN )

4 x SP1.0)

INP)

TFNSI^N

7f070]

,p rOMP'(FSS J">n

SUBPROGRAM|_ F njGTh

000113

UNUSED rO'JPUFr) S-»«CF043700

Hf>SF 1

HASF 2

BARF 3

BASF 4

BASF RHASF ft

HASF 7

HASF R

HASF 9HASF 10HASF 11BASF 12BASF 13HASF 1*BASF ISHASF 1ft

BASF 17HASF IS

00000?

su-nouriNE cok'pfs roND i

lESlbNS Thf s H f 4 P CONNECTOR SPactmc, foP » OT'FN poorl^m COnO 2CrmON NA"E (IP) ,SAREA ( 1 0) .OFPTmI 1 B| ,FL«/T1MCi .Fl TH|I 9) iWtPTH(lR) t CONO, 3

lr)Ar(IR) f IX(lH),|Y(M),'iSFCT(lM),Mr)S|BO).TSTFrL(->fl),rs(«>Olt CONO 4?ILC in (Hi ) .CL(PO) i IMCONIROl .Third ,Pi iThi»',i, ,Pi wIn(B0,?\ .NT, CONO 53SL Ai»n,^LAHlH,Mo,cnoo (H) i

. »TI ( 5. Rl , 3 1, CC (c . m .("•, SPAN (4 ). I OSP ( S) • COND 6

»T •" )•• I (R'1> «NA,| EN6TH,oO(01 ) iSllHLEN(on) ,NS,i'Nl n I I 1 TRi.n ( 1 01 .PROP I 3) ,0ONO 7

5FC« -il RESS (81 ,4 .?) f^FSMOM (Rl ,4) .'IF.SPfs (S.4) ,nr SS« ( 1 A?,4) inEARIS.3) iCOND 86CCSI (1) ,C('NSP( If,, 3, 4) CONO 9

139

OOOOO? COiil n/-'i\iF / )PT1, JPT 1 n

OOOOO' CO*«f 0/1*'i/l_Pf' M

no 1)00? ClM*f'N/fH»E£/AS t NCSt jPTh,

OOOOO? COtlON/Tf IJ/M«Ut»fHOOOOO? PE4i_ IX. IYi ISTF Fl i TLCON. TrtCON.MH.LFNGTHOOOOO? DI"I'-NSIUN LPCMln), SPAPF ("!.)< m«»«i«i, r(1A,3,4)

c itna our Thf REQJiRCn a^ratsOOOOO? DO -"<49 I • = 1 , Rl

000004 SPACf (H ' O.r000005 ?RR9 HOI 1) 0.0000010 DO .('Oil 1 = 1.40000 1 1 no -»?oo j = l . i *

00001? DO tr-00 K e 1M000011 4200 CO*->P ( ),«., I I = 0.0

C if S I nN Hf SuACTNr, FOR 7/R JNCH SHEAR CONNECTOR STUDS00002* IF IJflt .LT. <«| T,0 TO 6000000010 RFruwn000011 *0O,0 Dl4 = .'<7SO0O033 Zfl = 10. h • DIA»»2O0003S SL4-IA = SLArt^D • StARTH/^R

C OETEUMINE THE NU*irEP OF CONNECTORS AT Fatm SFCTlON000037 F". I « = ^0.0000041 DO (dOO I = 1 . NF00004? 14 - NOSI I )

000044 IF |F|*[0(IAI ,|_T. FmIU) F'-Un = FLWIOIIAIooooso lono cO'ji iNurO0O0S1 NC-i = 4

OO00S4 IF (l-vii.g , L f, I?.01 MCS « 1

O000S7 IF IfMlN .GE. 1S.0) -ITS 3 5

0000*1 5Z-« = NCS » 7»

C lETEMMINE IHF ACTUAL RFOUIREO SPACING00006h DO 1001 I = -1 . NA0000*7 1)0 <U10 J 1. in. ?

000070 IF ILPCH(J) .FO. 01 GO Tn 3 1

1

000071 IF (I .HE. LPTMli) .AND. I . I. E . LPCM(J»1>> r.o TO 301?00010? 3010 COJiI'llJE

000104 301 1 IA a NOSI I

)

oooio* [C • ? • I I

0001 111 ID a IC - 1

000111 IE (I ,KO, ilA) Rfl TO 101?000113 vp = nEsSHiir,?] - ifssh i ic <. i

00011S 00 = DEPTm(IA) PL*TH(Ii2) . HMixr H . Si «HT.i0001?? Sp - SlaHA • (On - Ch(I) - SlAHTh/o.i /iHroig, T )

0001?7 SPP = S/«/ ( /H • t;P)

OOOlll IF i] .FO. II ho TO 3003000131 10'? VP s DESSH(IO.J) - 0FSSH(ID,«)0001 1* 18 = nils (l-li00O14O 00 a l)EPTH(IH) PLATHl!-lf?) HAiJMCH S| 'nTH000144 SP = SLAB* • inn - Ch(I-I) - SL.AHTH/2. ) /THCnM 1-1

)

0001S1 SPl = SZ-VH/w i> SFM0001S4 IF (I .ED. NAI r,r\ TO lnr>4OOOls* SPACt ill = SPl0001S7 IF iSPd ,LT. c ^'M S'aCFiII = SPRnoo 1*5 GO 10 3001001)1*1 30'i3 SPACf (II = SRPoooi*s go ro 3" o

1

0001** 10T4 SPACt III = ->l'l

oonl7n Oil iu inol

CONO 10CONO nCOnO l?CONO 13cond 1*CONO ISCONO 16CONO 17CONO 18CONO 1<5

CONO 20CONO ?1CONO 22CONO 23CONO 2*CONO ?SCUNO ?*CONO 27CONO 2RCONO 2"»

cond 30CONO 31

CONO 3?C0Nn 33CONO 14CONO 3SCONO 3*CONO 37CONO 3R

C 'Nil IVCONO 40CONO 41CONO *2CONO 41CONO 44CONO 4SC >ND 4*CONO 47CONO 4RCONO 44CONO SOCONO SI

CONO 52CONO S3CONO 54COnii 55CONO s*CONO S7CONO SHC 1NO SRCONO *nCONO hiCONO *?CONO hiCONO *4cono 6=;

roNn *hCO NO h7

1 !U

0001 7i 1 II 1 ?

ooowi 30MC

OOOl 7s

000177ooo?n:>

oou?osooo?l

o

301 Sc

c

000?1

3

oo<>?i s

c

ooo?i s

000?2<looo??i000???

II ? ? 1 3 0^100'1??S

noo??so ? 3

00n?1n In 1-?

no"? '?

O00?34? 1 s

ooo?*? In 1 S

00fi?4'» lossP0n?4S000?4S 3 u 4

ooo?soooo?s?

? S 4

000?r>S 30^7r

3 OS 300H?S7oon?7i000?7?

0?7l000?7s000?77000300 40S000 30 3o o o 3 o s

OOOlOS000307O00310003]?00031s0003??000l?s00033100033400033=,00033s in»s00014100014snooisnO0II3SI 3 0fti

<j(>«of (i ) = o.oCO J I I NUf

itTEKMlNE RFOnIUEn SPACING Tn T^F NFaoFstDO <U)S I = 1, maNi j SPACE til / 1.

H0( I ) = N3 • 3.

IF I Pi, ( I ) .,jl. 74.1 BO (II = ?4.C n ,1 1 1 1 ii If

(•"ILL IHE CONSP a^pay rflTH 1hf copqfcT "A!MN 3 MS -

I

11- .In lilt (OOP ''"III PATH SPANDO »0S I I - 1 . «N

IMI ,<"l(NE lnr CPOSSOVFP. POINTS IM THF SO;,

IF imn ."t- . ii go td 3osnIf - I

II 3 IMGO in 1 '' I

ip ii . ii . ii ( ; <-> rn ins?I A = I

p, aIMl. M 1 I . 1

GO Ml I; S3IF I 1 .[,F . MN) fio TO 30S4DO V Vi j j = l , in

I A = | Pi II.JJI |

IF I 1 a .,,!. [nSP(MMl) nn TT 10SSCO J I 1 Nil*

1 1, = l A

GO 10 1 ,1

Oil iOS7 I = ?. I". ?

I A : |. PI i., (J) « 1

III - I PC«(.J*1 I - 1

IF il PC«< I) .(3F . inSP( I ) , AHJO.l PCM( J+n ,LE. T"SPCO * I I NUf

lit. Tfi'MINE TnF STARTING ANO ENDING rOnoOln,HMUII) = 14DMA* = II.

00 4t' J = 1 A , TP-

IF H't

S

MOM(Jt?) .LI. UMAX) GO TO 40SnDMA* = DFSMOMI J,?)MM 4* (II s J

CO j i l ru if

SC'I* = f II III I I A )

FC .n = ( ODHI [A)

J = I

oc 1080 k = ia, mIF if , F I) , | H l RO TO 30O1IF (AHSIPOIK.) - BllK.III ,LT. .IIOOOll GO TOIF iKi(r. ) . ot. i'ni<t| i) no Tn m«sxo x (Hi) (K«l ) -5.PACF IK) 1 « SlIPLENIKl /(SPATF (••(

NPn = < 11 / KO I r I

XO = WO (K) • MPP *0 (K)FC W = f OIK * XOfill I (i Ti 84xo = (SPACE (K)-Pn(if) ) » S'Mlfn(k) / ismrFrnMm = in / (to ( r

|

xo = P(i i i e (: uii

Fr w r i fop » xnCO"->P l,li I . 1 ) - miKl

COM) 6hCONII f>9

3 INCH TNTBrMEuT CONll 70COM) 71

CONO 7?COM) 71CONIl 74

CONII 7SFS C )NO 7S

CONO 77CONO 78CONll 74CONO B0

C 'NO 81

CONO *?CONll 81CONO 84CONII 8SCONO 8SC'ND 87CONO 88CONO 89CONO 40C'lNO 91CONn 0?conn PIO'NO 94C < "Ml > 9SCONll 9SCOno 97CONO 98

1 i ) ) fin TO 3 0S3 CONO 94CONO 1 on

TF FOP THF -OnnFCTOKSCONO 1 0)CONO in?CONO 103r (No 1 04CONO insCONO InsC'lNO l n7CONI) 1 n8CONO 1 04CONO 1 1"

CONO 1 1 1

CONO 1 1?COM) 1 1 1

no" CONO 1 1*CONO 1 is

1 1 • 5PaCF(*I ) COM, 1 ISCONO 1 1 7

C"NO 1 18

CONI) 1 19CONO l ?n

. spjrr iKtill CONO i?lroim '??CONII I?1CONII 1 ?4

. CONO 1 ?S

1 11

non35* en it- ij.?. 1 1 - sron000361 CONiHC.It.Ttl) = FCOODOOIht SOW = FCOH00U36S FC.M = CODh (k . ] i

nonihf- j = j • i

O0o3b7 0" ID 30*, 1

nom7n i(i"i xn conn' dm - scoq00137") Nrtfj Xli / i<0 (* )

00"376 *D = Xll - **<H e t'OK)000401 Ffiir. = rOOh(IH) - «D000401 C04iH(Jtl«I) x «n(K)000*10 CO-tiP(.it?» 1) = Sr'^ooo<> l 3 CONtH ( i. "ii I ) = f ro'i

* 1 6 J = J 1

000*17 GO H' 3i.no

000*?n io<<f FC'it = rrnF. « SOKLFMIKIOOn*? 1 ln«r Cf mi 1 ' if

ooo*?6 io^i cr ii |i ufr ai JUST IMF SpaCImos Fin Jul I CST SP/iki

O00«3ii 00 <1 oij J = 1 . If.

000* 3? J I = J

000*31 If IAHS ICO0lSP(Jt3tMM) ) .LT, .0011) r.C) TO 31 i

000** 1 3 I"f CO mi liiif

000**? Ill I J J * J.J - 1

000*** *n = if ..Mm - C^tS=IJIil." Nl

ooo*5o un 1 1 r.p j = i . i i

ooo*s? enm u.iiM.i = rO»iSp(j,3,MN) *n000*57 31'? COW IJt?.MN) s rnoSp ( j, ?, -1 N j Xp

C fiwrtlCl SPACINfi FnW INFLECTION POINTSc if tfkminf mimbb^ of pows aujacfmt to t«f t'-ififctton point

000*6* SU"J - (.43 • nil««l • SOPT(?50O. « Ffl000*7' PSl^I- = Ai « *(i,

000*74 N^lm' = P5LAfl/(.P5 • SH C) 1

ooosoi nsh = as • ir./;w i

000506 IF iKSFi' .liT. I\|C|A«» nslah = NSFR000511 N«« = f.siAH/urs . i

r copheci Imp roNSP ah^syOOOH s DO .051 I = 1 , MN000^17 on *osj » = it io000 S?n IF iiK'UI .f'J. 0) r,0 TO *ns]oons?i ia j ipcmijiooo5?i if il« .i.i. ir.spip ,ano. ia .LT. losP(i»l)i on to 4o53000533 00 10 *rc?000531 »P'I IM i IDSF'I I

)

00(^3^ IF ICOOkUAI .M. C0o(? ( Tfll »SPAN( T ) /?, 1 rin T- *n r *

000544 K K , ?

0005*5 HI) = OFSI'I.M ( I f 1 , I ) »SH 111 F M I I A) / I AuS (OFSMO 1 I I , . 1 . 1 ) ) ,

IA-t-> It'F V •'

I IA , ] ) ] I

00055? GO 11/ *1SS5 5 3 * H '- * Kr. - 3

00l'SS<. '> = 1FSMOHI t A-l , 1 1 »SiJMLFN(IA-l 1 / ( ARS(nFS"0-i , I A-l .1 ) I .

I AMI ll F ', |(IM I I/. . 1 ) ) I

OOOSfi? *1'-S [F II-, K . F . 31 OO I 4-irt

5 6 4 v< i - C'l'iSr'JitPttl - r .'

»o P.( I A 1 1 » o ) / r r\ s P 1 1 , 1 , 1

)

O0oS7^ x, = CO.SPlltlttl • IN»I1 « NPA)001601 C '>)> (l.Kr(tI) = r :".'Ss I I , KK < I ) - Xfi

"OOlSllS 1 Hi i, ^V101'f.os i»p^c do .osii ." = i. i^

CoNI) ?6CONO ?7CONO ?p

COM) ?9CONO 30C')ni) 31CONO 3?CONO 33CONO 34CONO 35CONO 36CONO 37roNo 3RCONO 39-

comi 40CONO 41CONO 4?CON[) 43CONO 44cono 4SCONO 4hCOnii 47CONO 48cono *MCONI) SOCONO 51

CONO 5?CONT) S3CONO S4C inn SSCONO 56CONO 57C"NO SHCONO 59CONO 60CONO 61CONO 6?CONO 63CONO 64COM) 65CONO 66CON.', 67Oni- 6Hcond 69CONO 701 Nil 71COM. 7?COMI 73

C INII 7*( '. 75t '. 76

( N 77t ». 7"r mi 79r • 80r . mo PIr ii R?i

-

F> 1

] I

J

6 7 K

00061 1 IF

nooMfi 40'-6 COooo6?o 4057 N<

000633 X!)

000640 CO

O00645 40 c ? CO0» 7 40K1 CO

cDO00065?

000651 IA

00065=; IB

000657 AR000664 P(3

O00666 PCooo67i 1^

000674 NH000701 DO000701 IF

000711 IF

0007?7 K.J

000731 4 0") CO00073? 4 OK? RO000734 J

000735 40»4 IF000737 RO0007*7 J

000750 60000751 40«3 RO000?6? NC000766 IF

000775 IF

001000 NA001004 NAO01005 NT

O01006 NT001007 KK001010 IF

0010U NA

001013 DO001015 NT001017 IF00l0?7 DM001036 MS

00104? SP001 044 NP001047 SP

001051 co001051 NT00106? IF001064 4 55 CO001067 GO001067 1*0001 074 NS00110? SP

001 104 'IP

001107 SP001111 1 *5 Krl

= JK - I

IMPS (CoNSP ( JK , I . I )) .IT. .iMioon RO T

"J I INU1.i m [cnomiA-ii »n - roimp (k ,kk, t 1

1

= CO'lSH ( <« I . I I » |N*n NPA)>)->H (K.KKt tl - rON5p(K.1,T) <nMl INUI

M I 1 NUFCOBPKCTION For; ULTIMATE STRENGTH40H0 I = I i MMa MMf > ( I )

3 no-> ( 1 a>

a SAKEACim Pi a th ( I ft . 1 ) »PLw In ( i a , n,),/ a am » PROP ( i)

<C = ?.1,?5 • FC » SI.arwO » Si.AMThIFCO jC .l.T. Pr,<)>/) Pf,rn; a PCO-iC

e j = i'i.iiv / i ,o5 » susi i

•. ll R 1 K = 1 . \l

(AHSICONSP(K,l . 1 1 ) ,|T. .00011 r-" Tl

(COOP 1IA) .LF.rnNSP (Kt?,I ) .AND. COOP I I A)= K

M( IMP4 = 1 .11

* 1

u ,t"0. ik i r,n tt 40B-}

4 = HUW (COnsp i i, i, i ) - CONSPi J.?* I

)

J l

III 4 < » 4

« i Bom (COOP(TA) - rOMSP ( J,?, 1 I > /

i|< a KOW » M~s 1

(AHSlNCON - OOP » NC5) ,(iT. ,00001) M

iNCOM .bK. NRFO) r,0 TO 40S6.) i a (ijhEu - NCON) / iJcS 1

F. = NADUur = n

» o

K = jr - 1

IKKK . f U. 0) RO To 1 '10

t a NADD / HK•tbSO J =

1 . <KK0) = NTOT « NAfu .mi, kkk .and. nTi)T .mf. lAnni naf= co.jspi j,3, 1 1 - roNSPi J,?«i)

> - DM / cOnS*p( j, |,d , naf

a IIM / NSP1 = SP / 3.a NP ) » 1

.

1-.H ( J. I . I I = SP- nt Dm / sp - -jsp . nafI NT ,i,F. MAIHH RO Tn 40Hf,

N I I NUFIII 4^1 V-,

= C OOP ( I A) - rnr.SJ( JK ,?, I 1

-> - I) / CON^P (.|K, 1 , I ) . NAFa D / NSP

i - SP / 3.

• NP J • 1 .

' 15

''F . I Ot.sPlK,?. I ) ) JK

-ONSP (J.I.I)

CONU 1B4"I t, k7 CONO 1B5

CUNI) 1R6/ pn- SP if , 1 . 1 ) C'OMI) 1 H7

rONO IBSCONh 1R9CONh 190COM) 1P1CUNO 19?CONII 191CONI) 194.

CONO 195P| UTn ( 1 A.?) »Pl »TH( I A.?) CONn 196

COM) 197CONO 19BCONII 1 99CONI) 200CONO ?0 1

CONO ?0?CONI) ?03<:oNn ?04CONO ?05CONn ?06CONO ?07CONO ?08CONO ?09COno ?ioCONO ?11CONn ?i?CONO '13CONO ?14CONO ?15CONI) ?16CONO ?17CONII ?1RCONn ?19CONI) ??0CONn ?2lCONO ???C'NO ??3COM) ??4CONO ??5COND 'P6CONn ??7CONO ??P.

CONn ??9CONII ?10CONO ?31CONI) ?3?CONII ?33CONn ?14CONO ?35CONO 316CONI) ?37CONO ?1SCONO ?19cond ?4oCONO ?41

rOMcn( J, 1 , I

)

rON - NrON -

-N|/ln"-N'OT«"AF

1 4 5

0011 1? TEM" b < ONSPI 1 t?» I I

0011 Ift |M 00 |M SC = |i 1

0011?0 lHh CONSPlMt*! tKCt II » CONSP (KR.KCt I

)

001134 IF IKH iFO. 1) RO rO 1H700113* KH i tt • I

ooiiiT go re lMH001137 |H7 CO«KP ( 1 . 1 . I ) = SP

0011*3 CON-«PU«?«I) = TFHP00114* CON '»•

( 1 . 3. I ) = C0NSP(1,9,|) Sp • >,c.p

0011544COntlH(?l?ll) = rmiSPl 1 ,T, I )

001157 40"h ROW = 1.0

0011M J a *JOOllh? 40^9 IF (J .hi, jk ) r;o TO 400n001164 Ron = ROW » (TONSPI J.liT! - CONSP [ |,5> , I ) 1 / rON«!P I J« 1 1 1

)

001 1 74 J » J - I

00117s on io 4nh400117* 4000 H0< = HOW l( O'lSP ( I, 3. I > - COOH(IA)) / CiNtn (J , | > II

noi?07 NC')g = "«"n » ncs « 1

001?14 If" 1A0SINC0N - Pnw » NCS) ,r,T. .00011 NCnn , nc^N - 1

001??3 IF INCOll .OR. MWF'i) RO in 45n0001??* NAOO = INHEO - Nf-Oj) / nrs 1

001?3' NaE = Nam)ooi?33 if im .ri, jh no Jo 150001P35 Mt< = KJ - JK00123* NAE = N1IHI / KKKO0l?4O J = rj001?41 NTUI = f,

O0l?4? tlT i

012 4 3 151 N 1 ' I I = M T I ) T N A F

001?45 if U,eu..ik»T .Ann. mtot.mf, nado) ».AF*N4nn-MTOT»NAF001257 D'1 - COuSP(J,3,T| - rONSP(Ji?iI)O01?h* NSP = OM / C0NbP(JiI,I) ^ A F

00127? SP J DM / NS>P

001?74 UP 1 = SP / >.

001277 SP = MP3 » 3,

001301 C0«J"»PCJi 1*1) = SPO01303 NT a NT » Dm/SP - MSP NAF00131? If (hT .RE. NAfni (50 TO 40 h o

001314 J = J - 1

00131* IF u ,F(], JK) r,n TO 40onO01317 00 IC 151

001320 iso n = (.()nsp( jk.t, 1 1 - ronj(j4)O013P5 NSP = I) / CUNSPl |K.l ,T) . NAF001333 SP » / NSP001335 NP * i SP / 3.

001340 SP * MP 1 « 3,00134? CON >P ( JK« 1 > I . II r SP

00134* CONiP( JK«1 ,3, J) - i-T-iSPI

|K .1, I I

00135? CO^ih (JK« I «?, I ) = ")NSP| ik»),3iI> - "ISO • So00135* COkIsF ( JK,3iI) = r.OMSPI JK*-I«?.D001 3*1 4="0 CONI I MUF001 3M 40"n CON I 1 Nl t(-

0013*4 0" «P I r 1, >>

0013*5 KSC1 = I

0013** 00 .1 ) = 1 , i

<

001370 IF (ARS (rt)NSP( J, 1 i II 1 ,|T. .oOOOl) RO Tn 3000137* n = CONSP <J. 3. I) - CnNSO(J,?,I)001403 NXO = D / C"'J< I | |. l i 1

1

CONO '4?CONO ?»3CONO '44CONO ?45C0Nn ?4fc

CONO ?47CONO ?48CONO ?49CONO ?S0CUM) ?S1CONO ?52CONO ?S3CONO ?54C0Nn ?55C"Nn ?SoCONO ?n7CONn '5HCONO ?5<>

COM) ?*0CuNO ?ftl

CONO ?*?CONn ?ft3

CONO ?fc4

conn ?65COM1 ?ftft

CONO ?*7C 'NO ?*fl

CONO ?f)9

CONO ?70COM, '71CONO ?7?CONO ?73CONn ?74CONn ?75COno ?7ft

CM) ?77CONn ?7«CONn ?79CONO '«0COM) ?«1CONO ?B?C nNO 'P3CONn 'R4CONn 3P.S

CONn ?fl*

CONO 3B7CONO ?«SCONn ?fl9

CONO 5<90

CONn "»1CONO ?9?CONn ?"J3

CONn 7Q4CONn pq<?

CONO ?"»*

CONO ?<>7

COno TinCONn ?qq

144

p 1 *Oft If I

ooi * i s If (

00l*?l KSCIool*?? IF I

noi*?* If I

001*30 COM-.

noun If I

ooi*«o Gn i

001**1 4? Com-i

001*50 COM->

001*51 GO f

001*51 43 COMj001*63 COm»001*66 *1 COM!001*70 39 IF (

001*71 on •«

001*73 D1 '»

001*74 CI It

001504 4S COM!0015)? KH *

001513 DO •»

00151S IF i

0015?3 IF (

noi5?4 IF 1

00153S CO-MI

0015*1 (SO f

001541 '.7 com-.

001547 com-.

00155? CO-M-.

001555 KH =

001556 4 6 CO'MI

001560 40r

COMI

001563 DO '»

001564 DO 4

001565 IF (

001573 xn •

001600 NXi)

001603 IF (

00161? xn -

00161h If <

0016?? CO * >

0016PS COM-.

0016?7 Git I

0016?7 400? If l •

00163S COM-.

001 644 CO M i

001647 GO 1

001647 40'<3 CO Mt

no 16^ *V'» CllMI

001663 If 1

001665 no »

00166h j i=

001 667 if i

00167S 4I1US CO-MI

O0167f- 4nofc J ) =

001 700 XI) -

001 704 DO •

AHS (NXDOCONSD ( 1,1,1) - n> ,GT. .00011 Mvn I MXn 1

IjXD ,GT. 3) RO TO 41

= )

J .FO. I) 1-0 10 4?AHSICONSPIJtl > 1 , T I I .LT. .0001) GO Tn 41

P<Ji 1 . I ) rniMSo( j-1,1,1)

CONSPI J«l , 1 , 1 > ,LT.Cn>MSP< 1-1 . 1 . T ) ) fn-isp, i, i . 1 ) rCONSP i

41P(1,3.I> = rON5P(l,?,I) « 1, » (-ONSPM ,1 . TlP I?,?, I > c fOMS? (1,1,1)

41

P(J.?.l) = rohSJ ( j,i, I ) - 3, o rONSP ( 1, 1 . T>

PlJ-I ,3,1) = COmsPIJ,?. i)

J NUEIvSCl ,E0. 0) (id TO 405 .1 = 1 . 1

6

5 K = It 3

h , I I = CONSPIJtK, 1

)

F (j

,

k , I ) n .

o

l

6 J = 1 , 1 6

AHSICIJtl ,1) ) ,LT. .0001) GO TO u()

J ,1'). 1 ) GO TO l, I

ARSic{j-i,i.T> - ci. it )«!)> ,gt. .onnTi r-o Tn 47F («»--l ,3, I ) = r I 1,3,1)G 4/.

f («", ltii = r 1 1,1,11f (K t,?t 1 1 * r(Jt?t I)

P(k !, 't I 1 = r I ).i. I )

Kls » 1

INUSlNIII

INAI AOJIJSTMFNTS OF THE fONNFCTOP SPin'r.300 I = 1 , MM39n .1=1,16AHS ICONSP ( J, 1 , T ) ) .LT. .0001) Go To 430"CO.ISPI J,3t I) - CONSP(Jt?tI)

=; X' / Cic SP ( l.l.pAMS IMXO«CONSp ( I, | , I) - XOI .GT, .000)1 wvn 5 NXO 1

MXn * CON'SP ( J, 1 , I )

CONbP (J, 1 , 1 , 1 ) .|T. POMSP I J, 1 , 1 ) 1 GO Tn <iq->

p(j.3,D = rnN53(j,?,n , xnP( J»l ,2tl) = CONSfl I, 3. I

)

1 4 IPOeS(l i.nSh ( J* I , l , l ) ) ,[T. ,0001) GO Tn '.or-,

I' I 1,3,1) * rr)NSO( l,?,l) Xo - rOMSP 1 i.i.TlP ( J* 1 ,?« 1 1 = ro\j«^p ( 1,3,1

)

( 4 •'"'

p 1 1. 3 , 1 ) ~ ro.vSJ 1 i,?, 11 xoIN Iff

I'M . f"'), 1 ) RO TO 1 1

IJUS I = 1 , 1 1

J

AHS t r iimsp i .1, -., mvii) ,|_T. .ooni) on Tn 4nu<

INUI

= JJ - I

I F_ .:, I 1 - r 0» HP ( I ), 1, m II

• I 9 r .1 = I , II

CONI) 300cono 301rofMD 30?COM) 303COM) 30*CONI) 30S

1*1

1

1,1) CONO 306cond 307CONO 30RCOM) 304f ONI) 310CONI) 311CONO 31?CONO 313CONO 314COMI 315CONI) 316CONI) 317CONI) 31ACONO 319CONO 3?0CONO 3?lCONO 3?2COM) 3?3CONI) 3?4CONIl 3?5CONI) 3?6CONO »?7CONO 1?«CONO 3?9CONIl 330CONO 331cono 33?COM) 333CONO 33*CONI) 335CONO 136conii 337CONO 33HCOM) 339CONO 340CONO 141

rONn 14?CONO 3 4 1

CONO 144CONO 345CONO 146CONO 34 7

CONO 1<,H

CONO 149

CONO itoCONO 151

CONO 1^?Cono "<^3

CONIl >S4C INO IS^.

COM 1 1=.h

CONO 1G7

1].',

00170ft CO-IlP < J. 3.MN) = r'i'iSp ( i , I.mni »n

nomi 40R7 CO M->R ( J.?.MN> = <-<>'lSP(.J ,Pi»N| Xnooi7?o 1 n CONI lNUF0017?0 RF ruHNooi7?i END

COM) 3SHCONO 35<J

COND IftO

COM) 161COM) 3ft?

SUHPRO'iRA^I LfN'J TM

002531

UNUSED (-U--1RII FK SRjCF034100

1

?

00000? " CO-MUM ,JAHE ( 1 8) .SARFa ( 1 h) ,DfpTm ( 1 B) ,Fl <in ( l cm ,Fi TH ( 1 R) .wthTmI 18) i CPUS 3

4

ft

7

^f iniwr ->nioii*f^i fiics'iijM i ri i ibi nir ^"<- a ( ^ , 4 > , "fssh i iftv f *. j ,iraHi^ t ji (Lkii^ 8

ftCOM (R) .Consp ( lft, 3.4| ,Cn\yPi_ I 1 ?»ft.?l CPns R

nooop? co

i

iON/une /jpT3, ipt i i CPns in00000? COMmON/TwO/lPCM CPnS 11

00000? CO-MON/SIX/FU CPOS 1?00000? CO»iil/N/t- H.HT/TST CPnS 1300000? CO<Ml>N/(EN/HAUNCH C^DS 1*00000? COM"tON/ElEVEN/Kra,KCt«;iS»SHStSLS»I5S, I. SS.HMn .JITST CPOS ISooooo? clmiOn/ ifen/pth.kt . i CPns ift

00000? KF4I. I*i It .JSIFFi , rLCON, IMCON.MR.LFNfiTH CPnS 1700000? DIlFNSIDN LPC" ( 1 0) .PTH (40 .4) ,RSm (40 , 4 ) ,phm ( ,,

~ ,41 CPnS 1800000? IF (1PT10 .OF. 3) write (h.lo4<)) CPOS \9ooooii loco format ( imi ,?ox. iihstart cpofS//) CPns ?o

C ^fcRO OUT Tl-F RF'JJTRFn ARRAYS CPDS ?1000011 DO w400 1=1.1? CRns ??000013 no v4oo j = l, ft CPns ?3000014 do <4oo k = i. ? CPns ?4000015 R400 COVPL UiJ.K) = n.O CPOS ?s000031 mn = ns - l CPns ?ft

000033 J = 2 CPnS ?7000034 ft30(i DO <(>01 I = 1. mf CPDS ?8oooo3ft no ho) jj = i, 4 CPns ?r000037 9oM pr-iii.jj) = o.o CPns 30000047 DO M'ftl I = 1, 40 CPDS 31000051 no -.eft) k = 1 , t, CPns 3?00005? 5(ih) pmil.M = p. 11 CPns 33ooooft? km = 1 CPns 340000ft3 NC * KH CPns 35

r DETERMINE IhF i'H ARRAY CPDS 3hooooft4 no -iiono I = 1 ( nf CPns 37noooftS IF (I ,1.1. 11 r.o 1 1 rjson CRns 3H000070 RS10 Pf-H(K8,1) = P| Mi'll, II CPOS 3R00007S PT>1IM,J| = PLwTDd. I) CPOS 40oooioo PTHiM3ti) = cnoRii) CPns 4i

1 If.

100101 PTHOHitl = C0OB(I«l) cpos 4?000103 GO IU 9i in CPDS 43000103 95nn IF I <>H S ( PL A T H I I , I ) -P TH ( KR , 1) ) . L T . , f| 1 I On .fl 0600 CPDS 44000113 kh » KH 1 CPnS 45000114 NC - KH CPDS 46000115 SO Id 9511 CPDS 47000115 9610 PTr|(K.H»4) = COO«(I + l) CPnS 4fl

0001?0 9000 CO'<l I lNlifi CPnS 49O001?3 KSS1 = n • CPOS sonooi?4 IF inn «F.Q« ]) r.ri TO 7no' CPns 51noni?s if (j .i.ij. li on in 700? CPns 5?oooi?7 no 'ooi 11 = ?, us CPns 53

000131 1 » 10SHI1I) CPOS 54000133 DO /(.0 1 JJ = 1. NC CPOS 55000134 IF ICOOH I I ) .fiT.PTH(JJi31 •ANO.COORI I) .LT.oTHl lJt4) ) r,n'TO 7005 CPOS 56000146 GO fO 7103 CPns 5700014S 7015 10 * JJ . CPDS 5fl

100150 IF it'TMII'J-1 ,1 ) ,LT. .1) GO TO 7006 CPns 59000153 KSSI = I CPns 60

000154 PTHIlO-l,l| s 0.0 CPnS 61

0011155 PT-UlO-li?) = r.n CPOS 6?000156 7006 IF IHnI l'J«) » 1 ) .I.T. .1) GO TO 7003 CPOS 63000161 KSSI = 1 CPOS 6400016? PTriiln«i»i) = o.i CPns 65000163 PTH(IO*1«?) » fl.n CPns 66000164 70^3 Cf>"tfINUf CPDS 67000167 70H COMflNUI CPOS 6R000171 IF (KSSr ,E(). 0) GO TO 700? CPns 6900017? Kfl = NC CPns 70oooi74 ktt = i CPns 71000175 NC = 1 CPOS 7?000176 no mho i = i , kr CPns 73000177 IF (I .i.T. 1) CO TO 7015 CPDS 74000?0? 70?0 DO /01? KKK r 1, 4 CPDS 75000?04 701? PT-MKTT.KKK) = DTHIt.KKK) CPDS 76000?15 go ro 7nl0 / CPns 77000?is 7015 IF (ARS(PTH(I«1) - »THU-1«1I> .LT, .oooil m Tn 701* CPnS 7Rnoo??? k t r = kit i CPns 79ooo??4 nc = ktt CPns so000??5 GO ID 70?1 CPns fll

O00??5 7016 PTniKTT.4) = PThiI.41 CPns fi?

O00?30 7010 CO^MINUr CPns A3r ->k!Nl THK ri-ir.l'-Ai ptm uroAY if dfootoFH C p ns B4

00OP33 701? IF IJPTln .LT. 3 ) RO TO )oo CPns A5noo?36 wPiit (6.ioooi • CPns as000?41 lonp FO-l-iAT ( 1 M0> 10» , 1 HH-IDIGIHAL PTH ABO/tV//) CPnS A7ooo?4i no iooi l * i . nc CPns rrO00?43 mil WW f I t I", 100?) (PTHtT.K), K c 1. 4| cpns R9000?61 ion? FO-MAT (?X t 1HF'l»TE Is ,F10.5,3H X ,F6. f, KX .nHS'TART e ,Fffl.?»lflX« CPns 90

I6mf <o = .f in.?i CPns 91noo?6i inn k'> a n CPns 9?000?6? KILL = :' CPns 93000?61 KPST = CPnS 94000?64 IF (NC ,FQ. 1 .AMD. AMS(OTM(),H) jt, .nnni, r,o To 10? CPOS OS

C -,1AUI THF. lono rip ihc o Lft TE CUTOFF CPns 96000?76 DO J300 1 = 1 . MC CPOS 97O00?77 KST = Kl< CPOS 9R00030) KB = n CPOS 99

L47

00 30 1 *T » li

00030? IF (IPIir .,F. 31 - ^* T TF ( ^. . 1<"> * 1 > I

00 3 1 1 ln'1 F0rt«Al ( / L *X . ? ] pr n I r l| > T T O'jS FOk I n .1?)000313 IF iF'TMIItll .LI, .1) SO TO 0)0000031*, if it li l .f i. ni fin to i9o000317 IF (AHSIftHt 1 ,1 )-PTH(J-l 1 1) 1 »GT. .oOOl) fifl TO '90

P003?S 30 Hi 9300O003?S 1P0 IF ( >ns ll'THI I . 1 1 -pTh i J-] . )) ) ,l.T. .orinl) «0 in 9">o0

000335 IF <i\sT ,KU. ?) RO To 9">S9

r itTFi'MNt 1HF PlATF FND CONDITIONSO00334 DO »33d K = i , bja

00033*, M = K

000337 IF ( A.MS (COOW ( I A) -PTH ( I . 1) ) .1 T. .(10011 I RO Tn "til000 34S 9330 CONI INI1I

000347 933) K'J - IA0003S\ KC = 1

0003S? IF (I .i j. 1 ) Pn TO 9 133

000 3S 4 IF (PlMll-1,1) .OT, .1) Kf = ?

0003157 9333 ISS = 1

000360 IF (Plll(I-lil) ,r,T, PToiT.lll ISS = >

000364 IF (IPIIF ,£(). 4) " « T Tt- (6.101?) K'l, KF, ISS000*00 101? F(M«AT i/S<,k^ii = .i?,?X,ShkC = , 13, ?x ,<,Htsc; a ,I?|000400 IF IMN .Fu, |) fin TO ^3?9

r '(ETfc'iiMlNd Tmf maximum ALLOkAmI F rilTOFF00040? DO «310 K = ?. mm000404 10 ' lOSP(K)000406 ]F irP-,1 .£Q. II RO TO 7701000410 IF (I no.j ( ID) ,(F .pTh ( j , 3) ,Arjn. COOf> ( 1 0) . I.F . P TH U 1 4 ) ) GO to 93|SOOO 1"?? GO 10 4 <1

0004?? 77"0 IF ((Oil. (ID) ,r-F, PTh(I-1i3) .AIiP. roimiiH) IF. PTH(I-1,4))1GO fO 4317

000434 931 CP«J I I Mill

000437 93?9 IF (6 1 LI .El). 1) GO TO 03]700044 1 DMA* = SUHLfN (Ml009441 IF (ISS ,FU. ?) ru-lAX a S'lRl F N I I A- 1 )

000447 GO It) 9(?10004SO 931s IF (KH . Fi. ?| r,o TO 93170004S? ND" = OFPTH(IM) 19.0004S6 = Mil) » 1.0000460 (IMA* -- court HI)) - . PTHIl.-O000464 KM - 1

000465 UO 10 9 K?l

00046S 9317 NOD = l)FPTH(TST) 19.000471 D = Mil) • 1 .

000473 DMm = i'ln(l.«) - nn'llim - D

000477 KPS I =

O0OS0O IF ( fv [ L I .FO. 1) I1MAII = PTH(Il3) - rflflHlini .

OOOS06 ll'l K, K 1 miPOOSM IF ( 1 P I 1 r, ,fj), u\ »^iTF (6«in?6) OmmO0OS17 10^6 F0-MA1 (6X,^Hr)MAV = ,K1S.?I00 OS 1 7 IF IMI.I ,tj, II .' TO ?->n

O0OS?l IF I I S T K V I ( K O I , fi T . rSTFFLIK 0-1)1 «« - K 1 .

O0OS?S ]F (j .ill. ?) PO TO f,->4

C (t TEMMlNE ThF SFCTIOM o-JOpFwTIfs /it TmF m ut F>in

00DS?7 TO = OK 1m(IS1I . PLATHlKKill PLATH1KK,?)000533 f,0 It. 6 ?s000534 60?4 TO -• 0.1

000535 6D?S SIl = [ S T F F. L ( l» K ) / AllSlTO - (" S ( K K ) 1

CPOS DOCPOS 01

CPns 0?cpos 03cpos 04CPOS OScpos 06CPOS 07CPOS ort

CPOS 09cnns 10CPUS 11cpos 1?cpos 1 3

cpos 14cpos ISCPUS 16Cpos 17cpos 1Rcpos 19CPOS ?0CPOS ?1CPOS ??CPOS ?3cpos ?4CPOS ?sCPOS ?6CPOS ?7CPOS ?«CPOS ?9CPOS 30CPOS 31

CPOS 3?CPns 33CPOS 34CPOS 3SCPOS 36CPOS 37Cpos 3MCPOS 39CPOS 40cpos 41CPOS 4?CPOS 43CPOS 44C-'OS 4SCPns 4*CPOS 47CPOS 4HCPOS 49CPOS SOCPOS SIcpos s?rPos S3CPOS S4CPOS ssCpos ShCPns S7

L48

00^4?oor;S430J0S4SooossononS54POOSAOnoosftsnooS7onoosTsn o o 6 o o

000604000607O0061?00061

4

000630OOOMl00063300063S00"64

1

64 6

noo6S'OOO6S40006S7000*63

000*77ooo7m00 70600:)7?30007i,0

00074400»7470007S30007^3O037S30007si.

00077'

00077'

000773001 004

010 0<.

001006noionooioi'0010 3",001 04*nolOM

1 S I

no) O^o

001 0S60010S7noi 07s00111 3

ooi i?i

PI

PI

IF

SI

SmAC41

SSssIP

If

IF

IFIF

GO' PLPLIF

IF

IF

TOIf

HP

C»I StTSH

caC"SI

SHSIr,n

COKlIF

1 ? 7 F 1

L5H

S"JO

3'-i

1 io

CA

IF'

rr.

IFPTPIIF

lc

IF

(.(

P'

I'

P I

I"

IF

n

I= PI

4 > D|

I Jp I 1

5 = II

-, = III

ML =

Sr( =

= I X I

= SSIJl'T I

i jr I i

IJl'I 1

IK I LI

I (US I

10 )•

= .> i

= p i

iP I H I

II fHIe JP1 I

= lin

'J .

a |)| ,'

i.l If

I^ISI„ = S .

* ? . "

LI. IC1H. ICrt

1 = SI"> B 1H> = Si

10 -r

glli IJ(

i.l. = '

I IPT I

-MAT I

->>=,CALL

LI. IF-I'M I M I

I 1 K 1 I

-< 1«T I

.ll IDS

1 1- I .

•1 I I - I .

1 l I . ))

(IPllIIPIlI KM .

I (' MlH I I i 4 )

l l .I

i l I « I .

UPTII Ll I

Pt

n ( «

U In

I'l .

S (K

N Ik

T«pL«I )

(OF

tjT.

i,r.

(.i

.

E ).

;. ih

. I I.l TO 4-3

k i / a a s ( T n - ci i km i

f ) / Mr,ll,l - fH (P,K) )

I»«|PlP!HI|tll/;,»PU/i,n.i

o P| l«»ll / 1 ? ,

. ?..«*1 SPC ?,»APHI1flPTMI 1ST) /?. P[ 1 )

«> SIS = ss9) S| S = SS0) SHS = SS1 i Ro to R oo

IKK, ill. I. T.. 0001 .A NO. I ,F". i SS = STS

"ll-llllMl I-) ,?)I.l) .11. "T.il 1-1 , I ) I P| I

I.l) .11. °TH( 1-1 t I ) ) P|.W

.br. Qi i.'i to 4907.. ( 1ST) . »'_T

l. ff) In = n.oI'H [SI ) /'. . PLT

I i ( O.n. 0.0. Dl rt t P|. TtOfPTiMTSTl

a r>lH I T

a PTH( t

, SA r A I -ST1 , IX I 1ST)

HF A I 1ST ) . >! T°^l W

(UEPTMIlSTl ^>lT - SCII f'ISl AH»IO/ 0.»HP) t SLAHTH»0. .0. iMiTSa .SJS.Sc.wAllN'l r I si AM»n/'<-*.SLA'3TH,n.,(i. 1 H,TSA.sis.<:r,.«AUijrhfrS'./I.HSlin . Sr)/AHSlTll - CSh)/JHS(TI) - <~Si )

1

1

.to.* >6HS

1

1 II . 3 )

. iHf

INihk ru

• ijf •

'(Hi IF

Thf f

'1. 1

)

I = PI= PThI

. E ';

.

• F.Q,

I . 1)

= PTHI. NT)I = fI

. F. O

,

.F.J.

fill 1*1

'.I WJ1TF (6.10?M SI«,S i »F10,3»?Xi 6HSI S =

SI '

ifl' .3.

sshSmS

InfF nlSlANCr IF RFoilTKFDII *PiTf (»,. 1 | 0) |)I ST•<rilT3FF iiISTamCE a .f|S.s//iIm «-W«Yr.o IT c)3f,o

h ( I - I , 4 ) > ) I S I

1-1 . 4

)

41 -<J TTI (6,|n,?| |nT.<

| l-l ,K i . K = |, 4|

4) < -J T TF (6.|i.l2l (PTH(T,<) a « n 1. 4)

;i I 1 n3^u

I ... i . Ill ST.n r i q jno

I i

)

4 1 .-lilt 16.1 002) IPTM I 1,«•)

4| .-UTF | f\ • 1 ? I ( P T H ( T • f • I

.4)-3TH(I»l<3)l ,(3I , .nonii

) . \ )

= 1.4i 9no

= n

CPns s«CPns S4Cpos 60CF>ns 61

cpos 6?CPns 63CPns 64CPns 6SCPns 66Ci'ns 67CPns 68cpos 6<J

CPOS 70cpos 71

CPns 7?CPns 73CPns 74CPUS 7S.

cpos 76CPns 77CPns 7Bc^ns TiCPns PO

nP,0.« CPOS «1

cpos R?cpo; H3CPns B4

n.CSL< SL) CPns AS•Shi CPns 136

cpns R7CPns RHcpos RQCPns 40CPns 91

CPns 9?rpns 93

10.3«?A« CPns 94ci'ns 9SCPns 96CPns 97CPns 9RrPn-, 99CPns >00

rpns >01

CPns P03c^ns '03

f^ns »04

c^ns ,>os

CPOS /OhCPUS '0 7

cpos 'OHCPCf, '09TMOS Mi(. >JI1S '1 1

rPiis M?rpns »] <

cJ ns '|4

(Ji ii MS

49

001 1 ?

1

KlLI.

0011?? IF (

0011?5 pr-ii

001 1?* PMl001 130 GO 1

001130 04 Pl-ll

ooin? pr-i<

001 134 PTh (

00113*. PTHI001137 KP-><

001 1*0 SO f

0011*1 Q-)5Q IF 1

00 1 1*3 IF I

0011*7 IF 1

00115? 93511 KF< a

001153 93ftR

C

001154 00 -.

00115ft tri =>

001 157 IF 1

OOllftS 0357 CO'N 1

001167 93«ft KQ J

001 171 KC »

00U7? ISS001173 IF (

00120ft IF (

001?10 GO l

001?11 0371 If" I

001?15 IF (

001??1 IF I

001?35 GO f

001 ?3(5 0100 CO Ml

001?*

1

c

NTor

001?*? DO i

noi?*3 DO ->

001?** 5060 PHH(001?57 Kl^-001?ftO NPU-J

001?6*f

OOP

001267 17s001?70 I/f001?7I If I

001?74 IF (

001301 OS »

001 304 Or »

00130ft IF (

001317 FTol0013?n KJPi0013?! IF 1

0013?3 MP>0013?4 1^ 1

0013?ft IF (

001 333 KT->>

001334 5000 KT^h00133^ If (

1 3*0 KlPr

-I

PTH(!*2tl) ,1 1. PTHlIiUl 60 To q;,

1.1.1) - PTHd.l I

l*\,g) a PTH(1.J|(! VM1I. 1 , 1 ) 3 PTHI I .'.1 I

1*1*2) = PTh< l*?., ?)

1.1,1) = PTH(1»1,31 - "I 1* 1

I,/, I = P T H ( I I • 3

)

I

9.100

1 .FQ. NC) no TO 9 3ft 5

PTH(I»1«1> ,fiT. ,1: r,n Tn 9300KP .LI. .5) RO Til 9lftfl

?

1

UTOFF THF RIGHT FNO IF RFUUJPFO357 K =

1 , N«K

AhS (C'jO^ ( In) -PTHI 1 ,4 I ) ,tT . .00001) GO To ^35ft

INUFII

1

= 2

iptio ,eo. *) "Pttf c f>. i n 1 2 > ko. Kc. i 5;*

KB , FQ. ?) GO TO 037191?9

FT H ( 1 1 1 11 .GT. ,11 KC « 2

PTHll.ll .LT. PTh(I.I.I)) ISS a 1

IPTIO .EU. 41 W«lTF (6.1012) KO, KC, ISS9 115

INUF= NC

i T UP 1HF PHH SPRAYft I 1 , N T T

OftO K = 1 , 4

1 ,K I b PTH I 1 ,«. )

t » =

= 37. ?, o OEPTHIIST)* NHOP • 1 ,

tT DP THF OPTIMIZATION PPOCEDllRF IF r»'n MATS i\RE TnD SHORT* 1

= NlOTFHHI 1,1) .IT, .1 ) I ?S « ?

PhhINTOT.1) ,LT, .1) J7F * NTOT - 1

PHH(

I

iS,U) - PHH ( I 7S, 11

PHH( |ZF,4) . PHH( 1 7T.11IS .GT. HOP .A'lO, Of ,GT. OOP) GO Tn So?.-= U00990000,3

is ,of, nrp) go to s n h o

3 1

1/s ,FQ. 1 ) RO Tn 5OB0I OP - US ,GT. dhh 11,4)

OF ,gf. nnPi r,^i to ^ooi3 I

PHH I 1 , >) ) r,n T^ eonO

CPns ?ift

CPDS ?17CPUS ?1«CPOS ?19CPDS ?20CPI1>, ?21CPOS ???CPDS ??3CPDS ??4CPDS ??5CPDS ??ft

CPDS '?7CPns '?HCOS ??9CPDS ?30CPOS '31CPDS ?3?CPDS '33CPOS '34CPOS ?35CPDS ?3ft

CPDS ?37CPOS ?3«CPOS ?39CPns ?*0CPDS ?*1CPDS '*?CPDS ?«3CPDS ?**CPOS ?45CPOS 'ftCPDS '47CPDS ?»fl

CPns '49CPDS ?50CPDS ?MCPDS ?s?CPDS '53CPns ?54CPDS '55CRnS '5ft

CPns '57CPns '5fl

CPns ?59CPns 'AOCPOS ?61CROS 'ft?

cpos 'ft3

CPns 'ft*

CPOS 'ft5

CPDS ?ftft

CPDS ?A7CPDS '6Hcpns 'ft9

CPns '70CRns '71CPOS '7?CPOS '73

150

o

1

3*1001 341no 1 3Sf.

00135100135300135400135500 1 3S6001360001 3h1001 364O013bSO013h7001 37000137?00137S00137ft001377001*01001*01001*040O1405001*07001*1 *

001*1*ooi*?nooi*?o001*?3001*?*0014?ft001*?7001*31001*3*001*35001**0001**3001**3001**50014ft3ooisoo

00150000151)3015 01.

00151000151 1

00151?0015??00|5?1001S?400153700 154000154100154700 1 547001551

5(1^ 1

SS^O

=•4

5S

Sft

50?5

39

103R

10T9

SROO

J 01

51 I 1

51 1?

"1

IFUK [P

r. f j

r.Pi

KPFIf

IfPfHP Mfin

PT*IF

IFPTri

PTiGOPTHN-T-t

Ki

DOIF

IF

en

GOPTHPlHpthPHKICO'1

NCIFWRIF(H[10

WR(IFFP*

15 H

?7H<

CALIF

IF

DOnoP'n01DnPbHHI .)

FT )

IF

FlMIF

00

* i\

IKPS(r kS( l/SI I /sM. 5

( IZS(KPF(KPFil/hI I/F(0 5

I UF= N

= 1

"(. I

(1

I AHSIM-

S' N(0 4

IKI,IM«I K.I I

(M .

= KII1MU= NB(1PTIf I

1AT1009il (

(KIP4A I

•_CAU

IFF

CALL_ FLIK IP(I- T

Ml 1

>! 1 1

I 1 . K

-.1 1?>! 1?I I ,K= N

I r

I IPT1*1

I iPl•O I

- OFi ri ) i'i n 5phi

i T . PHH( fJT0T»4) - HHM ClTOr . 1) 1 fin TO SlHl

I

F

HJ. P) fiO Tn tc.

Hi. 1 ) fiO To 54) s PTH( 1 75,41 - OOP,4) PTh I I 75. 1)

) a

FU.f Q.I =

.3)s

) -

I

Pi.M 1/5.1 ,1 )

0) RO Tn 5n?5l ) r-u To 5ft

PI ri I 1 7F , 3) OOP« PTH I I 7f, 4)

PTri( I 7F-1 ,1

|

* 1, MOTto. 1) C-n in 3 9

(PTMd.l ) -PTh ( 1-1 ,1 I ).bT..0001 I r,n Tn 3Q

1,4) = PThI 1.4)"H -

1

I)

I ) = PThI 1 , 1

)

?) = PTH I 1 . P)

1 ) = P T H ( 1 i 3 I

4) = PTHI T .4 I

1

.

.10lul1 =

. 10FH1M0E I

.1

OHPTEHGT.I =

K =

LT. 3

3B)

• IPX,1 . N

0?) (

• FP.• IPX,HE t N

?.?> .

Fl "PTI PTH,• F(j.

F l r t

i ro to 101

44HPTH ARRAY AFTFR rUTnFF A.'- LFK'GTH ApJ'iSr

PTHI I.K1 « K = 1, 4)

1) »HITF (ft.^ROOl KDF.KIPF ,Kn5,K TP5R7riTHF FLnPT SUBROUTINE TS r«LLFn A nUmp.fR

PLATF5 ARE TOO SriPPT. /15v,ftH«PF « ill,?ftHKPS = ,I?,?X,7HKTPS = ,l?iTn nFTFPMlMf THE SPLICE inr.TinNS

NCf COST.FT)n) fin in 5iooi fio To si in

I = o.nI = 1 . NTK = 1 i 4

= PTh I T ,K1-

( .EO, 4] WRIT! (ft. SI)lul . 1 ( » .P^riTnF niRrifNlp .nf. 4i fin Tn r?- l. Kin

PSh ARRAY, • //)

CPOS ••74

CPn5 ?75cpos ?7ft

cpos >77CPUS ?7HCPOS ?79cpos ?R0CPns ?«1cpos '«?CPOS ?R3CPPS ?R4CPns ?RSCPOS ?Rft

CPOS ?R7CPOS ?RHcpos ?P9CPOS ?90CPOS ?91CPOS ?9?CPOS ?93CPOS ?9*cpos ?95CPOS ?9fe

CPOS ?97CPOS ?9RCPOS ?99CPOS 300CPOS 301CPOS 30?CPOS 303CPOS 304cpos 305CPOS 30ft

CPns 307CPOS 30R

TMENT//)CPnS 309CPOS 310CPOS 311CPOS 312

OF TIMECPOS 313x, cpns 314

CPOS 315CPOS 31F.

cpos 317CPOS 31HCPOS 319CPOS 3?nCPOS 3?1CPOS 3??CPOS 3?3cpos 3?4CPns 3?5CPOS 3?ft

CPns 3?7cpos 3?RCPOS 1?9CPOS 330cpos 331

I 5 1

101551 H WP 1

101S71 «? TF

10 1 6 » 5HH1 F (H10160? Rl 10 IF

io lfcin KPFD01605 IF

n o '* (i * r,o

COl 6 (J

6

5i?« IF

P01607 l>p-

OOlhI 1 IF

noifii? K"F00161

3

5 3>'0 D')

PO 1 ft 1 s on00161* 5310 PTm00 t ft?f> DO '

ool6?7 no00 1 630 53?P pri001643 CO001644 54 10 DO001646 no001647 54h0 PT-i

001657 NC001660 on

00 1 ftftp DO001663 5441 PTh00167* 51^0

c

KH

001677 oo001701 IF

001704 IF

001710 KHOOWl' co^00171*. cov-001 7?1 co</

0017?4 COi/'

0017?7 G )

001710 H0"3 COv00173S "0 10

C

COg

001740 IF

00174? Wt< 1

001748 ioso FOl00174* DO0017S0 10'-

1

fcHl

001767 1053r

1 ?

FO-(

001767 DO00177) IF001771 00001774 10

00177* IF

oo?oos *?50 C3N0020U7 1 01oo?01

3

DOO02014 IF

L.LI00?034 IF

00204* *1 19 COX

It I i . 1 ' 1 IPS-'ltiKl, k n 1. u )

(IPTIi .GF. 31 «^llF (6,551111 FI'T«i-\ ( I iiO> 3r* . -"if TnT c ,F]t.5>if ikf ,ti. r i uo to 5i ?fl

= KPf - 1

IhPF .IU, n ) fid ro 5] ?01 1' b 1 u

lMt"> .ED. P) SO TO 5400= KI'S -

I

IM'S . TU. f ) RO To 54= MI'K

-> 31 I) I = It 4

-i-IIO K = 1 • 4

( I .K) = 0.0T3?0 I = 1 t NTOl-.3?0 K = 1 , 4

( I.KI = PriH 1 I ,K)

10 55 uO»440 I 1 . 40-,•,1,0 K = 1 , 4

I I ,M a 0.0= NTO-i4« l I = i , nr-i44 1 K = 1 , 4

(I.KI = PSFl ( I ,K1=

11 T UP IMF' COVFP PL4TF ARIlA**n(io I -

i . mc(Pi ii( 1 1 1 ) ,ii. .n oo to mo oni*pS(PTh< I ,) i-CHii-i , l) i .it. .(ioonn fin To R003- KH » 1

PL (Kll, I I J) = PTH ( I . 1>

"t. (K.ii?» Jl = Pin ( f ,4)-0 (Km, 1, J) = DTH (1,11*>L (Ki1,4i J) = pTh I T » ? )

I HO*l (Kit, ', J) = p[h(t,4II 1NIIF'

^F- 1 .J I Ihf: TOVPL ApRAV IF UEOllIHFn(IP III . L T . 1) 00 TO 10'K IhtlObO)iM ( I ho. i (i* . i phCovpi a-tnnr //il 051 I = i , i ?

IF (h.lOM) (fOvOL ( I ,K, I) , K B I, 4)1A1 tnx,* (Fl 5.5,5X1 1

«it r LIP IhF PI aT.H ANO ol^TO APPAYSil 1 I - 1 i NF(F"l .Fo. 1) Rn TO 10or' 5 II = ?, MN= IOSP(II)(I ,Fo. in- 1 .OP, I .FO. ID) 00 TO Ml"I INUFa (chop ( I ) . pons (i*n) / ?,»109 J J = 1 , 1?t*HS(CJVPL (J J. 1 . J) ) .LT. .00001 ,»Nn. auc CO* PL ( J 1.7, n..00001) 60 Tn 6007IbT .GF.. COVP| ( I J, 1 , I) .and. OT ,LF. rOvni (J |,2, n ) fin

I I Ml If.

cpos 33?CPns >33CPns 334CP'IS 335CPns 136CPns 337CPns 13F1

CPns 339CPns 340CPns 141

CPns 14?

CPns 143fpns 144CPOS 145cpds <4F>

CPns 347cpds 34HCPOS 149CPns 150CPns 151CPns 35?CPns 353cphs 354cpiis 155CPns 15*CPUS 157CPns 35Hcpiis 154CPUS 3*0CPns 1*1CPns 3*?CPOS 3*3cpos 1*4CPUS 1*5CPns 3*hCPDS 1*7cpiis 3*ft

CPns 3*9cpos 170CPUS 371CPOS 37?CPns 173CPns 174CPns 375CPns 176CPns 177CPns 178CPns 379CPns 3R0CPns 1R1cPns 3R?CPns 3R3CPns 3R4C^ns 3R5

) CPns 3B6CPDS 3R7

in fcloa cpos 3RRCPns 1R9

152

0020M *m7 hi jiniiiji = p. tin ~ cpos 1900020^4 pi. -hi 11. j) = o.ono cpos i9i002056 GO IU 6110 f.PnS 192no?os7 sp« cO'MilNUF CPns 193<>02o5t if (AhSU'T - rnv/PL( Jjt It J) I .1 T • .nnoon .0 to ,.noi cpos 194no?o6h if (ahsjih - covpl uj«?iJ> ) .lt. . *onni i w to »noi) cpos 39500207S PL*1M(I,J1 = rovPL I JJ. 1. I) CPOS 196002103 Pi.«IMI.J> = r.0«PL(JJi4tJ) CPDS 1970021m go rii 6110 CPns 19R00? 1 1

1

4010 kjii = jj CPns 199002113 IF <COVPL(JJ*l .3, J) ,LT. C0VPL(JJ,3i J) ) kist 3 1 J 1 CPOS 400002133 Pl<Uh(I,jl = fdvPL (K JST.l. Jl CPOS 401002131 Pl.ill (I.J) = C0VPL(K.|ST,4,J) CPnS 402002136 GO It. 6110 CPOS 403002137 4001 KJSI = JJ CPns 40400?141 IF ICOVPL (JJ-1»3.J) ,LT. COv/Pt. ( JJ.l, I) ) K 1ST • U - 1 CPDS 40500215] PUMHII.J) = rO\/PL IK JST.l, I) CPns 406002157 PL«lt'U.J> = fOVPL (K)ST,4. J) CPnS 407002164 6)10 COxllNUf" CPOS 408002167 IF IJ .£<>. 1) fin TO *200 CPn.S 409002171 IF UPT1 .&T. 9) GO T o M50 CPns 410002174 J » I CPnS 411

r ->KT UP THE Tnp PLATFS OVFR ThF TnTFPI'II* S' PPoqTS CPOS 412002174 DO il40 I = )f in. ?

.CPOS 413

002176 Ic (LPCM(I) ,FO. 01 GO TO 6l«S CPOS 414

002177 I* " LPCM(I) - 1 CPOS 415002201 18 » LPCMU + 1) CPOS 416002203 DO nl41 JJ = 14, IR CPOS 4]700220S PL4IH(JJ,1) PLATHUJ,?) CPnS 41fl

002207 6141 PL*lU(JJ»l) a PLWIOUJ.?] CPOS 419002212 6)40 COMIINUF CPnS 420002214 6145 CALL SFMlC CPnS 421

C PKINT IMF 5FCTION I NFOR^AT I ON IF PFOIITWF^ CPOS 422002215 IF (IPTIO .LT. 4) GO TO 63"0 CPOS 423002220 CALL PRSFC I NF .MOS . WAMF . PL * I . PL ATM . T STFFI . CS . Tl CON, PL , I MCON . CM, CPOS 424

lCOO*t,SUHLEN,0,Nl-Y) CPOS 425002236 GO fC) 6300 CPOS 4?6002237 6350 DO t>?51 1 = 1, 1? CPOS 427002241 DO "251 K = i, 6 CPOS 4?800224? 6251 COVHLII.K.l) = mVPL(I,K,?l CPOS 429002255 DO i?52 I = 1 , 'IF CPOS 410002256 PL4fH(I,l) = PlATHIt,?) CPOS 431002260 6252 PL'lDdil) = PlwT0(T,2) CPnS 432002261 62"0 REIJKN CPnS 433002264 EN'l CPnS 434

suhproi.dam lfngtm003304

UNUSED COMPILER SP4CF032500

SURGUT INE CP*'iFS CPWO

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I 1 A

It INIt T

(

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/(JNF/.JP/six/Fn/E IGH1 /

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>.lY(i«)iN<;FrT(iH),Niis(«n),T<Mc[| i in) ,rs(P0> i

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1

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1ST1FFI • TLCON, THCON»Mrt,LFMRrH, Tl T'-'T

1(41. TS<4>InF ALLOiVA»|.F WFLO STATIC STi-'FS";

3) - TS.) ,(5T« 1.4S) FVThF iop plates

r 3 . l r

.

I = 1,S(COVP(7 10

EHMINING STAPTfllti AMD FADING MODFS

Q) SLAHA = SLAHwD o S! AHTh1 ?

( I . 1 .« ) 1 ,I.T . .000 1 .AMD. AHS<rovR| if,?, Kll.LT. ,0001)

J = 1,

.'IF. n

V^i I I . 1

VPL (I .?MF.

III-

F>mINEI 'J.

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F'l. 1?S IC'IVP|

S (C3VPLI ,S,M

S (COVPLVi' I (1,1

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. c ) .GF.COOW ( J) . AND.Cn VP| ( f , ->,k i

.AND. fH .NF, n) GO TO 7H1

I F .C00-> ( J»l 1 1 [A:

I F .COO') ( J,l I I IF):

J«lJ

1HF FNO CONDITIONS OF THF PIATF(.0 10 qUl

I GO TO HO?(I,1.K)-CG\/PL(1-1»?»K) ) .GT., f>0ni) ^0 to ani( 1 ,->,ki -cojdl ( !« 1 ,1 ,k|

1 ,6T. • onm 1 r.O To Hr?= o.o"

( I ,5,K) -C0v/O|. <I*ltl»K)),GT..O01 ;

.K) l ,s»ravP|. ( 1 ,4,ki - rno ' ( 1 '

r,n TO R^o

LT, 0,0) kI

A

H 1; (0)

701/0

SIC iv Pi

Vl'l ( I ,?

( I , 1 ,K) -tOupl ( 1-1 ,?,K ) ) ,r,T,

.

r on 1 ) -.n to Rio.«i - 1 .^"covpi iI.4.ki . rnnui-i

T. O.r ) x I

= !H= I

= A

IL<

i3lS I (J= s

- 1

H\ (IJ)

7 1 or1=1,

1 = DFSIl«««*l T

ran 1 I a . 1)

CPwCPwrCPrtl

c^^rCPrfi

,CPwi,CP-.

ci'wn

CP»(I

CPwi

cpwiCP«IC w wi

CP-'CPWICPwrCPwrCPWDCPWICPwiCPWIC-'wi

CPwl

CPWICPu(|

CPWDCPwlCPwiCPWICHWICPWiCPwiCPWICPWICPwiCPwiCPWfCPWICPwitpwdCPwiCPWICPWDCPWICP voCPwrCPw.CPwiCPwiCPw<CPW'CPwiCPwiCPwi

CPwiCPwlCPwiCPwl

?

34

S

ft

7

R

9

10

1 1

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1 R

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3 1

3?33343S3ft

373R3^1

4041

4?43444S4h4 7

4H41SO

S?S3S4SSSft

S7SHS9

154

noo?47 on *3? 1=1,4 cpwo miooo?5i p->? T-iii(j) = DFSmom<I«,j) cpwo hir\on? t>7 t« sT''M'ix t T"sn cpwo ft?

POP?ft) If" lAMS(TH) ,r,T. A-iS(TLi) Go To mis CPWI) 63oon?6A 01 io 837 CPwn 64

r i)FTEMHINE Tmf »r Ln OFSIGN SlfJFSSFS C^Wli 65O00?ftft 70^0 DO a ? ji< = ), 4 CPwn 66non?7o no 'hi J = 1. na CPwn 6 7

noo?7i 7"3 "oi i) = oeS'iomi i, jk) cpwo 6«000300 71? INiiI.im = II.INT ( IT tSOtCOOHtKTtnP, LENGTH, Siltii FNI CPwo 69norsn if I* .F'i. 11 i>n to 710 CPwn 70000315 TMSI(l) = TMSTll) r'i(TS) / 15TFFI.MM C"WH 710003P0 IF (JPT < .GT. 4) GO TO 100 CPwn 7?0003P4 TMSII?) = roSTl?) » CH(TS) / IHCONMSI CPwn 730003?ft T-I-.M3) = rnsi(i) » rL(IS) / ILCOmiTSI CPwn 74000331 T^MUI = TOSTU) » rnllS) / IHCONITS) CPWO 7500033^ I--') I'' 7?(, CPWD 7ft

001334 7io to a riE'-i m < im ) . plaTH(IS»ii plath(T5,?i cpwh 77000340 T ^1 ~»

I ( 1 ) = TMSTin • (TO - C5IISM / TSTFFI.I'rl CPwn 7fi

000344-

IF (JPT' .GT. 9) GO TO 100 CPwII 79000347 TMSII2) = T>-1ST(?) • (TO - CH(IS)) / IHCO'ltfl CPwn «000035? TM-,113) a fMST(3) • (TO - CI.(IS)) / Il.rn'illc;, CPWO fll

0003S*. TMlll.4) = TMS1U1 • (TO - CH(IS)) / THrO"<Tci CPWO A?0003ftl GO 10 7^0 CPWO A3O0036? 1)0 TMSit?) i iMSTl?) CS(IS) / ISTEFI (15) CPwt) 14000361 T-t-)l(3l = O.n CPWI) R500036ft TMSIU) = T^slU) » CS(TS) / ISrEEL(TS) CPwn Hft

00037H 7?0 TOS = SrRMA*(TMST) CPWO B7000373 F = A'<S(TOS » COVPI (T.4.K) • COtfPL ( T . 3 , K ) 1 CPwO RH

r OfcTF.i-iMlNE THF Ai L0*AH|_F STHFSSF5 CPWO R900040? 51. = l>lsT(l) . T"ST(?) . T'<ST(3> CPwO 90000405 bH = TMSTdl . T"ST(3) . T«ST(4> CPwO 91ooo4ii7 IF (ArtS(SL) .(?T. .ooni .A Kn. absisii ,r,T. .«nnVi go to f,;n c iJ wn 9?0004?3 P = l>.0 CPWI) 930004?4 GO 10 610 CPWO 940004?4 600 R = SL / bH CPWO 950004?ft IF 1AH5ISL) .r,T. 44S(SP)1 '> m S° / S| CPwn 9ft

P0043? 610 S< a 1.0 • .3ft • (FJ/SB, - 1.0) CPWO 97000437 AF-. = 10. H « Sn / (l.n - .IS « K) CPWO 9H000443 ASI < = FV CPwtl 99O0044S IF IAFS ,LT. A5TR) AST>^ AF1 CPWO 100

r nETEKMJNE 1 «F ^T^r OF THF wtl.O CPWO 1010004SO I/J-. = F / (?.H?H » COVPL I I .4.M • ASTl^l CPWO 10?0004 c

;ft Olft = TwS / ,rft?= CPWO 103000461 IF lAHSlTwb - Klft«.0ft?5) .GT. .00011 Mlft = • "ft » 1 CPWO 104000470 T«fS = ,iift?b » MA CPwn 10S00047? T1<»» = FLTH(TSl) CPWO 1 nh000474 1 T -I = FLTH(IST) C''wo 10700047ft IF lCnVPL.(I»'1»K) .U, T1AH) TMAX b rov°l (I.l.K) CPwO lOHOOO^Oft IF I lovpl ( I . 3,e l ,| T. T-iAH) TTM s cnVPI il.1.«l rPwO 104OOOSlft T«M s [OPTlTHAM CPWO 110

r -.lone THE POOTHFT wfi n SJ7E CPWO 111O0OS?l IF (1*S .ST. T^tM) GO TO SOfl CPWO 11?000 c'?4 IF (UM ,11. T^'lh) ',0 TO =.03 CPWO )13O0OS?h cn/^l (I.s.K) = TmI'i CP«*n M4000^31 GO ii »U0 CPWO 11100053? SI1.3 COi/.'l ( I

.t ,A) - T"pi r» ( ii lift

OOOSlft IF ilriS .LI. TI") COVPI IT.^.K) = TT^ CPwo 117

1 55

(IQ0544 GO II 1 V(>0

nooS45 s^o cn/^i <i.'>.k) = twsr CALC'lLATt Thi- T-UrKHrSS nF ThF Se-a(_ wri n

P00S51 900 C p a = CUVPLIT.l.K) » COVPU 1 1 .4.K1000557 D5-> - O.o

C itTEKMINE TMF P'UnT df Ma.Imum ShFASP0O56U 00 'SO J a IA. In

000^6? IL a ? * J - ?

000564 14 a ? * J - 1

000566 oo /sj jk = i. (,

000567 751 TM-.IUK1 a DFSSHI IL.JKJO00576 IL = STKMAX(TMST)000600 JO /5? jk = i , 4

P0O601 75? TMSHJK) = OFSShiIo.iKI(10OM0 TH * 5THMAXITMST)00061? IF (AHSlTl.) .11. OSS) on TO 753nooMs oss = ahsul)000616 [C » J - 1

f> ? IT^Joooe?i n a il

0006?? 7F3 IF lAUSITP.) .11, HSS) BO TO 750ooo6?5 os-> = aiis i mi000627 IC * J

000630 I r = j

001^31 10 = IH

00063? 750 CCHII'JUF000635 IF Uip5iiOHUT.il .IT. n.o) oo TO 3ooo000637 IF UPTJ .or. *>) GO TO inon00064? IF If .fO. 2) 00 TO 301?

C itTFKMlNf Tmf 10? DESIGN STRfSSfS In THF oOSTTIVF RFOtOn000644 TSii) = nt- Ssh I In, l I »rPA» <DFPTH( ]M) +PI ATH I lo. -) -i-S ( IO

IPL'Uhl IC l ) /?.) / IStEFi ( IC)

000655 TSi-M s DESSHI In,?) »SL AHA" IriFPlHI I'M »P|.ATH( Tr.ai -CHMC) sl.ARTH/?.IHA'HCH) / (MP ••IHCONITO)

000671 T5M) = OESShi in, 3) »SI AMA»(nEHTHI I'll *PL.ATH I T-.2I -CL I TO SL.AhTH/Z.lHAiUCH) / (3.0 « MR » ILCON(TO)

000705 TS(») = OESSh I In,* > »si_AHA» (OFPTHI IM| .PLAT'i I l^.?l -CH I TO SI AHTH/2.U'A.uCh) / <MW • iHCONIICfl

000721 GO 10 3'UUC i)ETE»MINE ThF HiTTOM OFSIGN STRESSES T

ki t.jF POSITIVF >EGTON

00072? 301? T S « I ) = DESSHI In, 1 1 "cPa" (DEPTH! IM| £>( ATHlTr. -•) /C-CSI IC) ) /

i isrttLUCi000733 TS(^) = OESSMI ln,?l «rPA»(OFPIH( (M) ,p L ATH( ir.^l /^.-OHt ID I /

I HC iM ID000743 TS(1) = DESSH I In, 1) »rPA» (DFP1H I IM) .01 ATH I IC . ->) /?.-CL I IC) i /

II LC INI IC)000754 TS<*) = DESSH( In,*) »rPA» inEPTMl IM( olATH I IT,-') /'.-CHI IC) 1 /

llHCuM ID000764 00 10 31-01

C >tTE*MlNE THF OFSTON STRF^SES IN THF MFcatIVF REOIOm00o7hS 3000 IF If ,EQ. 21 Go TO 3010000767 CO-c.1 = CPA • inFPTHdM) PLATHdr.?) - CSITCI PI aTh I t C . 1 > /2 . )

1/ I-ilEEMIO000777 00 10 301 I

001000 3010 CO^-jI = CPA • (nFPlHiIM) P| ATh I I r , ? I /? . . rS i I c) ) / TSTEFL ( IC

I

0O1U07 3011 T5(l) a DESSH(in.l) • CONST00101? TS(.M = DtbSniIn,?) < CONST001013 ISlll a DESSh<IO,3) • CONST

CPwn 1«CPWO 10cpwd 20c^wo 21CRwn ??CPwi) 23CPwi) 24cpwo 25CPWI) 26C°wi) 27cpwo ?fl

CPwo 29CPWO 10r.Pwo 31CPWI) 32cpwo 33cpwo 34CPwO 35c^wo 3hCPWO 37CPWO Ifl

CPwi) nc^wn 40CPwi) 41CPWO 42CPwi) * 1

CPWI) **CPWO 4SCPWO 46c°wn *7CPWO 48CPWI) 49CPWI) 50CPwn 51CPwn 52cPwn 53CPWI) 54CRwn ssCPwn ^hCPwn 57cpwo 5RCPWO 59C pwn 60CPwn 61CPwn 62CPwi) 61CPwn 64cpwo hSCPwi) 66CRwn 67CPWO 6RCPwn 69CPwn 70CRwn 71CPWO 72CPWO 73CPwn 74CPwn 75

156

10 1 01

s

001016

00 1 031nol 024ool 026001 0400010*?ooio*?001 044ooiosoO010S50010S7

00106?001067001071ooi mi001 10S001111001116001 120ooli??001 12600H?7001127001131001131001136001137

lor 1

?7iO

2 7 PI

7«07<<0

101

102(-4(1

TSI-.IU£ T

TS>) =

CALSI. = T

SP = T

Jr ( uf\

AF-> =

go ru

[F (AMAF-> =

ASS I =

IF ( Af

It T

TWS =

Nlh =

IF [AHTwS =

C0i/->1 (

IF (Tw

CO <l INIF 1 1\

IF UPK a K

GO I (J

DO 10?COi/pL (

COV-L

(

HEfohNENi)

= l)f Sv< (10,4! • r-i'isr

EMMINf inf total orsiRN stressSi i "AA ( T S)

C"|ATl ihf FATIGUE ALL riwAHl E STPFSSsin • tm?> rsiDSll) IS(1I . TS( 4)

S(SL1 .GT.,0001 .A'in. asS(SP) ,oT..oooi i r,0 TO ?700Sr. • 10. f

?7o|/ Si*

S(SL) .GT, A3S|SP)I 1 S» / ?lSr. • ln.6 / (1.0 - .SS • P)f <J

S ,LT. ASST) ASST * afsEHMINE THF *FLO TmTC*NFSSAKS(TSn) / (1.414 • ASST)TwS / ,06?s

i

S(T«(S - (M16 - II • .0625) ,LT, .noil) Nl* b N16 - 1

N 16 • . 6 ? s

Itft.K) > T»Ss .it. ,)B7Si rovPLi I i6.ki • .istsUf

• EG, ?) GO TO «40T3 .ST. 9) r,0 TO 101

1

430II = 1 . 1?

1 1 .5.2) « rOWPL ( I t •»• 1 1

11.6.2) = rOv?(. 111,6,11

CPwO 176CPwn 177CPwn 178CPwn 179CPwn 1R0cpwo 181c°wn 182CPwn 1R3CPwn 1 R*CPwn IRSCPwn 186CPwn 187CPwn 188CPwn 189CPwn 190CPwn 191CPwn 192CPwn 191CPwn 194rPwn 195c p wn 196CPwn 197CPWI) 198CPwO 199cpwo ?00CPWD ?01cpwo ?0?CPwn ?03CPwn 204cpwo ?05cpwn 206

SUBPROGRAM LFNOTH001330

UNUSEO cO M PIl.FR SPaCF036500

slh

000002 COM1DAF?ILC3SL«4TMi)

5FC.bCOs

O0000? CO-t

00000? roi00? COt

00000? HFa00000? OH

"(OOT1NE UEFLFCCALCULATE THF RFfJulRFn OEFLECTTnNS FOR Tnr FTNA| OES111 iN NAME (IB) , SARFa I 1 R| .OFPTmiiri .FLWlni 1 u, ,Fl TH(is) ,WF(18),IX(lH),lr(lR),NSF.CT(l8),NOS(R0).TSTFFl(ao),CS(o0l'iN<80)«CL(ROI,HCON(oo)tCM(80),P| ATH(fl',?i.Pl w ID (A 0.2 i

-iwn,SLAHlH,MP,C0 0P(Hll,PH(5,Rl,1),cr(=;.ci.F",SPAN(4),It I (8") ,N4,I EnGTHiPU(O) ) .SnBLFNiari) , MS,"UI n (91 , TBI. 0(101".1RE5S(BI,4,9) . OES'IOmi Rl ,4) iOFSOF»(S.4t .nrSSmlft?,*) ,1119) .C3NSP(16,3,4) .COVPL (12.6,?)10N/ONF/JPT1, IPT1

n

10N/U/IDEF(?0) .OESnFF (20,4

)

.nOEf , PESCFN

,

hrYCiom/e/IPT?l ix.iy.is1fei .tlron.lhcom.mr.lfmbthtNSION Til

1 H , II . STIPE (10)ZERO OUT T>'l PE1JTRFO APRAYS

;n

I 1h ( |HI ,

.

.NF.I0SP(5J . utrL,PROP(3) iDEFLFARIS.3) ,()FFL

OEFl

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1

2

3

4

5

6

7

8

9

10

11

121314

15

157

00000? DO «*00 I = 1 . ma00004 W ilH J = li 1

00000s QHfO T IL < 1 . J) = D.(

oooois no -«*-oi I = i, mopfO000 1 1 DO ^h!\ I 1=1,4nOOO?') 9fin] DES'iEK(IiJ) = n,n

r -MM I HE MMnlM 1; IF PFOllinEo

000030 IF ( 1 i- T 1ji ,(,F. 11 W«ITE (ft. 9700)

000037 «7n0 HHiM ( l Hi «??HDFFLF.C TIDM LOADINGS...//)C ilAWl |H[". | OOP FTP FA^H OFFtFCTTON OFT'I'rri

O00"37 On ibdO I=i, mhFF000041 I a = 1 i H F ( I )

000043 DO v'iflU K = 1 i 3

C KTFKMI^E 1HF HFNnlNri ^OmfNTS DIIF TO a IIM|T I "An000044 IF UP! j .liT. 9 .ANT. K ,EQ, ?) (50 TO 75"O0OOS4 DO ->b\ J = 1 , NApoooss »»^ = o.''

oooosft rm <b] i j.i = i , nsoooofto in * InsiMjji0000ft? IF u .If. ID) (;n 10 9S110000 ft4 v* = WH N I L i j I • I n t k ) » I Coop ( n . rnnPiinnO00O7S 9S1 1 C01-I 1MUI

000100 SP = O.I

OO01PI IF U tlil. I A I SP c009(J) - conn n A)

000 10=. PO ( II = l»H - =F0001 10 9510 COll INuf

r itTFKMINE 1HF M/EJ A^RAYoooi i ' rm <b] 5 j =

i . nf000114 Ul 5 ISIFEL(J)00011ft IF I* .!"• <?> HI = ILCON(J)0001?1 IF <r .F'Q, 11 l)| ImCO-kj)oooips I'inrii j) = mni it nn( i*1>) / (?. • fi » miooom osi5 rOM i 1 f-i»e

r .itTF*"MNF_ THF !A\ir,F rJT AT THE LEFT FMnoooi3>i l»P = o,o000137 pn -('-If, I a 1, Nf000140 nP = </h . rnoflljl » SUHLENIJ) • (I FNGTH - roopi.il - SllRl FN ( J) /?.00014*, OSliS CONI INHF'

0001SO TAlc = wP / LFNOTHC '1FTFWM1NE INF OCFiECTTOM AT F*CH ANALYSIS PniNT

00.lis? TILMiK) s o.'O00015S TILINA(K) = 0.0POOlftO DO Jb?n J = ?, NF0001ft? »|P = 0,.i

O0 0lh3 I R = J - I

oooihs on v',?i jj = l , ih

C ilOHF [HE DEFlFCTtONS AS the lNF( HEMHF rnrF F t C I FNTSOOOlftft 9s?l FiP = wp*T^0ET i J I) »sj H | F'-M JJ)'» ICoru ( i) .rnn'M i I) -^"Hl fmi.j.m /?.)000177 9s?o tilu.m = r a i t o riouij) - ^ooo?07 9ftno en 4 1 1 NllE

000?) 1 7'iO CONI INUfc

r i.wAll THE INFLUENCE LTNFS TO iiFTFnMIMF TmF OFFIErTTOtS000?) 1 CALi. LOAO(TIL»TRLOi OnLO. 5UH| FNiNA» IPT?,I fill", r'lOH, !»,«H^FFL»NS,

1 IOSP«SPAN,S rnpF 1

000??7 IF iIPM*" ,GF, 3i WITF (ft.97nl > Ia, (STDdF(kK). KK a 1, 10)o ? 4 >> 9 7 - 1 F •< 1A 1 lls,x,ir(Fli.n,xn

r .11- IFi'-MNt THF nFSl -'i nFFi.FCT |OnsOOP'4*, pri ,|f (!,l) = STo^ciil

UFFL 16llFFL 1 7

DFFL 1H

RF.FL 1<J

OFFL ?0DFFL ?1

DFFL 22OFFL ?1OKFL ?4lit'FL ?SI1FFL ?hOFFL ?7DFFL PHDFFL ?9DFFL 30OFFL 31

DFFL 3?Itf'FL 33DFFL 34

DFFL 3SDFFL 3f.

DFFL 37DFFL 3HDFFL 39DFFL 40DFFL 41OFFL 4?OF Fl. 43OFFL 44UFFi. 4SDFFI. 4*1

OFFL 47DFFL «

in FL 49OFFL SODFFI SI

loFFL S2DFFL S3OFFL 54DFFL 55DFFL S6OKFL S7DFFL 5HDFFL 59DFFI 60DFFL hiDFFL *>3

DFFL fi?

DFFL F.4

OFFL ft 5

DFFI ftft

DFFL 67DFFL f>8

OFF[ *i9

OFFL 70OF F L 71

DFFL 7?

DFFI 73

1 58

000250flf|i?5?

000253ooo?54nou?5s

P00?*Snon?h7ooo?7?ooo?7S

000277ooo3oi00030S000305OOP307000311O0P33100031100033100033?

95S0

9v>o

9710

971 1

«70??0

Dt'S >f

POS *

SE'i =

no -<5

IF IS

If (S

comi i

ne:-»>f-

DE"> •!

crni i

hi.

if uwR( if

FCMirt

00 ' I

1« =

k.Pf If

F0-J1ACOM 1 I

RE I ifi

EM')

F (!

0.

0.SOTonTOWNiie

F (1

f (I

MueINIPT1

<(•

T I

I 1

I Of

(>-

T (

NUf

N

,3) = STOWFdnl

r,

K = ?, 7

fc(K) ,GT, ROS) °0S = STORf(K)f (K) ,n, SEr,) SFG e STORFIK)

,2) a Pns sTflOF(H),4) = sfg » sTni'FCl

IHE PESTON nEFl.FCTIONS IF OFQ'ttraFO

.LT. T) BO TO ?o.4710)1H0,21hpfSI!9n INFLECTIONS...//)1=1. MnFFr (I)

.970?) if. (DESnFF(I.K) , k i l, 41IS.4X.4 <F1?.9,4») )

Of Fl. 7*DFFL 75Of. FL 7iS

OFF!. 77OFFL 78OFFU 79OFFL BOOFFL RlOFFL fl?

OFFL S3OFFL R4OFFL B5OFFL B6Uf'FL B7DFFL HRDFFL R9OEFL 9Of FL 91

OFFL 9?Of FL 93OFFL 94

SUhPRP'ioAM LFNGTH00101 1

UNUSEO rOMPIl FH S^-iCF

041 100

RU-WOUTc »<H 4

c itFL00001>- HFui LLO0OO1*,

1 HI 1 <) , w

"0001 is OT «0 I

000017 WA ( 1 ) =

0000?0 «0 l»i ( 1 1 =

r c»i r

000023 <P r 0.

000024 110 11 J

000025 1 1.)f 1 (J00003*, >1 * J = WHoooosn 1 »L' =

r rwr00005] MM = ns000051 DO i2 J000055 11 = I n

000057 IM = 10h 7 [C = 10

ooooiss DO i3 K

00 P*-

7

Willi I

000074 1-3 M ( J) =

oooi i ? » 1 i >l =

I OF EoSf 1 (WO.SUi*LEN,LFNGTH,rnn«,Ne-,TM T ,F",«, IOSPfS FOP Thf IMiTial VALUES IN ThF Oil -/AT-JX VhIcHfttions or a simplF hfam at thf suPPnnT pointsr.r, thUN KU IfJ) 1 ,S ML FN ( RO) .TOOK (HO) ,T«1 (ROl . TOSP (5) , SPA'A ( 5) ,wr- (S) , T^ioFI («0 )

= 1. 4

o.oo.o

ULATE TAMRFNT AT THE LEFT F'-in

1 . NF

) = (HO( ]) *Rr)(J»H ) * (?»*TMJ (.|)«FM1TMOFI ( j) oS i^i FN I J) » (| tN(;lH-rnn«( iI-hhRI FN I 1)/?.)•P/LENGl

H

"I Alt DFFLFrTlONS AT THE ImTfRITH S'IpdprtS- 1

= 2 * MNSJMJ-] )

SP(J) - 1

SM ( J)

= I«. Hia

( ]) . TMOF T (K ) • SIiBLFN (K i

K'(( ]i»T'.inM ml. 1 IRLfN (Kl » (rnnR ( ID -rnOR iK) «SiiB| f

"' ( J) wo ( j-l I

SPAN, HI) FUST 1

ARE THE LOST ?

FNSf 3

fust 4

(4) , f NST 5FQSI IS

F )S1 7

FIST 8

FUST 9

F'IST 10fST 1 1

tosr 12EflSl 13fust !*E"sr ISf >*sr 1«F is

r

17f '1ST 18FUS1 14f-iST ?0f (JSI ?1f ' 1 SI ??F jS T ?3

1 K | /?, 1 y si ?4EuSI ?s

159

II 01 1 4

oooi??nool 33

norm

«H ( i I :

«2 p r i i-i i

!>< I IKN

L'NO

> ( J) WH ( J-l )

Coni- i t r ) » 7 A|

*'A (J-l ) 0Su»"l( 1-1 )

- i.'M (J)

t'JST 26FUST 27FUST ?BtJSI ?4

SUHPrlO'iOAM (_FN1>TH

O00334

unused ruMPn r« s^aceC4?40n

rooooT000007

7

nooo?npooopooooo??oooo?srooo?70000?700003?000034

000037rooo*ii0000*1OOOO*?OOOO**oooo*soooos?oooossO00OS700006OOOOObl

nooob*0000660000730000770000770001 0300117

0001 17

ooni?i0001??000133

00013*000137oooi *o0001 4<i

1 00OC/0

19^0190?070

97?

071

9"U

OH?*"0

20 r

?ori

?9r4

SUi-<iiiJ

i if T

COM 10NDl Irr.S

IF IIPF O-ciAT

DO 1^0IF illP L „ =

GO 10

CC N I IN00 <70SITrld

iiET

si r-.( i

K a C

IB = 1

DO v7 1

DO 47?IF I AHCONI INsi t-kk

K - K

19 s k

CONI INHLA

CALL S

IF I IP<K | I t

FO-eiAIDO -<MWrt[ IE

FO-l-iAT

no ^oDO -"*0

rpi 1

1

j

DO ^"»0

ill T

pcr«i<i1 = I

IF I AH

I = 1

I HE Fl.OPT (PTn.Nr.COST.FT)IMTZE THF iotatIO'iS OF ThF Cm/FR Pi^Tr sp, iCFS/uNE/ JPT ?, [P r ) i

ION STTHUn) , ?TH I 4 0. *) , PC TS ( *n ) , rnsT (o. ,ri|«(ii ,TP("1,*0)TIO ,r,p. i, «9tTE(AilOP)

< 1H1 1 in* , ivhFnTky TO FLUPT//)I = 1 » HC

Hiii?) ,lt. *.o> so Tn ivooPfHUt?)1V0?UF

[ > li KC1 = 0.0fHMlNE THF STTh ARRAY) = PTH(I,i)

I = 2i NCKK = 1 , THSlSTTH(KK) - BTHUiUI .LT, .00011 f,f T" 971UE) = PTHI 1,1)

1

- 1

UF

CF THE STTH ARRAY IN ASCEMOINfi DRDP^OkT (STTh.TH)THi .LT. 3) (50 TO 400(6, 4H0)

( 1 ho, I o* > 1 5HSTTH aRRay //)1=1,1*

<'.,9b?) I, STTnlII< 1 OX, I?, si

,

Fin,* I

1 = 1 . Mi"

J* = 1 , THK) = o.r.

11=1.1°FriMINE THF STARTING SECTION1 =0.0

s (PTH< i,i)i ,r,T. ,nnni) fin Tn ?o^31

FOPT 1

FOPT 2FOPT 3

FOPT *

FnPT SFnpT 6FnPT 7

Fnpi 8FnPT 9

FOPT 10FOPT 11FOPT 12FOPT 13FOPT 14FnPT 15FOPT 16FOPT 17FOPT ISFOPT 19FOPT 20FOPT ?1FOPT ??FOPT ?3FOPT ?*FOPT 25FOPT 26FOPT 27FOPT 28FOPT 29FnPT 30FOPT 31FOPT 32FOPT 33FOPT 34FOPT 35FOPT 36FOPT 37FnpT 39FOPT 3SFOPT *nFOPT 41FOPT 42

1 60

ooou?000U7

00015100015?0001600001610001M

000161000165000170000313

00021 3

000215000220

00022200022*000226000232000236000237

0002*00002*20002*700025300025*

00025600026?000273

3 1

000306000315

00031500031 7

0003?*000331OOO 3* 1

U 3 * ?

0003*3

000350'000356

000 1563 6 ?

000 3f>h

o o o i n

no 10 ?90*290J lb = I

C 0tTE><*IN£ THE FNUlNU SECTIONI NC

290b IF (AFtSlPTHlI.il) ,01. .0001) 1,0 TO 2905I • 1 - 1

(30 TO HOh2405 IF 3 I

C HE6IN TIE OPTIMIZATION OF IMF COi/tk PLATES00 *0OO I U. \f

PLl EN PTHI1,*) - PTM( l,3i

IF lIPTIv .£0. *) wollt (6.101) IS. it.

I

iPLW.PLLFN101 FOHMAT 1 1H0,5H!S = ,I2»*»5hIt • .I2»A.*MI ,I2i*i6HPL* * »F5.1i

IX.HriPLLtN = ,M 0.?)C INITIALIZE In! STAFtTlNG CONSTANlb AND COSTS

1)0 *0Ul K « 1 , 1H

*001 cl IK) * 0.0IF ( 1 .£0 . IF) r,n TO 4500

c vapt rut Thickness of thf ao.jacen! sectionDO *01 * « 1 . 1H

TCT * 9 '999.

IE (STTrt(K) ,r.T. PTm ( I * 1 * I ) i GO To *020IE (AFiSISTTH(k) - PTH(1*1»1>) .LT, .000011 GO TO *0?nCT (M * 0.000 10 *0 1

c vaht me thickness in thf oesion section*02u 00 <,030 KK = 1. in

IF ( ST Til (KM ,1,1. PTH(llll) GO TO *0*0IF (AHS ISTIrtlKM - PTHtl,!)) ,Ll, .00001) GO TO »n*0(,0 10 *U30

• 0*0 IF (1 ,nf. IS) t.O TO *0S0C OETtrtHlNE THE COS! OF THE INITIAL SECUON

Tma* * TOPI (SlTHlKKl )

CEk e CU5T (b) *H w»fOST (U) ,5«TMAA»«<: , PLW 1'CnsT ( 7)

rbw = 2. "COS) U .) .?.• HLLEN "(COST (H) «.01759*»C0ST (71 )

IF (AhSlSTTniK)) .CT. . OOOOUll GO Tu *0*1Cbw - C^'ST (bl .Pl.w»COSl (U) »PLW"TMAA»»^«COSI ( 7) /2.CO TO *>l*2

C lit H'lilNt thF msi UE THF BOll Wt-Ll) IE heooi^eo*0*1 1H • SI IHUI

IE (SIT" (KM ,LT, SllulK)) Th STTlllKKl]E (AE)S(STTri (KM - STTh(Kl) .LT. .Ouudl) Go TO 40*1CHw = COST lb) . Flw« (COS MR) ( , 12S*TH»,2H8676i»TH«Z» »COSTI T)

)

i,() 10 * )*?

*0*3 Cm = D.OC nlll '<-U \it Tut maTEH1«L roSl Of TuE Pi Ale*0*2 C'T = PLLEN «Pl.w»STlh(KK) »C0SU1) «*90./172rt,

C liETfHMINE |n| KHAL COST UE 1HF btCTlONre - Cel . Ch w . CF ti Lsw . PCTSIKMgo ro ti/i

C Hi lC'«^lNt Thl rnsT OF Ti^ bF AL HtLOS*0bu IF (Alib(STTrl(Kh)l ,| I . . 000 00 1 I i>0 10 .,0 55

II lAMbtsl iriir I I ,i 1, .uuonii GO 10 *0S6CSw * .'.* PlLfN » ICOSl (Ft) .017b94»C0ST ( 7) I

r ' « ~ 0.0

FDPT 3FOPT 44FOPT 45FnPT 46FOPT 47FOPT *ft

FOPT 49FOPT 50FOPT 51FOPT 52FOPT 53FOPT 54FOPT 55FOPT 56FOPT 57FOPT 58FOPT 59FOPT 60FOPT ftl

FOPT 62FOPT 63FOPT 6*FOPT 65FOPT 66FOPT 67FOPT 68FOPT 69FOPT 70FOPT 71

FOPT 72FOPT 73FOPT 74FOPT 75FOPT 76FnPT 77FOPT 78FnPT 79FOPT 80FOPT ftl

FOPT 82FOPT 83FOPT 8*FnPT 85FnPT 86FnPT 57FnPT 88EnPl 89FnPT 90FOPT 91FnPT 92FnPT 93FnPT 9*FfiPI 95FnPT 96FOPT 97

161

000374 t,0 10 4 i4 1

000374 4055 If lAbSISI lrt(K) 1 .IT. .U00O1) tin Hi »u'j7

C UF1fcXM|NF In) fOSl OF ThF APPmOUmATE FND WFLOS000400 J»H « I OP I (SIlH(K) )

000403 Ct* = COM (o) «3. .Pi w»tUbT (H) .FLW".5° I max ••-"'COS I 17)

0004 ib rc a cf « « pctmkk)00 04?ll (H) TO 4 J 70

0004?) 405b Tmia = IPPI ISTlli(KK) I

0004?5 CtS - C JS I ( M .n w<.f uS I (o) ,s» I MAA u "2 B COST ( 7) »PL«00U41* C^w * 0.(1

000417 rSW = r".° Pi I f. N « If ob I (ii) « .0 l 7S^4«COST I I ) )

0004 4 3 (iO TO *u4 2

000444 40">7 FL = I'CISHM00044* 40'0 If (IPI1II .to. 4) *-Mlk lb. 102) STTnliv), STTh(Kk). Tr

0004*5 HlZ FOwiAl O* . t'lHl ill TknFSS ON KlLnT - iE lO.b |2A i20HTHlfKNFSS ON LEFT1 = ,F 10. >»?»i 'H( (1ST = .Fill.?)

0004FS U 111 .<",!. Irll r,o 10 4030C SlOi't Trir. llisl r,h|) UiF T>llLI*.NtSS

000471 Tl-I = It

000471 |M' « M00O473 40 30 fONl |NUt

C SIOHf lot THICKNESS KFODIHtU IN l^f IP AHHAY00047b TP ( I »K J = b I in ( it-Pi

00050? CT Ir ) = TCI

000504 It (IF-TI" .hi, 4) VMlIt lb. 1101 UUI i TP(l.K)0005?? 110 foi)maT ( IrlOt lnX.7HC')Sl = ,F 1 b.b.bAtbhTP = .MS. 5//)O0U5?? 401 C^'j 1 IMIE.

C DE TFi<m| s£ THl Pfls a*kayooosps no 40^n **< = i . |m

00OS?h 40*0 PCTsmuM * CI ^M(l000532 IF IlKllO ,UT. 41 l,(l 10 40011

000534 Wh II) C>, 4 1 I

O0OS40 4lU FOllMAl I lMll» lflhPCTS AHHMY//I000540 wHTTt CmIOJI (f'CTS<KIMOi k*K ~ |i ID)

0005^3 10J FOI'hA I I 4 I M 5.5 .'-X ) )

0005S3 4000 COM lNUt.

C vAUt Int IhlCKNFSS 0) 1 HI LASI StCTION0005*0 4500 00 tlUII K s 1, (H

0005b? U ISTTnln] .il. PlHIIt.ll)) 00 10 »l?n0i)05h7 If l»HbtSrtrt(K) - Plullt.ll) .LI. .000001) 00 TO 4I?0000573 PCTSir) = .0

00 05 75 GO T.I * 11!

C DF TF.x'MNt T mF rnsT Of ThF LASI StCTION000575 *U0 Cff = SllHlMo Pi * o PILtN " CliSl i 1 )

o*iJi)./17?H,

000*0? C^w = ?«" PlMN " (COST (HI » .01 7b9,<•(.0 <;,I 7) I

000*07 If (If . f_i. I-) CSV. « Lbw . ?. • COjIibi000*1 4 T^x = I 0P1 I'M lh(K| I

000b?0 CI* c COST(t>). P| « »r(»Sl (H ),'j" IMAX»«?«COST ( 7 | o Pi w

000*31 PCTSli-l = BCTs(K) . CPL . CSW Ltw000*3* ]F lit .ED. ISI PrTS(R) = PfTSlKl'. Cf «

000*4? 4ioo continue000*45 rCT « 9'<99^ .

C lip 1 F»<M J ME iHfc THICKNtSS of ThF L«bl SECTIONono*4h no 4 1 in « = i , in

000*so If (AHSlPCISlKl ] .IT. .ooonnil r,u lu Ml"000*54 IF IPC'^I") .1.1. T r 1 ) GO TO 4130000657 TC T = P(.TS(<)000**0 ICt' c k

FOPT 9BFOPT 99FOPT 100FOPT 01FOPT n?FOPT 03FOPT 04

FOPT nsFOPT 106FOPT 107FOPT 10F)

FOPT 109FOPT .10FOPT IIIFOPT 112FOPT 113FOPT 114FOPT 1)5FOPT II*FOPT 117FOPT lift

FOPT 119FOPT ?0FOPT l?lFOPT 1??-

FOPT l?3FOPT ?4FOPT ?5FOPT l?bFOPT ?7FOPT ?8FOPT ?9FOPT 130FOPT 31

FOPT 3?FOPT 33FOPT 134FOPT 135FOPT 13bFOPT 37FOPT 3»FOPT . 39FnpT 140FOPT 41FOPT 4?FOPT 3

FOPT 44FOPT 45FOPT 4*FOPT 47FOPT 4f<

FOPT 49FOPT 50FOPT 5]

FOPT 5?FOPT 53FOPT *4

FOPT 55

162

OOOftftO *1300006ft")

oooft6s000hft70U0ft73 4bO000h73000700 55200007?) ssai0007?!0007?7 4350007?700U733 5522000751 552 3

000751 420O007M0007S*0007S5001000 <tbo

c

ooinoo00100?00 1001 41 10

00100500 100ft

001013 4 14(J

00 1 1ft

001021 S|)OU

00lO?l0010?3 41SU0010 3?.

00 1034o o 1 n <* ?

no lius00 104ft

0OlO4ft 4 1 bO1 <i h

o o l o s i

oo 1 ns* linu10 54

oo loftn 1 11'

I

ooi 1 14 1 1U2

0011141117 1 »4

001117 4^.1

n u 1 1 1

7

001 1?0

CONTINUEIF (1PT10 .LT. 3) GO TO 42011 a It - 1

rfhlTf (h,4t>0)

FORMAT HHOtlOXi JBHFINAL TP »HH*Vj...//|1)U 5520 I * Is, ITWRITE (6t5bil) I. ( rHll.M, K I« lb)FORMAT (5X,l2,5x,10(F7.*,3X)

)

WHITf (ft«455)

FORMAT UH0ilnX,3HHCALCUl.ATlONS FOR IHE.LAST SFG*FNT //>riO 552? * » i , irWRITF (ft»55iJ3l K. S I TM tlV > • PCTSIMFORMAT 15X,*hi\ = , |?,2X» 7HSTTH o iF1Q,5,2A,7hCOST ,FI5.5)CONTlNUr.

Plh( IKiI) = S1THUCHIFl « Pcrs(lCH)IF (IPTin ,GF. 3) WHITE (6,4h0) It. STTHUCHli FTFORMAT ( 1HU »?1 MlHlTKNtbb In SEGMENT i12,JH o ,F10.5,|5h WITH

IT » »F 1>.">)

DFTtR«|Nt THE THlCKNtSSFS OF TMF HEMAlNlNG SECTIONSI = If

IF (IS .Fi). IF) GO TO *lftOl)U 4 140 K t 1 , |H

ICR - K

IF (M*SlSrirt(K) - PTH(lil)) ,(T. .000011 GO TO AlsoCOM I MJt:

wR 1 1 1 (",5000 )

FORMAT < 1 HOt 1 OX i?0MF HHOH FOUNU IN FLOP!)slopPlHI 1-1 . 1 ) a TP( 1-1 , ICK)H Tm ( I - 1 » ? 1 » PL *

IF (APVfTrtM-ltllJ ,LT. .00001) PTn(l-1.2) » 0.0IF (1 .FU. IS I ) 60 10 41M)1 = 1-1r,o r n h 1 7 o

CONl I Vlr.

IF (IPI IT .LT. 31 Gil 10 h70WH I T F 1 <' • 1 1 )

FOwv.0) ( 111 I lOXtlRMPTH ARHAY IN Ft-0pl//|no i 101 i = i , ncWHITF I". 110?) PTh(1i1)i PTH(lt?)> PlH(Ii3), PlH(l,4)F"UHMA1 (2X,*mriaTf IS >F10.s.)h A , t 6 . 2 , I OX , mhS T APT a ,F10.?,

IfthF'NlJ = >Elu.:>)»N ! 1 t 111 I 04

)

FORMAT ( IMOi lOXi IshKFTUNn To CpntS//)rum i nulRt 1 IIHN

FWi

— rnPT 116FOPT 1STfopt 158FopT \**FOPT lftO

FOPT lftl

FOPT 1ft?

FOPT Ift3

FOPT 1ft*

FOPT lft5

FOPT lftft

FoPT lft7

FOPT lftB

FOPT lftO

FOPT 1T0FOPT 171FOPT 17?

COSFOPT 1T3FOPT 17*FOPT 175FOPT 17ft

FOPT 177FOPT 17*FOPT 179FOPT l«0FOPT 1*1FOPT 1«?FOPT 1«3FOPT )R4FOPT 1*5FOPT lRft

FnPT 1*7FnPT 1 HRFnPT 1R9FOPT 1^0FOPT 191FOPT 1«?FOPT 103FnPT IP*FOPT |QSFOPT 19ft

OX, FnPT 197Fnp t l^RFOPT 199FOPT ?noFool ?01FnPT ?o?FOPT ?nl

SUHRhOuI'SMI E NG7H.

ll U '770

IINUSF D rilMR Il.fc ) SH,\tf

03 f 000

163

SLMhOIJTINE ICALC <A.R,n,C,H,AS,IS,HP,HA,l EF.lTOT) ICALC CALCULATES MOMENT OF INERTIA FOr A PARTICULAR SECTION - ICAL

000016 REAL ITOT, LEF, IPARTi IS ICALC CHECKS FOH COVER PLATES JCALC CALCULATES I FOR NO COVER PLATES — ICAL

000016 IF IA ,<iT, ,000) .OR, ,GT, ,00011 flO TO |A ICAL000027 IToi • IS ICAL000030. LEF « M^ ICAL000032 RE r»)hN » ICAL

C »ETS INITIAL ZERO VALUES ICAL0Q0033 10 AL* 0.0 - ICAL00003* A.M 0.0 ICAL00003* DL » 0,0 ICAL000035 OU • 0,0 ICAL

C CALCULATES VALUES FOR THE UPPER PLATE OR SLAB ICAL000036 IF (A .LT. .0001) GO TO II ICAL0000*1 AUt* • A • B ICAL0000*2 DJ * MA IH R)/?. ICAL

C CALCULATE VALUES FOR THE l.OWER PLATE ICAL0000*6 11 IF lU .LT. .0001) GO TO 12 - ICAL 2

000051 ALP • C ICAL 2

000052 DL » (H C)/?. ICAL 2

00OOSS 12 ATOI AS AUP ALP - ICAL 2

C CALCULATE DISTANCE FROM CFNTHOm OF STEEl SECTION TO THE ICAL 2

c ctNTKoio of the overall sfction, also caiculate i For section, ical ?

000060 DI S I • (AUP • Dl) - ALP • DLI/ATOT ICAL 2

00006* LEF * HP UIST ICAL 2

000066 IPahT . |S . AUP.H»8/)2, AlP*C»C/)?, ICAL 2fl

000076 ITOI o IPaRI AUP'Ou"? AlP»0L»«? - ATOT»MST»»2 ICAL 29000111 REfJhN ICAL 30000112 ENO ICAL 31

SUHPROGfiAM LENGTH0001*2

UNUSED COMPILER SP«CE0*2500

HEAL FUNCTION ILTNT < PT , RO . COOR , I SW ,nP ,L FNflTH , SnBLEN)C INTERPOLATES REHfEN POINTS ON ThF INFIUfmCF LlNE

P0001? OHtNSluN RUIH1), COoRIRlli SUHLEN(RO)00001? RtAu LEHGIH000012 INlf.GFH PI

000012 IF IIS* .EU. ?) r.O TO 5?0C CALCUiATES VMUE OF INFLUENCE LlNF TO Thf RIOhT OF POINT PT

00001* SP » COOR(PT) DPC *tTUHNS A 7fRO IF THE POINT IS OFF THF OlODEd

U I N 1

II. IN IKIN 3|L IN «

IL IN S

1 L I N 6IL IN 7

ILIN AU IN 9

1 6 1

00001*. IF (SP .or. LENGTH) RO TO Sin0000?? GO 10 51?0000?? 510 ILI'O = 0.00000?3 RFfoHN

C 'JETEKMINES Thf SjaFLFME^T LOCATION0000?!, 5'? J = M 1

0000?is 513 IF icnow(.l) .Gf . SP) GO TO 51500003? j = J 1

P00033 GO 1° 51300003". 515 K = J - I

C IMEKPOLATION FORMULA000036 ILI-il = KUIK) (HO( j) -oo(K) ) « ISP-COOPi' ) 1 /Sn U f NIK)00005? RM'iHN

C CALCULATES v ft |u f" OF TNFLMFNCF LINF TO Iwr IFFT OF PojnT PT

00005? 5">0 S^ = COOK(PT) - OPC -<t TUi'NS A /fmo IF THF POINT IS OFF Tht cicOF)

000054 IF i',p .L.T, 0.0) RD TO 5??000056 GO 10 5?5000057 5?? ILM1 = n,0000060 prf.iHN

r ilTFKMINES Thf S.IRFLFMFNT LOCATION000061 5'5 J = PI - I

000063 5?7 IF ICOOH(J) .U. SP) GO TO 5?6000067 J = J - 1

000070 GO u 5?7000071 5?6 K = J 1

000073 J = *

000071. K. = J - I

C 1 1 If <POl_AT ION FORMULA000075 It I *1 = R0(K) (HO(J)-RO(K) J

»I SP-fOOR (K ) ) /Siml.EN ( K

)

O00I11 RFf.lfM

00011? END

ILIN 10ILIN 1 1

ILIN 1?ILIN 13

ILIN 1*ILIN 15ILIN 16

ILIN 17ILIN Ifl

ILIN 1"ILIN ?0ILIN ?1

ILIN ??ILIN ?3ILIN ?4ILIN ?5ILIN ?ft

ILIN ?7ILIN ?HILIN ?4an 301 1. 1 N 31

ILIN 3?ILIN 33|LtN 34ILIN 35ILIN 3ft

ILIN 37ILIN 3BILIN 39ILIN 4(1

ILIN 4)

SUBPHnGRAM LtNGTH000133

UNDSFO CUMPII ER SP4C-F

04?600

S HhIiUT I NF ILF'KOP (Rri. S. IRLF N,NA .KOP, /VNFG. " P<">S , M«XO|_ .MlNOl )

OOOn 1 3 DIMENSION KUIK1). S-fRlFMlRO), KOPI1MC LFTMihlNFS TmF PROPFRTIF* OF A r.TVFN tmfiI'F'CE

| TNF000013 MA * iL = 1

000013 mjxil x I

00001

5

ANF . = 1,0

000016 APi)-> = n.O1 >, 0M4* = -.000]

000017 0M I •« = .i0010000?! DO ->70 I = 1, 10

0000?3 5 '0 K1"l I ) = n

C IfTEHt'I'NE THF CR3SSOVFP POINTS0000?6 KOP ||)=1O0O0?7 J = r

ILPH 1

ILPH ?

ILPu 3

ILPH A

ILPH 5

ILPH 6

ILP-i 7

ILPH H

ILPH 4

ILPH in

ILPH 1 1

11 PH 1?ILPH 1 3

ILPH 14

165

oooo3ft00003?0000340000*30000*=,0000<.7000047"0005100005ftooooe30000f<500006700007?000074

00007=,00007ft

00010?0001050001050001070001 11

0001 1?0001 14

00011ft

0001?1oool??P00)?4P001?SO00l?7000131000133O0013S000137000145OOOlhO

1 ft 1

OOdftTOOOlhSO00173000?10oon?i i

ooo??o000??3ooo??s000?33000?33000?34

5M

550

555

554

5*<?

^3

i;ft4

5ft?

5F05*1

NED')

IFKOJ

GOIF

IF

IFKOJCOKONK

0"IF

IF60O'l

MAGOOMMICO

Of)

IFIAIHA

noIFIF

IFA

GOIFIFIFA

GOA

COIF

IFCi

PF

Ef

a NA-.SO 1

(ARS<-MJ) s

J

10 55I I .F

(H0(1I ^H5 (

»»< J) D

J

t I IMUF•M J) =

M = J

• lETE-.5? I

IKI( I

[Ml (I

fO 5^A* = .

K.Jl =

10 5'.

I i = H

I'll I

-J I I 'Mill-.

IF TF"->ftO .K

IK .F

= IU)R

a KOR* o.o-.ft? I

II ."1

I I .F

iahSI= bllHL

11 S<

I 1 .1.

HOIftHS (

x A«SU10 5 ft

i A

II 1NUFI A .(,

(A .L

Nl INIIF

I it-fj

>)

- 1

* <?. NFRO(I)) .r,T. 10.0»»l-ft>) GO TO 551

1

1

o

0. 1 > (.0 TO 550)»RO(I-l) .GT. n.o) (50 TO ^5nHO(I-])> .LT. lo.0»»<-6)) GO TO 55n

I

1

MA

MINE MAMMIIM AND MINIMUM OPOINATF I "NATIONS= 1 . Fl A

) .GT. OMAX) GO TO 555I .LT. OmIM) GO TO 554

(MI)I

?

(1(1)

I

MINE ThF POSITIVE ANO NEGATIVE ARFA5 IJNnfH THE LINE= 1 , NKOP

0. NKf'P) (.0 TO R6I<K)

("II -1

- IA. IP

F . I A I GO TO 5ft3

'). ll GO TO c,63

"("(I)) .1 T. )0.0*»(-ft)) CO TO c,fti

FMI-])<>POII)«AHS( c!0(I))/<?.»(AP5(Rn,T)) 4 ARS(RO(l-l)>))4

F . IH) GO TO c;f,4

,EQ. MA) GO TO c.ftft

K0(I*1)) ,lT. lo,0»»<-6)) GO TO Cft4

RLENI I ) »RO (

I

)«ABS(Rn< I) >/ <?.»(»R5 (RO( 1) > ARSfRol T«l ) > )

)

?

(r(0(ii »0( i l ) ) • SUSLFN) T ) /?.

"

1. 0.0) aRo5 = A»05 . A

t. 0.0) ANFG b ANFG A

ILPR 15ILPR 16ILPR 17ILPR lfl

ILPR 19ILPR ?0ILPR ?1

ILPR ??.

ILPR ?3ILPR 2*ILPR ?5ILPR ?6ILPR ?rILPR ?RILPR ?9ILPR 30ILPR 31

ILPR 3?ILPR 33ILPR 3*ILPR 35UPR 36ILPR 37ILPR 3BILPR 39ILPR 40ILPR 41

ILPR 42ILPR 43ILPR 44ILPR 45ILPR 46ILPR 47ILPR 4HILPR 49ILPR 50ILPR 51ILPR 5?.

ILPR 531LP.J 54JLPw 55ILPR 5ft

ILPR =.7

ILPW 5RII PR 59ILPH ftO

ILPR ftl

ILPW ft?

II PR ft3

SUHPRO 'RAM L F NbTrl

00O?77

UNIJSFO TO-'PII FH S^nl F

04??U0

166

RC»i. FUNCTION Impact (Type .("P. IOSP,* Si«ci.r ran. COOS)C oITEWminES Thf Ixp»CT FACTUM

00001? D! ""'NSInrj IOSP(^). SpANii,). rOCmifln00001? INfMiFH TYPE00001? MN a NS - 1

000013 U ""'N •E ,J » 11 c.o rn 7nnoOOOOIS IF (TrPf .NE. (.hpFAC) (40 TO 600

C IMPACT DISTANCE Fort ThF RFACTIOn TNFI'iFMrr LINES000017 IF INP «Nt. 1) Rn Tf) <i01

0000?0 OlN'> = SPANd I

000021 GO (0 6500000?? f.0 1 IF INP .NE. NM 00 To 6m?

0000?4 D I M •> » SPAN(NS-l)0000?6 GO lO 6SI'

0000?* 602 D I ^>i - SPAN(NP) * SPaN(NP-I)00003? GO 10 65000003? 600 If (TYPF .NE. 4HMOMT) Go TO 610

C It-PACT DISTANCE FOR THE MOMENT IMFLUFmCF i TNfS000034 DO ill I e 2. NS000035 IF IIOSP(I) .LT. NO) (JO TO 611000040 IF ll'fAf) .LT, O.il Go To 61?000041 DI*» = SPAN! I-i )

000043 GO 10 65(J

000044 61? IF !&P .LT. ( IOSP( I-l ) *TOSP( I I ) /?) oo To *?c000051 DIi.i = <5PAN(1-J1 • Sp AN(I)»/2.0000056 GO 10 650000056 6?5 01 -J . = (5PANII-1) SPAN (

I -? ) I /2 .

000063 GO TO 6Sp000063 611 COmiIMUE000066 610 IF llVPF . NE . 4HSHFR) GO TO 6?0

C, IMPACT DISTANCE FOR THE SHEAR IMFLUFNCF i tNFS000070 DO »?1 1 = 2. NS000071 IF (IOSP(I) .IT. NO GO TO 6?1000074 IT = lOSP(I)000075 J.I = IQSPlI-ll000077 DI M'i = COOR(II) - COOR(NP)000104 DO*(.> = COOfl(NP) - COOR(JJ)00C110 IF iDONo .GT. DING) OlNf, DONG000113 GO 10 650000114 6?1 COMIlNUF

C IMPACT DISTANCE FOR THE DEFLECTION TNFUIF-CF LlNFS000117 6?0 00 h3o I = 2. NS0001?1 IF <NP .GT. lOSP(I)) GO TO 6300001?5 D I Mi = SPAN(l-)

)

000l?6 60 10 6S()

000127 630 COMflNllF00013? GO 10 650000132 7000 DI M i = SPAN! 1

)

C lf-PACT FACTOR CALCULATION000134 6 C HT » 50. /( (DING/1?. ) 1?S.)000137 IF IhT .GT. .3) hT r .3000143 HT a HT 1.0000145 IMVaCT = HT000146 REIJhN000146 END

I"PT 1

I'<PT ?IMpT 3

IMP! 4

I"PT 5MPT 6IMPT 7

IMPT H

IM PT 9

MPT 10IMPT 11IMPT 1?IMPT 13IMPT 14IMPT 15IMPT 16IMPT 17IMPT 18IMPT 19IMPT 20IUPT 21IMPT 22I"PT 23I <PT 2*IMPT 25riPT 26IMPT 27IMPT 2HIMPT 29MPT 30IMPT 31IMPT 32IMPT 33IMPT 3*IMPT 35IMPT 36I "PT 37IMPT 3HIMPT 39IMPT 40IMPT 41I'iPT 42IMPT 43IMPT 44IMPT 45IMPT 46IMPT 47IMPT 4fl

IMPT 49IMPT 50IMPT 51IMPT 52I 1PT 53IMPT 54IMPT 55

1 6

SUHPHlriRAM |_FM.'TH

ooo?n

UNUSED rU^PIlFK Sr'nCF

042*00

SUljrfOU

C ->'U

oooon coiicn000011 CCMniONOOOOll DUi-.NS

C CHFoooon if up000017 IF lIC

000021 RE' "HN

000021 7003 If (*T0000?* RE MhN

C »T000 025 70 r 4 DO /GO

0000?7 DO "SI000030 PLT-iAV

000036 6919 PLWiAV0000*3 70H0 IS4vt (

0000*7 CHI i =

000051 WMI < =

000051 00 '00

000053 00 10000005* 00 (00000055 70''1 SAVFII00007IS RE r iRN

000077 EN)

IT1NF KFEPfNE .NOS.PLATh.PLWID.COVPI ,CMTm,UmIN, IPTft)iRFS ThF ArrFOTAHLF GIRDER)/f OUR/wTOT.TC><;Tl/l- OUR/^TOT.TCXiTl/A/lS«VE(«0>.SAVF(l2»6.2).PLT5«V<nn,?i.P|.wSAv(«0.?>ION NU5(flp) ,PLATH(R0i?l •PLWin(OTO > ?) .rr"'P| (12, S, 2)C* IF THF r,I«TFR 15 *ETTFR Than Thf PorVlnuS RTRnFoTh ,QT. .*•) RO TO 7003OST ,LT. CmIN) till JO 700*

OT AT, hMTNl r,0 TO 700*

RE THE ACCFPTAflLF RIROFRI = 1 . NF

9 J = 1 . ?

(I.J) e PL ATHl J , J)

1 1 . J ) = f- L W I ( I , J )

I) * NOMI)TCOST*TOT

1 I » li 1?1 J " 1 . ft

1 K a 1, ?, J.KI a COVPL ( I i J.K)

SUBPROGRAM LFN^TH000120

UNUSED (-OHPII ER S^aCE0*2500

K.FFP 1

KFFP 2KEEP 3

KEEP *

KFFP 5

XFFP 6KEEP 7

KFFP R

KEEP 9KFFP 10KEEP 11

KEFP 12KEEP 13KEEP 1*KEEP 15KEEP 16KEEP 17KEEP 18KEEP 19KEEP 20KEEP 21KFEP 22KEEP 23KEEP 2*KEEP 25

000021

000021000021000021000021

000023

.LFMG TH, COOT, NP. TYPE. LOADLOAD

OPMOl .STnPr (in) .

LOADLOADLOADLOADLOADLOADLOADLOADLOAD

1

2

3

4

5

6

7

a

9

1011

I 61

OOOC?'. Rl 1 sT.)-e idc -.i r u

000030 no loo i

000031 Rr o Ri 1 1 ) =

0000*0 CALL ILHOQ004T ir hype000055 If l>N .

000057 DO IHhOoooobn Ir U.r> .

oooom I r I 1 I L (

P00071 IF (Till000077 ]

RfrO CO 11 INUF00010? 1R50 Ai.ir •=

000104 IF 1 JPT 1

c >tAO

000107 uol f* 1

oooin if i unuoooi?s ST Mr I 1 1

00013O SIMt ( 1 i,

000131 GO Id HO

c oEAOooom R"l UOL = T.I

00013* IF (UOL00014? ST HI [ 1 1

600145 DO «li2 I

00014'. BTS BO ( 1 ) =

000155 CALL ILP000164 IF ( fYPf

00017? IF (f"N .

000174 00 1 Hft

1

000175 IF INP .

OOOPOO IF cTlUooo?(>6 IF (TIL (

000?14 IBM CO Jl IMJF000?1

7

18^2 Al )l = ft

000??1 AC4 - Ufill

oon??3 IF (ACA000??7 STO-if ( 10

c -.tT .1'

000?3? am IF UPT1000?36 00 '105

I

000?37 Po5 R0( 1 ) =

000?46 CALL ILP000?55 ir drPt000?63 II- I r* N .

000?65 DO ifft?

000266 IF If P ,

000271 IF I 1 IL (

noo?77 IF ( 1 1L(0003(15 186? CO ^l IN'Jr

r -if GIN000310 BH IF ilPT?00031? AC1 = UN000313 IF iTYPf

r CALCd000317 IF < I • N L i

'

00032? HT = |,00003?4 GO |0 pi

= o.oP THF STFFl 5FCM3M INFLUFMr-F L1 K 'F

: li NlriLCTil)Pop(no.5iiMi fm,na.rijp,anf(mSpos,m^«oi Lmt*K)L)

.HE, 4H5HF-}) GO TO 1H5"FO. 1) RO T1 1850II = ?, «NNK. TObPlIM) GO TO lPf.0

NPfl) .GT. 0.0) » p l5 = AP05 - Sljqi FM/NPt/2.4NP«1) .IT. 0,0) ANFG = ANFG SU«I FN I MP- 1 ) /? .

POS ANFG•LI. 91 GO TO HOI

LOAD "FACTION FOB a NON - rnMPOStTF CFTTION( (t( 7) TBI 0(RI rfll.O(lO)

,LT, l.iNI. n (4 ) ,IIMiO (5) tUNLO (9) ) 1 101 si IHl O ( i, I UNI ( 5 I

= UOL • ATOT) =0.0I

LOAD ANn LO< viO'i ILJ5 BEftCTIOM FOB rn.<P05lTF ACTIONLO(H) TB| 0(i0)• LT. liNL, (5) .UNlOI V) ) UOL » IINLOI^l , l|M(.0(9)

= Uni ATOT= 1 , MA

TILI1,?)WOP (BO.MIHIEm.na »KOP, ANf G, AP05,M*xm . MI'.OL).HE. 4^c;HFB) GO TO l85?

FO, 1 I GO TO ) 85?II = Pi mNNE. IObP( III) GO TO IflhlNP»2) .GT. 0.0) ftP05 = AP05 - Sllnl Fm.mPi /2.0UP » ? ) .1.1. 0.0) AMFfi ANFG 5liril F-. . NP-1 ) /-3.0

POS . ANFGLO(4).1 T . IP|_0(7) ) ATA TRL017II = ATOT « ArAP THF HIGH MODULUS INFLUFNrF LT'" r IF PFollIBFD.GT. 9) GO TO R04= 1 . NA

TTLIT.3)BOP |BO,SllP|_FNlNAiKOP, ANFG, AHflS, w\«ni MT' OL),NE. 4H5HFB) GO TO O04

FO, 1 ) GO TO 804II = 2, MNNF . IOSP III)) GO TO 1 Hh?''Bill .GT. J. 01 4P05 = APOS - 5Ual r. iMPl /?,0NP«3) .IT. 0.0) ANFG = ANFG • IIIHIF'iNP.II/JJ

THE l.IVF L OaO IOAOINGS

,EO, ?) GO TO RTOI

ii( 1)

• F 1. 4HiO"H AOR e I.NlOl?) ^LATE THF I^^ATT FACTOB("I .IT. . 1 ) GO TO 11-00

'.I

LOAD 12LOAO 13LOAD 14LOAD J5LOAD lr,

LOAD 17L'AO IRLOAD 19LDAO ?0LOAD ?l

LDAD ??l.OAO ?3L'lAll ?*LOAD ?S1 OAO ?f>

LOAD ?7INLO(V) 1. 'IAD 2fi

LOAD ?9L OAD 30LOAD 31

SECTIO.MLOAI) 3?I OAO 33LOAD 3*LOAD 35I OAO 36LOAD 37LOAD 3RLOAD 39LOAD 40LOAD 41LOAD 4?L'UD 43l.UAO 441 OAI1 45LOAD 4F,

i dad 47L^aii 4RL Oftl) 49L"AO 50LOAD 51LUAl) 5?LOAD 53LOAD 54LOAD 55L OAO 5hLUAD 57LOAD 58| OAO 59Lu»n 60LOAD 61LO«n 6?LOAD 63LOAD 641 OAO 65I OAll 66I "Al 67IHI 6R

I "4,i r.9

69

0003?4

n 03 <. n

0003^3O0035400<)3S«,

00036000036)00P3t>400036700037000037?00037300037500040=;00040500040700041?00041

4

0004160004?*,0004?600043100043300043500044=;000447000451000453000463000463000466000471

000477000502

0005040005?0000523000^3600054100054400056000057400057f,00060100060Snoo6?o0006?300063600064100064400066000067400067s00070100070S

I a^n ht

1 «fl1

RnM

R'7

«13

flf<>

R14

SIS

B0681?

H30

STSPIKIf

00IFIFIF

LM

DOIF

GOIF

LM

00IF

GOLM

DOIF

LM

DOIF

GOCOSPST

STST

RRPRRRSRIF

RRTRSR

IF

STHP.

PRRRSRIF

RRTHSRIF

STIF

rot CULit (?)

K * =

I I YPh

I ^ N . F

rtOfi J

(MNOlIMINOL(J .NE

•- IOSPIj iospiton k

(HO IM10 81?(J . fiF

3 IOSPI= IOSPIHl3 k.

<HO(M10 R 1 ?

= insPIa IOSPI<u «(HO(K)

3 IOSPIa IOSPI*15 K

< h ( K.

)

10 81?m i iNueK". = HO.Ml (31

CALCULOHt (R)tMt 19)INTERS* I L I Na HR* TUN= RH »

(PR .L= ILIN3 ILIN3 RR .

IPH .L)-tl (4)= ILIN= HR= ILIN= RR .

If-R .G= It IN= ILIN= RR .

it-R .G>-<t (SI

HPT?

( 1 (TYPFOTE ThF- rfj o

.NE. 4h'J. II G3 1 . MM

.LT. T

.'ST. 1

. 1 ) PD?)

3)

L, *.LT. S

,N".TOS". ,>l

c;.

<;PArj.STn'5(r(i'ii*f,'> u l

P05JTIVF SNP MffiATTVF I vjf lOArjNoSC iinlo 1 1 I

• APOS AfR » "'>f">xni i)

mO'-'T) go to ri?n t D «i ?

nSP(.i) ) GO To H06OSP (.1*1 ) ) GO TO R06T" R07

p£<] SPF< » RO(K)

TO ro=). MN) Rl

MN - 1 )

^ N)

= I. , M

.LT. SPfx) SPFK = HOIK)

J-l)J)

= L. M

•LT. SPE«) SPFK 3 POIK)J»l>J«?)3 L. M

•LT. SPEK) SPFK 3 RO(K)

IMINOL) SPEK= riT • (UNLO(l) • ANEG ACR • SPO,ATE THE STIFwALK LOADINGS= APOS » U>J( 0(7)= ANFG • UNlomTATE LOoDI^r;S ( POS AND NFR RASFO o> A 4 FOOT SPACING)T (MAXOL ,RO,coOR,l , 4R.iLFNGTH,SU'3LF"iHO (MAKOL)

TIMAXOl ,R0.c00P,?,4R., LENGTH, Sliol^ i

RO(M««OL)T. SR) PR » SRT IMA»OL.RO.COOR,1 »?4. , LFNGTH.SIiql F»mT <Mi\>Ol .R r>.c00R.?.?4, ,LEn(STH,5IIRLFi> \

TR1. SP) PR s SR= rij • IINL0I6) » PRT (MTC'Ol , HO, (-003, 1 ,4fi. ,lFNRTm,Sih>i F"\HO(HlNnL)T(MUOL,R0,c0OP,?.4R.,LFNGTH,SliPLF''RO

(

MINOL)T. SP) PH 3 SRT (MTKOL .RO.roOP, 1 ,?4. .LENGTH, Sinl F> \

T ( HTnOl, RO.cOOP, ?,?(,., LENGTH, Si 101 F »hTR

T. SHI PR 3 SR3 HI • UNLO(ft) • PR• £0. 1 1 GO TO A70

L'lAO 70LOAD 71L"AO 7?LOAO 73LOAD 74LOAO 75L'l«n 76LOAO 77LOAO 7BLOAD 79LOAD noLOAD 81LOAO 82LOAD A3Load 84LOAO 85L'JAO 86LOAO 87LOAO 88LOAD 89LOAO 90LOAD 91

LOAD 9?LOAO 93LOAO 94LOAD 95LOAD 96LOAD 97LOAO 98LOAO 99LOAD 100LOAD 101LOAO 102LOAD 103LOAD 1 04LOAD 105LOAO 106L n AO 107LOAD 108LOAD 109LOAO noLOAD inLOAD n?LOAD 113LOAD 114LOAD 115LOAD 1 16LOAD 117LOAO 1 18LOAD 119LOAD 120LOAD 121LOAD 122LOAD 123LOAO 124LOAD 125LOAD 126LOAO 127

1"0

o o ii 7 n ?

" 7 1r

.

O0C71100071?00071";

000717

0007?n0007?3000741000755000763000766

0007710010070010?!001031001034

0010370010*?00105700106?00106500107000107ft001100001100

00110500112100112400112700U3?0011H001151001 15400115700116100H63001 16ft

001173001?01001205001210001213

001P140012170012350012400012*3001246001253

->Ta)T fri£ ThurK Lt»l! M li

POS = 0.0Sr i* = 0.0PF<4 i .4

OCl\ r TwL'> (Si TP' 3 (4)

OC-I = TMI (6) TPI 1 14 >

>UV£ Th£ TPUf* f'POM LFFT TO PI~,MT

R34 PALRHSPTTi

IF

If"

HPSPTT,

IFIF

FAlHPPALIF

IFIF

IF

60831 IF

R12 RPTTlIFIF

spTTlIF

IFK =

R33 IFK =

IF

IFTTlIF

IFGO

835 CAlPRPALIF

IFIF

IF

(P

AH A

LC"LTh|_

ILINILINHAL

TL .

TL .

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?, TRLO (4) . LFNGTh.ShoLF-(2)

: BAL» PAL".01 GO TO SIS

GT. PFBA • SEG) GO TO 835kIGGLInr Thf 8ACK AXLET ( J.RO.rOOP,?, OCA .LENGTH, Si irl FN)

PR • TRLOOlGT. POS) Pis = TTLLT. SEG) «Eg * TTLIfJ.PO.COOP.P.OCR.LFNGTH.S'iRLEN)

SP • TBLn(3)GT. POS) B^e; a TTLLT. SFG) SEG = TTL

D po TO ni5

K) .GT. COOP(J) - OTA) 00 TO BIT" > .IT. COIR(J) - OCb) GO TO R3K

onui • T'<LO(3>GT. POS) POS = TTLLT. SFG ) SFr, r TTL

THE <-FCONO ««L r ON THE POINTo (?) » PO( J)t < j.M'.rom, i . tqlo<4) «i fngth.smplf-. Hi- • TRLO I 1 )

GT. POS) POS = PALIT. SF G I

SFr, i DALJ) - TP|.0(5) .IT. 0.0) GO TO R4-LT. PFSA • POS) GO TO 836

lo»p 1?RLOAn 129L A ) noLOAD 131LOAD 13?LOAD 133LOAO 13*LOAD 135LOAO 136LOAD 137LOAO 138LOAO 13<J

LOAO 1*0LOAO 1*1LOAO 1*2LOAD 1*3LOAD 1*4LOAO 1*5LOAO 1*6LOAD 1*7LOAD 1*8LOAO 1*9lo«o 150LOAO 151LOAO 15?LOAO 153LOAO 15*LOAO 1S5LOAO 156LOAD 157LOAD 158LOAD 159LOAD 160L'lAO 161LOAD 16?LOAD 163LOAD 16*LOAD 165LOAD 166LOAD 167LOAD 168L°AO 169LOAD 170LOAD 171LOAD 17?L'lAD 173LOAD 17*LOAD 175LOAO 176LOAD 177LOAD 178LOAD 179LOAO 180L'Hn 181LOAD 18?LOAP 183LOAD 18*LOAn 185

1 71

noi?5600l?57

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RO"=i J 1= = TTLSFO) ",, a ttl,ML,r"iR,?. TOL') (61 tLF NGTH.S'WSB » T-ltO)P05) »OS = TTLSF(3) 5FG = TTL

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"L4TF. FOR THE mamwOm SPACINGINT ( J,PO,rnOR,-3, TRL O (6) tLFNGTH.Slml F-

I ' T (J.PO.rnnP,?iOCB»l FNGTH. Sii«I fm:.| TPlO(?) o hn T&LOlll » SR.01. (-061 PTS = TTL.1 T. 6F01 SFo = TTL

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1

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"IJ) Poa ,3T. I.FNGTH) r,0 Ti sac.1. T . PF -JA • POS) GO TO .14?

43,',T. IfOl o SFOl GO TO '<!*<=<

T WIGGLING Tnr Ha or aiLEI'iT ( J.PO.rO^R, 1 , nr A .I.F I'iGTm , <i in| f> i

AL KH o 1 RLO ( 3 I

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M » SL o 1 J n { ( )

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^ = J, '.A

LO40 1 A6L o»r> 1H7L 'AO lRfl

L^ATi 1B9L040 190LUdO 1<»1

L'-'M) 19?LOAD 193L 'AO 194LO»n 195L'lAO 196L'lAO 197L'lan | 9RLOSO 199L"AO ?00l )»n ?01L'Jao ?0?L OA0 ?03I "An ?041 040 ?06I "AO ?06I 0411 ?07L>JAO ?0HL'lAO ?09LOAD ?lnL >AO ?11LOAD ?1?IOAI1 ?131 U40 ?14I 411 ?151040 ?lh10An ?17Li'AO ?1HL '40 ?19I 040 ??0i i*n ??11040 ???I 04(1 ??3L"4H ??4L'TAn ??5LOAO ??6LOAH J?7

L 0411 ??«1.040 ??9L'lAll ?30LOftn ?31LOA11 ?3?L04T '331 "4n ?34L "All ?36LOAn ?36L JAO ?371 "40 ?3«1 'iftll ?3RLO*n ^40L"A 1 ?4 1

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1 72

001 647 IF (COOH (k ) .! i , roii> (ii . nr«| r- o in "4'.

001*55 IF i( on < (M ,r-T. COIR ( ji nrH) On to P4C

00166=- T r i = PAI •' IK! • TRLP(31001*70 IF ( 1 TL .KT. POS1 P i<; = TTL001671 IF iTTL .1'. S£ 31 ",, i ttl

001676 R44 CO^II I NHSr PLACf THE SFCONn h»lf om tmE POTmT

001701 H<.5 CAL - T-l '' (?) « P(ll J)

O0170'i RR =• IL INT ( J.W0irOOR,?,TRL0(4 ) « LF.nGTMiiSijm f

0017?? pa l i c«i • ^p • r«un 1 1

1

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001 730 IF if AL .il. SFR.I 5Cr °al001733 IF ICOOH(J) . TRlOtil .r,T. if.n&JH) r,n TO Mt

00174? IF |FA|. .1 [. pfRJ • POSl G1 TO J46

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00?n?o TTL = f-'»| SI 1 o T3LOI3)002071 IF (111 .'ST. P051 °0s = TTLoo?o?6 IF ( 1 tl. .11. SFR) SEG a TTL002031 00 <<. 7 ' = Ji MlO02031 IF itMOrflrt) .IT. COO«(JI OTA) RO TO »4-"

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O07051 TIl = P«l RO(K) » Tl<LO(3)002054 IF ilTL tGT. POSl 005 = TTLO02O57 IF (1 TL .LT. SFfi) 55r, i TTL00206? a« 7 COm 1 l'JUt

002065 mc,o J - J - 1

002067r

IF U . >f . 1 I RO TO S4 1

CALCULATE !nf I«->ACT FACTOR00P07O IF (1 RLO tl) .11. . 1 ) RO TO i «0200?073 HT - l.n

r jTOHt TrlE " A x T -t i vi POSITIVE A 'JO MFRATf'F002075 1R1? STOHt (6) - HT <• POS002100 SlUI ( 71 = HT o CFG00210

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LOAO 770LOAO 771LOAO ?7?LOAO '73L"AO ?7«LOAO 775LOAD 776LOAO '77loao ?7HLOAO '79LOAO ?«0LOAO ?R1L JAn ?R2LOAO ?«3LOAO 7R4LOAO 7R5L OAO ?86

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• Eo.j o

Q »

16fl.

s>oi

GDI

.E J.

0.0so or

hThF ;ni T T =; OF THE APnuF ToaiF ur TNrwFS.)t n B " 7nFOP u &T ION1 GO TO 170

01 Si P| l • SL a P*I . 5PL. "01., Sii , •

! , OIL3. ftFl 0.4)(H HH| Q = P|.l • .S6H HIS .00. L^IS ,FO, AHHSlC) 1 : PLL • . 71<.H N^n .OP. LOlS ,Fn, 4HMS-1 ) n = t'Ll.

? I GO TO I7

S

.0=33lf>.

?6.

OIL) • °LL • ?»

1 ).-'i TO 1 7ft

•Sis .on. LriS .F'fj. i.H«f i 'O rn 177

= Ih'l.

= 01= S| L H *

KF«n 767PF40 P6RWF40 ?6<J

HF»0 P70HF40 »71PF4PI »7?WF«ri ?73PEAO 374nr«r> ?7Sffjo ?7AHFAn 377HF AO ?7«HFAO ?7<>

HFAn ?P0HF All vai

HFAO ?p?HFAO ?«3HF AO ?P4HF AO 3RSHFAO JHft

HFAO PR7HFAO ?PSHF An PP.9

HFAO ?F*0

HFAO ?91HFAn ?9?HFAO ?F)3

HFAI) ?Q»HEAO 5qsHEAn ?Qft

HFAO P97HFAO ?9fl

HEAn ?9<J

HEAO 300HFAO 301HFAO 30?HFAI1 303HFAO 304HF An 'OSHFAn 306HFAO 307HF An 30BHFAIl 309HF AO MOHFAO '1 1

HFAn 31?HFAO 31 3

Hf A 314HF A 1 31SKll' i)6HFAO 317Pr An MPKFAI MQKF All >?fl

HF AO >?1

l» «> 3??kFah 1?3Hf A <?<*

187

Q013?l GO 10 1 7h HFAO 3?50013?? WO IF (IPT? ,E(J. II SO Tn i 79 HFAD 3?60013?* PF»> I5.1H0) no|0(I), ] b 1. 101 HEAD 32700133ft 1«0 KOH«AT (10F7.3) HFAO 3?H00133ft 179 IF lIPT? .EU. ?) GO TO I 7ft HEAD 3?90013*0 PF « i (5f]Hl> (UMlO(I), T = It 9) HFAO 33000135? 1«1 FO-MAT 19F8.4) HEAD 331

C conVFR' I hf iofln jnfoRmat [ON Tn units "F tN(-hfS head 33?

00135? 17ft IF (IPT* .Ed. PI BO TO |9D r FAD 333001353 IF (IPT-i .EQ. f' ) GO TO IBS HFAD 334001354 TPl_d(4) = tRL0(4) » 1?. HFAD 33500135ft TPL>US) = IHICK5) » 1?. HEAO 3360013S7 T«L')(6) THlO(m • )?.

N HEAD 337001360 UNLdUl = UNLO(l)/!?, HFAD 33«001361 1P5 TR|_M7) = TH|0I7)/1?. KF AO 339001363 TRL'MB) = IHlOmi/l?, READ 340001364 T»LK10> = IBLO(10)/12. PF An 34100136ft • • UNLM4) = UNL0(4)/1?. READ 34?001367 UN|_ MS) = UNlfi(5)/l?, PFAO 343(101371 UCLM7) = JnlOI7)/1?. HFAD 34400137? UNLM9) = UNl()(9)/l?. HEAD 345

C ">hINT THE LlJAn INFORMATION HFAO 346001374 190 CONflNUF HEAO 347001374 wPIll (f>.l9b) HFAO 34B001*00 195 FO-MAI ( lMl »TC X «?4HL0AniMG INFORMATION //) HEAD 349001400 IF ilPTS ,£U. 0) w-UTE lft,?nn) LOTS HEAD 350001407 ?P0 FOkiaT I 1H0?30Xi?5HThE nfSlGN IS bA^FD D'i a .A4. HH IOaOtng///) PEAIi 351

00 1 4 07 IF (IPT? .EO. I) (in TO l Q l PFAO 35200l*ll K'M It (<>.?0l I PFAI) 353QOl'lS ?"l FO-MAT (40Xi?5HTRHC* LOAO INFORMAT TON. . . // 1 HEAD 35*001*15 WRIlt (6.?0?) 1R[ 0(1 ) ,TPLO(?) PFAO 35566l*?5 ?0? FOH-iAT (box, IPHF TPST AXLE LO/\D = .JMiFB.^'u K

I

PS/SnX , 1 'HSFCOND AHEAD 356lXLF IOaii = »?tx ,fH. 3,bH KIPS) HFAD 357

00l*?5 TP => THL0<4)/]?. HFAO 35B00l*?7 WPlIt (ft,?03) IP HEAD 35900143S ?f'3 FOP1AT (50X.40H5PACIMG BETWEEN FIRST AMD SFrnNn AXLE i*X,F8.3t HFAD 360

15H rtt T) HEAO 3ftl

001435 IF I IPTb.CU. I .OR. LDIs, FO.4HHSl5.nH.LnlS.fi). OHMS'") Gn TO 19? HFAD 36?001450 GO l(i 143 HFAD 363001*51 19? TPI b TKL0(5)/1?. HFAD 364001*53 TPr = Tl<t0(6)/1?, HEAD 36S001*55 WPllF (ft,?04) TRlO(3)i TP] 1 TP? HFAD 366001*67 ?r-4 E<mAl (5|',X. 1 H H I H I P AX|F lOAl) a i'M,FB,l,^J K T PS/SO X , *4 HH J N I HUM HFAD 367

1 spacing of Sftono Mn third axlfs a ,f«. 3.cw ffet/sox«*4mma*imum shead 36b2PaC|NG OF SECOND AMD THTRn AxLES = ,FR.3. c h rFFT) Hf AO 369

001*67 193 TP I = TW.O(7) • I2« HFAD 370001*7] TP? = T»l.D<8) o 1?. HFAD 37]001*73 !Fl = THLO(IO) » |? t HFAD 37?001*74 WRIlt (l.?U5) 1P1. TP?. TP1 HEAD 37300150ft 205 F0-HAT ( 5il X , 25HSIIPFR T MPn<;F : l DFAp |0/>0 r .lo»,FB.3,BH K iPc/ET/50X, READ 374

12]HiilRDFh DtAD WFlliHT = .?3X.FH.3,Ph k I PS /F T Sf 1 , HFAD 3752??mi>EaO »'l IGHl OF SL/iH = .??a.Fh.3,bh «|'"-/ni HEAD 376

00150ft IF (IRLO(O) .r.T. .11 WRITE (ft.Pnft) HEAD 377001514 ?Ph FP-<-iA7 (SiX,?9h>" IMPACT FACTOR Wl|| pr HSF"///) HEAD 37B001514 1

cj1 IF (1PT^ .EO. ?) GD TD ?49 HFAO 379

00151ft fcRliF (6,?10) HEAO 3B00015?? ?)0 FCH1AI I lM0f39X.p7Hl.ANE lOADINu INFORMAT T"'i. . . / / I HEAD 3B10015?? TP ; UNL'Ml) " I?. HEAD 3B?

188

001?.?'.

00153ft

00153ft00 154000154?00154300155S001557001567

00156700157S001610

00161000161?00161400161S0016170016200016?300162300163100163100163300163S001636

00164100164]001657

001657

0Q165700166?001673

001673

001717

?!

?1?

WP1 FO131?3&IPTPTPWPTPwPFT

134IF

9 IF

b FO

?6?6

27

?7

30

no

13"

001717

0017170017?0

130

0 IF

PPPP.

PPEMFCGO

(' RF1 FO

PPPPEMFC

COWR

5 FO162FR3244?RCO

IF

RF1 FO

MP.

ICO? FO1213313NE4175F8610-71Q'81H-CO

IF

IF

t (ft.PllAT ( '•> n x

,

ONCl'NlrtAGMCe NTRA

UNLO (4

UnLO (S

UN| (I {1

<6.?051 >r.L I 7

t (*.?1?at I'mGncf '-I RaUNLO IB)

TRl.o CJ)

AT (|M0,tAD THE1P1H ,EQ(1 ) = ?o(?) = 1?

(3) = 36?qoijo.

.4 • FP270(5.?M

)

AT (F10.(1 ) = .5(?) = .3? 9 p .

.4 • FPHINT THEINUtt (6.?75AT ( ImO.f'FSS = ,

t4H KSI/ooulus oILOxAHLEINUEEAD Th£IPTh .&T(5,1301)AT (9FB.HINl IhEt ((,.130(7) .COSTAT (

1

m t

,

OST OF «

F8.3.9H15X,

ER.3t9HtlSH DOLDOLS/wELOOL'S/CUDOLS/ININUFF.TFHMlNEIPT7 ,tJ1PT7 .EO

TP, i i'l| 0(5), UNLO (3i

H| 1«FIAnf L "AT I MR b ,'4«,F r'

FOl< MOMFNT =

FOR S>"lFAR =

,

1

3X.FQ.. 1 4K.FB.3

TP3

p i

iinD I

OAT• 1 ?.

• 1?.• 1?.1 PI , T[

• 1?.TP1 , UNLO ( 6)HSTOFanl.K lIVF LOAD = ,?3X,F(i IHTFPSTaTF IPAOING = ,10*.T . .1) WHI TF (6,?(16)I . .1 .AND, UNI O(R) ,| T, , i 1

»,14HlMPAfT IS lNCLDPFO JN T

TFRI'L PROPERTIES IF PFQIToF1) On TO 260

)

?r>

TFTF

)

1

)

)

)

I

?1

TF

.r-

.L30KA

.0

.0

.0

r/i noo .

PROP ( T)

?)t, u ppnp(i)•5 » PH0P[3)

C/ 1 .

HATFRIAL properties

) PROP(l), PROP(?>, PROP(3), F

3<jX,??h*a1FRTA|_ PROPERTIES.../17X.F8.3.4H KSI/^OX,?^h»LLOn««SnX,

l

ShYTFLO STRFSS ,?9X,F0.f elasticity » >i8x,F)o.3,4h k

COMrWFTF STRESS = tl6x.FR. 3.

4

.=.Rh KlPS/FT/^nx,>.rH 'TPs/>;ox,,'N K'PS)

«. • .8" KIPS/FT '50X,Fn

,

3.CH KIPS)

uoITF (6,?1S)Hf ANALYSIS)n

m, Fr/= -' X,?7HALL0WA'<LF HFI F ShfaR STRFSS = , 1

3./. H kSI/SOX,ST /Sn* ,

H »ST 1

COST INFORMATION IF REO'iTRFO0) GO TO 1300(COST II), I 1 , 9)

?)

COST INFORMATION)?) rnsT(i),C0ST(?),C0ST(3).rnSTif ),rOST(S).CoST(6)(H)

39X.24HUNIT COST INFORMATION.,F SFrTJO'j s 23X.FB.3.9H OOLS/IrnL ^/L^s/snx ,

>

FH.3.9H OOLS/LBS/50X,?7HrOSTOf I S/LRS/<^0X.33HC0ST OF rONNFTS/fnNNFCTOR/io* . 1 HnFI »FO wF|nD/^nx .24HCOST OF WELD M/iTFRlAIt> of wEl n/snx ,??HCOST nF »Fi

n

OF lFMGTh)

.?' X,FR.3,1 rNGTH ,2?X .FR.3.

IMF NUWpFR OF rrCLE INFOR-ATIO' ANO PRINTC) GO TO 3300?) GO TO ?301

HF AO 3R3HEAP 3R4RFAO 3RSHFAO 386RFAO 387RFAO 3RRHFAO 389HFAO 390RFAO 391HEAD 392HEAD 393READ 394READ 39SREAD 396REAO 397READ 39RREAO 399READ 400REAO 401HFAO 40?RFAO 403HF A[) 404RFAO *05RFAO 406REAO 407HEAD 408RFAO 409RFAO 410HFAO 411RFAO «1?RFAO 413REAO 414

NUlNRFAO MS9X REAO 416

HFAO 417HEAD MRHFAO 419READ 420READ 421REAO 4?2HFAO 4?3HFAO 424READ 4?S

, READ 4?6RFAO *?7RFAO 428

= .READ 4?9IFFEHEAO 430

, RFAO 43111X.HFAD 432

RFAO 433REAO 434HEAD 43SREAD 436REAO 437READ 43RHEAD 439HFAO 440

189

0017?? RF4P(S.?30?> NCYff PFRCFN HEAD 441001731 ?3<-|? FO<»AT (I10»F10.?> HEAP 4*2001731 UB|lt (bt?303) PFHCfN.Ni-vr HFAP 4*3001 7*1 ?3P3 FO-f«AT ( inl ,?ox,5?HTHt pfSIgm CYCLF IS Pf BF"fo uNTIL THc FINAL MOREAP ***

1MEMIS/21 A,?2HAfiF CHANGED LESS Than ,F6,?,??w PF°PEnT. ThF MAXIMUMREap 4*52/21 ».?0«NUMHEP PF CVfLFS IS , I2t ) H. ////) HEAD 446

001 7*1 GO 10 ?150 HEAD 44700174? ?sm «E«.i (5.2304) NfYC REAO »*8001750 ?30* FCHoAT (110) RFAO 4*9001750 PE-*('£N * 0.0 HFAP 450001751 WRIlt (*.2305) NpYC REAP 451001757 ?305 fo-mat tiHi,?ox,40HrHE design cycle is rfpf/>tep A TOTAL OF ,1?, HEAD *5?

17H I1MES.////) REAP 5300i757 GO fO ?350 HEAP 454001760 23O0 NC'C = 1 HFAP 455001761 PE-iCtN * 0.0 READ 45600176? W"[iE (h,2306) HEAD 457001766 2306 FO-MAT (lHlt?0X.^0HTHE DFSIGN CYCLE IS RFPF<\tFD ONLY OmCf. THE HAHEaD 458

1SIC/21X.52MSECTION r, F Jio>*l NFP IN THF PFSTGN rYCI F IS RFPFSIGNFD/ READ 459221 <.*8HliSING THF NEW DESIGN LOADINGS ANP Tmf program IS/ REAP 46032H.16HIHEN TERmjnaTfO.////) READ 461

C DETERMINE THE RE3UIRED REFLECTION LOCiTInnS READ 46?001766 ?3S0 IF (IPT4 ,NE. 01 GO TO 7400 HEAD 463001767 DO "'OX I s 1 , « N HFAP 46*00177) 10 = IOSP(I) REAP 465001773 DT = COOR(ID) . SPA*J(I) / ?. HFAP 466001776 AS = 994999. REAO 46700?000 DO -'402 J => 1. NA REAP *6RO02001 IF (AHSfCOOR(J) - nri ,GT, AS) GO To ?40? REAP *69002007 IA a J HEAP »70002007 AS a ARS(COORU) - OT) HEAD *71002011 240? CO 4 1 INUF HEAP 4720020H IOEF(I) * I

A

HEAP 473002016 ?4"1 CO-il INUE HEAP 47*002020 N0r> a MN HFAP 475002021 GO 10 2450 REAP 476002021 ?*00 IF i IPT9 .NE. 1 ) GO TO ?*60 HEAP 477002023 IS = 1 HEAP 47800202* DO 24 10 I = 1, MN HEAP 479002026 = .? HFAP *Bo002030 10 » IOSP(I) HEAD 481002031 ?4?5 01 a COOHI Iu) . p • SPAN! I

)

HEAP 48?O02035 AS = 99V999. HEAP 483002037 DO -»4

1 1 J = 1 , uj RFAO 484002040 IF (Ahsicooh(j) • ni) ,gt. a<u no to ?4ii REAP 48*002046 IA » J HEAP 486002046 AS = AHSICOOPIJ1 - IT) HFAP 487002050 241 1 CO il INUF HF An 488002053 ID'> I Ml = I A HEAP 489002055 18 » IH . 1 HFAO 49000205* IF (P ,LT. .41 GO T -> ?4?1 REAP 491002061 IF (l ,LT. .(•) no TO ?4?? HFAP 49?002063 GO 10 24 1 HEAP 493002064 ?4?1 = .5 REAP 49400206* GO iu 2<.?5 HfAli 495002066 ?4?? D = .8 NF«'i 49*002070 oO 1 u ?* >5 HF AM 49700207O ?4l c o 'i r ui HF Al 496

90

I0?n7300207s00207s00211?

?4'?4f^

c?4sn?4^S

"0211?00212S

00212S00212*

NDiCf s IB • |

sn ro ?«snREno |S,?»K',| NnpFi (IOFFUli I = 1. NnFFE0-MA1 IIIUi ?(<n>

kPinT Thf PFoujofn dfflFction inraTin**wllt (b,?45S) (inFF(I), I = 1, NOF.F)

EO-eAI I1HOi?0X,boH0FFLFCTIOnS aRf FOUNDi...//?4x,?cniRE luh'N

EN )

*t tmf following points

HF4D 499RFAO SCOHEAD SOIHEAP So2WEAO S03HEAO S04.HEAP SOSREAP S06HEAD S07RFAD SOR

SUHPSO'iRAm LENGTH003*7?

IJNUSEn rOMpjLFH S^oCt'

O3100O

00000?

O0000?00000?noono?nooon?00000?00000?

00000?000001000004ooooosOOOOOfc

oooon

000017

O000?lnooo?i

oooo?4

0000?h? 7

O0003*oooii 4 ?

0000x7oooo"--?

0000S4POOO^f.

SU-M

COiiipae (

2ILO)3SL4-1CO i-i

CO i"

CO" "

m It

HE 11.

INIr

ISAH =

wP 1 I

T H ) I

IE I

IE c

DO >

IF I

K =

r

IE I

c

po >

Th ) I

IE I

IF

CO>

ISlr

C cI i

OUT I

FKT.CON '.

!H) .

N(HHnil. s

UN/H( N/1[1(1/ I

NS10I*.

Of K

t T I

= 0.u.

F =

f =

jpt i

JP1 3

1ART5 I

HFC*1 .)

1-

hf CKMIS (

hEff(> M\F =

IHOIf =

[1(1 I

1 Nl JF

F TSt'L(l

I =

OF SF w

I

sf is t

AMf ( 1 M)

\> ( 1H>

I . C L ( P f

I AHlH.FNF./ JPT

3

<*o/|_prM

I N/HAUNN L P CMIT. IS

NAMEM I IAI

ir

Ihf CONDITIONS FOR USING K»l r To SOl.VF EO ) I VALUEI . SAO£a< 1«) iHFPTHdb) .FLWin(lO) .Fi Tun n> , wrRTHUS) .

> 1 Y (1 *) iNSECT I 1

B) , NOS f «0> .TSTfFLCIl tCSCOl •

') . IHCON(RO) .cmIho) , P| ATHfon.-a! ,Pi win ( «o,?i . ne.•'P

i. fPTln

In)

TEFL, IICON. JHCONi MR

7FHD VAlHFS

o

.

.

.LT. Q) T^«1D1 * SLAfJWn / (3. » MR1

.LT. 9) T^njD? c S| Afwl) / MPHerman loop for each sohelf^fnt

= 1 . MEPRcviOUS SECTION FOR SIM.Il.aoi TY In thf CURRFNT 1NE

(J . 1 ) On To 7 ?

1•

FOR SIMTIf-t STEFL SECTIONSI ) .ne . MOS Ik ) ) on To 2?FOR SIMILAR TOP Asm HOTTOx rniyfn Pi .TF^= 1 . ?

AhS (PI A!h I I ,KK) . PLATH(K.KK))f ,oi . , nonoi ) on To ??AHblPt »|M 1 iKK) - 'LhID(K,KK)lF .OT. . n on n

i ) on To ?.2

I VnlUFS In THOSF OF Thf MmTLI" SF'-'IOo1 = 1STFFI. («)CS (Kl

SFMC 1

SSFMC ?

SEMC 3

SEmc 4

SEmc 5SFmC 6

SFMC 7

SFMC FI

SFMC 9SFMC 10SFMC 1

1

SFMC 12SFMC 13SEMC 14SFMC ISSEMC lhSFMC 17SFMC IP,

SFMC 19SFMC 20SFMC ?1SFMC ?3SFMC 2?SFMC ?4SFMC 25SFMC 2*SF MC 27SfmC ?8SF MC 20SF MC 30sf mc 31SFMC 3?SFMC 31SF MC 14sf «r ISSf MC 3fi

191

nonnf-n II C ' ( I i = Ii f I> (K I

00 HUM CMM = ri imnOOOfil Ihful ( i i = i,.r r>n in i

000064 C« l i ) = ChlK)00006ft GO i( 2 U

00006ft ?? Cf «i If Uf

r CALCULATES" 1 Wftl 'FS whF'j 1I-.F-F It NO 51MTI «i< sfcTTOnooooftft ?n j Nfs i i

i

000070 hv * nFPTh(J)/?. • PlATH(If?l000071 C«IL ICALC(P| . »I.r>f I • \ 1 tPI *TH( 1 i |i ,Pt to- T ri ( I .»\ .PI ATHII ,?) ,PrPTw(J) •

15AWFAI Jl , I M I) ..u . " . ,CS I I 1 . ! MKH rll)00 1 14 D - (. .

oooii'. if UPT3 ,OE. lni "in Tu ??s000 1? 'I c = t.00O1P1 TS» = Si. HFA(.i)»|.|»ii|l«ll 0>

'l % TH ( ! . 1 1 RL<"" 11 » .')"PLATH( It 'I

0001?7 H * ?. • (DEPlhM) • PLOTHII.?) - rtiTi)000134 CAi.i ICAI.C (ISfclni t^UAHT'Htn.r.htTSAi fSTFFl i I i ,rs i T ) ,H«iif(- i.Ci (I).

1 I L C iM I I )

00015ft CALL ICALC <TS»»ln?»«LARTH.D»C«HiTSA« TSTFFI ' ! 1 .f*S i I ) .HaUliC'iiCH 1 1) .

1 IHCilM I ) )

000P0 1 G r i' P 1-

000?0? ?? c. ILC.HMII =• I SI F Fi 111

000?04 ' lHC>.r ( I I = 1ST! Fl IT)

000?0ft CM l l ) : fMII000207 CL I i ) = CS I I |

000?1 ] >s CO* i 1MIF

C CURHtCT FOR ThF CnMPoSTTF ACTln'i

000214 IF UPT I . liF. 101 <i0 TO 3d000?lft 00 ll I s li 10, ?

000??0 14 a LPCM1 I

)

000??? In = l PCM [!) . ]

000??4 IF (1A ,FU. 0) fin TO 30000?25 Ori il j = IA, InO00??6 iLCOhl Jl = TSTFFL ( Jl

0X>0?30 IHCnN(J) = ISTEFI I J)

000?31 Cmi il = CSU1000?33 CL I I) = CSlj)000234 31 CCN I iMilt

000?40 30 COmiIMUF00O?4O Pf r.lf-N

000?41 EMO

SFmc 37-jt- mc 3«SFmc 34SFMC 40SFmc 41st wr 4?bFMC 43SFMC 44SFMC 45SFMC 4ft

SFMC *7SFMC 4F3

SFMC 41SFMC 50SFmc 51SFMC 5?SFmc 53SFMC 54SFMC 55SFMC 56SFMC 57SFMC 5FI

SFMC 5<»

SFMC 60SFMC 61SF MC 6?SFMC 63SFmc 64SFmc 65SFMC 66SFMC 67SFMC 6RSFMC 69SFMC 70SFmc 71SFmc 72SFMC 73SFMC 74SFMC 75SFMC 76SFMC 77

SUBPROGRAM l FN(jTH

0003?0

UNUSfO cOmPTL fH S-aCE0*?000

Si'-wUUT INI SO| V/F I -'.i f A.P. '.4 I

C >OLVFS Thf m»tfm« Eo lATInN FOR T .F

000010 DMrt-M'i'l A(S,t), P|c,R|), MAVt(^,5|000010 ?i I FOrt^At I// 17M S|l.r. j| jn wATn|> //)

000010 ?i ? FO-HAT |2(I3) )

9F M" I I• I'iFL'iFNCF I ImES

SOLV 1

Si.LV ?

SOLV 3

Solv 4

SOLV 5

i 9;

noooi o

OOOOllooooi?0000?10000??0000?!O000?4oooo?s0000?h

0000?7000030000031000034

00003S00003*000040000045nooosn00005|oooos?000057

0000610000h3000066000071OOOIOO0001010001040001 1 1

0001 1*

0001?00001??oooi?*i00013?00013700014000014?

000144

00015300015h00016k

00016700017..000175000?00000201

?m

?io

21 5

?19??n

??5

00DOMAINISNHMhaiIN

DOTSNil

MM

DODOIFTSNMMMCOIF

DOTSA(A(

DOTSPI

PiIFDCTSA(

A (

INMAMA

If

-.1

a?c•>t

Vf

4 ^

a*r ll

)r A

<t

/b

ft *

a *

ill

-M

?1

I A

9

ft*

ft*

•H 1

If.

.10

-u3

viAl.KA]

a

>J1A

i ih

in->?

OSS i

FFH(TBI*THE

NGUI A

K UU1

3 1-

3 J =

I I . J )

a .1

F = "

LlMI'MlriN Tfl UNIT MATI'I* WITH CT> ir is imkIFf.l M(\r«I> Sl/F ON Mr MS. P TS T..r PTOHT HAM) SlnEwlTh N/l m UMNS ANP NS ko*";, FVFnvTHTi'fi IS SrHiHHlEOA Mflr-yx ofiO ThF PFSlJLTS «HF ON Top Of P. IF A ISH ThF PHO-jRAM STOPS,lHf PFOHIOF.O VARIABLES1, 5

1 . ?

= r

ik. 1

i *,tU)tX

I

\<ti (

it

? 3 (] IF I A

r A.

'lit

'lit

ILL

CI

i IN

(1

(J

: J

*P|

WR I

CAl

?40

?4l

J :

If

J =

TS

oi u ihe 501 hi jom t nop6 I = 1 . NA I 1 . 1 )

= I

- T

1EHMINE THF LARGEST ELFMENTJ - I « M

fi m = I , n

HSfAU.Ml ) .LT. TS) BO TO ?loA R 5 ( A ( J , M ] )

= J

NUtMAA ,EU. 1 ) GO TO ??PTriE SImpl*" wn* Ano column OPERATIONS

B iv -. 1 1 NA (^MAX,K)X i K ) = A ( I , K )

) = ISH = l, I

P(nMAA.K)X.M = PI I ,K)) = IS"A* .EO. I| GO TO ?105 K = 1 , N

A ( P. , 1 I

) = a in ,mmax )

M A « I s IS=. INDEX .

I

INl'F ». 1 I a MM A *

INOFXt2) i= i

TEKMINE ThF SINGULARITY CONDITIONhS(A(I,I)) ,OT. HITTLF) 00 To 740IT If" A SINGULAR MATRIX IS FOUNDIf i?01 )

16. ?0?) 1 , [NOFXHITNTINUE Ti ( ROW mo COLUMN OPERATIONS

* 1

.tO, N) i.o TO ?4 3

. to. I.

' ) 00 To ?4

3

- 1

All. I) /A ( f , T I

Soi.v 6Son/ 7

S"LV H

SOLV • 9

S>'LV 10SOLV 1 1

Si LV 1?

Solv 13SOLV 14SOLV ISSOLV 16SULv 17SOLV 1 R

S ILV 19SOLV ?0SOLV ?1

SOLV 22SOLV ?3SOLV ?4SOLV 25SOLV 26SOLV ?7SOLV ?fl

SOLV ?9SOLV 30SOLV 31

SOLV 32SOLV 33SOLV 34SOLV 35SOLV 36SOLV 37SOLV 38SOLV 39SOLV 40SOLV 41SOLV 4?Solv 43SiiLV 44SOLV 45SOLV 46SO L v 47SOLV 4«SOLV 44SOLV 50SOLV 51SOLV 5?SOLV 51SOLV 54SOLV 55SOLV 56SOLV 57SOLV 58S ILV 59SOLV 60SOLV 61

SOLV 6?SOLV 63

193

o o o ? o s

ooo?l

1

o o ? nooo?l 3

ooo??iooo??ft

? 3 o

00073100P?3?

non?'nooo?4i000?'.'ooo?4ftooo?4»-

n|)ii?t'i

ooo?ft4ooozft7

n o o ? ft ft

000?6ft

ooo?7oooo3< l

ooo3nft0(131 »

000311O0031?0003)

4

00031ft

0003?!0003?}0003?^0003?.,0003?700033?00033100033ft00O34 l

00034'.

00U3470003ft?0003S3oon3ftft

00n3f><-

o i.i 3 7 ft

00 4

0004 I

4 3

o o 1 1 4 o *

00 4 0ft

4117

0004 l n

I) 4 1 p

00041 ft

0004??4 ? 7

P0:i4?7

?- 3

?4 4

?46

/i I I . ,i| = IS

fid 1(1 ?41On J4<, i=i.T •• =

p<l..I • =

?'-7

?ftft

?hft

( I..') /A I I ,

= IS

If

?0"5

T I

J =

IFII

J !

TOTO1.

Tft

I In= I

r

= « I

i •

i I .

1 J .

J -

= n (ft

2 fl(|

= («

= 1

V

0) r.n n ?s?

N)

I*

> ni;?

Tl ?c,?

1

1

II

I J)- IT

» M . Jl - ISr;r> ii. ?si0( .".ft i = l,

r- *

PK..Iir ur, -i

11

'

' (-* i) -

IS' . I

'.I

I

1 I D(l ,

I''

IF

OfTl

Ift

IF

J

IF

IF

J =

T'l =

Tn =

Tv =

Tft j

M<>r,r, i

I 1

i l" .i ..

Jr-ft * =

= i I- . I )

* I * I

lift .Fi/.

p . 1

II .' i .

I J 1 1 I)

•

)| 1,1 TO ?6ft

In,

h. | 1 i.

i\ r-n

1*11rn

r.n

TO ?h?

3ft?

Tn ?< 3

i - 1

M'.Dill. )

)

' K.J)rv - n

I) = TS?' 1

D ' ->t ft I - 1 .

Tft s Pin.. J) -

P ( * . J | = is

Cft II 1 Ml i:

II I I i . ,'

i*

tl IIJll

I = INDI X

Ir" l! .P'J

1 = 1-J = > 4 V

M = f fi v

rs * cij. c i

t. I r . I ) "Ul.ll

.t'O. o

)

Cjlii«i<;

» i

r,-\ Tl PROTl I. F II i [ '. TMftl

P(

P|

61

:. ll

I

I If?)I I • 1 I

= 1 .

:I' ( M , I

(,n T i ^ft ri

.1 I- lb

II ? J ''

V>LV **V'LV 6=.

S'lLV 6ft

SJI v f.7

Sui v ft«

S ILV 60SOLV 70

501 v 71

SOLV 7?S'lLK 73V>L V 74S'.| v 7*bi'l. v 76S iU 77S«'l i/ 7HSOLV 7450| u »05olv FU

S'H V P?S ! v RTS-'LV P4Sn| v B=,

^OLV H6VI J H7S"L v fl«

S iL V H<J

Si'LV "90

S'H.v <Jl

SULK 0?s a v ^3S'H i/ 04S >Lv Qft

S'lLV 06ft LV 07s ii_v OB•» il v 00S. L v 00S'H v 01S'J| V 0?S iLV 03ft ILV 04ft i| v o=;

SOI v 06ft 1| V 07ft 1 V OHft LV DOb Lv 10

S"l. V 1

1

V'Lv 1?

s ii v 1 3

ft ii v 1 4

S 1 V 1ft

S 1 V 1*

5'H V 17ft M i |fl

S l| I' 10ft"! 1. ?ft

| V ?1

npn4 In F 10

OOOSO 7

ijnusf r i ru ipri F" c -j ji f

P4) ?un

19-

S '(. v 1??

oo o " <> ~

pop Opsn o (i n h

ronii 1

1

oond nnotiPl*n o n o l =,

P0»P1 s

POOP'nP000P1ooo"?"tPOOOlnP o Q fi 9 i

00003?P000?<.noon 1^

000040POOR* 3

P00044POonfc^

P0UP47POOOS..POPOVSPOOPMPOOOM

Sil-IHl oT I Ut; Si>i< 1 IPU.NIOIli-'NSIi'f PAKuni, T-iK.ii. P(4i>D' 1

l 1=1. N

I I'M I) = 1

Mi [It = -| - 1

DC •> k = 1 . rvtT np,1 = r - k

!'.« = 1

D" < I a l» ,1

I >l = I'M!)i.m i = u>(i»nI* i F-n HOI) .if'. »AQ(iiTll I lifl I" 1

I 1 = |l>1

I'll) = loll• KM 1*1 I = IT

[Si = ?

T CHI I 'MJf

IF Msn , F U . I ) mi T n ] n

? CO 4 t 1 Nllf

i p or, i i J s l,

• *

I" = !'ii l i

n Piii = • /. - < l a i

DO 1 1 I - 1 . I"

i? p « «( ( ] ) - >. ( I )

PF I II- il

t J )

5"PT 1

SORT ?

S"RT 1

S"RT 4

SORT s

SOflT ASORT 7

sior H

SOBT 9

Sort IPSORT 1 1

SORT 1?

SORT 13SORT 1*SORT ISSORT 16SORT ) 7

SORT IBSORT 1«S iRT ?0V'PT ?1SORT ??SORT ?1S RT ?4SORT ?sS0R1 ?h

CljHPFn <p4'.- |_' NOT.

i

000??^

uniisf o ro 'Pi i f M r> J ''( f

P4?700

n o P 1 f.

P00P1 ^

n (i 1 7

SlM-tOUT I NF ST 1 f FI I" , iu 1 MS, nf SPf A ,nns,ri TH.Fl .. I n . • F H !H , DF P 1" . PHllP . SI)

I F li if !•<! S I T

itSl •-S IHf nFASjMfi STIFFFNE.RS wwFRF r-Fci'iT wp. s'lDhrl'SIW. I )SP (t

l ,'IFSPF A (S. i ) . K|_ ( <, ) , Pf AU l= . 11 .N"? I B '1 ) ,F[ r" | | «) , SI I

IFl « 10 U«) .wf -tTF< I) "1 »nEPTH ( 1 R) tPHOPd) S T 1

D(' J^O I = 1 . f « ST I

OO ^c n \ - \ . ~\ s 1 T

195

00002n

OOno3n

P0003100003?00004?000045000053000055000060000071

00007*.00010300010400011

1

0001 1?

noon?0001 ?

1

0001??000)3"00013?

00013?0001*3000147000 1 5.1

000151000160

00017-;000?01000213000??3000225000??7000231

00023?000?35

000237

0002460002476on?56000263000270000275CI0027700030?000307

00031?

gin Hf «

D'.

9^1DPRL (

TMHIh

I"tf

S5IF

9"5

9"7

9"fl

W 10W 10If

wlo60

TMITmI

If

MIGO

8SIF

THI&o

COLCOLl?.oCOLSI.

FACSIIF

THI30

Bf.'«

Bt»

WL

FYIF

SSKRPRMpa r

IF

fatIF

TR

I I 1 . Jlf3lN•4t,n

I

CHFC"* I «

k) =

SI

= IDS•i n n -i

il .1

= TMw(AHS(.ItSll

if TF"•1AA =

= * .

( In Hi

* W 1

Id 9l.

i)fc IF"i = S

(> a

( I H I C

CK =

10 9"•If TEHa THHIRSCIS =

10 9r

It IfH= 1

I = 1

»»ID»R = S

* IDE= RRnn c I

1CSTHOf =

10 911

->t T u

-KI.I-1(1.2it SI 1,

= 4 .

if TEH= 1?.(AHS I

= 1.

a OFS= OFS10

I AHS (

1 = S

((•(VIS

O A L C 1

1

= TM"

, P

I (THE= I . f

10 SFF= 1.4

OFSHFO (

Ri'AX (RL

PI I)

( IH)U. N5)

/ ( WEHlHSS) .1 1

'J OF ThMINE Th

IFLwK1

.25) .

O .?5S

MINE THOhT (PRO.25K .OF.ThICK7

MINE AN/ ( ( win-If.. ,R(

TnlCK <

6

MINE ANn.O «

.5»wF_HlThICK* (

U«T(CPLRTH(IA)P( 1)«(1MR /COL A

• LE. f

ThICK .

6

THF p

= WTO= THITup r

(0FP1MIME Th4

R*OP

(

1)

.36P A( 1 ,

1

Iff A( I . I

Hm 7 RPHell ,GTSK » 1 p

.LI. t

1 A It Th/ ( .707

(ip n.i F ach <m 'HP ik r

IF 6 SlIFFCi im I S fciuior

l.i")

)

T a = MOS I TH - 1 )

( T A I o (OFRlH(lA) . -> . n » fit MM)). . 75oPP'iP (?) ) Gl) TO qi?F BFAPTNR Si TFFf fif u

F w T 0TH hf Thf P| IMF(l/M - wrqTH( t a) ) /? . "

r,T. rtJOMAX) GO TO 004

F MTMTMU-1 T-HrKNF55M(3)/33.) • W!0 / 1?.

TmINI r,n TO 9r6,06?5

CHECK TMF BFARTNG =TRFS51 ,?";*WEHTH(IA) /2, I »TwICK»?.niopROP (3)i rM TO 90R.0*.?!=

n CHECK THF COLUMN STRESSfrThiiai»»? . win • thick • 5.0H(IA)«»4 » (THlCK»wtn»«i) /•. *

KTDA?,»WfhTH(TA) /?, )••?T/COLA)- ?. * FLTh ( T A ) ) • . 7S/COI '

.-SL»SL»PR0R(3)/(3Q.47«3^»fm m /,. ? 5

A) CO TO 909.06?^

FAH ARRAY

CK0NNFCTING wFi n5H ( I A ) - ?. • F L T H < I A ) 1

F ALLOWAULF WFLD MFTAI ST.'^Sc;

- 36.0) . G T . 1.45) r» s 14.^« (FU/5H, - 1.0)

I « r)FSRFA(l,?l . orsRFfi ( 1 .-1

1

) OFSRFMl.M » nrcrjF A 1 T . t 1

. HO) RflTjn = HP / Pu

. n / (1.0 - .55 » RATIO)v I FV = FATSf wFLn ThTCKNfSS» F V « WL

1

sr TFsi I p R

ST If inSt IF 1 1

St TF 1?St If 13ST TF 14

ST IF 15St IF 16ST IF 17St IF IBST IF 19ST IF ?0ST IF 21ST IF 2?ST IF ?3ST IF ?4ST IF 25ST IF ?6St IF 27ST IF ?BST IF 29ST IF 30SI IF 31s r IF 32ST IF 33ST IF 34SI IF 35SI IF 3*ST IF 37St IF 3HST IF 39ST IF 40ST IF 41ST IF *2ST IF 43ST IF 44sr IF 45ST IF 46ST IF 47ST IF 4BST IF 49St IF 50ST IF 51St IF 5?ST IF 53ST IF 54ST IF 55ST IF 56St IE 57St IF 5BST IF 59ST IE 60ST IF 6!ST TF 6?ST IF 63ST IF 64SI IF 65

196

0003180003?10003?=.000331

r

N18 = TH/.Oh?'!H[ u-< (1,3) = Nl 8 o .0825IF (HEAw(IO) .IT. .?S)GO 11 900

St T uf' 1HF H c aP AURA00033?00033=1

qn? hf«-< (l.i) = o.rBr«Hii,?) = o.i

00033800033700034?00034?

9f

HFA< 1 1 , 3) = 0.0CO"*l 1NUFRF ( iKN

END

SUHPROhrAm000*77

LfNi JTH

• 08?bRFAR ( 1 , 1) s .?=.

' FOR NO STIFFFMFO

smfSllFSIIFSMF5T!FSTIFST[FSllFSI IFsiiFSTIF

6<S

8768697071

7?73747576

UNUSED COMP] i F" SV-U E

041500

0?

00000?00000?00000?00000?00000?00000?00000?00001000001400001 8

O0001 7

oooo?o

00003400003*000037000040000041

00004 ?

O0004 3

000044

000084000077000077

so

CoIDA?IL3SL4T»1

5FC6C0COcocuCOHi

PIIF

IFDO00DO

lHi-0 ST

DOPLPLPLPL

onOnI*

7

1GOIFGO

Of? IF

HCHKTHF STripSSfS AT FACh ANALYSIS' onT'T

PI . SARFa < 1 «) »DFPTH(]R) ,FLWTn(iPi ,FI TH() p)

I ,IY (IS) »NSECT(lH) ,MOS(«0l .TSTFFLCOl tCSIBO I , IHCON (°0) ifHlBm ,P| aTh(HO,->\ ,Pi win

(

ho, MR. CO Ok (.ii ) ,^i (S.'M , >) .rrrs.ci , F".SPAN(I FmGH»pD(Hi ) »Siit)| FM( on

) .NS.UNI n(Q) ,Tp|.n(

4.?) , hf<;m()m (ri ,4) ,PFSPFA (S,4) ,rrSSH(l6?,«(18,3.4) 1 CnvPL ( 1 2.(>»?)1 3, I RT 1 n

L . TLC l>MHCOM,MR,LF"r,Trtn I , TlST (4)

TS*TO) 3 Sl.AHwO / (3. «

TS*j F)? = Si AB*D / ufl

rtROUTINF STCALCULATES

1 ION NAME!]r ( 1M) , I > ( 1H

C''(> (Bl.) ,CL (

As»0, St. ABlHOf I (8(0 .NA,,->lf?ESS<81,-.1(4) .C'NSPM <bN/0'lF / JPt ^(.i-i/ I WO/LPliON/Sl »/FllM>tUN/ I F n/H»ai. u.n.is•IfcNSIUN LPC

( JRT ) .LI.I JRI I .LT.(BOO I - 1

11' J = 1

i B K = 1

rtrISS* I » J,KIstr, in I HEMOO I = 1 .

n = n.r,

« i = ,

( -i = 0.0«-l = II.

f

)1 T F i'I1 1 Nt IhF PI.ATF THICKNESS AT FApH NOncrBC3 K = l , ;

-10 1 J = 1 . I

>

IAHS IC"VR|_

10 BO

3

(LOOM ( 1 I .r,

l( B'll

I r> . K . ? )

,Wf hTh( )fl)

00) <

,?) iNFi4) .IOSP10)

)

J (5>

U('C

UFI 1

9)

9)

M/l

4

?

OOP TO CALCULATE TmF STRFSSFSMA

ij.).«.)).Lr..oooi,ANo.AfiS(rovP| ( j.j.kii.lt.

E .rnVPL ( J? 1 .K) . AND.CDOP ( I ) ,1 F.rriVPI (J,?,K))

on Tn Rio

STRCS1RCSTRCSTRCSTRc

) . 1 use (Si • STPC0) .PROPI3) .STRC,aFAR(5.3) .STRc

SlPCSTRCSIR C

SIRCSIRCSIRCSIRCSIRCSIRCSIRCSIRCSIRCSIRCSIRCSIRCSIRCSIRCSTRCSlRCSTRCSTRCSIRCSIRC.000 1 )

STRCGO TO R0?STRr

STRCSIRC

1

2

3

4

5

67

fi

9

10

11

1?13

14

IS18

17

Ifl

19

20212?23242526272B293031

3?3334

3S

197

oooioi PI 1 1

oooios P! «l

oool in G J 10

0001 10 H 1P L M

O0O1 14 PL « 1

0001 17 SO K0001?1 R 1 C0 1 1

1

0001?? R r 3 C n m f 1

r r.fi

nt»oi?4 It =

oooi?6 lc 11

O0013O 1 r |/1

1 1 1

0001461 • I 1 •

[F lA] 1 T

0001641 • I 1 • •

J.I =

oool 66 HP =

000171 CALL1SC»"»1

000?0S IF U00"?1

1

If 11

n o o ? li H a ?

000?1

7

ISA =

000??^ CALL000?17 C'»LL00n?s? oo 1

1

000?S1 R?1 I A =

ooo?ss p?0 SIS =

ooo?S7 5C =

ooo?6i IF (j

100?64 jp (1

000?66 SLS =

oon?7" Si. =

000?7l SH-. =

P00?71 S I =

000?74 go a-

ooo?7s s <o SL-> =

O0O?77 Si. =

3 H SHi ==

100301 S,l =

oooir? RSO IS =

000104 Toil

0003C7 T '1 S I (

oooll? Tt-,1 (

00031' 1X11 (

0117 1 I-. l I

nool?? T"-> =

0001?4 ST-lr^

r iiF

P003?6 AS f H

ll'r W000341 IF i 1

00034' ir 1

1

& 1 4 7 af -. =

0003S3 IF | jB

ooni^h 9-1 5 T-»- i

000 IhO ]r I,

- rnvPL ( Jii.K)= C0vPL(J.4,KIH. 1

c rovPL t.'t itK i

= i nvPL(ji« ini8i3

MUENUFLCUi.ATE ThF SFCTIHN PPOPEHTIE^I

• M). \A) RP TO M?lMSlPl ri-PL«TH( I «il) ) , LT. .0001 . anO.ARSipi Tr-PLaThIia.?))00'' I ) tin To H?nus (Pi rT-Pi ATM (I a. 1,1) ) ,1 T..0001 «»wn.ABS(P| n>-P| aTh < ' a-i , ?) )

00' 1 I SO In R?lNOS 114)0F.P1H UJ) /?, * Pl.TR

I CALF (P| Tl ,P| wT,PiTR,P| WH, DEPTH) |Ji ,*f Fa * JJ) , M <J |) ,»P ,n. ,

S)

PT i .

G

X . 1 GO TO MilFS'iUMlI.l) .LT. O.M GO TO H3i. » (DEPTH MM * PI.T3 - SOSAOFAIJJ) . PLTT»PL*T . PiTpodiwoIC»LC(TSWtni »SL'AHTh,0. .0 « »Mi TSA ,ST5,"!r . uAUHCH,<;i » 51.^1

ICALC (T ,-cTO?.S| ARTH,0. ,0. »H,T«;A,STS.Sf .H»hMCHi«;H,Su|S)

T - 1

TsTF tL I T A)

C S ( I A

)

PT i . GT . 0) GO to RIOf S lOH (1,1) ,L T . 0.0) 00 TCI RIO

II CON( I A)

r.L i ia)

InC'INI T A )

CHI I 4)

llsn

Sissc

si s

SFNOb ( I A)

= i)FPTH(TS) P| TT . PLTHI CM iTE IHF HOTtom FTRFW STPFSs1 ) = U[S«{i« ( 1 .

I ) » ST / SIS>) - OESwOMd.?) » sh / Shs3> = oesKOM, r, i| « sl / s lsM i

- ,iesn om 1 1 ,<. i° sm / sms

S 1 U lAnI 1 MST )

s ( 1 , i , l ) = Tl;S

TF»"i|T'F ThF ai.lowariF MoTTuM ftpFR STRr^SF^= n| I Ow (r>F S'mO" ( 1 , 1 1 ,FLW1 (1 1 1 S) ,| PC". ' 'So . 1 «"S .PPOP.roflH,M.S IHLtN.I M, 1 I

.i- U. 1 1(-n T I to 1

.i-O. n«) rcn to qo i

HnSFAl(Ti"ST«F'l,STUFSS(lil,l) t PRnP(i))F S . i T . f s r p ) a S T i; = A (• s

s| I

• 1 » r> I = n , O

•«S I s TmF ssi

i , 1 . | | | . -,T , (. i.v, ( 1 ,T,M ) STPrSSll . I .?) = 1.0

s PC 3As TRC 17s rue IRs TRC 19s IPC 40s IH C 41s roc *?s or 41s ST 44s TRC 4*s PC 46s rwc 47s PC 4Hs 'PC 49s RF ^0s PF SI

s T SZs l) C S3s PC S4s "(. '5

s «r S6s rue S7s [RC C.M

s wr SOs RF 605 PF 61

s PF 6?s PC 63s PF 64s fPF 6Ss IPC 66s PF 67s «r 6Hs OF 69s or 70s PF 71s or 7?s PC 71s OF 74s wr 7Ss or 7*s PC 77s wr 7Hs Of 7 l>

s PF HPs Or . «1

s Of »?*! PF M3s o r 84s PI- MSs RC Mns Rf H7s Pf 11 H

s u( R9s or 90s PF 0)"( Ul J^s «C 93

! 9 -

1 1 fill

n 3 6 7

000373000377000*01"OOfcCI 7

oori.1 ?

" * 1 ft

OOOft]

S

ooo4?nP o n ft ? ?

nOOft?^O004310004 3 >

n o ft ft "i

P0nftft4o ft ft s

00T451noofts?nooftfcn

O0O466ft 7 ft

00047*.

5 UPdOOSlHOOP^O*.

000507OOO^l 1

OOOM?o o n s l ft

noo^l 6

0005?o0005??P005?100<15?4

OOOSpsP005?sP0'>5?7

5 3

00053?00053300053ft00053sO0C5..5

0^5000055?ooo^M0005Sft

5 fr 7

O00S7S5 7 7

nOO'i0 4

O0OM17h 7

ej.il

*53

KM

f r-6

(1 .1'

I 1 ,M

MVO J

A .

IF

IP

ii.

ME I

Ot c '

DE5>Dts-D E S m

IA« ( T

'.'I

I Mr. 1

DP(1)•

! )

. Nilt- a r ( T

I 1. A

?•?)TRESSa IE 1

• bT .

1(1.1r _

0. S

(3F5M

OES*D£5m

• 'AX (1

TRESS

S T u r 5 s

»(

T

n Tn - sri / s is» (T'lTn - 5H| / Shso

(t mn - st I / 5i q

o |llTn - 5 H ) / ShS

om( i ,i

)

[1M( i ,?)1 >>

I I . 3 1

o,M< i .4]v ST I

= - ) . ii • inshF A| LT'A^LF Trip Fl-rp STRrSS^s

(,n 11 qo3r. n n nm

"ST.f'l,STPFS5(T.?,l),PI>nP(-U)SliJ) AbTR s At <-

= , "

(I t ?.l)).r.T.»STHI STnFSSIT.P.'i = 1.0hF C^IC'-IF TF 5T..tbSFc IE MfrfSc.PyQ I GO T n a 5 1

) .U T . n,r) fin lo R5tF

I T T HA tNF-i bl.AHTH

O'WI.?) '

1 "I I . 3) •

C" (1.41 '

VST )

= -1.0 •

= o.r(1.3.1)

I

( T 'U n

( T ;i T i-

l TtiTn

5M1Si I

Sri)

(SwS

r si 5

(S.JS

MR )

Tns

,RT. FT I STorSb ( I . 1. -"

111) r n ,n

*I?) = .0aTE THF ShEaR STRrssf b

IA)

^TH ( .1.1) « wfRfH | J l|

. 1) i,p ti B60

. Ha i fin 11 8611 - l

1

= 1

• NA - ?

1 '

8 IH

K = 1 . ft

) = IH 5Sh ( IR, » i / A«FHI flX(TI S T )

> n 1 . „

) = UESSH ( Tt. . <.) / nwFHrcinX ( T>-s I l

( I . «. . I 1 = A H 5 ( T 1 I

SIT,') .TT. A-IS(Tlt) STRESS! 1 ,4 , 1 ) , A'.- IT')( I . . . ? ) = n . n

S isrn£ssi t .4 » ) ) ) .fit. phiipi^ii stpcss i t. I*.?) = i , n

F i it f

j

s roc Q4s or OSs wr 06s RC 07s "C 9fl

s or 09s WC 00s PC 01s rc>c 0?s MC 035 r«r 045 Rf 05s IRC 065 PC 07s r«c OSs rue ORs r»c 10s RC 1

1

s RC 1?

b RC 13s rRc IAs rpc 15s RC 16s RC 17s RC )Hb «C 1R

s RC ?0s MC ?1

s RC ??5 'RC ?3s RC ?4s RC ?5s RC ?6b RC ?75 "C ?«51 RC ?oS RC 30s PC 315 PC 3?S RC 135 RC 3ft

S RC 3SS RC. 36b Rr 37b RC 3"5 RC 305 RC 40b PC 41

S »C 4?S Rr 43s RC 44s Rf 455 nr 46b or 47b zr ftH

b f»C 40s Rr 50

199

SUHPPT<PA» i_r MjTm

hni">E r) rd'-Pii f* S-

040100>(.e

Fi PviC 1 TO'i

c he Tf>c Ihr C

000003 o; ifi.si'i

oooooi TFl- = 1

000004 Pa-iI = 1

00000* PAH; - !

noooi n A Nl = PA

noooi? IF (fcHSl

000017 st-hax =

oooopn RF r.lHN

0000?1 ENU

SlIVMA* ( I^S^IMINf.5 Thc n^,r>M STurSS at a piinifimponfnt nrST'iN S'Mf'.bE^ rou t-iat

n rsssuiSSS( 1 I . t<;s^ ( 3>

F -P . TSSSI?)Fmp . T <;ts ( 4 l

s

HIPnH?) .r.T, ArSianS)) AIjS = o ( UjrtNS

. t V r *

WIT

STrmI

STrm ?STrm 3STrm *

S'Pm 5STRm 6STRM 7

SIRM R

STRm B

STbm inSIR" 11

STRM 1?

SUHPRO"RAm LFKiGTH000043

UNUSED (""••Pit F H SP..CF

041100

SJHxt'ilT I fJi

r ,it TfflM

00000? COM<U'N' l««

1D1F ( 1*) . 1

2ILOI (80)3SI ft -iKl.SL

4T till! 1 mtibFC.->lWFSSbCii-Ji (9) ,C

00000? Cl»MiON/i>U

00000? C.lMiON/1 «l

noooo? CU'HON/Sl00000? COHtUN/FI00000? C fmi>N/iFO0000? C'11iO\/Ftnoooo? COM HON/ 1 E

00000? Rf«L IX*

1

00000? DI«4tfcSIONr IMTI*

noooo? MN a NS -

000004 T T N = •

00000S KLL =

00000* Ml :

000007 OP = O.lj

L TFPM1MIMF THF C 'Toff DISTANCE fib a rt*T« u

\ »teME ( 1 H) ,<;«oc-a(1P) ,r>FPlh ( 1 Ht .FLWIHI 1P\ .Fi TM (

1 R) ,WrUTH(l«> t

XllB) , TY< 1R» »NSECT (lB) ,mos (ROT . TSTFFl ( "0) iC.s. (nni >

tCL (I'D , IMrnN<Hn> .fH (Pn I ,P| aThi n , ->. .Pi I- I n ( HO . ?' • NF .

AtilH.MP,rnno(Hi i , a ti (s,hi ,-n .rns^ .f -.Spai-u ) . in«;P(5) •

• N^tl FmIjTm«B'i(«1 ) t 5llRL£N (Oil »N5>«NN| n (<: I , Tat O ( 1 01 . PPOP ( 3)

(81, 4,? I .OESMOm («1 .4) innoFMI.Ai .nrSSuil"*?, 4) ,mFar (5,3)insp

1 1 f.,3,4) ,cnv/PL 1 1 ?>>>•?)E/JPT3. IPTir(1/lPCMK/FUliHT/TSTN/HAUNCHF.VEN/KO.KCtSISiSHS.sLS, ISS. IJ,"!S.r>--'. x.nTSTEN/PTh.K T . I TTV» ISTFFI ; ILrON,THCON«MR,LFvftTH,TI ' »

Lfr«(|rU TMSTI4), PlMI4n.4lUI/f ThF BFniJlBFn VAHlAHlFi;

1

1FBM 1

TFBm ?TFRM 31FRM 4TFRM 5IFRM *

. 1ERM 7

.TFBM R

TERM BTFRM 10TFRM 11

TFRM 1?TFRM 13TFRm 14TFBM 15TERM 16TFRm 17TFRM lfl

TFRm 1"TFRm ?nTFRm 21IFRM ??TFBM ?31FBM ?«

200

ooooio AV = VIr If If

POOOl

1

L.n -.t-nl

ooooi i II- lIOSooooi «. IH = Ml

00001ft \Y IAhS

oooo?4 r a = i o

rt ? ft IK IK')

U 3 ? AV - An00003ft SB >1 CON 1 I Nil

000041 SR-1? C "> m 1 I Nil

00004 1 IF I Mloooo<.s Tl = 0.00004*, DO ->t

OOOOSo 5ft. 10 TIM IK)

0115 7 GU i s

0000^7 55'Ui 00 it S)000061 DO ->05?.

0000ft? so 1-? Rll (KK )

P00071 50M T'ls 1 1 K )

0001 04 56M1 CO i 1 Kill

0001 04 QMS = 1

0001 Oft IF (1 MS000 1 117 TM-SI (1

)

0001 1" T M S 1 1 ? )

oooi ip Tn-ii 1 1

)

rool n IMS 114)

000114 60 rc 5

0001 IS 5700 I M S 1 l 1 )

OOOl 17 TM-il (?)

0001?o TM S f ( 3

)

nooi?i T M S 1 1 4 )

00 01?? S7i> 1 TDS = S

r >E Tf

P001?S Asrwi =

oooi?* AS) -It- a

lSUHLl N,000143 S 11 M =

00014ft SUv =

000150 IF (AMS0001ft4 H a I .

oooies GO IU S

U 1 6 S 5100 PA fill =

POO 1 67 If- 1 A H S

000171 si io SK = 1.

ooo?oo IF (KC000?0? ASF 1 =

000P04 ASP -i a

ooo?os GU 111 S

OOOPOft softo A > 1 =

OOOPlft ASF -1 a

ooo??i IF lUMS000??S TF"!-* =

000??ft AS»- I =

000??7 ASI- -i a

000?30 SOft 1 ir uj000?3? AS = AS00u?34 IF (ASF

IIHINE 1 hi- MOMFNT A'jO STHFSS IT Inr Pn«II = ?. 'iv

y ( I ) . fo, hi r.n to shp?SP( 1 )

(C')OR (KO) -COIP ( I R) ) .r.T.av) oo to c..r>i

^H I I )

• If. IA) [A = 1A . 1

S U"OOw iroi - ronu( I -i)

)

F

r

.F'i. II I' = "1

K = 1 . 4

a DESMOM(KO,k)61 1

K = 1, 4

K|l = 1 • WAB I

£SM()M |KH,«I= ILIfil (kO«RO,CO0R> TS*iDP«I rnr.Th . Si m. FN)

I-

mST I 1 I

. L 1 . P.n) SO Til 5 700= 1 MST ( 1 ) / S I S

a IMS1 I ?) / SHS= I MST (1) / SLS= I MSI ( '. 1 / SHS

7.'.1

= IMST ( | ) ' SS= TMST I?) / SSa TMST (1) / SS= lMST ( t, I / SSTRMA* ( TMST

)

i.MTNt TnF A(.LOWAU L F STHESSFST^OP I 1 )

AiLuw(lMS,FLi,iIO(lST),LPCMtToSP.IA.MS.PROp,roOH,OFSMOM.m . 2

)

f'lST ( i ) t TmST (?) TmST( 1)

I MST ( 1 ) • TmST (II Ti'ST I <. )

(SrtIN) ,r,T. .0 0) ,A fJ |i. ahsismaX) ,si, .0001) GO TO S100

I 10

S •! I N / SMAKISi-AKI .IT. AHS(SMIM)) RATIO a SMW / SMTKli .?"<<> I F J/S«, - 1,0).F'J. ?) 01) TO 'iOft"

1?. / [1 ,n - ratio)AS. I

061,5S»PH('P (1) /() .- ( ,55»pH0P (11 / (SK»i 1.6) -1 ,1 •RATIO)sk •

i1 . > / |

t. . ,ft? » :jat TO)

,01. p.n) 01 Til SOftl

ASK T

ASEBIF MP• F I ) • ?) TO hOBOIRI1 ,LT, A5TUT1 AS a ASFT

T ) p« ?STF RM 26lt»4 ?7IK rm ?«Tfrh ?RTERM 30TFHM 31

Tl- Rm 3?1FPM 33TFHM 34IK RM 3STl-RM 36TF MM 17TFHM IRTFRM IRTFRm 40TFRM 41TERM 4?TFRm 43IFRM 44TERM 4STFRm 4hTF Rm 47Tl RM 4HTFHM 4RTFRM SOTFRM SITl Rm S?TFRM S31 t HM 54TFRM 55TFRM 56TFRM 57IFRM 58TFRM 59IK RM ftO

TERM ftl

TFRm 6?TFRM 63TERM ft4

TFRM 65TFRM ftft

TERM 67TERM 6fl

TFRM 69TFRM 70TERM 71IFRm 7?TFRM 73IFRM 74II RM 75TFRm 76IFRM 77IFRM 7HTERM 7RTERM HOTERM fil

IFRM fi?

201

00"? 1

no"?*

noi ?»O0i'?s

noo?s

ooo?s00'>?snoo?.sno»?f.

000?f,

ooo?*noc?7ooo 30

00031P0'» 31

ooo3)r o 3 l

O0"31"00??noni?O003?O0033n o 3 3

00^3300034"0O34000340003S

0.3S

noo3S00»3SO003S0003fr

000370003700037

000374

0004000 4

00041O00410004100041

4?0014?noi 4?"0i'4 3

043'i 1 4

"or 4<,

up I] 44n o <« a

so'.q

S0';0

SI DO

M ll h M».,,,, o (.-. a nsH'H

11" it'sf .l i . ,.<• t <> i />>; = nsf H

ilMll i u I T ! Mr. .icF thf PLnTF. my iiti^", n\ i • n.f ASl'ifi

-.1 . p si Zc ii''i' imii n PunCfc nnuF

(.r .) [F i i 'S I ..) ,il, .0 00 01 I SO rn SO St-

ir , ,il,.s) ,ii, isi r,n TO ~"S7i, i i( S • in

s o <\ 7 1 > < = I SSr, ) ii s • • • *

s o r. « (Si = 1

-a = 1

T F i I". . -I (J . 1 I I S* r ?

PO U '• ' '

Simf, 1F IAhS I I Ob) .1 1 . AS.ftNO.XLL«R>»0) fin Til fio

Ir i . <s i I . iSl ,11 . (i S. 4nn,«i.L . f ii.

1 ) r.n TO n«:if, i il s 1 ?.

d I = n

.

y< s I .

IF i Ink .£0. ?) vis = -l.ou )

-. - B <4P 9

•

7 = .s[f ,„..•, (', p.,)-/ » I .11. .OOOll HO T:> (.000

V « V » <*,

1 ! = OPQP e ML * V

Jf I I - inl a WAX I".3 = -ima »

IF (».-. c,(.. p - \, ( t) ,lt« . n O p 0l) i.o rn i"" 1

n i io s-.', i

So.'? IF ilf .il, VI M i/ns = npJr" [A(»S( II. - Wsi .Li. 1,51 fiO TO S'OSIL = II

i/ = .s','1 It 5l<Jfl

SO 'IS 'iT-,1 r »a • -I

[r ( >I<S(SMS(|1IST1 -DMA*) .RT.l ) GO In ftSOfl

IF all ,r"U. i i r.o rn hsooIt lAMS(inb) .i i. os) fin to f-'ioo

Pi. = OP.ii him oma« it opnUIPFO

TT v r I |ri . l.iJ 4 » = H*'AX Pm»</TTN

I- i M .-'.'. l) fin tt 7oonIt iIjmah .GT. rno.<KO|.piHiin-nn r,"> T'i «haiGO it 7 0,5

7 1 l'i"' = rOOH(KO) - p1h(1TT-I.ii1-11 = 1

','1 ic 7i.o?.

7o io i' ii "a< . (>! , ptm( i Tt»i it) -coon i kid i fin t.i . - r -i

(5(1 lu /.'i?

7o 3 i.'3» = i'[H( ITT + l ,4) . riiP|K')l-, T I = ,

7 V 1-" IIPlll .t"0. '.I i^TTF (ft»l| O-IAX

1 l)MM IIin. 7p.|iMA < = ,ni,1|

v = . s

(, i ll ^i -

S S C'YI IW'i

1 F BM B31 f BM H4IFBM AS1 F Pu Rf.

It Hi R71 >-P'< ORI t BM rq1 \ BM 9Tl BM BlIFrtM q?Tf BM "31 f BM 04Itfia isIFBM PhIf BM B7IkPM 9Rifbm qp1 r B-* 00IFHm 011FB" 0?rfrm 03IF Uu 04!F«M OSIt BM OF.

IFww 07T F PM 08IFB'1 OPTFRM 110Tfrm 11

TEBm 1?IERm 131 F B M 141FRM ISIFBM its

IFBm 17IfD- IPIf HM 19IFBM ?01 p RM 21ifhm ??it bm ?3n bm ?41 ERM ?sIf B 4 ?fr

IFBm ?71 1 BM ?fl

If BM ?BIf Bm 301 - Bm -*\

1KB ' 3?1 • B 1 331 . .. 341 t UM ISIt Uu 3h1

i u - 371 > " 1»

1 B •> 1J1

' '. 4 1

202

000445PE I it N

EN i

1 F q -i U 1

IF «M 1 4?

SUMP^iViO*'-- L f Mi>TH

00PS67

unuse n ronpii f* sp«( f

040400

ooooo?

ooooo?nooocooooo?ooooo?ooooo?OOOOO?ooooo?ooooo?

ooooo?000004ooooosooooi o

0000?o0000?^000031O00033000037

4 4

O0004h00004700005sO000S7OOOOh?ooooos

h 5

OOOOl-'.

00007700010?oooi os

10 7

oooiis0001 lh

Pfcr'O

RS^O

flSTl

R5 V

CO1042113SI.

4T I

bFChenenCOcoCOCOCOhi

01

noDOPLPLIFIFPLIFIF

DO

ISIF

KFTl

1?(30

KEIF

Tl

I?IAIF

60I

i\

-ULIlT

IH)0>r <H

a 1 .• n

,

.it- 1 (fl

••THE-. i I'll

Ml'N/»-ION/1 IdN/* 11 i-i/

<-lON/rfip'l/

«L I *

It-.NSI

• 1 HO-ifiOO

•tooA I h ( I

«ID(I1JPTIJP1

1 = 1

ULw(F LwHI fil

i<)00

It TFI

t =

UF.S=

- ng= HEI H

= 1

(DES= OF= DE= 1

l»HSI I H

= I

IMF.'••I

. I*

I

,

SLAi 1 t

SS<

iCOuUF1 «n

SI >

( It)

r, I.i

I FN. 1

f

(IN

)Hl

Nt T

Ellh(IH)C L ( h

BlHiNft .1

HI ,4

NSPI/JP1/LPC/F(l

hi nE/is/nai• IS!TMSlI IH= 1

.

= 1

.

= r

=

LI.LI.

1 5

hf HCOuiUFfl THICKMFSSFS T Ki < ir , sn.fl.FMFMT),"!= M 1 -II ,riFPTM( 1 H) . F L Wl n I I ' v . F I TH( 1 u) , w-MT" ( 1 HI i

,IY( 1 »> iNSECT (IH) ,Nin«; («M .i^Tin |iif.| ,r<;|pfi, ,

(i . [hcon(«oi .thihoi .°i Ar^io , -• .mi b. in ( ro.?i . nf t

Mil, COIR ( P.1 ) ,RT| (5,»l.-i>,rri'-.ci,F '.SPIH.UI . Il)SP(S) ,

F •i-l'i.i.' Ii-

i ) i miHtEM(R' 1 iMS.HMl W91 . Tui O ( 1 Oi .PHOP (31 ,

,?i iOF^mOm (R1 ,4) fnFS"FA(<5il> «nrSSw(l6'«*) t"FARCi,3) i

1 fc, 3, 4 I ,ri«Pl I 1 ?ih. ?)

3, IPTl

n

l • Il.ror., THC(i^iMK,LF-,r,TH

LPC* ()0)nF^Ir,N a PairsF

TS/irnl = S|_hhwo /

MP

(1ST) . r, r . | 3. " ) »L» = 14.

'

(1ST) .r,T. If.. ) "L*. = ls.nTHE | pop FOp ForH F| EMEMT

I = 1 . nF-UnE OiTirai mimF'jT LOC«TInN T ^' r«r

mom ( i . 1 1 ,i t . o.n. on.nf smQ*i i i » 1 . 1 1 ,i r.n

SMUMil.l) . TfS'iou ( T . ?> • DFSMOWI T •»)

SMOM(I.l,p t DFSMn«( 1*1 I?) . OFS— MIl

SOI

i'l 1 ( I . 1 ) . r.F . , ,TR. OES 1PM[ y . I , 1 I

.r.i

SMM(l.l) 1fSM(l>. ( I , 3) • [irCMOMI!.',.smpm

( i •i . i i . dESmOm

(i »i ,T) . nFV'i'Mi'

F| FmFkjT

i) r.n to psnn

1.3)

I r, i Tn tSO?

Ill)•>" 1

T. a < S ( T ? i ) In I 1

Ti-TIF 1

TnnE ?ThoF 1

THOE 4

THOF S

TrtOE f>

THOF 7

T«DF fl

ThOE 9

l H OE 10MnE 11

T>mF 1?TmOE 13T'inF 14ThOF ISThoe 16Ihi-iE 17ThOE IHTnr.e 19TnriE 20Thoe 21IHOE 2?TmoF ?3ThOF ?4T"OE ?Sthoe 26thoe ?7i-nt ?BThOF 29IHOE 31

f^OE 30THOF 32I'inF 33thoe 34THOE 3SThoe 36ThOE 37I hoe 3HTHOE 39t'-OF 40ThOF 4)I"OE 4?TH11F 4 1

ThOF 44

2 5

nooi?n

nooi ?ino (i I ?3o o o 1 ? <•

"ooi it

oool i?

000113oooi 37

O0O1S30001SS0001 hi

oooi6s000171noo?04000?17ooo??3ooo??ftooo??7000?31000?3?000?33000?34

000?34000?3700024?000?44

00OP47000?53000?54O0O?61000?6400P?70

000?71000??4000?7S

000304000310

P003?S00033100033S000 3 3hO003430003SO00035S

C003SS0003S7000363

BS MBS1 1

7-m

BS40

BftM

BR'.?

IF

CI*J

IF

IDE

Pi.

PL

i HPC A

1 II.

IFif

TSM

CAC5TOTOG">

I SESFS 1^

SkCO

TX1 1

TMTM

AFASIF

TOIF

GO

EFOJTM

AFAS

IDFIF

AFASIF

IF

IF

GO

IF

IFIF

( I if- s-

-, I A K T

I I 1 NIK-

= 'I

(I FS"»fl()M ( I

-.1 4PI

II = ]

n =

if Tf .<

= PFH1.1. ICtt

I.SFCC(I FS'i

( JPT3» = S"* ?. «

LI. 1CALL TCA= l>EP

= TDro 7u

Ch = s

Cl = S

C 1 h =

C I L =

*r 1NUFnt TE'<

-.1111

sit?)> I I 3 )

-.111,1

'it TEH1 = HArub =

(AHS (

S = STI AHS (

10 BS"ETE*

s = osHb61

->! (K I I

• lETEPSh = H|H|. =

~>^l'M,S

(AHS (

", I = H

r-(T =

(*HS((AHS (

( AHS (

Id HS'JSF 1

l*H .

I ARSI|AHS(

1.1(1.

1HE1.1) .LT. 1.0) 1 A =

P| :. T V TfTF ""I 'Jf. 1 ICl'l

OM(Ift,ll ,LT. 0.0) n<;*N = PFSMOM ( 1 A . ' 1 . PFSMOM ( TAf 1) t

ft.**)

aITh K n P| ATFS

INlH(

LC,SE0-M

• GHK A

(0

LC (

LC (

fH(

1

ECCFCCSECSEC

MlN= P= 1)

=

= D

MlNSFAPi'0

&FSP'-IA

I OS4?MlN

KI

M[NASFALLU4LAt- S

ASFP <0

AF S

EFSPES4l

'IEI- .j.

PI. T

PL!

E Thf SfctIOm P-(OPEWTTFSISTI /?. . PLTR(P|k,PLTT,PL*.PLTH.DFPTMiIST).SAJrA(tsT).TX(I<;T),HP,Cl)I a. l ) ,l T , 0.0) nn To «sunT. 9) RD TO 7"0( l c T > P|_W • (P| TT P{ TBI

EPTHITsF) olTB . SFCpi1st. ]n) 1 Si.AHrH,n.,n.,H,Tsi,SFri.SFrc.wAiiNrHiSF'-i. ,secIL)TSl..In?.SLAMTH,0.,n..H,TS/\,SFrT . Sr p P H A UNP H . SE PH , SF C I H )

1ST) . PLTH . PLTTP|. 1 T • SLAHTH HAUNCH

I

I

E ThfESmOmESMOmESMOmESMO"E THFT I1M<;

P( 1 )

) .LT* (Tms) .LF

BOTTOM ST"FSSES IN POSTTTvr SECTION(IA,D » sErc / seciI I A,?) o SEpH / SFPIHI I A,l) e SFCI / SFCTI.( I A .4 ) « SECh / SFPTHA|_L.OV»Aml f STPESS

1,F I. 1 000, .PPOP (3) )

. ASTPH) ASTPH = ARS(AFS)T)

. AHSI ASTPB) ) GO TO BS41

E Thf BOTTOM STRFSS IN NFP.ATI'/F nrGIPM• SKrr / sECl= 1.4UFS^Omi TA.KIlE THF ALLOWAHl F STHESSAT ( TMST,Fll.-l 00 0. ,PF<0P(1) )

0"*(DFSMnW( I A . i ) .F| will! 1ST) ,lPf1.T-Sp. TA.NS.PHoP.COOP.EN, I M,]

)

H) ,|T. ASTP-M ASTPB = AUSIAFC")AT (T 1ST, FN 1 1100, ,PHOP I T

)

\

P ( 1 I

T) .IT. ASTPT) ASTPT = AQ<:((1FST,

) .GT, »RS( ASTH^l )' GO TO BS4?) .(T. AHS(A9TPT)) Gil TO OS4'

Wv/fl HALTING TO vaHy ThF PLATr S|.fI ) r,n TO R7io

H) .IT. .000) 1 SO TO RSVH) .GT. 1 ,S « FLThIIST)) P,0 TO Br. a O

InnF 4ST"OE 4hTnnf 47T»'OF 4BTHOE 4<J

ThOF SOInnF SI

THOE s?ThoE 53T-inF 5*1 hoe ssThdF Sr,

TnnE S7THDE SBTHOE S9THDE hOTHOE ftl

1HOE f.?

THOE 63THOE 64THnE 6STHOE 66THOE ft7

THOE 6BThdf 69TMOE 70THOF 71TnnE 7?THOE 73THOE 74THnF 7SThoe 76THOE 77Thoe 7F»

Thoe 79Thoe BOThoe BlTHOE B?THOF B3thdf B4thoe ASTnnE B6thoe 87THDE BRTHnE B9TnnE 90Thpe 91thoe 9?I hOE 93Thoe 94TnnE 9STnnE 9ft

Thoe 97Thoe 9fl

TnnE 99thoe 100TnnF 101THOE 10?

I

00037100037?n o 3 7 ?

o o U 3 7',

3710004H110U4I'?

I 4 04C 4 1

"

00114 I 1

0004 1 '

O0041 S

0004?10004??Ofl')4?l

I) 4 ? h

r o c 4 1 i

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{' . L F . II ' "I T i' »fc 1 1

C.'LI. t-'HSFf ( NF . '. 1\ <' A"F , I * I P

1 C'i) <• 5U»H H.r.frucall F'McOv (rdvPi i

k/P II I I hi 100)1 i FllrfiM I Ml

)

CALL PK5 I!F </*>! "FA J

l

call Pwi'0i»(iviSirn |"So iMrs)»>•

I 1 1 ('-. 15 1 Hi "T"T , rcnsTima F'w-iAT (]Hi)i]nXi ismTotai hFTCHT :

IF 1 i.c

)

IF (1PT'- .'J I. .51 ''il TO PfcMWF- lit |h| I5H?) rnlNFCMlM I 1 "Ui 3p» ,7M(- -1TN = ,Fl?.?)go n jo]

i

MR lit |h. TiH?) *Ml 'j

FLM-I«T (I HO. IPX , 7M-JMTN E ,Fl3.?)Cfl <l I I MlIF

REIuKNFN I

plaTh, istffi irc.ii. ri«,r;i i inn in, cm,

if l s, s. <-». i ifji nT »i cost =

?6 Ii

?61 1

I.F NbTM

U^IF 1 17U'-IF 1 3«UN IF 139U .IF 1 «nUN IF 141IINIF 14?U'JTF 141UNIF I 44UN IF 145UNIF 1 4hUN IF 147U~IF 14RUMJF 149UN IF ISOUNIF 151UNIF 15?UNIF 151UNIF 154UNIF 155UNIF 156•HIF 157UNIF 15HIIMF 159U i T F 160UNIF 161UN IF 16?

UNUSFT fO"PII FH SP*CFP4010P