THE\EFFECTS OF EARTHQUAKE EXCITATIONS ON RETICULATED DOMES/

by

David A.“Uliana„

Thesis submitted to the Faculty of theU l

Virginia Polytechnic Institute and State University

in partial fulfillment of the requirements for the degree of

MASTER OF SCIENCE

inU CIVIL ENGINEERING

APPROVED :

D . S. M. HolzerD

Dr. A; E. Somers, Jr. Dr. R. H. Plaut

February, 1985Blacksburg, Virginia .

1/6E

ACKNOWLEDGMENTS y:2éär The author would like to express his gratitude to Dr. S.\‘ i

M. Holzer for his guidance, unlimited patients, and helpful

sugestions throughout the researching and writing of this

manuscript. ·The completion of this thesis would have been

impossible without his help. Gratitude is also extended to .

Dr. A. E. Somers, Jr., and Dr. R. H. Plaut for their help-

ful comments and for reviewing this thesis.

A special and most sincere thanks is extended to David,

Gloria and Morgan Young for being my family away from home,

to Mun Fong Chan for being an exceptional officemate and

consultant, and to Annie Crate and John Volk for their

friendship through the difficult times.

The financial support provided by the Department of Civil\\‘\~

Engineering and the use of the Virginia Tech computing fa-‘

‘—~a.. cilities are also greatly appreciated.

ii

‘ TABLE OF CONTENTS

Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q i i

Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q V

-

Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q

QChapter· Page

I Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q 1

Objectives ................. 1Q Q Q Q Q Q Q Q Q Q Q Q Q 3

II. STRUCTURAL MODEL ............... 8

Introduction .............3. . . E 8The Tangent Stiffness Matrix ........ 9Dome Models ................ 12

III; Q Q Q Q Q Q Q Q Q Q Q Q Q Q

QIntroduction................ 17Newton-Raphson Method ........... 20

_ Convergence Criteria ............ 23Discussion of Stability .......... 26

IV Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q

QIntroduction................ 31Modeling Earthquake Excitations ...... 32Damping Matrix ............... 34The Newmark-Beta Method .......... 36

Linear Analysis ............. 36Nonlinear Analysis ............ 37

Discussion of Time Steps .......... 39

V Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q 4 1

Q The Finite Element Program ......... 42Comparison with Previous Results ..... 42Checks on Some Assumptions ........ 58 Q

Small Lamella Dome ............. 59Static Analyses ............. 59Dynamic Analyses ............. 66

Large Dome ................. 68Static Analyses ............. 68

4 Dynamic Analyses ............. 83 _

iii

‘ TABLE OF CONTENTS (continued)' ESS

Comparisons of Stresses for Both Large andSmall Domes ............... 90 U

VI. CONCLUSIONS AND RECOMMENDATIONS ....... 100

Conclusions ................ 100‘ Recommendations for Future Research .... 101

REFERENCES .................... 104

Aggendix gage” A. FREQUENCIES OF VIBRATION FOR THE SMALL LAMELLA

DOME ................... 110

B. FREQUENCIES OF VIBRATION FOR THE LARGE LAMELLADOME ................... 111

C. PROGRAM LISTING ............... 114

VITA . . .......... . .......... 189 ·

ABSTRACT

iv

LIST OF TABLES

Table pass1. Maximum stresses of static analysis for numbered

members of the small dome. ........... 63

2. Maximum allowable stresses and buckling stresses fornumbered members of the small dome........ 64

3. A comparison of maximum stresses in numbered members _of the small dome for dead load only....... 75

4. A comparison of maximum stresses in numbered membersof the small dome for dead load plus 10 lb./ft.2. 76

5. A comparison of maximum stresses in numbered members· of the small dome for dead load plus 20 lb./ft.2. 77

6. A comparison of maximum stresses in numbered membersof the small dome for dead load plus 30 lb./ft.2. 78

7. A comparison of maximum stresses in numbered membersof the small dome for dead load plus 40 lb./ft.2. 79

8. Maximum stresses of static analysis for numberedmembers of the large dome. ........... 82

9. Maximum allowable stresses and buckling stresses fornumbered members of the large dome........ 84

10. A comparison of maximum stresses in numbered membersof the large dome for dead load only....... 92

11. A comparison of maximum stresses in numbered membeisof the large dome for dead load plus 20 lb./ft. . 94

12. A comparison of maximum stresses in numbered membegs yof the large dome for dead load plus 40 lb./ft. . 96

v

LIST OF FIGURES

Eigum pass1. Member end displacements for a typical truss

element. .................... 10

2. Large lamella dome. ............... . 13

3. Small lamella dome ................. 15

4. The tributary area for the top node of the domes. . 19

5. The Newton—Raphson method for a one degree—of-freedom system.................. 22

6. The Modified Newton-Raphson method for a one degree-_ of-freedom system. ............... 24

7. Equilibrium path for a one degree-of-freedom system. 29

8. One degree—of-freedom plane truss presented byNickell. .................... 43

9. Displacement vs. load graph for the static analysislof the one degree-of-freedom truss presented by

. Nickell. .................... 44

10. Displacement vs. time graph for the dynamic analysisof the one degree—of-freedom truss presented byNickell. .................... 45

·_ 11. Ten member plane truss presented by Noor and Peters 46

12. Displacement vs. time graphs of joint A for lineary and nonlinear analyses of the ten member truss. . 48

13. Axial force in member B for the linear analysis ofthe ten member truss............... 49

14. Axial force in member B for nonlinear analysis ofthe ten member truss............... 50 _

15. A comparison of the stress-strain relationships. . . 51

16. Large ten-bay truss presented by Noor and Peters. . 53

viM

17. The displacement of joint A for the linear analysisof the ten-bay space truss............ 54

18. Axial force in member B for linear analysis of theten-bay space truss. .............. 55

19. Displacement of joint A for nonlinear analysis ofthe ten-bay space truss. ............ 56

20. Axial force in member B for nonlinear analysis ofthe ten-bay space truss. ............ 57

21. Small lamella dome with numbered members. ..... 60

22. Load vs. displacement curves for uniform load on thesmall dome....4................ 61 B

23. Load vs. displacement curves for nonuniform load onthe small dome.................. 65

24. Accelerations, velocities and displacements for theEl Centro earthquake of May 18, 1940....... 67

25. Displacement of joint A for dead load only on thesmall dome.................... 69

26. Displacement of joint A for dead load plus 10lb./ft. on the small dome............ 70

27. Displacement of joint A for dead load plus 20 lb./ft.2 on the small dome...........·. . . 71

28. Displacemegt of joint A for dead load plus 30lb./ft. on the small dome............ 72

29. Displacement of joint A for dead load plus 40lb./ft.2on the small dome. ........... 73

30. A comparison of the displacements of node A forseveral live loads on the small dome....... 74

31. Large lamella dome with numbered members. ..... 80

32. Load vs. displacement curves for uniform load on the .large dome.................... 81

33. Load-displacement curves for nonuniform load on thelarge dome.................... 86

viil

34. Displacement of joint A for dead load only on thelarge dome.................... 87

35. Displacemegt of joint A for dead load plus 20lb./ft. on the large dome............ 88

36. Displacement of joint A for dead load plus 40lb./ft.2 on the large dome............ 89

37. A comparison of the displacements of joint A for thetwo live loads on the large dome......... 91

xdii

Chapter I

INTRODUCTION

1-1Dome structures, in particular reticulated domes, have

demonstrated their usefulness as strong, light-weight cover-

ings over large areas such as stadiums, industrial buildingsÜ

and exhibition centers where large, unobstructed areas are-

required. They enclose a maximum amount of space with a

minimum surface and are economical because they require lit-

tle material as compared to other structures. Several

different dome configurations exist. Some of the more popu-

lar configurations are the lamella, the geodesic, and the

Schwedler domes.· —

Many studies have been performed by various researchers

to analyze these domes under static loads. They have re-

peatedly demonstrated the domes' strength and economy for

Civil Engineering applications. The author found no refer-

ences, however, that presented results for dynamic analyses

of full sized reticulated domes. Due to an increasing in-

terest in earthquake resistant design of structures, dynam-

ic analyses of these domes are definitely needed. .

This thesis is a study of the behavior of full sizedt

domes, designed under static criteria and subjected to

2

earthquake excitations. Static analyses are performed on

two lamella domes. The axial stresses and strains in all

members are determined for several distributed static loads.

Dynamic analyses are then performed on the same structures

with the same distributed loads. The dynamic loads are in

the form of earthquake excitations to the bases of the

domes. Axial stresses and strains in all members are deter-

mined and compared to those of the static analyses. The

displacements of several nodes for both analyses are given

and effects of the earthquake motions on the stability of

the domes and their members are determined.

A finite element computer program written by the author

(see Appendix C) was used to perform these analyses. The

program can analyze geometrically and materially nonlinear

behavior of space trusses subjected to static or dynamic

loads. The direct integration procedure used is the New-

mark-Beta method and the nonlinear solution technique is the

Newton-Raphson method. The program can calculate the dis-

placements, velocities, and accelerations of all nodes as

well as the axial stresses and strains of all members at

each load or time step. The ability to determine if any

member reaches its buckling load or if the dome becomes glo-

bally unstable is also present in the program._

1 l

3l-2LIIEBAIHBE BEYLEHU

2A literature search revealed that there is little re-

search done on the dynamic analysis of space truss struc-

tures. No references were found that addressed the topic of2 earthquake excitations on reticulated domes. Severalrefer-ences

were found that closely relate to this topic, though

none use the space truss specifically. Penzien and Liu (43)

and Tanabashi (52) address the solution of nonlinear struc-

tures subjected to earthquake excitations while Berger and

~ Shore (8) and Carter, Dib and Mindle (10) present the dynam-

ic response of nonlinear structures.

In order to cover the thesis topic more carefully, three

subjects were searched for pertinent literature. These sub-

jects are:

1. Analysis of space trusses

2. Methods for structural dynamics solutionsl

3. Modeling earthquake excitations·

A review of these subjects provides a review of the thesis

topic.

One method of analysis that is used to model large space

trusses, such as reticulated domes, is to replace the truss

with a continuum model. The continuum model may then be j

solved with familiar methods of mechanics. Forman andI

Hutchinson (16) and Crooker and Buchert (12) present methods

4

to replace a space truss with a continuous shell. Renton

(45) models a repetitive space truss as a continuous beam

and Noor, Anderson and Greene (40) offer approximations for

beam-like and plate-like lattices. Conventional finite ele-

ment analyses of large systems would be expensive and time

iconsuming. These methods allow relatively inexpensive anal-

yses of large repetitive structures.”

Force and displacement methods are popular for analyzing

(trusses since a truss model may be defined by a finite num-

ber of forces or displacements. Methods such as Maxwell-

Mohr and matrix analysis are relatively simple for linear

models. Goldberg and Richard (19) and Hensley and Azar (22)

derive analyses methods for material nonlinearities while

Epstein and Tene (15) and Jagannathan and Epstein (29) con-

sider the geometric nonlinearities. A mixed formulation is

provided by Noor (38) who considered both material and geo-

metric nonlinearities, and a geometrically nonlinear stiff-

ness matrix for a space truss element is derived by Baron

and Venkatesan (2) with perturbation techniques. Reducing

the number of degrees-of-freedom for these nonlinear prob-° lems is desirable for many analyses. A discussion on the

reduction of the number of degrees-of-freedom of nonlinear

problems is given by Noor (39).l

5 g

For trusses that should be modeled with imperfect mem-

bers, Rosen and Schmit (47) and (48) have both an accurate

and an approximate method to include the imperfections. If

the effects of transverse loads are desired, then a frame

element is needed. A model for a geometrically nonlinear

pin-jointed frame is presented by McConnel and Klimke (33).

The pin-jointed frame has the characteristics of a truss but

permits bending strains. For dynamic analyses of nonlinear .

_ space trusses, which is required for this study, Noor and

Peters (41) use a mixed method.

Several techniques exist for the solution of structural

„dynamics problems. Among some of the less familiar methods

are the Finite Strip Method (11), the Runge-Kutta Method

(27) .and the Fast Fourier Transform Method (20). These

methods have not proved to be as popular for solutions of

multi—degree-of-freedom systems as modal analysis and direct

integration. Der Kiureghian (13) presents a probabilistic

approach to linear modal analysis and Nickell (36) presents

a deterministic approach to nonlinear modal analysis.

For solution of nonlinear problems like the space truss,

direct integration proves to be much more suitable than mo-

dal analysis, according to Ref. 18. Several different di-

rect integration procedures exist. Some of these methods

are the Central Difference method (42), the Wilson-6 method

6

(54), the Newmark method (34) and the method proposed by

Ginsburg and Gilbert (18). Two important factors to consid-

er when using direct integration are the stability and ac-

, curacy of the solution. Nickell (35), Preumont (44) and

Bathe and Wilson (7) discuss stability and accuracy while

Hinton, Rock and Zienkiewicz (24) and Bathe and Cimento (6)

present methods for increasing the accuracy and economy of a

solution. Atalik (1) makes solutions more economical by

constructing linear approximations for the element mass,

damping and stiffness matricies for nonlinear problems.

Earthquake excitations may be modeled in two ways. Eith-

er an actual digitized accelerogram may be used or an arti-

ficial accelerogram may be produced. Real digitized data,

such as that given by Haroun (21), are available for many

earthquakes. Data in this form, however, may not be useful

if it is digitized in time increments that are not appropri-

_ ate. Liou (32) offers a numerical method for redigitizing

seismic data without producing superficial frequencies.

An accelerogram may be generated artificially if it is

more desirable than the available digitized data. Earlier

methods for producing artificial accelerograms were mostly

deterministic. Bernrueter (9) finds maximum acceleration

only, St. Balan, et. al. (50) generate an accelerogram as aW

series of trigonometric functions and Wong and Trifunac (55)

7

0 use a Fourier transform method. These and other determinis-

tic methods have been replaced by probabilistic formulations

due to an increasing interest and understanding of the vari-

ability of earthquake ground motions._ Some of the most re—

cent research on this topic is presented by Kubo and Penzien

(31), Kameda and Ang (30), Housner and Jennings (27), Trifu-

nac (53) and Iyengar and Iyengar (28). These studies2

demonstrate how to generate artificial accelerograms through

probabilistic methods.

Because of the distinct advantages of reticulated domes

and the increasing interest in earthquake resistant design

of structures, the thesis topic should be of increasing in-

. terest in the future.•

Chapter II

STRUCTURAL MODELy

In this chapter the tangent stiffness matrix for a geome-

trically nonlinear space truss element is presented. It is

derived by the familiar principle of virtual work. This

y chapter also presents the domed structures that will be used

in the analysis. p

2.1Areticulated dome is a collection of one-dimensional

elements assembled in space so that their joints lie on a

spherical surface. These one-dimensional elements may be

modeled either as truss elements, where only axial elonga-

tion and contraction are considered, or frame elements, for

which torsion and bending about two axes are also consid-

ered. For a space truss each element has six translational. degrees of freedom. For a space frame each element has six

translational and six rotational degrees of freedom.

A space truss element was chosen for this study for the

following reasons:

l. Members of a reticulated dome are usually joined in a

fashion that more closely resembles a pinned connec-N

tion than a rigid connection.

“ 8

9

2. Dynamic nonlinear analyses are, by nature, time con-

suming. The space truss element has fewer degrees of

freedom and is more economical.

The geometry of a reticulated dome and slenderness of its

members allow for the possibility of large displacements and

rotations although the strains that develop can be small.

This results in geometrically nonlinear behavior which is

the result of a nonlinear strain-displacement relation and

equilibrium being formulated on the deformed structure. For

these problems strains are not generally proportional to

displacements. The nonlinearity must be considered in the

formulation of the stiffness matrix. .

92.2 IHEIAblQELNIMAIE.lX p

The tangent ustiffness matrix used in this study was

derived by Holzer and is presented in detail in Ref. 25.

The undeformed state and the deformed state of a typical

truss element are shown in Fig. l. During the deformation

the element may translate and rotate significantly with only

small strains being produced. Expressing the displacements

of the element as the sum of rigid body displacements and

deformations is desirable. The initial, undeformed state is

labeled I.S., the rigid body state is labeled R.B.S. and thei

deformed state D.S. The tangent stiffness matrix of an ele-

ment i is given by F

1i 10

2

Z: == == ——

. / 6, / 'd dz /

_ //.5. d

d 54

l

Figure 1: Member end displacements for a typical truss ' l

element.

I

11

. 2l _ 8 Ü 1. K · tzzrzzü ( ’. J k

where U is the strain energy of the element. The resulting

matrix is the sum of the familiar linear stiffness matrixfor a space truss and a nonlinear matrix. They combine to

form the tangent stiffness matrix for an element given by

. zi --1.K1 L _ K_ (2). _gl il

where

L. 7 c c c cLO_ 1 1 2 1 3· Fi = Y-

1 —Ül (1 CK) C (3)C 1 L 2 2C3O1 L. 7svm -——i -(l-C“)

-· ‘ _ L 3O.1.

and I O

- EiAi (4)Y Yi = T7l

For each member 'i', Ej_is Young's Modulus of the materi-al, A_ is the cross-sectional area, Li is the deformedlength and L0_is the undeformed length. Cl, C2, and C3 are

lthe direction cosines in the global 1, 2, and 3 directions,

respectively.O _

~ 12

2-3 DQME MQDEL§(

Two structural models are used for analysis. One dome is

a large lamella dome used in a study by Richter (46). A di-

agram appears in Fig. 2. The dome has a 100 foot base, a 14

foot height at the center and lies on the surface of a 200

foot diameter sphere. All of the members are tubular with

an outside diameter of 6.00 in., a cross sectional area of

3.18 in.2, and a cross sectional inertia of 15.64 in.4. The

material is T60—6011 aluminum (49) with a yield strength of

·35 ksi. and a modulus of elasticity of 10,300 ksi. The la-

mella dome has three rings and ten radial sections. This

structure was chosen for several reasons:

1. Data for the static analysis is readily available.

2. The geometry of the lamella dome is relatively easy

to define.

3. There is a natural truncation ring at the base of the

dome.Two

different boundary conditions are used for this dome,

one for the static analysis and one for the dynamic analy-

sis. For the static analysis a complete dome with a tension

ring provides the most realistic model. With the tension

ring the dome has 150 members, 61 joints, and 149 degrees of

freedom. It is constrained in the vertical direction at ev-T

·ery base joint, in both horizontal directions at the top of

I

~

14

the dome (to avoid translation of the dome) and in two other‘ _ horizontal directions (to avoid rotation of the dome). For

the dynamic analysis base joints are pinned. This model has

120 members, 61 joints, and 93 degrees of freedom. Since

each base joint is constrained in all three directions the

tension ring is rendered useless and the members are not in-i cluded.

For the second model a smaller lamella dome was desirable

because:

1. A comparison between similar domes of different sizes ·O

could be made.

2. Fewer degrees of freedom will require far less compu-

ter time; therefore, more extensive testing may be

performed.

The dome chosen was a truncation of the larger dome at its

second ring (See Fig. 3). All element properties and dimen-

sions are the same as in the larger dome.

As before, two different boundary conditions for this

dome are considered. For the static analysis the dome with

n the tension ring has 70 members, 31 joints, and 69 degrees

of freedom. It is constrained in the same manner as the1

«

larger dome. The fixed base dynamic model has 50 members,

~

1

p 16 T

31 joints, and 33 degrees of freedom. This 33 degree-of-

freedom dome requires much less computer time per run and is

used in a majority of the dynamic testing.

A geodesic geometry was considered for comparison with

the small lamella dome. However, a small geodesic with the

y same number of joints and the same overall dimensions as the

lamella could not be defined without severely modifying the

geodesic geometry to form a base ring. The geodesic geome-

try has no natural truncation ring for a shallow dome.

Also, a limit on the expense of the dynamic analyses was de-O

sired, therefore, the geodesic dome was not included.

Chapter III

STATIC ANALYSIS

In this chapter a description of the static analysis pro-

cess is given. The nonlinear solution technique used is theNewton-Raphson method. This description is followed by dis-

cussions on convergence criteria and stability of domed

structures.

3-1Adescription of the static analysis process is included!

in this study. The reasons that it is included are:‘ 1. Static analyses are the most common analyses for

space structures.

2. The dynamic analysis is actually reduced to an equi-1

valent static analysis at every time step by the New-

mark-Beta method.

3. A static analysis should always precede a dynamic· analysis when designing a structure.

' The static procedure was used in this study to determine

the nodal displacements and the element stresses caused by

several distributed live loads. The live loads used are 10, 7

20, 30, and 40 lb./ft}!. These values represent the maximumV

snow loads for most regions of the United States according

17

1 18

to Ref. 17. Several loads are used in order to show a com-

parison between loads, displacements and stresses.

The distributed load must be transformed into a series of Yconcentrated nodal forces in order to include it in the ana-

lysis. Each force is equal to the snow load times the

tributary area around the node. An example of the tributary

area for the top node of both domes is given in Fig. 4.

This area is the projected area on the horizontal plane and

is equal to 250.8 square feet. The tributary area for each

node in the first ring (node type A of Fig. 2) is 154.2

square feet. The tributary area for each node of the second

ring is 145.8 square feet for node type B of Fig. 2, and

149.1 square feet for node type C. The same areas apply to. the small dome of Fig. 3. A load vector may be formulated

by multiplying the distributed load times these areas.

Transforming the distributed load into a load vector is a

realistic assumption for many domes since suspending a load

carrying sheet from the joints of a dome is common. For

these domes the snow load is truly applied to the nodes.

For many other domes, however, rigid panels are attached di-

rectly to the members. In these domes bending strains de-

velop that cannot be neglected. A paper by Renton (45) ad-

. dresses the modeling of space trusses for beam-like behavior4

and McConnel and Klimke (33) discuss the analysis of pinned-

919

1

/°’ ·“

._•

,K VV [

„: ··‘“ A ¢•‘Z«;%§%•:••*11{~

°RRo„1EoT1oHow THE HoR1ZoHTALREAHE FORTOP@—TRlBUTARY AREA. (g5o.6 SEH.)

Figure 4: The tributary area for the top node of the domes.

20

end space frames. In this study, however, the bending ef-

' fects are not considered.

3-Z MEIHQD „The basic equation to be solved in nonlinear analysis is

. Q _ A+AAF = 0 (5)

Q is the external nodal load vector which can also be writ-

ten as (A+AAfQ where A.is a scalar andQ”is

a constant vec-

tor, and k+AMF is the nodal force vector that results from yelement stresses. When Eq. (5) is satisfied the system is

in equilibrium. A nonlinear solution technique is requiredl

since k+AÄF is not a linear function of the nodal displace-

ment vector )‘+A^q. This description of the nonlinear solu-

tion technique is given for the static analysis. The reader

should understand that the technique is the same for dynamic

analyses where t may replace A.

One of the most popular techniques for the solution of

nonlinear equations is the Newton-Raphson method. By apply-

ing this method Eq. (5) becomes

K(i)Aq(i+l) = Q _ F(i) = R(i) (6)

for the i'th iteration where K(i)is the tangent stiffnessO

matrix at q(l)- A complete derivation appears in Ref. 3.

212

Eq. (6) is solved repeatedly until a new equilibrium state

is obtained with a sufficient degree of accuracy (See sec-

tion 3.3).

The Newton-Raphson method requires a known equilibrium°(

position (qO,Q0) to start the iterative process. Refer to

Fig. 5 for a graphical representation of a one degree-of-

freedom system. The load is incremented from Q0 to Q where

a new equilibrium position is sought. The tangent stiffness

matrix K(O)at q(0)is determined and Eq. (6) is solved for

i=0 and R(0) =Q-F(0) . A new equilibriumpositionq(i+l)

2 q(i) + Aq(i+l) (7)can be found along with the nodal point forces F(i+l)

corresponding Residual forces

R(i+1) 2 (Ä 2 Mm- _ F(i+l) (8)

are determined and a convergence check is performed. If

convergence is not reached then the tangent stiffness matrixK(i) is computed and Eq. (6) is solved. This process is re-

peated until convergence is reached.

A modified method can also be used. The tangent stiff-

ness matrix K(0) is found for the first iteration only and

Eq. (6) is solved using K(0) for K(i) for every iteration.A

A graphical representation for a one degree-of—freedom sys-

zz

.l

Ko Kl.

Q :I ‘ER*· I f' II I · I

II I| I| II II ·F=I

. I: |

I |·

QO °·· ;° II „ II ; II I I

I I [Ä ld I ZX QQ ICI (LG). Figure 5: The Newton—Raphson method for a one degree-of-

~I

freedom system.

D 23

tem appears in Fig. 6. Using a constant tangent stiffness

matrix eliminates the need for the costly processes of com-

- puting and factorizing the stiffness matrix for every itera-

tion.

3-3 §.BI.IEBlAMathematically, the Newton-Raphson procedure will con-

verge to an exact solution; however, it will not do so in a

finite number of iterations. A condition referred to as aconvergence criterion must be defined so that the iterative

process may be stopped at an appropriate vector q(i+l)in Eq.

(7). The convergence criterion may be a check on the magni-

tude of Aq$i+l) or on the magnitude of the unbalanced force

vector R(i+l{ It must assure that the desired accuracy

ofthesolution is found without excessive computational ef-

fort. Once the condition is satisfied and convergence is‘ achieved the Newton-Raphson process is ended and the analy-

sis proceeds on to the next load or time step.

Several methods exist to check convergence. The·simplest

is convergence of the norm of the change in the displacement

vector °

||¤9(i+l)|| < 9

(9)wherethe norm may represent either the Euclidean norm

= Aq§j_+l)2)]-/2 (10)

’ 24

ÄK7·°Q " "'°'”'” ” ° I-. ° _-

I I. I I I

I · I. I II I I .I I I .I II I I' I I I I

I I I I

I I I I

I I I II I I I

I I III I I I ' I ‘

QI I I I I‘ "" I ' I IO I I I II

I I I I |I I I I I I‘ I I { I I

A10) I

Figure 6: The Modified Newton-Raphson method for a oneI

degree-of-freedom system.

25

‘ or the largest absolute value of the components of°Aq(i+lÄ

It is apparent that the norm is not a dimensionless quanti-

ty, therefore, the value for e must be determined by consid-

ering the dimensions of the actual system. This creates a

problem in that e may need to be changed for analyses of

various systems. To avoid this problem the nondimensional

criterion(i+l) _ (i+l)

. (1+1) .may be used. Again, ||q || is the norm of the total

displacement vector and may be either the Euclidean norm or

the largest single component of the vector. The criterion

used throughout most of this study was that of Eq. (ll).

Bathe (6) suggests using e=0.00l for this criterion.

A check on the unbalanced force vector is similar to the

methods presented above. The simpler check is on the un-

balanced force vector

('+l)l i- °

IIRL ||<eR (12)( '+l

äwhere ||R“L )|| may be either

. 1) . 2 l/2IlR(l+ ll = (Z R$l+l) ) (13)· JJ

or the largest absolute value of the vector components.l

Here, too, e may need to be changed for different systems.R

66

26

In order to nondimensionalize this quantity, the unbalanced

force vector must be divided by the restoring force vector4 to create the ratio

(14)

When this ratio is small enough then the R(i+l)vector is in-

significant and convergence is reached. This would guaran-

tee thatFLi+l)

is close enough to Q to assure convergence.

The value of eR could remain unchanged for different sys-

tems.

3-4Reticulated domes are very strong for their light weight .

and are able to resist great static loads. For example, the

large lamella dome used in this study was able to resist a4

static load of 24 times its own self-weight. The geometries

and relative lightness of these domes, though, make them

susceptible to instabilities. A reticulated dome may become

unstable long before yield stresses in the material are

reached. Special consideration of instabilities may be re-

quired in order to effectively design a reticulated dome.

For the space truss the possibilities of member instabil-

ities and global instabilities exist. For a truss member

the internal force increases linearly with axial deformation

27

in compression until it is near the buckling load. In the

vicinity of the buckling load a real, imperfect member ex-

periences transverse deflections that increase significantly

for small increases in loading provided the material remains

elastic. The truss elements used in this study, however,

are modeled as perfect elements that do not allow transverse

deflections. In order to include a more realistic behavior,I the compressive loads are assumed to increase linearly with

axial deformation until the buckling load is reached, after

which the compressive force is held constant at the buckling

load. The buckling of a member may or may not result in a

global instability that is defined below and is usually less

catastrophic. One reason for this may be that the buckling

of a member could redistribute forces in the structure andl

adjacent members may compensate for the loss in stiffness.

Global instabilities result from a decrease or loss in

stiffness of the structure and exist in two forms: limit

point instabilities and bifurcation instabilities. Either

of these can be determined mathematically using the tangent

stiffness matrix. For the nonlinear problem the tangent

stiffness matrix is updated at least once every load step

while for some analyses it is updated more often. Instabil-

ities cause the stiffness matrix to become singular. Forl

the bifurcation instability, the Newton—Raphson procedure

7 ( 28

may be used to trace beyond the point and over the unstable

post-bifurcation curve. It cannot be used, however, to

trace an equilibrium path beyond a limit point. The inabil-

ity to proceed past a limit point is an inherent weakness of

_the Newton-Raphson method. To analyze the dome past a limit

point other methods such as the Riks—Wempner method (26) are

required.

A practical description of both types of instabilities is

presented by Supple (51). He states that under increasing

deformation the dome may gradually lose its stiffness until

a complete loss of stiffness is realized. At this time a7

dynamic jump occurs to a highly displaced configuration that

·is usually symmetric. This may be a limit point instabili-

ty. A graphical representation for a one degree-of-freedom

system is shown in Fig. 7. The complete inversion of a

domed structure is an example of the equilibrium state after

a limit point instability. The dome may also exhibit a sud-

den loss of stiffness and displace into a configuration that7

is different from its initial configuration. This is the

bifurcation instability. The suddenness of the loss in

stiffness is what differentiates the bifurcation from the 7

limit point instability. The bifurcation is shown for a one

degree-of—freedom system in Fig. 7. The equilibrium con-7

figuration reached after a bifurcation instability does not

29 Vr

stable path

'K limit point -

I—~ __, __ __ __ __ new ”_= j equilibrium//’

\\F<' C) configuration.

unstable/\*

pathbifurcationpoint

:table path "

Figure 7: Equilibrium path for a one degree—of-freedomsystem.

30

have to be similar to the equilibrium configuration after a

limit point instability.

Chapter IV

DYNAMIC ANALYSIS

In this chapter the equations associated with the dynamic

analysis are presented. The dynamic finite element equa-

tions are given first followed by the method used to include

earthquake excitations. The direct integration scheme cho-

sen for this study is the Newmark-Beta method. The method's

application to linear and nonlinear problems is given along

with the damping matrix formulation and a discussion on time

steps.

4-1„The equations of motion ufor a multi-degree-of-freedom

system can be expressed

Mä + cq + Kq = Q (15)

whereT

M-the mass matrix yC-the damping matrix

_ · K-the stiffness matrixq-the nodal acceleration vector

q-the nodal velocity vectorA

q-the nodal displacement vector

Q-the dynamic nodal load vector

31

32

The type of analysis chosen for this study to solve Eq. (15)

is the direct integration method because it is suitable for

the nonlinear analysis that is presented in section 4.4.2.

Direct integration is an incremental procedure by which

the displacements, velocities and accelerations are solvedi

at successive time steps At using the displacements, veloc—

ities and accelerations of previous time steps. At each

time step there are 3n unknowns that must be computed.’ They

are q , q and q. The direct integration method used in

this study reduces these to n unknowns by making an assump-

tion about the change in 'acceleration over the time step.

The result is an effective static formulation that can beeasily solved at each step.

4.2·

The base excitation of the structure may be included in

the analysis as known displacements. The finite element ·

equations may be written

Mba Mbb üb Kba Kbb “b Qbg (16)

if ua are the unknown degrees of freedom, ub are known baseexcitations and Qa are known nodal forces. The first set ofequations is

33

Maaüa + Mabüb + Kaaua + Kabub = Qa (17)

Both u and u are displacements in a fixed global refer-a b _

ence frame. Only the displacements in the relative refer-

ence frame, however, result in strains in the system.

Therefore, substituting

“a = q * " (18)

is convenient if n is a vector having the same magnitude as

ua and entries for the horizontal degrees-of-freedom equal

to the base displacements . The vector q is composed of no-

dal displacements in the relative reference frame. Eq.,(l7) _

is rewritten

II=

•· ••i

-Maag+ Kaaq Qa Maan Mabub (Kaan + abüb (19)

A computer program written by the author was used to prove

that·Kaan+ Kabub = 0 (gg)

for the domed structures used. If the mass is also assumed

to be lumped then‘ Mab = 0

(21)· and (19) reduces to ‘

(22)

34

The subscripts 'a' may be dropped since it is‘understood

that q applies to unknown degrees of freedom. One can see

that the effect of the base excitation can be modeled as a

nodal force vector of the mass times the base acceleration.This equation is commonly used in the literature.

The self—weight of the structure is also included in this

study to provide more realistic results. Self—weight is de-

fined as the product of mass and the acceleration due to

gravity. To account for this an acceleration of 32.21

ft./sec.2 is added to each vertical degree of freedom in the

H vector. This results in a constant downward force at

each node which is equivalent to the effect of gravity.

4-3 DAMELEQMHBIXThe damping matrix, C, is unlike the mass and stiffness

matrices in that it is not constructed from element damping

matrices. The damping matrix is only intended to model the

energy dissipative properties of the system. At best, it is

an approximation, however, it should be included to realis- ’

tically model the behavior of a structure.

For Rayleigh damping the damping matrix is approximated

by a proportion of the mass and the stiffness matrices. It.·

can be represented as

C = uM + BK, (23)

35

Values for czand B are determined by solving the two simul-2 taneous equations

By

C! + = =1.,2where—wi

are two frequencies of vibration of the structures

and €Q_are two damping ratios either determined experimen-

tally or assumed.· For structures with many frequencies

Bathe (5) suggests using average values for wiand fi. Engi-

neering judgement may be used to assume these values.

To accurately model damping all of the frequencies of

each structure are considered. Lists of the frequencies ap-

pear in Appendix A and Appendix B. A computer program writ-

ten by Dib (14) was used to find these frequencies. Since

the frequencies of both strucures seemed to be divided into

two groups the average frequency of each group was taken for

wi. A damping ratio of 1% was assumed for the lower wi and

a ratio of 3% was assumed for the higher wi. These E val-

ues were not experimentally determined but were chosen in

order to represent light damping characteristics. For the

small lamella dome the average values for wi and w2 are1.725 hertz and 21.376 hertz, respectively. They yield an a

value of 0.0259 and a B value of 0.00285. For the large la-B

mella dome wl and w2 are 1.608 hertz and 19.198 hertz whichyield an a of 0.0241 and a B of 0.00306.

B

h36

4-4 IHE NEHM8BK;BEIA MEIHQD 24-4-1 Linear Aualxsia

Given the conditions of the nodes at a time t an expres-

sion for the accelerations and velocities at a time t+At can

be derived with the Newmark-Beta method found in Ref. 34.

The resulting equations of this method are

*‘*^'°é3 = (1/ßAt2) <‘”“^"q — tm (25)and

t+^t<ä = tv +· (1/26At) ("+^'°q — ta) (26)

where 9

t .d = tq + tqAt + 1/4 täAt2 (27)

and

- tv = té + 1/2 t&At (28)

Once Eq. (25) and Eq. (26) are derived, linear analysis

by Newmark's method is straightforward. Substituting them

into Eq. (15) yields

(1/BAt2)M(t+Atq—td) + C(tv+(l/2ßAt) <"*^‘*q-"d>> (29) 3

+ K t+Atq = t+AtQ

37

At any time t+At,!b+Atq

are the only unknowns in these

equations. By rearranging the equations the following form

is realized:

· t+At _ t+At^K Q · Q (30) Nwhere

IK = (1/BAt2)M + (1/2BAt)C + K (31)

and

t*^*°é = '°*^*Q + «1/:A·c2>M*‘6 + C((l/2BAt)td - tw G?)Q is referred to as the effective stiffness matrix and in-

cludes the apparent stiffness effects of the mass (inertia

effects) and the damping. A y

4-4)-2 Nsnlinsa; AnalysisIn this section the reduction methods presented in the

preceding section are combined with the Newton-Raphson tech-

nique presented in Chapter 3. The Newmark-Beta method is

used to reduce the dynamic problem, then the Newton—Raphsonl

technique is used to iterate to the solution. The same cri-

terion for convergence as in the static analysis applies to

the dynamic analysis.K

38

If 'k' is the counter of the iteration then the displace-

ment vector

t+At (k) t+At k—l kQ = q( ) + ^q( ) (33)

will be found at each 'k' by solving for 4&q(k) until con-

vergence is reached. The equations of equilibrium for the

nonlinear analysis are

+ + KAq(k) = t+AtQ _ t+AtF(k-l) (34)

At this point Newmark’s method may be implemented. Acceler-

ations and velocities are found by substituting Eq. (33)

into Eq. (25) and Eq. (26). These termsbecome—

k tl) + Aq( ) _ d) (35)

and

respectively. By placing these into Eq. (34) and rearrang-

ing) the following formulation is reached:

^ (k) _ ^ 37KAq - Qeff ( )‘ where

Ö ff = t+AtQ_t+AtF(k-l) _ [(1/BAtz)M (38)e

+ (1/2ßAt)C]t+At§(k-1)-Ctv

39

·c+A1;ä(k-1) __= (t+Atq(k-1)_td)(39)and

12 = (1/BAt2)M + (l/2ßAt)C + 12, <‘*°>

The Newmark method becomes unconditionally stable when the

constant—average-acceleration method, or ß=1/4, is used ac-

cording to Ref. 23.

4-5 9.E TIME §I.E1°§Choice of the correct time step is critical in dynamic

analysis. The time step must be small enough to insure an

accurate solution but not so small that excessive computer

time is needed. Since the Newmark method for B=1/4 is un-

conditionally stable the choice of the time step will be

with regard to the accuracy of the solution. Bathe (4) sug-

gests using a time step At=Tn/10 if TH is the smallest per-

iod of oscillation of the structure to account for the res-

ponse of all modes. For many structures, however, he states

that the primary response is found in the lower modes so

that the higher frequencies and mode shapes may be neglected

and the time steps be lengthened. In these instances the

time steps may be increased to 2;)/10 where TP is the period

of oscillation of the highest frequency considered. Using ·

TP instead of Trlmay increase the time step dramatically and

and still maintain accurate results.

E40

As can be seen in Appendix A and Appendix B the

frequencies of both the small dome and the large dome are

divided into two groups. Only the mode shapes associated

with the lower group of frequencies were assumed to be need-

ed to effectively model the dynamic response. For the small

structure 1.952 cycles per second is chosen as the critical{

frequency because it is the highest of that group. For the

large structure 1.842 cycles per second is chosen. The cor-

responding periods of oscillation, Tp, are 0.512 seconds and

0.543 seconds, respectively. In order to obtain an accurate

solution the time step should be at the most TP/10 or about

0.053 seconds. Also, Wilson, et al. (54) states that for

iearthquake loading there is little justification to use time

steps less than 0.05 sec.‘ The available earthquake data from the El Centro earth-

quake (21) is digitized in increments of 0.020 sec. At a

· time step of 0.020 sec. At/BP would have a value of 0.0377.For Newmark's method this would result in less than 1% per-

iod elongation which is acceptable for many engineering

situations according to Ref. 23. Also, if the time step

used is reduced to 0.020 seconds the earthquake data would

not need to be redigitized which is a complicated process.

.Therefore, for the purpose of convenience and accuracy the‘ time step used in this study is 0.020 seconds.

Chapter V

RESULTS

The WATFIV program that appears in Appendix C was written

by the author for use in this study. It is a finite element

program to model space truss behavior under static load or

dynamic pbase excitation. Nodal displacements and axial

forces in each member can be determined at each load or time

step in addition to nodal velocities and accelerations. The

static analysis capabilities are strictly nonlinearwhilethe

dynamic analysis may be either linear or nonlinear.

Also, Rayleigh damping-may be included as well as a choice

between lumped or consistent mass matrices. The nonlinear

solution technique may be either the Newton—Raphson or the

Modified Newton—Raphson method.

In this chapter results of the program are compared to

results of other researchers to check the program's accura-

cy. Following this, the displacements and stresses caused

by the static loads on both the small and large lamella

domes are presented along with the displacements and maximum

. stresses caused by the live loads and the earthquake excita-

tions. The digitized acceleration data of the El Centro

earthquake of May 18, 1940 was chosen for use in this study

because it was the most severe data available. A comparison

41

42

4is then made of the axial stresses of all members for both

the static and dynamic analyses. The percentage increases

in stress due to the earthquake are then given.

5.1 THE F.LN.I.I.E ELEMENT RBQQBAMui;11 Rrsxious äslilxs

Few sources were found that provided results for a dynam-

ically loaded, nonlinear space truss with which to check the

program. None were found that modeled base excitations.

The simplest comparison found is offered by Nickell (36) who

analyzes the one degree-of-freedom plane truss shown in Fig.

8. In this study, the spring is replaced by a long truss

element that exhibits the same stiffness characteristics.

(The first test performed was a static analysis. A graph of

the load P and the vertical downward displacement of the

joint is shown in Fig. 9. A dynamic test follows where P

increases linearly from 0 to five lbs. in 0.1 sec. and is

held constant thereafter. Both Nickell and the author use a

time step of At=0.1 sec. Results are shown in Fig. 10 and

for both cases the author's results are nearly identical tothose of Nickell.

A larger two dimensional truss system shown in Fig. 11 is

presented by Noor and Peters (38). The horizontal members

have cross-sectional areas of l.6X10’4 m2 while the diagonal

43

P

gi¤7 }„l-—————————g YOU

Ibßn.-—"‘

Figure 8: One degree-of-freedom plane truss presented byNickell.

E44

50 ’°

A- L\11c1<EL L p F "

20

YF .O „~170 _ "

7 2v DISPLACEME/\/T ID.

Figure 9: Displacement vs. load graph for the staticanalysis of the one degree-of-freedom truss‘ presented by Nickell.

45

ISO ^‘/\//CKELI.' ° <>·UL /A/\/A

B25 . 2

$0

E75U4 ’

3.60 · 2Q. '@.26 __

2 2 6 4 6 .7T/ME 666.

Figure 10: Displacement vs. time graph for the dynamicanalysis of the one degree-of-freedom trusspresented by Nickell. «

5u

i46 p

I-~—ll.Om————{————7.0m———•{O.75fT7

P

Figure 11: Ten member plane truss presented by Noor andPeters

· 47

and vertical members have 1.3XlO_4m2 cross-sectional areas.

The Young's modulus of the material is 7.17XlO N/mz and the

density is 2768 kg/m3. These values are the same as those

of aluminum. The load P is an instantaneously applied load

of 4.5X1O4 Newtons acting downward. The critical time step

for stability of the mixed method presented by Noor and Pet-

ers is At=2.63X1O-4 sec. The time step used is O.625XlO”4

sec. Results for both linear and nonlinear analyses are

available.

The displacement of joint A with respect to time for both

linear and nonlinear analyses is presented in Fig. 12. Foru

both cases the author's results match very closely with

those of Noor and Peters. ° Data for the axial force in mem-

ber B with respect to time is also available for linear and

nonlinear analyses. Results are shown in Fig. 13 for the

linear analysis and Fig. 14 for the nonlinear analysis. The

author's results for the linear problem are nearly identical

to those of Noor and Peters. Results for the nonlinear

problem, however, differ slightly. A probable cause is that

the stress-strain curves for the material nonlinearity are

different for both cases. Noor chose to represent the curve

as a polynomial whereas the author chose a bilinear approxi-

mation. A comparison of both appears in Fig. 15. Overall,

the results for the two dimensional truss structure show ex-

cellent agreement with those of Noor and Peters.

48

.60 A-NOOR AND PETERS6- 0114 NA

Q.46LL12 N ONLINEAR ———•··—L5 [,3

TIY„1G;U) .~.75 ‘

__ -4-——————L [ NEÄR

2 4 6 IOTl /\/IEA {T7[[[/.5CC.

Figure 12: Displacement vs. time graphs of joint A forlinear and nonlinear analyses of the ten membertruss.

49A-

/\/OOR AND PETERS0- UL/A/\/A 0>< 704

_2O

/</LL /

·/ xS><Q 5 x

Ü 2 4 68TIMEm2//26600

Figure 13: Axial force in member B for the linear analysisof the ten member truss.

so

xz0" “Z6 ’ ·

• = = = =LL!A [ä (ÜÄOLLL!<c25 „Q A - /\/OORAND PETERS<

08 l.· 0-ULIA./\//X ·

· 2 « 4_ _ 6 8TIME {T7!//IS€C.Figure 14: Aäiää färce igbmemäer B for nonlinear analysis

.511

A- /\/00R AND PETERSo —— U!. /A/\/A

5040

=

A 50

'·<-/)Lu .CKI~co 70.002

.004 .006 .008 .070STRA/N

Figure 15: A comparison of the stress-strain relationships.

i

52

A large three dimensional truss structure is presented by

Noor and Peters (38) and is shown in Fig. 16. The longitu-

dinal members have cross-sectional areas of 0.8X10°4m2, the

diagonals have 0.4Xl0i4 m2 cross-sections and the battens

have 0.6XlO-4m2 cross-sections. The material properties are

the same as those of the previous problem. The time step

used by Noor is At=0.45Xl0_3 sec. and the load is 5000 New-

tons instantaneously applied to the four center nodes indi-

cated in the diagram. Again, the results for the linear and

nonlinear analyses are available.

The displacement of joint A in the direction of the load

for the linear analysis is presented in Fig. 17. The axial

A force in member B as a function of time is graphed in Fig.

18. Both analyses yield nearly identical results. A com-

parison of the displacements for the nonlinear analysis is

shown in Fig. 19 while a comparison of the axial force in

member B is shown in Fig. 20. The results show some devia-

tion of the displacements possibly due to the fact that the

material nonlinearities are different. The graphs exhibit

good agreement in the linear range of the material; however,

when the bilinear assumption of the author applies the dis-

placements deviate slightly.

For all tests the results of the author are in close

agreement with those of other researchers. The only appre-

„ 53 ”

5 m.’? n -.@6 ‘

7.5 m(Ä•·••°fi'

II.

1_$ • ]‘|_§ '“_ l*‘ ?Q? •« 1..: ¤ :1.:

„.Figure16: Large ten-bay truss presented by Noor andPeters.

54

_Ö A -A/OOR AND PETERSE O - UL/LA NA LH7,352

’

A rf ÖLU 2 ...9O \ ,„ \( .~

V) Ü UC3 }4f§ w

0.2 Q2 Q5 0.4 - 06-T//VIE 86C.

Figure 17: The displacement of joint A for the linearanalysis of the ten-bay space truss.

ss

A-NOOR AND PETERS0- UL IANA n

XIO5 0 .AI} //n• 2 0‘ / 1. 1.

Z ., x ·· ..Lö SO [ \ \ LQ: \ \E~'2O6 6.X . \ .<( /1 \ 1. L

x ° ‘0

Q7 Q2 [ 06 0.4 Q5TIME S€C. —

Figure 18: Axial force in member B for linear analysis ofthe ten—bay space truss.

56

7.80‘Q

R7.35 x \E Ö

. <(A’

4. CO

E 45 p A-/x/OOP AND PE TERSo-UL//Ä./\/Ä

Q7 Q2 Q3_ T/ME S€‘C.

Figure 19: Displacement of joint A for nonlinear analysis6 of the ten-bay space truss.

57

.><10$260LL}.U -0- 6- -6 60:

-JE{270 A-/\/OOR AND PET/ERS

O.7 — 0.2 0.5T/ME S€C,

y

Figure 20: Axial force in member B for nonlinear analysisof the ten-bay space truss.

58

ciable differences arrise in the nonlinear problems and maybe traced back to the bilinear assumption of the materialbehavior. _

Before the dome analyses were performed several tests

were run on the large dome in order to check some assump- .

tions that were made. The first test was to determine ifthe use of the Modified Newton-Raphson procedure provides

appreciable savings in computational effort. Two short .static analyses on the large dome showed that the Newton-Raphson procedure required 405 seconds of CPU time and the

Modified procedure needed only 140 seconds. Both analyses

gave identical results. Because of the savings and accuracy

the Modified method was used for the remainder of the test-

ing.

Next, a check to determine the accuracy of Bathe’s sug-gested convergence criterion (See section 3.4) was per-

formed. A static analysis was run using a very small dimen-

sional criterion in. The same test was runusing the nondimensional @=0.001. Both produced identicalresults but the latter used 12% less CPU time. Therefore,

. the criterion that Bathe suggests is used.

59 _

Finally, for the dynamic problem the effect of earthquake

motions in different directions was desired. Two dynamic

analyses on the small dome were performed with the excita-

tions in two perpendicular directions. The results for both F

were identical probably due to the high degree of symmetry

in these domes. Therefore, the direction of excitation does

not affect the results.

5-2 SMLL LAELLA DQME5.2-1 S.t.a1;isAna1y.as.a

Static analyses of the small lamella dome that appears in

Fig. 21 were performed. The nodal load vector Q included

the self—weight of the structure along with the live loads.

The domes are modeled with an additional skin of aluminum

sheet that has a thickness of 0.162 in. in order to closely

approximate the weight of a real dome. With this, the dead

load is about 3 lb./ftkz. In addition, live loads in incre-

ments equivalent to 10 lb./ft.2 or less are added until

failure of the dome occurs.

For a uniformly distributed live load the small dome is

able to withstand 77 lb./ft? plus the dead load before a

singularity in the stiffness matrix is realized. A load-

displacement graph for the downward displacement of node A

and node B appears in Fig. 22. This graph shows the singu-‘

eeebberr.

615

— S/NGULAR/TY80 7~00E@-„

60N.ät 61006 @60‘40

Q .6E5Q1 20 · . ‘

. 2 4 6 8‘ DISPLACEMENT en.

Figure 22: Load vs. displacement curves for uniform load onthe small dome.

62

larity occurs without a significant loss of stiffness. The

instability is sudden which would indicate an unstable bi-

furcation. The analysis is stopped after the bifurcationbecause it would constitute a failure of the structure.

Stresses at failure in the numbered members are presented

in Table 1. Only the stresses in a quarter of the structure

are·given due to symmetry. Stresses at various other static

loads are presented in the next section where they are com-

pared to those of the dynamic analyses. None of the members

reached the elastic buckling stress before the global in-

stability. The maximum allowable stresses according to the

Aluminum Association (49) and the buckling stresses for the

numbered elements of Fig. 21 appear in Table 2. ·

A nonuniform load condition was also tested where a full

live load is placed over half of the structure and one half

of this load is placed over the remainder of the structure.

The load-displacement curves for nodes A, B and C are given

in Fig. 23. Node B is in the fully loaded region and node

C is in the partially loaded region. The stiffness matrixof the dome became singular at 67 lb./ft„2 plus the dead

load. Nineteen members reached the buckling stress before

the bifurcation. A complete presentation of the results for

the nonuniform loads will not be given because a dynamic

analysis is not available.

63

TABLE 1Maximum stresses of static analysis for numbered members of

the small dome.

ELEMENT MAXIMUM STRESSNUMBER AT FAILURE (KSI)

1 -5.4112 -5.4483 -5.4214 -17.300 U5 -17.3026 -17.2987 -8.8838 -4.6299 -4.657

10 -8.88111 • -4.65312 -4.63613 -8.88014 -4.64315 27.69816 27.70617 27.706

· 18 27.70119 27.701

64

TABLE 2

Manimum allowable stresses and buckling stresses fornumbered members of the small dome.

‘ (!<SI> <1<s1>”

1 -5.10 -9.89—

2 4 -5.10 -9.89

3 -5.10 -9.89

4 -12.34 -25.43 ‘

5 -12.34 -25.43

6 -12.34·

-25.43

7 -5.10 -9.89 _

8 -4.26 -8.28

9 -4.26 -8.28

10 -5.10 -9.89

11 -4.26 -8.28

12 -4.26 -8.28

13 -5.10 -9.89

14 -4.26 -8.28

15 -12.34 -25.43

16 -12.34 ‘ -25.43

17 -12.34 -25.43

18 -12.34 _ -25.43U

19 -12.34 -25.43

65

80 ‘ QSlNiULAR/TY)/x/00£@ 6

8

Q 60 © NN · Q**“ Q“*— QE ./N ~006@£40Q

2 TOQ4 2

2 46 6 6° DISPLACEMENT }n.

Figure 23: Loacähvs. dä.-splacement curves for uouuniform loadon e sma l dome.

. 66 I

5-2-2 DxuamisAnalyse.;1Dynamic analyses of the small dome subjected to the El

Centro earthquake of May 18, 1940 (21) were performed for

five different load conditions. An accelerogram of the El

Centro earthquake appears in Fig. 24. The load conditions

are:

l. Dead load only.

2. Dead load plus 10 lb./ft.2 live load.3. Dead load plus 20 lb./ft.2 live load.

4. Dead load plus 30 lb./ft.2 live load.

5. Dead load plus 40 lb./ft.2 live load.

Nodal displacements at each time step are calculated inad-·

dition to the maximum axial stresses in each member over the

entire analysis. The analyses are limited to four secondsof earthquake data because the largest ground accelerations

occur within the first four seconds.

In order to include the live load an additional mass isadded to each element that is equivalent to the mass of snow

on the tributary area about each member. By including anacceleration due to gravity (see section 4.2) an effective ·nodal load vector is achieved. The initial nodal displace-

ments of the structure due to this gravity load must also be

included. If they were not then the load would act as if it

were instantaneously applied.

67

03,0.2 I »Ol I ' I · ’ IO O I IIIII

I,, [ I lv ..n n.A.,_lnn. A ’*,~

:; , lvgy 'V ,q, ·. I[I"!1!' ‘, N-0n I __ I I ·f02 ‘ ·_ ,*0-3 4-—y_•o.3zg · — Ground Accelerotion, y

6“ II Ii . I Al.! In lt I,6 ' 7 " V T ' " Y1 ' I-;

-69°•l5.ß8 in/sec Ground Velocity, y

·I6 y,-6.28m. .6

. 4 ”s „s 0

-4Ground Displocement, y

0 6 IO I5 20 25Time, Sec. .

Figure 24: Accelerations, velocities and displacements forthe El Centro earthquake of May 18, 1940.

68

The nodal displacements in the relative reference frame

are calculated since they are the displacements that cause

deformations. The time-displacement graphs of node A in the

direction of the earthquake excitation for all five loads

are presented in Figs. 25 through 29. A composite graph of

the displacements of the four live loads is also given in

Fig. 30. Tables 3 through 7 provide a comparison of the

maximum stresses. For all loads the maximum stresses in the

numbered elements (see Fig. 21) for the static analysis are

compared to those of the dynamic analysis. Stresses in mem-

bers 15 through 19 are not presented for the dynamic analy-

ses since they are the members of the tension ring which are

not included in the fixed base dynamic problem.

5-3 LABQEILQME5.3-1 Ssasisßuzalxsss

The analyses of the large dome are similar to those of

the small dome. For a uniformly distributed live load the

large dome is able to withstand 72 lb./ft.2 plus its dead

weight before a singularity in the stiffness matrix arises.

Load-displacement graphs for the nodes A,"B and C Qf Fig, 31

are given in Fig. 32. As with the small dome, this dome ex-

‘hibits bifurcation instability. The stresses at failure for

the numbered members are presented in Tablel 8. Stresses

69

10-Qoz

-~ t1.0 1.5 -0

-.02 . _

in,.

0t_O _3.0

-.02 _in.

.02

· t3.0 4.0

‘Figure 25: Displacement of joint A for dead load only onthe small dome.

70 I

.02 . °°°

2_O t1.5

-.02tu.

QOZ

t2.0 . 3.0

-.02 '

in..02

° t3_o 4.0

-.02Figure 26: Displacsment of joint A for dead load plus 10

lb./ft. on the small dome.

I

71 g

in..02 - '

· 4 __

-.02in.

.02

-.02 '

in.

'“

-.02Figure 27: Displacezgnent of joint A for dead load plus 20

lb./ ft. on the small dome.

72

in..

.. · t1.0 2'°

-.02 —

in..02

d2.0 -5 3"° t

in..02

3.0 3 .4,0 *5

3 -,02Figure 28: Displacement of joint A for dead load plus 30

lb./ft? on the small dome.

73

in..02

__ __ A _

‘•O2

in.

2 0_5 3.0 T1

-.02V

in.

.3.0 3. 6.0 t

-.02Figure 29: Displacement of joint A for dead load plus 40

lb./ft.2on the small dome.

74

im ..„....... ,. ]_g_]_b_/ ftzz

.......•-- 20 11:./ E1;.2-- —-- so 1b./ ft.2.....----# 40 lb / ft 2 ·/xl

•.• |••‘

••·

·I Ä

•

1.5 2· 1:•• • ••°

~ ·\'/

§\\.,./-Ä

in._md " Q‘~®/geo

, ' _, LO 1:°= y — \ //

in./~.

I^

'

3.0Figure30: A comparison of the displacements of node A for.several liveloads on the small dome.

75

TABLE 3

A comparison of maximum stresses in numbered members of the °small dome for dead lo.ad only.

ELEMENT MAXIMUM STRESSES (KSI)NUMBER STATICDYNAMIC1

-0.1724 -0.49977

27

-0.1724 _ -0.6953

3 -0.1724 -0.7683

4 -0.3775 -1.5300

5 -0.3775 -1.0935

6 -0.3775 -1.3778

7 -0.2248 -0.4164

8 -0.1170 -0.69007

9 -0.1170 -0.6041

10 -0.2248 -0.6106

11 -0.1170 -0.5218

12 -0.1170 -0.7187l

13 -0.2248 -0.6977

14 -0.1170 -0.5987 {15 0.6954 N.A.16 0.6954 N.A.17 0.6954 N.A.

'

18 0.6954 N.A.”18 0.6954 N.A.

I 76 1

1TABLE 4

A comparison of maximum stresses in numbered members of thesmall dome for dead load plus 10 lb./ft. 2.

«‘ ELEMENT. MAx:M¤M sTxEssEs (xs:)NUMBER sTAT:c DYNAMIC

1 -0.9344 -2.05332 _ -0.9349 -2.05053 -0.9347 -2.04704 -2.0470 -4.22465 -2.0470. -4.45166 -2.0470 _ -3.46897 -1.2199 -1.4644

1

8 -0.6346 -1.7334 e

9 -0.6346 -1.733010 -1.2199 -1.464411 -0.6346 -1.734012 -0.6346 -1.711513 -1.2199 E -1.386014 -0.6346 -1.826615 3.7715 ·N.A.

n15 3.7715 N.A.17 3.7715 N.A.18 3.7715 N.A.1 19 3.7715 N.A.

77

TABLE 5A comparison of maximum stresses in numbered members of the

small dome for dead load plus 20 lb./ft. .

NUMBER STATIC ¤YNAM1c1 -1.6696 -2.4123

p 2 e -1.6706 -2.40983 -1.6701 -2.49834 -3.8358 -4.89065 -3.8358-5.13706

-3.8358 -5.21277 6 -2.2403 -2.01458 -1.1650 -2.3430

6 9 -1.1657 -2.2771 618 -2.2395 -2.145311 -1.1658 -2.4295 —12 ” -1.1657 -2.228713 -2.2395 -2.2861 614 -1.1656 -2.339615 6.9397 N.A.

E 16 6.9399 N.A.17 6.9398

9 N.A.18 6.9398 N.A.19 6.9398 N.A.

78

TABLE 6A comparison of maximum stresses in numbered membärs of the

small dome for dead load plus 30 lb./ft. .

ELEMENT MAXIMUM STRBSSBS (xs1> ·NUMBBR STATIC ¤YNAM1c

1 -2.3857 -3.36362 7 _ -2.3874

2-3.3866

3 -2.3865 -3.41724 -5.7541 -6.7501S -5.7539 -6.91136 -5.7541 -6.97797 -3.2925 -2.82838 -1.7134 -3.18441 9 -1.7146 -2.9653

10 -3.2912 -2.931611 -1.7147 -3.2442 E12 -1.7143 -3.022713 -3.2913 -3.073114 -1.7142 -3.155015 10.2090 N.A.18 10.2090 N.A.17 10.2090 N.A.

_ 18 10.2090 N.A.19 10.2090 N.A.

n

79

TABLE 7A comparison of maximum stresses in numbered members of the

small dome for dead load plus 40 lb./ft? .l

NUMBER gTATIc DYNAMIC1 4 «3.l233 -4.33092 I -3.1233 -4.29753 i -3.123 -4.5087

2 4 -7.5331 -9.11665 -7.5331 -9.53516 -7.5331 -9.72537 -4.3104 -3.68368 -2.2447 -4.6477.9 -2.2447 -3.9668

10 . -4.3104 -4.0932ll -2.2447 -4.778612 -2.2447 p -4.069513 -4.3104 -4.356714 -2.2447 -4.492515 13.3654 N.A.15 13.3654 N.A.17 13.3654 N.A.18 13.3654 N.A.19 13.3654 N.A.

363

81 A

8 . S/NGULAR]7-Y

&NODEN60

ä xx/0066 @ AND ©W- 4 O ' I· Q

WO~¤ 2

2 4 6 8W

DISPLACEMENT m.

Figure 32: Load vs. displacement curves for uniform load onthe large dome.

82 ·

TABLE 8

Maximum stresses of static analysis for numbered members ofthe large dome.

ELEMENT MAXIMUM STRESS ELEMENT MAXIMUM·STRESSNUMBER AT FAILURE(KSI .NUMBER AT FAILURE(KSI)

1 -5.331 21 -2.232E 2 -5.331 22 -5.513

3 -5.333 23 -5.513

4 -11.860 24 -2.2325 -11.860 25 -7.447

6 -11.860 26 -2.2327 -7.370 27 -5.513

8 -3.484 28 -5.513

9 -3.484 29 -2.232

10 -7.370 30 -7.439

11 -3.484 31 -2.23212 -3.484 32 -5.511

13, -7.370 33 32.355

14 _ -3.434 34 32.603

15 -9.654 35 32.357

16 -9.657 36 32.356

17 -9.655 37 32.60218 -9.655 38 32.35719 -9.655 39 32.357

%20 -7.447 40 32.603

n l

834

for other loads are given in the next section where they arecompared to the dynamic results. The maximum allowablestresses and the buckling stresses for the numbered elements

of Fig. 31 are given in Table 9. Again, none of the members

·reached the buckling stress before the global instability.

For the nonuniform load the stiffness matrix becomes sin-

gular at 45 lb./ft.2 plus the dead load. Fig. 33 shows the

load-displacement graph for the downward deflections ofnodes A,B,C,D and E. Nodes D and E are in the lesser loaded

portion of the dome. In this dome, unlike in the smalldome, no members reached their buckling stress prior to glo-

·bal instability. I

5.3.2 Dynamic AnalyacaDue to the cost of analysis of the large dome the loading

conditions are reduced to three. They are:

1. Dead load only.

2. Dead load plus 20 lb./ft? live load.3. Dead load plus 40 lb./ft? live load.

- Nodal displacements at each time step are calculated in ad-

dition to the maximum stresses in each member.

The time displacement graphs of node A in the directionof the earthquake excitation for all three load conditions

are shown in Figs. 34 through 36. A composite graph of the

84

TABLE 9Maximum allowable stresses and buckling stresses for

numbered members of the large dome.

‘ (xs:) „ < KSI)1 -5.10 g -9.892 -5.10 -9.89

3 -5.10 -9.89

4 -12.34 -25.43

5 -12.34 -25.43 g6 -12.34

4-25.43

7 -5.10 -9.89

8 -4.26 -8.28

9 4 -4.26 -8.284

10 -5.10 -9.89

11 -4.26 4 -8.28

12 -4.26 -8.28

13 -5.10 -9.89

14 4-4.26 -8.28

15 -12.34 -25.43

16 -12.34 E -25.43

17 -12.34 -25.43

18 -12.34 -25.434

19 -12.34 -25.43

85

TABLE 9 (cont ' d)

ELEMENT MAXIMUM ALLOWABLL BUCKLINGNUMBER COMPREQSIVE STRESS STRESS ‘

20 -5.10 -9.89‘2l -4.65 -9.03

22 -4.65 -9.03_ 23 -4.65 -9.03

24 -4.65 -9.0325 -5.10 -9.8926 -4.65 -9.0327

3-4.65 -9.03

28 -4.65 -9.0329 -4.65 -9.0338 -5.10 -9.8931 -4.65 -9.0332 _ -4.65 -9.0333 -12.34 -25.433* -12.34 -25.4336 -12.34 -25.4336 -12.34 -25.4337 -12.34 -25.4336 -12.34 -25.4330 -12.34 -25.43*0 -12.34 -25.43 ”

86I

50 . gNODE7v001s©406

SSO

2 7Q<L'O·~*7O

7.0 62.0 :20 4.0. 6.0DISPLACEMENT m.

Figure 33: Load-displacement curves for nonuniform load onthe large dome.

I

87

in.-.02

6 6 2-0.+.:.

-.02in.

QOZ

-.02in.

002

3.0 4 3.5 6.0 ”°

'°•O2 AFigure 34: Displacement of joint A for dead load only on

the large dome.

F F88

1:1.OO1

1..0 1_ 2.0 C

*0•1

in. „0.1

2.0 3.0 t

-0.1

in.0•1

3.0 6.0 t F

-0.1 ‘

Figure 35: Displagéement of joint A for dead load plus 20lb./ft. on the large dome.

. 89A

111. '0.1

2.0 6

-0.1in.

l ti2,0 2.5 .0

TO-1

in.0-1

*

·

, 3.5 _ 6.0 t

—0O1

Figure 36: Displacäement of joint A for dead load plus 40„ lb./ft. on the large dome.

90

two live loads is presented in Fig. 37. Tables 10 through

12 offer comparisons between the maximum stresses in the

numbered elements of both the static and dynamic analyses.

The tension ring elements are not included in the dynamic

analyses.

5-4 9.EEQRBQIHL.é.B§EEJ@§EELLD@.E.$The allowable stress for all members according to the

Aluminum Association (49) were calculated. Allowable ten-

sile stress for all members is 19 ksi. Allowable compres-

sive stresses are found in Table 2 for the small dome and in

Table 9 for the large dome. These compressive stresses are

very low because the members are unusually long for their

cross-sectional areas.

For the static analyses all members of the small dome

were over-stressed at failure. These over-stresses ranged

from 6% in members 1, 2 and 3 to 74% in members 7, 10 and

13. No members, however, reached the buckling load or yield

stress prior to failure. For the large dome, half of the

members were over-stressed at failure. The over—stresses”

ranged from 5% in members 1, 2 and 3 to 71% in members of

the tension ring. Other over-stressed members were 7, 10,

' 13, 20, 25, 30, 22, 23, 27, 728 and 32. As with the small

dome, no members reached their buckling stress and none

reached the yield stress of the material.

91A in. -———— 20 1.b,/ ft.2

.. - 40 110./

1.5tn,0.0

0

in.

0.-0 0Figure 37: A comparison of the displacements of joint A for

the two live loads on the large dome.

I

92

TABLE 10A comparison of maximum stresses in numbered members of the

large dome for dead load only.

ELEMENT MAXIMUM sTREssEs (xs:)NUMBER sTAT1c 0xNAM1c

1 -0.1786 -0.61092 “ -0.1787 -0.64753 -0.1787 -0.58354 -0.3594 -0.91855 -0.3594 -0.96196 -0.3594 -0.89957 -0.2235 -0.47558 -0.1159 -0.47759 -0.1159 -0.5595

18 -0.2236 -0.465111 -0.1158 -0.4421

E 12 -0.1156 p -0.358213 -0.2236 -0.505914 -0.1158 -0.464315 -0.2558 -0.626415 -0.2558 -0.628417 -0.2558 -0.746218 -0.2558 -0.737318 -0.2558 -0.8282

93 !

TABLE 10 (cont'd)

¤·¤¤¤~¤·NUMBER STATIC DYNAMIC20 -0.2264 ° -0.3024

21 -0.0622 _ -0.473522 -0.1722 -0.477623 -0.1721 -0.471324 -0.0622 -0.417725 -0.2264 -0.290926 -0.0624 -0.346027 -0.1722 -0.5168

28 -0.1722 • -0.490829 -0.0624 -0.3659 230 -0.2262 -0.2864 „

31 -0.0623 -0.3277

32 -0.1722 -0.514733- 0.9694 N.A.

34 0.9808 N.A.

35 0.9694 N.A.

36 0.9694 N.A.

37 0.9808 N.A.

38 0.9694 N.A.39 0.9694 N.A.40 0.9808 N.A. l

94

TABLE llA comparison of maximum stresses in numbered membärs of the

large dome for dead load plus 20 lb./ft. .

— MAx1M¤M STRBSSES (xs:)STATIQ DYNAMIC

1 #1.550-6.43232

' -1.550 -6.43593 -1.550. -6.1703

44 -3.154 -8.30035 -3.154 -9.8866

h 6 -3.154 -8.9202. 7 -1.959 -5.8969

8 -1.008 -3.60169 -1.008 -4.2084

10 -1.959 -5.191511 -1.008-3.528012

-1.0081

-4.033613 -1.959 -5.953114 -1.008 -5.058315 -2.263 -7.6324 U16 -2.263 -7.569117 -2.263 -7.723718 -2.263 -7.150718 -2.263 -7.2858

95 _

TABLE ll (c¤¤t'd)

EEEEEEENUMBER_ STATIC DYNAMIÜ

,20 -l.983.' -3.5416

21 -0.547V V-3.8718

22 -1.508 -4.101023 -1.508 -4.3558

E 24 -0.547 -3.3052

25 -1.983 -3.194526 -0.547 -3.353027 -1.508 -3.8117

28 -1.508 -3.9527 'V

29 -0.547 -3.1650

gg -1.983 -2.7943 .31 -0.547 -2.950732 -1.508 -4.8165

33 V8.506 N.A.

34 ·8.506 V N.A.

35 8.506 N.A.

36 8.506 N.A.37 8.506 N.A.

38 8.506 7 N.A.

39 ·8.506 N.A.40 J 8.506 N.A.

V

l96

TABLE 12A comparison of maximum stresses in numbered memgers of the

large dome for dead load plus 40 lb./ft. .

1 NVMBER s·1·A·r1c: owmxxc ‘

1 -3.021 -8.8923

2 -3.023 -8.7624

3 -3.022 -9.1952

4 -6.430 -13.1460_ 5 -5_43Q -14.6910

· 6 _6•43O -12.41407 -3.973 -8.14688 -1.981 -4.33689 _l_98l -4.5931

10 _3_975l

-8.165711 -1.980 -5.1791 .12 _l_98O -4.435913 _3_975

c -8.712214 _l•98O ‘ -7.001015 -4.895 -8.610216 -4.895 ' -8.6628

‘ 2

17 -4.894 -9.691918 -4.894 -11.647019 -4.894 -13.4650

I

97

• TABLE 12 (cont'd)

RRR20 -4.033 -5.3766

21 -1.149 -5.2154 622 -3.037 -6.3230

23 -3.035 -6.4656

24 -1.149 “ -4.6812

25 -4.033 -4.0493Z6 -1.153 -4.397627 -3.063 -6.5516

28 -3.036 -6-3407

29 -1.119 -5-6663

30 -4.029 -8-7535R

31 -l_l5l -7.4687

32 -3.036 -8-8381

_ 33 17.387 8-6-34 17.520 8-6-

35 17.388 8-6-36 17.388 ‘ 8-6-

. 37 17.569 _ N.A.

38 17.388 8-6-38 17.366 8-6-88 17.570 8-6-

98

In the small dome no members became over-stressed up toand including the static load of 40 lb./ft.2 . The highest

stress was 6% under allowable. For the large dome , also,

no members were over-stressed up to and including 40

lb./ft.2. The highest stress was 8.5% under allowable for

the tension ring members.V

For the dynamic analyses significant increases in maximum

stresses were noticed for all loads on both domes over the

stresses in the static analyses. Members of the small dome

experienced average increases in maximum stresses of 303%,

121%, 51%, 40% and 47% for the dead load only, dead loadplus 10 lb./ft.2, dead load plus 20 lb./ft.2, dead load plus

30 lb./ft.2 and dead load plus 40 lb./ft.2 , respectively.

The maximum increases in stress of any member for the loadsgiven were 514%, 187%, 108%, 84%, and 113%, respectively.

The stresses throughout the analyses remained within the al-

lowable range for all cases except 40 lb./ft.2 where members

8, 11 and 14 were 8.5% over-stressed but still remained be-

low the buckling stress.

Members of the large dome experienced average stress in-

creases of 236%, 261% and 191% for dead load only, dead load

plus 20 lb./ft.2 and dead load plus 40 lb./ft.2, while themaximum increases in stress for any member were 661%, 608%

and 549%, respectively. These increases resulted in many

99 1

over-stressed members and even some buckled members. For 20

lb./ft. members 1, 2, 3, 7, 10 ,13, 14 and 32 were over-

stressed to a maximum of 26% over allowable but all below

the buckling stress. For 40 lb./ft.2 all members were

over—stressed except members 16, 17, 18, 25 and 26 to a max-

imum of 90%. Ten elements reached buckling, however,all of

these elements were outside the quarter region of Fig. 31.

A final note on the results should be given. At no time

during the dynamic analyses did either dome become globally

unstable. All analyses were able to be carried to comple-

tion. This may be because the entries of the force vectordue to the earthquake excitation act in a plane parallel to

the ground. For shallow domes like the ones used in this

study horizontal forces are probably less likely to cause a

global instability than vertical downward forces.

Chapter VI

CONCLUSICNS AND RECCMMENDATIONS

6-1The question to be answered by this study is by how much

does an earthquake excitation increase the axial stresses ina reticulated space truss such as the domes in Figs. 2 and

3. The stress increases due to the excitation were signifi-

cant especially in the large dome where the average increase

was about 200% over the stresses of the static analyses.

For the small dome the stress increases were smaller but

still over 40%. Earthquake excitations cause stress in-creases that must be considered in the design of a dome in a

seismic region.

Even though these stress increases appear to be large,

these domes exhibit surprising strength characteristics un-

der dynamic loading. Many studies have shown that these

domes are strong for their weight when subjected to static

loads and for dynamic loads they again appear to be strong.

For example, the large dome was able to withstand a distri-

buted load of nearly six times its own weight before its

members became over-stressed under the base excitations.

The small dome was able to withstand an additional load of

nearly 13 times its own weight. This is impressive and it

100

101

demonstrates the strength and usefulness of these domes in

seismic regions. Overall, the lamella dome is a strong

structure and able to resist base excitations based on the

results of this study.

6.2 BE§QMENQAIlQN§ EQB EHIHBE‘EE§EABQHAlthough the basic questions of this study were resolved,

many other questions were raised during the research that

were not answered due to the constraints on time. Several

extensions of the thesis topic that address these questions

are given. Other students may wish to pursue these topics.The computer program developed for use in this study may

be refined to make it more versatile and economical. It may

be modified to include various types of dynamic loads such

as blast loads or wind loads to provide more complete dynam-

ic analysis capabilities. The program may be refined to in-

clude different material nonlinearities so that different

materials may be considered and more accurate results pro-

duced. Other direct integration methods may also be includ-

ed. The Wilson method or the Houbolt method might be suita-

ble for other structures. A study to find the most

economical direct integration scheme for these domes is also

a possible extension. .

. 102 A

The most time consuming step in a typical computer analy-sis using this program is arranging and inputting the data.

The program by Dib (14) produces the necessary data for a

lamella dome or a geodesic dome and numbers the elements and4

joints to provide a reduced bandwidth. The two programs may _be combined for a more efficient program.

Additional testing may be performed to answer some in-

triguing questions. A geodesic dome or other popular dome

configuration with the same weight and overall dimensions as

the lamella could be tested with the same earthquake data.The results may be compared to the results of this study.

Also, the nonuniform loads mentioned in section 5.2.1 may be

included and dynamic analyses performed. A comparison with

uniform loads would be possible. The methods presented by

Rosen and Schmit (47) and (48) to model imperfect members

could be included in the program to study the effects of

member imperfections.n

The frequencies of the structure are calculated using the

stiffness matrix of the undeformed structure and the mass

matrix of the unloaded structure. By increasing the mass

with the live load and changing the stiffness matrix with

the initial displacements caused by the live loads, the fre-

quencies should change. A study could be made on how the

frequencies change with different live loads. Any changes

103 I

in the frequencies would alter the damping coefficients andtime steps. The amount of change in these parameters should

I

be determined to see if they are significant and to what de-

gree they affect the analysis. If the time steps would vary

significantly for different loads then it may be advanta-

geous to generate an artificial accelerogram to accept the

varying time steps.

The last question to be answered is whether the bending

strains should be included in the analysis. Perhaps the as-

sumption of the space truss element is not accurate. In-

cluding the live loads may require that a space frame ele-ment be used. The program may be modified to model a space

frame element and comparisons between the frame and thetruss can be made.

REFERENCES

1. Atalik,T. S. and Utku, S., "Stochastic Linearization ofMulti-Degree-of-Freedom Nonlinear Systems," EerrngnegeEngineering eng Etrnetnrel Dynemiee, Vcl- 4, nc- 4,April-June, 1976, pp. 411-420.

2. Baron, F. and Venkatesan, M. S., "Nonlinear Analysis ofCable and Truss Structures," ggnrnei er rne ErrngrnreiQiyieign, AEQE, Vol. 97, no. ST2, Feb., 1971, pp.679-710.

3. Bathe, K. J., "Solutions of Equilibrium Equations in .Static Analysis," Einire Eienenr Erggednree inEngineering Aneiyeie, Prentice-Hall, Inc., EnglewoodCliffs, New Jersey, 1982, p. 489-491.

4. Bathe, K. J., "Solution of Equilibrium Equations inDynamic Analysis," Einite Element Ergeegnree inEngineering Aneiyeie, Prentice-Hall, Inc., EnglewoodCliffs, New Jersey, 1982, pp. 537-542.

5. Bathe, K. J., "Solution of Equilibrium Equations inDynamic Analysis," Einite Element Erggegnree inEngineering Aneiyeie, Prentice-Hall, Inc., EnglewoodCliffs, New Jersey, 1982, pp. 527-530.

6. Bathe, K. J. and Cimento, A. P., "Some PracticalProcedures for the Solution of Nonlinear Finite ElementEquaticnc," Egmnnter Methgge in Annlieg Meeneniee engEngineering, Vol. 22, no. 1, April, 1980, pp. 59-85.

7. Bathe, K. J. and Wilson, E. L., "Stability and AccuracyAnalysis of Direct Integration Methods," EerrngnegeEngineering eng Etrnetnrel Dynemige, Vcl- 1, nc- 3,Jan.-Mar., 1973, pp. 283-291.

8. Berger, B. S. and Shore, S., "Dynamic Response of, Lattice-Type Structures," Qgnrnei er rhe EngineeringMegnenige Diyieien, AEQE, Vcl- 89, nc• EM2, April,

1963, pp.47-69.

9. Bernrueter, D. L., "Estimates of Epicentral GroundMotion in the Central and Eastern United States,"Brgceedinge gf tne §ixth Worig Cgngerenge en EarthgnageEngineering, Earthquake Engineering Research Institute,Vol. 1, 1977, pp. 332-335.

104

105

10. Carter, W. L., Dib, G. M. and Mindle, W., "Free andSteady State Vibration of Nonlinear Structures Using aFinite Element Nonlinear Eigenvalue Technique,"

Vol- 8.no. 2, Mar.-Apr., 1980, pp. 97-115.

11. Cheung, Y. K. and Lau, S. L., "Incremental Time-SpaceFinite Strip Method for Nonlinear Structural

Vibratipus.Dyuamlta,Vol. 10, no. 2, Mar.-Apr., 1982, pp. 239-254.

12. Crooker, J. 0. and Buchert, K. P., "Reticulated ShellStructures." Qi the ASQE.Vol. 96, no. ST3, Mar., 1970, pp. 687-700.

13. Der Kiureghian, A., "A Response Spectrum Method forVibration Analysis of MF Systems," Earthguakaand Dxnaä. Vol- 9. no- 5.Sept.-Oct., 1981, pp. 419-455.

14. Dib, M., "Analysis of Reticulated Domes With AutomaticMesh Generation and Bandwidth Reduction," Thesispresented to Virginia Polytechnic Institute and StateUniversity, Blacksburg, Virginia, 1985, in partialfulfillment of the requirements for the degree ofMaster of Science.

15. Epstein, M. and Tene, Y., "Nonlinear Analysis of Pin-Jointed Space Trusses," Juurual ut tta StrugturalQlylaluu, ASQE, Vol. 97, no ST9, Sept. 1971, pp.2189-2202. 7

16. Forman, S. E. and Hutchinson, J. W., "Buckling ofReticulated Shell Structures," lutaruatlgual Juurual gf.S.<il.i.d§ and . V¤1- 6. ¤<>- 7. July. 1970. pp.909-932.

17. Gaylord, E. H. and Gaylord, C. N., ed., StrugturalEugluaarlug Haudbogk, Second ed., McGraw-Hill BookCompany, New York, 1979, pp. 19-11 to 19-13.

18. Ginsburg, S. and Gilbert, M., "Numerical Solution ofStatic and Dynamic Nonlinear Multi-Degree-of-FreedomSystems." Qdmpnizar Maäißa in Applied M;nn.aeai¢Eugluaarlug,Vol. 23, no. 1, July 1980, pp. 111-120.

19. Goldberg, J. E. and Richard, R. M., "Analysis ofNonlinear Structures," Jaurual ag the StructuralQlylaluu, ASQE, Vol. 89, no. ST4, Aug., 1963, pp.333-351.

106

20. Hall, J. F., "An FFT Algorithm for StructuralDynamiee," end £_¢;nLlSu aQyneniee, Vol. 10, no. 6, Nov.-Dec., 1982, pp. 797-811.

21. Haroun, M. A., "Corrected Accelerogram and ComputedVelocities and Displacements," NISEE, Mail Code,104-44, California Institute of Technology, Pasadena.

22. Hensley, R. C. and Azar, J. J., "Computer Analysis ofNonlinear Truss Structures," Journal ef rne Structure}Qiyieien, ASCE, Vol. 94, no. ST6, Proc. Paper 5997,June 1968, pp. 1427-1439.

23. Hibler, H., Hughes, T. J. R. and Taylor, R. L.,"Improved Numerical Dissipation for Time IntegrationAlgorithms in Structural Dynamics," EarthgnakeEngineering eng Srrugrnral Eynamice, Vol.5, no. 3,July-Sept., 1977, pp. 283-292.

24. Hinton, E., Rock, T. and Zienkiewicz, 0. C., "A Note onMass Lumping and Related Processes in the FiniteElement Meth¤d„" end éggnreltu tQyneniee, Vol.4, no. 3, Jan.-Mar., 1976, pp. 245-249.

25. Holzer, S. M., "Notes on Geometrically NonlinearAnalysis," Virginia Polytechnic Institute and StateUniversity, Blacksburg, Virginia, 1984.

26. Holzer, S. M., Watson, L. T. and Vu, P., "StabilityAnalysis of Lamella Domes," Prgceedinge er e Synnoeiun -en Lena Spee Beni äßä, Geteber, 1981. pp-179-209.

27. Housner, G. W. and Jennings, P. C., "Generation ofArtificial Earthquakes," genrnei er tne Engineering

ASQE, Vel- 90. ne- EMl, February.1964, pp. 113-150.

28. Iyengar, R. N. and Iyengar, K. T., "NonstationaryRandom Process Model for Earthquake Accelerograms,"

Vol-59, no. 3, June 1969, pp. 1163-1188.

29. Jagannathan, S., Epstein, H. I. and Christiano, P.,"Nonlinear Analysis of Reticulated Space Trusses," EJeurnal er the Errnernrei Qiyision, ASQE, Vol. 101, no.STl1, November, 1975, pp. 2641-2658.

1107

30. Kameda, H. and Ang, A. H.-S., "Simulation of StrongEarthquake Motions for Inelastic Structural Response,"

s;f1‘—heiizs:11Iu.*.l.<§.¤ Q;1...>fe@¤egnE..;r.rL1seathaEnginggning, Earthquake Engineering Research Institute,Vol. 1, 1977, pp. 483-488.

31. °Kubo, T. and Penzien, J., "Simulation of Three-Dimensional Strong Motions Along Principal Axes, SanFernando Earthquake," Egntngnake Engineering gnd

7. ¤<>- 3. May-June. 1979. pp-279-293.

32. Liou, D. D., "Frequency-Domain Redigitization Methodfor Seismic Time Histories," Egrnngnake Engineeging nngllxpgzliss. V¤l- 10. ¤<>- 3. May-June. 1982.O pp. 511-515.

33. McConnel, R. E. and Klimke, H., "GeometricallyNonlinear Pin-Jointed Space Frames," Mnngniggl Mgnngggfg; Mgnlingn; ßggblgng, C Taylor, E. Hinton and D. R.J. Owen, ed., Vol. 1, p. 333.

34. Newmark; N. M., "A Method of Computation for Structuralpi 'csQiyigign, AEQE, Vol. 85, no. EM3, July 1959, pp. 67-94.

35. Nickell, R. E., "Direct Integration Methods in 0Structural Dynamics," Qgnnnal gf the EngineegingV¤l- 99. rw- EM2. April.1973. PP- 303-317.

36. Nickell, R. E., "Nonlinear Dynamics by ModeSuperp¤Si’¤i¤¤." lim J.r.s_r_Su tues.Qynnniggang Mgnggiglg Qgnfenenge, Las Vegas, Nevada,April, 17-19, 1974, Proc. Paper No. 74-341.

37. Nigam, N. C. and Jennings, P. C., "Calculation ofResponse Spectra from Strong Motion EarthquakeRecprds." gf L11: gfAngrigg, Vol. 59, no. 2, April, 1969, pp. 909-922.

38. Noor, A. K., "Nonlinear Analysis of Space Trusses,"Qgngnnl gi gne Struggngal Qiyigign, ASCE, Vol. 100, no.ST3, March, 1974, pp. 533-546.

39. Noor, A. K., "On Making Large Nonlinear ProblemsSmall," Qomnute; Metnods in Ann1igg Mechanics angEnginggging, Vol. 34, no. 2, Sept., 1982, pp. 955-985.

I

108

40. Noor, A. K., Anderson, M. S. and Greene, W. H.,"Continuum Models for Beam and Plate-Like LatticeStructures," AlAA Jedrpel, Vol. 16, no. 12, Dec., 1978,pp. 1219-1228.

41. Noor, A. K. and Peters, J. M., "Nonlinear DynamicAnalysis of Space Trusses," Qempute; Methods lp Appliedepd Val- 21. rw- 2. February.1980, pp. 131-151.

42. Park, K. C. and Underwood, P. G., "A Variable-StepCentral Difference Method for Structural Dynamics.-Part 1. Theoretical Aspects," Compute; Methode lpApplied ani S aps.1 V¤l- 22. rw- 2. May.1980, pp. 241-258.

43. Penzien, J and Liu, S.-C., "Nonlinear DeterministicAnalyses of Nonlinear Structures Subjected toEarthquake Excitations," Eagthqdeke Epglpeeplng epßepkeley, Report no. EERC 69-1, Jan. 1969, pp. 210-288.

44. Preumont, A., "Frequency Domain Analysis of the TimeIntegration Operators," Eepphgdeke Epgineepipg epdSppuepupal Dypeplee, Vol. 10, no. 5, Sept.-Oct., 1982,pp. 691-697.

45. Renton, J. D., "The Beam-Like Behavior of SpaceTrusses," AIAA dppgpel, Vol. 22, no. 2, February, 1984,pp. 273-279.

46. Richter, D. L., "Developments in Tremcor AluminumDomes," Analysis, Desigp epd Qepetructiop pg BracedQomes, Z. S. Makowski, ed., lst ed., Nichols PublishingCompany, New York, 1984, pp. 521-539.

47. Rosen, A. and Schmit, L. A. Jr., "Design OrientedAnalysis of Imperfect Truss Structures- Part I-Accurate Analysis," lppeppeplepel dopgpal fe; MumeglcelMexhpple in Vol- 14. 1979. pp- 1309-1321-

48. Rosen, A. and Schmit, L. A. Jr., "Design OrientedAnalysis of Imperfect Truss Structures- Part II-7 Approximate Analysis," lptegnetional Journal fo;Mumepleal Mephede lp Epgipeeplpg, Vol. 15, 1980, pp.483-484.

49. Speeiflcations ;o; Alumlnup Spgucturee, Fourth ed., TheU

Aluminum Association, Inc., New York, N.Y., 1982.

109

50. St. Balan, Minea, S., Sandi, H. and Seibanescu, G., "AModel for Simulating Ground Motion," Rggeeeginge ef eneSixthen”Earthquake Engineering Research Institute, Vol. 1,1977, pp. 523-528.

51. Supple, W. J., "Stability and Collapse Analysis of_Braoed Domes," Anelxsis, Design end efßnegeg Qgmee, Z. S. Makowski, ed., 1st ed., NicholsPublishing Company, New York, 1984, pp. 141-146. .

52. Tanabashi, R., "Studies on the Nonlinear Vibrations ofStructures Subjected to Destructive Earthquakes,"

ef theenEngineeging,Earthquake Engineering Research Institute,June 1956, Paper no. 6.

53. Trifunac, M. D., "A Method for Synthesizing RealisticGround Motion," malletin ef the Segietxgf Amegige, Vol. 61, 1971, pp. 1739-1753.

54. Wilson, E. L., Farhoom, I. and Bathe, K. J., "NonlinearDynamic Analyses of Complex Structures," Eegthggekeend §.t.¤.agt,1.u:.el Dxnemies, Vol- 1, no- 3,,1973, pp. 241-251.

55. Wong, H. L. and Trifunac, M. D., "Generation ofArtificial Strong Motion Accelerograms," Eengnggekeend Dxnemite, Vol- 7, no- 6,Nov.—Dec., 1979, pp. 509-528.

Appendix A

FREQUENCIES OF VIBRATION FOR THE SMALL LAMELLADOME

FREQUENCY FREQUENCY FREQUENCY FREQUENCYNUMBER (HERTZ) NUMBER (HERTZ1

1. 1.3993 18. 14.6974

2. 1.4014 19. 17.9737

3. 1.7227 20. 17.9742

4. 1.7290 21. 19.8414

5. 1.7523 22. 19.9268

6. 1.7764 23. 19.9268

7. 1.7995 · 24. 20.6390

8. 1.8205 25. 22.2076

9. 1.8999 26. 22.2037

10. 1.9515 27. 25.3070

11. 2.4822 28. 25.3088

12. 7.6420 29. 25.7914

13. 9.4609 30. 25.7914

14. 9.4612 31. 28.0129

15. 14.4240 32. 28.013316. 14.4240 33. 28.999117. 14.6974

11O

E

a

’ Appendix B

FREQUENCIES OF VIBRATION FOR THE LARGE LAMELLADOME

FREQUENCY FREQUENCY FREQUENCY FREQUENCYNUMBER (111:12*1*2) NUMBBR <H12:R·rz>

1. 1.345 22. 1.752

2. 1.345 23. 4 1.754

3. 1.359 24. 1.798

4. 1.359 25. 1.798

5. 1.364 26. 1.8286. 1.367 27. 1.828

7. 1.367 28. 1.841 ·8. 1.395 29. 1.8419. 1.395 30. 1.842

10. 1.417 31. 2.687

11.l

1.417 32. 4.906

12. 1.423 33. 6.560

13 1.479 34. 6.560

14. 1.730 35. 8.360U15. 1.735 36. 8.360

16. 1.735 37. 8.43017. 4 1.742 38. 9.56318. 1.742 39. 9.563

19. 1.746 40. 11.636

n 20. 1.746 41. 11.63621. 1.752 42. 12.384

111

112

Appendix B (Continued) 4

FREQUENCY FREQUENCY FREQUENCY FREQUENCYNUMBER (HERTZ) NUMBER (HERTZ)

43' 12.384 64._l

17.9064‘* 12.442 65. 18.0624S' 12.443 66.

518.062

46' 12.443 67. 18.89247' 13.412 68. 18.89248* 13.412 69. ,19.66649° 13.775 70. 20.851SO' 14.372 71. 20.851Sl' 14.372 72. 21.500S2' 15.038 73: ‘ 21.625 _58* 15.609 74. 21.625S4' 15.609 75. 21.94455* 16.891 76. 21.944

5 S6' 17.071 77. 22.37057* 17.071 78. 22.37058* 17.359 79. 22.762S9' 17.359 80. 22.76260' 17.437 81. 23.3916l° 17.437 ' 82. 23.80462° 17.540 83. 23.80463° . 17.540 84. 24.337

113

Appendix B (Contiuued)

FREQUBNY FREQUENCY FREOUENCY FREQUENCYNUMBER (HERTZ) NUMBER (HERTZ)

°85. 24.337 90. 25.592

86. 24.792 91: 25.592

87. 24.792 92. 25.858

88. 25.285 93. 26.198

89. 25.285

i

Appeudix C

PROGRAM LISTING

114 ‘

ll5

************%***1+***** 4*1+********* C*1+******1+** I--I·· Lu Z*********** 4 I• •-• >•***********

. 1 • I-!-• 4 -1***********

GV)! -1 1V!-11+}********* I-ZU Gu.! II-••-eq

*********** _UOCJ I-C ZV? •-•*1+ *1+ · LU•-4-1 L9 O I-+-** 1+* >I-G CQ. Z UI•-••-•1+*

**4 U.1LUZ•-4 I- Z-¤·«¤· lu ·••··»

<c:< »-I-Om «.u•-·?:•-·**

UV? 4 1+* LUI- • 'ivßu-•4 X20**I4Z 12 1+* W-1< • -1 I-LU P- ··-•**UJ¤.OCLL14 1+* 4LuC •-• LUU-141 >·I•**Ut/7+-•</3G•-• 1+* U • 1I1U -13«~#*4 I--IZ-1 ·¤··¤- cuz „ •·-•L|-JZ •c.¢ ·-•1+*-1444lUD 1+* UJ4*··• I- CI--I•-·• •4Q•~*·l+¤. I- E •«I•·¤· m Z C: LU •-·•LuZ···•*·I•u'>LI.•-•I·~ •<I'** SDI-vl LU ILULJ>· •ZO~·**°"*C'9U••·•I4®** ZLU I I-··IU-I •-•>~LU**C• X U 0*** LUZ LU LU+-41 1-JLU-1I *1+ I/IU.1 4C-1** •1*·• -1 Z 4 LU G!·I·*-IZ •I-U•-• ·|··l· · muu-1 LU 1I-Lu mm UZU. >¢UJZZ ZLUQ3**G¤·-nt/I4/Iu.40** LU* Ol-L1 L1. 1>4•-• \.UV74c0*1+CI-4ZOQ 1+* -1* •-••··•U.1 C) 4CDI-.1 I.‘4¤·u»·••·Z<!c¤¤ ¤c·¤··••· mx •-::3 z an u.:.1c**

1 •-·•¢h>-\U1+* <* 4 LU 4 3221 U.1 I-**1U1¤I-LUGZ1+* •-•* 1wU. LU U-IcQ¤Z_r:§}"1+*O-JI-CIA £** 1* LU 1 Z-·•UU.C Z•-•-1·1I··¤·u.•.u :mZD·¤··I•· <*‘ ..1u>¤c < I--

Ca-·•~·•4 -_**

UC LULUI/51+* >* LUZO LU4„z~OI-• 4 LU:}**L1.:UUJLU1I·• 1+* U•··•U. -1 I1D~O4 OV)-1G**>4+-MI-•·¤• •** UC 4 I-·•LUU.~O1 -I4/I¥LU*1+-I U4¢/'11¥** 44L9 2 -1 ~¤LU LUU·I+·I+CJ¤u.1..': 31** LI.* u.:Z c: LI.LuC~O-1 <.'J¤:::c**V>Z"!G-I C3*1+ :1+ cnc-· •-~ C:‘e.><:~¤u.• zr-coz*1+ 4GI4 3** Lu 3 I- L.:L¤~¤L.J •-•v‘I 4**G 3+-*** 1+* N1CJ U 14N•'*U -1 LU**1-III:/'1¤C><¤.L/7«I·II· •-•O-1 UJ LU ••4 >£l«UII·-·1+* UJ 44*-U•"•** 2* I-U.-1 VI I-U. U>I-2**Z•-•LUU.1 I--!/5%* C3* LU 4 I .L1.1OIIII 'J~ 4**LUI-1 LUL/>LU** •-•* 13 U'! Z GLAGI-**+-·•-•D>•I :*1+ I-•* UOLU L/7 4LLJ4 v'1I¤·•I/I*‘I‘I-U+·•-1I-·UJI-** v-•·I+ vl-IZ C 1C„I-• LUU.3 Z**¤OU¤' Z ** 2* •-•-IP·• 1 4>~LL1 I1¤.C**1-1D4vI•-•Z** •-•* Q4!-· U Q.!-G I-¤.DU**3UJ¤¢..ILLJI·-•-•-1+1+ u.* I I I I**

>I-DZ 1+* I.U* I I I I .**17 tfIU•-IUJ** C* I I I I**4•· •-•SUI/7** I I I I**1I/IL/II··1<'l9** I'1+*¢„9I-W1!-LJLL1 1+* I I I I1+*OZ34I-- 1** I I I I**1UJ1¤.LUI-O** I I I ·•' **¤.!'I--•Q4U.** I I I N

** 1+* I I I •*1+ *1+ •·•~ I I •··•·I+*· *1+' CD ·•~ I -**

1+* ~¤• **1 I UJ1+***—I·1+***** -1 ·• I -1 ·*********** LU 4 4 at*********** U UJ I- U*********** U 1 LU D*********** 4 4 G G*******1+********-}*1+**************«II·**********UUUULJUUUUUUUUUUUUUUUUUUUUUUUUUUU

I

116

IAP- .IA>· LL U. LL

V7 •• U G I CI I"UJI- O U 4 I-·• Z GZG LU Z Z id U LLI L/I-•• ZGZ I/I G 4 4 Z E Z Z Q.U D .1 I-O G 4 I-I GCII.UU)I-1107 4 U MG .I M •-•<I-•U.1O-·• th • •-• 4.1 4 LI. ~ I-C.II/IC)‘ •¤• •>• Z I-U<3 *7 4.1 GI-·I-LI •·--I 4 Z LU • M Lu•··•L9•

Q 4 •LU Z LULU Q Q LIJIZLIJ42 Z > >· I> •-• Z I- I-L.)•-Q;I/HAQ •-e cz- Q I-*-I I- Lu Z I-•4I·-D

LIJ<h•-·• Q. - LUI- I- 4 M •-• I1-I CJ••ILUI-• Z OU M MU I•- LU O LL ILUZZ4 4 ¥ ZW C3 GI-U -• M *7 IDMUUU M O LUQ. Q. U UJ Z G4:} IDMLIJ ·-·- ZU'! U ZV! X M LL-D MMLLIIJLOCJII-' I ·I$ LU •-• IAQLU LU Qv-• Lu Q.M•"'• U 4 LUM In VI•-••··•M ..I I-· OLUM•M •-• I- I 4 I-II/II'- MI/7 4 LUU ZMGU.1•·-IJJLU LU LU I·•• I- IA)-UUJ G•-• O I•LU DD I• Z .4 m Lh vv >-...4u.4I >< Q 4::: zQ··~I·-Z-• >· Q u.u4 .I4MI¤- u4< ..• z-~_ Luv:M4G 4 Q>< LL 4Z•-• I- G ·-Q u4•..J•-Iu.LLJ u.I cc ·•· 4 •··• 24QG 4•-I Q ICJ«.n•-•I-I-U L/E 4 Z Z UJ M-I I-M)LI.4Q — Lu.: LU QLUG •-•.I I Q c...44Icc •. Z< Z uv-•I...I O4 I- Q.; I- <•

I-Q. X I •-Im -••···«II·-4 ccm U4 Z22-• •-• WG Z I-4° OG 2 O DG4¢.QGG)- M •• G-1 M 4ZMZ G-1 I- LUG GI/B •-•

OI/IM I- *UG LU I->•GCJ UU I-I UIUI/I

Q LU 4 4 I-• I/IO •-• LI.! I-GJ Q.•-¤>•GC> Z I ZM LI.: ·I-•I·- LULLI I- C<I--I

. IICLU Q. G Q I IZ4 II 4 II I-M44•-Q G .I •-•Q •• LLII- I-I- Z II-ZN-IZ Z 4 I-Z GQ-•NZ•-• •-«•••~ MZI/E4• G •-• ‘G U4 I-LU CDU II O•"7 u;C3-••'-O Q. LU MIII|Q.X M‘>• UI- U~¤•I-Q Z II MN MI" ZLI1-

G--• ILJZI-‘·••U1 LU 4 ¤-•• LUI-/ILIJLUG •-I G ~• I-LLJZZ-I.1I·-· G -• O-I GU-IULJULU••~.• GI-Q ZZUJ4:t4Z LUO•··••- ¥I/WQ. • ZM • -·• ZZUD•-I LU U LULU I- GOI-U4•-•Z P- LLI•-G I- LLJLU>-DOM I II ZI/IIIIDXG U IGG U ZIMCOLUM I- -• I-I-· •···••··•LJUI·•C3<U LU I-*7U LL3 4I-U~·•

I I I I II - I I I II r-n I I I II ·· I I ' ' «m I II U I I I II • I I I II •- I I I II -·• I I ··~ II - I I •-4 I‘ I N I • II U I ·· M I••• •· Lu M ~• I

'> ·- U -CD I-•• •-• rn Q. M Z•-I ~·• G Z G D~• •-• I G G G

U U U U U U

_. UUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUU

117

I--4Q I ••’ ‘ •- I- 41-. I- I Z G•LL14 GZ LU Q IIn r- GQ cz: zur- I-•-• w Z II··•LL• I.'•4Z ZG I-IG LLIw..I•-I U.122 Z •-I LULU I-•••I-U • E4 •··• I-• ZZ!-U w •-·• • I-UZ 4 w Z>•ZI-IJI •·-• UL9 Z I- BCI-L14 •-•..1GI3 • 4G I-LJ U ZILU 4•-•I- w ..1•Z I- LU 4I-• ZZI- I-•Z Z tw¤.• Lu I- E O . •—•<•-•¤:<ID LU mut I Z ILLZ 4 GG U Q •-·•Z

LUG 4 •-I LLIC34 ZLLIZ •-U X CLL1IG Z Z I-IG-wG LL.1 LDI--I·L9 LD 4 I- tw wI··-UI/:•-I E ZZZ Z t U www - •·~•I/IZ •·-Lt.1mw •·-• •·-• w II-LL1 ZI-LDw>-•-• Lg >ZI- t Q. 4 Z I-I/IZ DGZ>•..I4 G LLJZG-- Z Z G •-• I- L'G·-•..1<¤c GG_ •··•Z 4 4 CQ C1 ZIU • •-IG4ZI— >• ZUI-•-• G G Z •-IU4 • ><L54Z4w I- 44LL. 4 Z 4l -4 4DG4 •·-• IU-ZZ I I ..1 G wI-U2 • IG; UZ U GGu.1•-• LD L3 LI. I G Z U-II •·-•1- 1-• •-1. w ZZU Z LL1Iw•·-•Z1'E.' I- LUZ°•-4Z'L-U LU I I- w•-• w II-II-4** w IG4 •.I .-1 I- Z I- Z CB ZI- I-4Z>< 4 I-I-O >· >· LL1 >•‘C‘«

E •·-•-

I-)-4 -1 4LAG 4 4 LL. I LL.-JU. LL: 4wr-mwCD! LU I-LU•·-• Z Z G LL1 GG Z Z•-•••··•--• G-•ZG Z LUG I- L1. QLu> Z Z r- G ZI-G LI. In- - C2 LLJZ. I-4 •·-• •-• Z z Q4I• C •·-• N GI-LL, LU hl •-IUI-Z Z• • w I'.!4G G CI Z I·•lLL1G I *2-• •·-• D I-ZI- u.1 LI.! we t 4wZ-·• I- Z- *- •-I •-•4w w In Zw w ZZ I-• (.9 •->< >< D ZUG 3 D U•-·• I1- •-• Z4 Z X4 4 G LDZw Zw w CQZOI- w 4Z I CJ 4•wl LIJ Lu 1-•>· I4!-GD -1 Zt l E IZ>l G D ..1 LU GLLJIt LU LL: G_ZG -1 .J w4 Z UltI w U.1 w LUI-GI- 4 4 IZ I-• t4G I I I IUUw > > I-4 I- 44ZU I- I- I- I-LLJ 'I I I I I I I I I>I I I I I I I I

I I I I I I I I I .I I I I 1 I I I-I I I I I I I I II I I I I I I I II I I I I I I I II I I I I I •~ I II I I I I 1 N I II I I I -·~

•·~ • I II I I I •·-• 1- •-•··~ I4 I I I ~·• ~• ~¤• I-I ZI 4 4 I I- U >< ~·- G¤. I- ..1 I- c. z < G .1.1 LU .1 ..1 D LU :2 G In4 CG Lu LU w ..1 l I lG G G G G IJJ u.1 LU LU

UUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUU

118

\ .

Z Gu: x LI.CQu.2ZI·-·I •-•C> u.u.II•·-I-•I'.'3•-•··•IU ZI- In U-IZ II- I-~¢/IG) I" MX |¥•·• ZMc:<>·<::D¤: <ä u.I•-I •·- I- 4ä IZZ!-· I-- Z ZZZ GZ LLI •. Z•-•)•·-•5QgM •-• U.IIJ.I·-EJ GI Z C3 LuQGZULUIG Mb X2 ZI.L<Z III-LU •·-MLU Q.Z•-·•<_|..I LU M: •·-••··• •·-••·-nz < ...I•-·•.JOU.LI.I<LLILUI LLICB Z bb Z >~ZLU ..I U3Q.Z2UC3¢¤I- 2*-* I-M )I/H/IZ I„I.L’J LLII-•< Q.-I/ICD•·-• C: LLZ <u.I Q IAO I-•~x I•-•I.> LULUe,,:•«|ZZZ>- LLI- ZM Q:Q<I-L QI-I.&.I b I-Z ZU-I <¤ I-IZ CD QLIJZ ."J<b UJM MCJGOILUU I·-G MQ. )O O ZULI. ZU•-•Qzzzcz Q mu wc: mzu.II·- ~•Q< DZ u.:U•··• <•~LLI LU) <I .J ¢.L•·•• ZI-.II- •-•U I-I- ZQ. ZQBI-Q Q O Mu.! •-•v‘!v!<U¢/9—•)• ZZ U. •-I U.I•u.IUJLu IJJ > bLI.I•·-••-•UJLLII.I.DZ LULU LI.)- Z¤M><•—•<..'>>- <.'JLI..IUXZ>v'5I-LOG ZZ •-IZ UJCBI-)•-•LI.<!CJ <tLI.O LI.¤!I.I.Iu.ILLv'IuJ¤:•-e u.zU.I I-u.I G2 XI-011 QELUM C)C7 I- LLIu.Q.I··• ..J•J• MZ < QC!I—QCJI··•• O>t•‘ I„L\„I.I<ZZ <t UJLUX ug gI„IJIJJ</><)I-MQ b .7.,/IZ•·••I~

MZ •-• LIJLI. OIO-JZZMUJUJ MXUJ LuI-I- m•u.I3 nutte: Iu. I-I-·Q< Q.: Püx caZ I-UM ZUG IUI-• I-•··• M < Gbb .1I*-Q<•··< ZI-•I-IZGQZ-·• b<< Q UJ •ZOZM<IZZI-··I- )O•dI-<2I-CDU. I-UZ Z >·~Zt/)LI.•-•ZUJ-•U<&LI<! ZQ. UJ•-•I·•|-LZ Z GLIJ•• ZCDI-·•I.I.Q Z LLIZZIM Q.!-< C5 QZM ILLI-IM <I-· LUZI/I<I.I.MZ< U Lu.IU.I •Q.&/IZGU ILOM Z•-• C12!/II-•¥<•·-•ZI.L„•-••-•Z¢J7<t I<M••~<•-••·•Z LLUJ 21,07 D •-• C3 ZI-LI .JxMI.I.I bGI/76* I/I><•-•Z I-U Z CI->• Q.) Z MLLI¥• LULI.:GLUCJZUJGI-•·• QQII •-e ...1 ZI-LLIZQMQ. I.uu.I¤..ZQ I-ZZMGZZM< <UJI.I. I-xd LU ZGUJLIJ I.I.I>Z I-LLIJ 2b••-•

Q.•-•I·- czI-··•- <CJZ I-bGLLCJZ<U.J~<u.> )IL!/IGI·-LIJQ.•/YZ O<I~ UI„I.< <!LL Zu. ZCI- I-•CJ GO Q.<I<LuU-J I-OM O MILUO<LLM~M)tßP-Z UI-• -II-• ZU MQ. •-IQU <:¢¢¤b¤~<M•C<MP-xzw: cz ::.1 u.I•-·I I-- cc C7OUJIZ <UJ< >- < LLIMZM en IT.! I-bZbZ •u.II‘ Z ::3 G)<>· )UI-IJ<G·~ZI-2 <•CD < Z4 Z M ZI.I.I.JcQLI.»··••··• •-• ZM.; Z >·3 LU I.LI>I„IJ ~·•.IM OLLIG O•CJ-I I Z G' u.IMIJ.•··•<U..I Q.) bu. < 3 •-• U.:LLILIJLLH-·•LL¤ Qt Z.JLu VBILLU I-IIMILIJ U.) LU<I I.IJI• . • • ZITI¤•·~•I-LI.<OI-• II->I-• <¥b•-• N M •-•

I I I-I I I II I I II · - II ' I 'I I I II I I II I' I- II I •·• II I G II I ~ I

··-- I •-• I•~¤ I ~·¤ b·-• I ac ZLL •~ Q Du. ~o ..I C'.:LU gju, O I •-·

UUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUU

I

1

119

WI-J: asWLI4 Q ‘ MLIJLLILJ LU nn: •• an12 ac aus-- ca 2 u4

_ M IJJ 4 LU •-• ZZW Q c¤LL 1 . I-6LLI~·• •-·•Q • OC) M Q I--I WLLI W W LU 3ZQ Z1 1 IG- LU 1 C7

UJ QU-I D UL!-I Q UJ 1.I1 LJQ LJ •—•I·- QDV" I" LJ II/7 X M •ILW wm Q I: •-•>< In u.:ww GZ I cz-• Z >WQ O I- >-LJ I-ci O .JD • CU Z >< Q4 4+- LJ G

LU- I- •-·• •-• Lu I4>< WM1 LLI 9 4 1 1 IM LU •

•4LL-I WQ I-· 1 I‘• LLIZ VI 1 cz)Q .4 •·-• Z I- 4 I-··•·-• WW•·- ZGUI--I Q M W I LU 4W4 O M •IG4 L3I·- 4 2 IQ X4! I- •-·•I-LIJI Z 1 O W 4LLI Z LLI ¤LLII-W -WL') I- LJ W ¤c•-• LL W < WIW GMZ W LU 4.J CDI-W Q Q I-

LLI Z •-• Z LIJ Z GG Z4 I3 ZLLLI-I1 4I-DG G 1 LL M LLILI-III I 1 Lu*'*•I4 GZ! LJ I-I-I LL LBP- GI- 4 G IQ- •-< • I I- Z.! >-WQ .4 u. u.:ZP-W ¢GQ‘ >< I- 3 ‘|- MD I-•••LU L- JLu G LLII •-• Z W Q£• WG LL• LULJZW I4G 1 M P- 4 W LLIZI GW I•-II- I-Q2 I- Q Z Lu QW•-• IQ: •-• I- LLUJ4W LI4 4 *1 M > .I•·-W I-LJJ LLIW Q C}II- III I Q I- >~ D)- M

9 I-1I-U Z LL '1 •-• Q-J LLJI I >< ..I.I 3 ILLI-II •-IQ LU Q I- LL‘3< I- •-• << Q

ZLJM W Q LL LJ I-OZ 4::--• ut >Z Q CM P- LUII II O Z D LU Z...I4 LJ I- 4 Z LJ

>· P- LJ O LL LLILLI •-·•II II 4 Z .4Q.ILL 4QQ M 1 LL XQLJ Q Z DU fß 1u4Z•- LJG-G I- I- LU LU Lu •··• ZQQ Z-- zuZOO mit Z Lu G3 QCUJI- •-•GG W •-•|-· LL QI cc Z Q<< •-• cz I LIJ LJIJ-I4 II W ><< .4 ZOLLLLI ZQQ Q •-·• D I zum- QD': < <•- < LuLLGLJ r-••-••-• '5 Q Z I- M~W P*—|-I Z ZW I II I I I I I I I I I II I I I I I I I I II I I I I I I I I I I

I I I I I I I I I I II I I I I I I I I I II I I I I I I I I I II I I I I I I I I I II M I I I I I I I I *•I 7 I I ^ I I ·‘- I I •-•I • I I '7 I I *1 I I •·

. I M I I •· I I • I I ~OQ en I I •¤• ( I •-• jf I •-G LL! I I M Q Q ~• 4 I LLII C2 1 I LL Q G W .4 I Q4 O M D LL I' I W >< Q CJQ LJ CJ Z HJ 4 Q 4 4 Q LJ*"• '7 *5 "5 2 J J I I Z I

LJLJIJLJLJLJLJLJLJULJLJLJULJLJIJLILJLJLJLJLJLJLJLJLJLJLJLJLJLJ

I

I120

‘ C O · QLU LU LU MQI- I- I-UC I- C3U.•<< <u.!——QZ •<t <zv:•·-Q QLDLLD LU• •-Q MU.!D<L•LZLLI-M ¤3¤. QL •-A1CDI/7D<U.I•-·••••LU OD M

>< •··• 112 I-I-I·-I Z I-I--1I-I U.!LhUJU~•U>< CDI/I•JI-LUG U-• LU1 Q)-c¤ <•-n Z U.!LU:¤•-• LU Ma‘ I- .I U.!1I1 u.¤QZ I- >Q•···•< „.l<•-IIO I- JZ •-ID CJLUIC3Z -JZ-JI-I-UJ< -I•-SIZ-J-I •JI-U.!•-•<~··• UI: •-•I-U.!Q•·-•O Z L/I..|~··-MM 3 ZRLLUJI- 3 >M3M O U.!< DM LU O> M LUCDI Q ZULU X¢>< ZI/I XI LXW LU •··• •LUZ •••~·••·-·•LUI-U·-ILU •-•I-•I-<•··•I U.! I--L/7</1.1*3

~ U. 1I···•1CJZIZ 1 Z11I- 1 •-LU•-• U. I-ZI-DUJZU. I-I-<I|I- U. U, 3)-• I-• <LU<I·•Z U. •<DI-Z<Z CDI-·..J<!I- I zI*'I\¤IJ ¤-•• ZOI-/'ICDI•··• LL. U<$.'I- M UJ ZU •I-Q IZI- CI 1LU>Z v'•Iv7¤<uJm;u_v1<D¤3m¤. u.1> <LL! LL I/II·•M<.JD I- MDUUJMUJ M EDOZI-··Z Q LU u.!Z¤...!u.!< u.aQ ZLUI- LU Z O4UJ IZI-Z M<IO 2Iw ZM LU IDLU•-•D•••..I Z U.fJU.LU•··•>I-·Q. U.I-ZQLL 1 ZZI- U.!U! G LLGLLIO D••U. •-•LULL>·• U: •-<tU.Z•·-••••-•I•·-•I·- QM Mu-•Q<•···••-·•1</I U.! LUI-QCDOu. I-VII-·L¤•··· LULUI01-II-LUZLL„h•WI/I Q I LUC1 <•-•M:¢/IUJIZU4LUMM·I—LU~M>LU I-I-IMC.] MUW O .;I···•-..!LS>• <QIG LUU LL I·-•s..L•LUI- I-UJ •->·LU1LU•-• U. Z-JUJC Ol-U G O I-ZUU ZU U.•JIIIIZUJMO<ILI-2]:+-1 ZI-IJULUQ LUZ —•<I·-I-I—x—~Q•-..!zI-t:•-—-I-·•<t¤. cc :•-<·-••..u ZLU CZ < LU CJ ¤.M LU .C5 O<I I I I G U)-Z O -I•··• IE U Z 1LUZ¤. LUU UC •-I •-•C •-• .*3 CJL!JI·-LUG.Z In-- Z 2 I-—> I-··Q u.•···• LUI-II II <!I II LUI- C3I-< Z Z 1 XI-M1 <I->·• >· >->- >· 3 LUOU.!<<r 1LU UMU. U. QLL LL E LDLUZI LUI Q Pd •··• •-4 hn •-• •-e LU.} I-U.! QZ Q1C Q 1Q Q >< I--ILU Z Z' U.! ZOO CD CC) O < Z<ICJ•·-• 3Z •-LL! Z LL.! Z Z ~·•UI--4./I-I ZI I I I °I I I I I{ I : I _ II I I I II I I I II I I I II I I I II I I I I•- I I I I~·-• I I I•· I I I IN >• I I- I• U. 0 Z IU •-• LL! Q IZ CD Z O IP- C3 X U LU

Z Z I Z Z

UUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUU

121

_ •ZZQi-! LLI an•··•< I In C:I-Q C I- IV! U-I4I-• Luth I4 • Q:QV7 I-•-4Z I·•£Z' LUO •"•LU th z- Z -• cc a za vsP-•LI.I D O)- LL.1¤~ <LL1•- •·¤•I LUI-•I CD •-•-I Z6-••~ LI-III-• I-I-· QI—• •-• I-LU Luv-• I--1 LUM 3 > <> ¤¢Q• Q Q•• MI QDQ( LU Q*·• U4 OLLLUQ D Oaa.1 cz LLII-· zccz I.1.a..1a GLI.1 -·•·-·I- cx. ..IL.> •-GQ LU •·-tJ>•-•Z LULLJ G LUU >Z I-UI.IZ•-I LU UG. LU LU •>gJ• ILILU ><c¢¤< I uv! ¤¤•I.¤ cc--•<Z QQ LUQZQ I- 4LLI MQ Ol- CD ¤.UJ Z

I--•~ cg ...I·-·•L1. I-••I::¤ LI.

QOM Q• Q -.II/I UUZUJ UJLL LL1I I-UI-I LUI/I Z- •-•>·IL u.1u.IDLu II- I1 I- th I··M 4•·~ 3-IO >ZOQ

-I-C3 I"O U-Luth LLLIJ U.I 4 QU-

Q 4ZUJ 4Q >·Z I-ZLU ULLIL9 U U.-I LL.LU •··•Q I- I-•-•• (4LIJ ZI LL• O4 GLU •I-L- •-M •-•Q• I Q! •··•I·-LLIO •Q' Q

QJGLI-O I'-QLÖIJJ I IP QK •CD • C) • (LIJZ (thI·-th -.• CZ C)

QQ Z .1-LU QLLIQ4 CJ-• LL I·~LLä I····K QQ4 Q•‘·• LLI..JZ OZ Q .-I >-LL; -II- UU Ua u.:Du. LU >c¤a I-•-·•aI.1. I-ccm: LU LUCDMZ GQ DG U—II- •.I•-• U -• >LU >th z -·-• zw -CLU LIJZ zu <t cu.: ILL1_ th LU•.-J LUth I-QLI.1 >GGU ZZLLIQ th I¤·-°I- I·••

LU I- Zth••·• ZD ZIQ ZLLIZ QDI-I th Z ZQ Z MGB ~v LUGLI. U •··•LU LU•-•_ILU ( LU2 LUL9 ••'• ZLU Z I ZQ-IQ I-I-Q.I I £•-• EILLI O •-•QI I-• UJ•LL •·-C„‘¤.Iu

><(•·-·I··· LU LUC "J I-•I— • ULUO OLLQLL LUI¤•I··• •- UG U

zU7I¤¤ MZ (1 ( (L1.: •-I.II-• (LU 4U- U- •-••3 MD ..1*-•LIJ G4 Q LLIt.J3( I JM ..1O O ( LU-• ¤.QLU .I€-ÜO >><1 Q.:) Q

QZU-J QI-· I/IQLQ GZ4-I •·••I-LI CI II V7 V7Q Q I··•°"‘V7 I-4 •-·•IU UE'C( I- XLL1 •-• •-•LU LL1 M 3 MQ COLU •-•4-IQ ULUÄZ LI, Q• OCC G- C3 LU C I-..1 O LU¤¢Q..J LL. Q.Z Z LULUQ LUI- LU• ( LU.-I LL<I-Q. LU LLIL1.1 LUD D Ivsa II- IOLL I->IL: LLD(¤. 0 II-- II I

I¤•DLL I-•-•ITUQ I,f)$I¤• LI.IGI( I-—M I-

I I I II I I I ··~ I I I II I I I

•-• I I I II • I I ¤- I I I II I I I Q I I I II I I I G I I I II I I I • ·_I I ‘I II I I I ··~ I I I II I I ··~

•-• I I •·• •·~

I I *"• -• CL ¤~ •• ~• ~•I I - L9 0 •-• •-¤ I- I-_ I I Q. •-• • U —• v; In -I I LU M ¤~ Q LL Z D

G I a Q •—• < LI. •·-• ..1LU '7 ...I -1 ~·- Q LU 1 Q.Z Z O O O CI O C3 C?

UUUULJUUUUUUUUUUUUUUUUUUUUUUUUUUU

II

I

122

' .C: uuG I II I- Z x • I-I·- C: < •—· 4LU I Z LU • LUGUI I- Z ,, •LUZI-Z

G Z I- I- <I-VI •-•Z•-• •-LI; G G •J 2 G••-• ••-•I·•VIGL.: LL u.: an I Zi!-ZZ Z at ··~ I ZLUI- ·Z¤CGZ-•u.: •·-• cz O Q LU 42 I.L1LI-IILULL u.1Z G LL LU .1 -I•-I CSI-GI LLIILU Z I- >· LU •I-U ZLUDUJG II-•LL G U Q1 G •—• UJCJI/SUSE I- >-L; I- LU G ct • 2 ZLUI Z 44 G-J•- U > I- I- • •-• GI3 GZ-J LLZLUQ LU •• LJ L/1 •-•

•-••···u.•--•¤.m G4>

>•cgI¤-· LU u.1 • VI I- I- G IALU •-•...| LALUZ > Q V) •-Z4 GG•·-•I- MC}-< GLIJILU gg Lumccj 1',!ZLiJLUQ<! LUZQx 4LhI-S' I- VI UJ x-•Z

-I-¢/72 Z I-LIJLU .

I- G>¤~¤•I.u Z •-• U I-USG-<h Zi•-•.-I-• 4IQ.Z .J.JLUU LU I I/7>•U¢h•-• LU 24*3 Zu-•LnLU 4 4 2 LI- LU .I -•Lh¢/7 ..1•ZGZ •-• LL1U ..1ZU'I..I LU LL- I Z<U¢fI>-ci L/ILUGC SLI-IZ

‘4<•-nd. U LU iZZ>•.Ji "**"I-ZG IILU G th 4 I!. LL I4!-•..I<U GI/JLU U CDI-•·I GZLI.-••-I G •-• G4ZU LU>-GLU G LUI- Z4LI.G</IQ. • XI-4Z4G Z.-! II- UI-x_•• LUILI •-un u.• I <I>¤4 ¤:4m•·-Z• 47.3Z V!LUZxZv‘I•- > I- ZG-I UZ OZ•-¤ •-•</I >· I-•-• u.1>•-¤ •··•>··¤ .1 L9 ‘ I Q-2 I1.4 QCJI ncwu1/I•··•.J• •-I CD Z IUUUJ•-2'l1‘°. UJ 4c:iG GI-ZULU<.J Ih LU IiII—•<•-• CLU•-••··• U clixLL! ¤„UGZUZ< • •I ••I-GI-4Z>< ~·•I GI-UZ GI-I···01 xLUZ•¤••Z4GL/I U'} x I->•4 I- GI-LU &Um2 2l-L, ><t •-•-Ins •- mmImmc:z'. >· •<<z.1 .:2

¤.u.Q.1I¤tU¢/IZ •-• LLI•-I·-•···•—«—• :cZZ -• u.1¤:LL!u.IZGU44>••-• Z x 4•-••-~>·¤£C I-I-32• G 4L/I LU JZ i I-•~ «~ x 4I¤..LU wl-

G. 3UJ LUZUJ4i In-4 N GI-x GI- L2.1zu 1-I¤tczI···•Izc: cz • •· ¤.ZI·-••¤£4 LLJGLLI- I-4LUI-•JI-4 LU E- P- I'·•‘•L/II-/IQ.-J IIUJGUB In uJI¤- •• Q. i~• -• LUG G¤•LI-J IZ

LU•AZLI„··~ ¤·~ LL! Z4 4 I-··Q•-lU4¤i I-xt}.LU >4•-•44 Q I- an •·-•Z' I 42 GZ‘ Z Z -I G In Xd) Q LU>·•·••LL1LL1LL1 LIJLLLL1•-· lU• • Z 4 4•-• •-• IZX-III ILUII-- vv-• N -• Z Zw In •·-44•I·-·I·- I-GN

I - I I I II I I I II I I I II

I I III I ‘ II I I I I I

I I ··~ I II I N I •-I I • I MI I •-• I ~•I I ~·-

••· Nl-. an )( hd )(•-• · u-• 4 ~·• •

'~• U Z gß •••LL O U Z MLL, I •-• LU ~•LU Z UI ..1 -*Z I- ><

UUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUU

123

*+6+6*hä*2 -

C3 +6*CD Q *+6I Z +6++I-LLI< *äLUI +6*Ihm -II--II-VI * **¥LLI.U • ++4+¤cCDZ ~•-• ++4+. < I-- • +1-*Zß-U

**3LU< 1 *äUJI-Q. LU +6* ·ZI/IZ C9 .*4+ ·G Z +6+6UJLUL.) LU *4+I> • SI ·II-·II·I-•—•1 • 4+4+I-Q •··• LL 4+++LL<LL • D 4+* ¢'~ •·•O1 ä* LU 1LU I- < 4++6 Z •-•I/II-·• Z •-• 4+% . I-• <

·-1'-•Q LU I- 4+++ ..4 ¤. ‘•-• 1 O• Z 1 +6ä A-4 LUIIZ U4 LU +6* I-• I IL9 b-LJPQ •-J Z -II-ä < U LJ

Z <!LU•-• U4 u-• +6*‘ I-•-I+II <··~ <LU LLLUZI- +6* 3*1 LL:•·-• LU•-I C} < LL J +6* ¤„*C) •I- ZZ!-• O < +++6 Z·%LL 1N 1.Z*"'•O3 Z 4+ä •-•ä C!~·- OG O I/I5}. VI O +6* LU ' I-LU LLZ •··¤•1IZ I/I •-• 4++6 Lu Z L/7•-• I-·<¤.G LU _I- +6* 1 I.LI•-Ü I·•LL: /LL <LU<U 1 U +6* LL ZZ ZZ

ZQ.1 +·~ LU +++6 <-I6 »-•• I-I•-•Q •··•¤.ILL In th *+6 I—·II·•• ...4- <.I1I" $(2G +6* <*L|J •• P-! BC !•*

Z O Q V7**

G*I·• I/I 3•· I-ZIDC CI-I-LU ..I In +6* CD •-·• I.ULU•-4 4/ILU1LU U<3IA LU G +6* Z I/I ZZ~·• ZZ•·Ih ILU< •··• 1 ää >- • Q O ZQ <I-ZLU >· LJ ·II··II· .4 ·-IZZ QZD

I I I ·I·ä < *7 nO•-• O2. I I 4+* z z •-4-.-; I--*2I I I ·l·+I— < •· I/II I I ·II·II· LU Q -~I I ·II··II· >· Z Q .4I I I ·II··I· ¤:I I I **

LLI •~ ¢~ •~I I I ·II··II· > ·-•

~M

I I I +6+6 LU·- - I 4+4+•—~ I- I ·II··II· cz—· ~• I ä* GI- 1 I 46* LLA I- "‘ +6*D In ·-· ·•I·-II-In Q ·-· ·I+·II·> -I "• ää>• N 4+*ää

«l~*· *+6

+6*

I

124

0-·•

" 41F-W•·~ Q

*7 -1 G•· P Q. ¢~(G • Z Qsu é ¢¤ •¤~ < QQ •—·• ac Q Q -Iß ~•• O •~ I--C C ··~ I I C LU••CJ ¤~I W U I-~¤. IWu •-•¤: •·-• < LU E• • W LU Z ZD LU

I"* I•'* P >• ¤• >- -4 U"'• U'7 LJ•·•·• -4 ° I LL. W U- .¥ • Z GG <• <- < G •···•

•-••···• M LU LU Q.

Z LUN U„.I•-• Z LL G W G < I M ILU ~• N < G P CD I •'• LU <MG M • LU I -| I I! P- LL GÜ" GM CD•• U Z • < • LU • LL •< LLC u.•-• •-• •-• Z Z Z Z I- •·-• u.;

G •-• I" -4 < < •—• -• -4 G ILU LUU LUG <! •J -4 LL! •-•G Z• ZG I- 03-·~ >< LJ Z •··• G .I I-G •-•··-

•-et W UJU4¥ < •-~ G •· <I •.4 ..41 ...JLU ~·· ZZ~·- E Z Z II < ac I·-LJ • • • Q1 • < •

I-- I·~ ,4Z Ind 3•~ •-• •-4Z< I Z G G LU Z LU•-4 '7LI4~• LL:U4••• IIGQ < >- G G GB LU G~•• ZZG ZZ}-• II ¥-CP .4 G I I U• g • (

_|U L- |-• an -• an

G •-IZG •·-•ZLU LU LU O LU LU U4 G Q• IIGG IIGM LJ U G G N I I GGQC ··~ - u ·•~ u. uC: C: I J: r~ oc > •-•

G G U LU GU G•• •~

·- LL. •-• I~‘!' Ih ~O •-• G I-I LULJ ILL LL•-• •-•

ULJULJUUULJULJUUUULJUUULJUULJULJULJUUUUULJ

I II

125

LL:C•-»

. 2 >¤:. O CDC .

Q ~ MLL.LLI ^ Q.LU Lß thM ~·• OZ

- LL •J ZCJU4 <!•-•LL U P--Q LJ v:<

4 OMLU • Mu-IU4 •·~ LU-JM 4* N?-UL3 ~·• UIJJ .4 IUC4 Lu I-4 °

U •-«I LJ xu.U 4 Cl4•·~ • LUU4! ·-·•·~ ZMMQ •-·•UJLLI ~·-~·• .4cS

-DU ..1.4 E

M < :.:4:44 :443I ~¤• 4/1LIJ LJLJ D-ZQ. Z ••• UU U4 ••~E QM!. 44 .4I-•O *···•C3-

••• Q.ZLu ‘· U •-•u.Q. •~··~ $LLIZ• nn Q h,|!~• Qu-••¤•

••GLUONZZ• .4-J •-•~¤ G•-••·~ LUU4 L/QLLLUQ. U..4:t UU >-LLM

4 Z ~·- UU 43n-•. n- Q 0.43Q. •<<: In/H-·LU U LLJ<tLI4¤ •• .4 Z¢'O • Z-Z• •~•·~ <<LI4 .Q an •|- ¤¤~ •¤•~O „ .• nt udn-•Z¥ nnen ••

4 •-· NZG- .4.1 LUI ¤- Xldnvg UJUJ Ü"Q. Z UU O.4 O ¤ uu 24 L.! Q 44 --Q

l§v¢'! uh

¤~ •—• -• •-e

. Uuuuuuuuuuuuuuuuuu

126

° *4%-*4***

•¢• ••

**••© • |_,|,jQ_4}* • •·•Qm Q. •QU.xh* ·~

•~•·~U\•-• •I QOQ•·¤·‘·¤· O oo-•-· •·cw ¤c‘•.J..JC3*4|· Ih mU\•Q. ‘ ><LU%- O"7C3I4%-* bd ••-•-IQL,L| 4Z• Q•·•·¤4l-I- ·•·~~•··~~·•~·•¤‘\Q

• I><>< U><">• '4%-* QOOQ.•-••·-•..| Lu Q._X4 •QZLLhh •„nIt¤ZZ~•G Q LL|•Z q_.,.1•u,,** •-•M•-•I-U •>¢• C3 •U0 ZCDC*LU••4* ••••-··~Q•~ U Q2-• OILUccx4%-* M•·~O •N...JO 5* O•-V3 U•Z •·•-

**—•QL{\•¤••QL|,’\ ••-• §'fZ• •(,§ •§-(/7

*4%- QU\•-•QOI•-l QN UJ•LL <'h•|J.JV7Qäh x-•~·•LQL.\ •~• Q•~ •~U-Ha. U.LZD-J4+* O•U···••-·••·~LD xx LQQLU •u.. •·..J>-4%-* QN••-•—•cnZ LLll·• ZCD:¢ NLuOQ.•**4 U-·u.|-LI-LLI •V3 LuU• ULLUJCJH-*4%- •£.)®LL-JO--I OG JZ!. ••Z •Q,,*4%- •-Z~•LU¥Z!•• Z.! U.I•4 •·-•><><b••Q**

O•··'4-l¢UO• u.I>• •·Q¢!J U4!.'</QV7*4%- U\!ZuJ•DU•-• -I• QQO nz •Z>*4- -¤•~U·-c¤ •·O wQ ¤cZ• U¤.U•-••··||·* -"*UQ•·•·~L¤ ••I CD•G •·LUZ'£Nhä- ¢‘¤O<w-Q•··• Qx CJU.„• w••-•C¢><·I-·¤· ¤•¤••·-nom- ¤c• www ..:Q:••hh ••—•••«m,-4:,9 Q•1 •»u.x•··• ;gQ•L|,•-•4%-* •-•·Qu.·-·•—-Z Q°Z Mzw UIwu.><·I·* *'• Q~JL¤U.•·I·-•u.2 U• g,:•·Q^ DLUQu.¤•_**

O U7~•r-¤LL|¢V7..J •O •I.IJ-Id QS•CGL9*•I- lß v-lL|J~¤•O|¤-Stu Mw- NGO)- •L'äU•Z·••·«l·

•-·• —-c•o•·w..•• oz uf: •w <2$¤.w*4%- • NQ~•~QQ.•- •• •UQ.Q |•··u.•Q..J*·l· G ULJ•~O-JCBN NLU •-•'7LIJ..J LU.JQO|-4%-4%- L!7 •I~OI.¤>-•• Q2 U•Q>·- mU.!Q••**

•¤¤l ¢•!~••¤| •¢~cQ!**~• O-L9••·~Q|.n •·-•U CIUJQDN 4l-•C!Z4%·*••·V7 =!\Q•xQLt\•—• UZ Q-|..J •>< UJQ..m•-Lu·h··¤·Nw •-•u\·-<m•-•... ••·-• :¢CD·:• qggwcn-4%·4|•|< --•O¤3•·-•~·•>< UJI ZUIZ•-4 44/7<••-II·*OZ •-·••·L¤O~·•P·-•< ..J• LuD-•>< •¤Z¢.9><*4%-•• g)¢H•·-••|·—¢./72 ¥LI.I IQL30• -l•••-eq**I•• •~••••-&Z§D UO D-••U.JLD LU}-LLQAZ _*4%·|O ·•wu.cID•-••·· DO <u.Zz U.JU.QL5**4LQ QQILLQVQZV7 QU •~LIJLL•U-| ULLJUJ-J•·•·l·*~•-A It\QLU•·•'>C3• •I •·•xU.IUJ-I 4Q>¢CJV7*{ • •¤•L,Ju,~¤••••••• <• (LLZP •·**·l-@0 ~•‘7•Q.•·•·-N UJQ •~• U‘l•**¤'\UJ4•••Q¤’7Q• xC¤ OU I ‘**«J**LJLU•*OO-\l7O 42 LU•-• 4**4~••-•¢O!h •N•¤It'\ ~·• Oh- Z**LULLO4L¢\•-•-><~¤-¤ |•• LU 4 >¤*·I-Qt!-LI •-•~•Q •L')•·• 'BU ULIJI- Q·¤··Il· uJU2—·•-¤.n•~•-·•><OZ: •-·•¤w*4%-I--! OQQ.-*¤¤tn4l¤•¢ C3•-• .Iil-·l·•-• ¢°'•°G3•-•~•QI••'*LI.|P• IQ.: CJ.:

UI.J Q4 LL**¤¤äL92uJQ¢I3><QUJO• •-U4 U •··•4%-*-J-JLUUJ LLJQ,4 Q~U LU Q. ‘**&4|-I Z4-J 4 V7 QOQ4%-*ZLL|Z•···• XUJ4 LIJLL -I Z!·•Z«u··¤·•-·•¤c•-•Q Emu ¤:•-• w www:*4* 4%-***** * 4%-** ***4%--1%-*·*•I'*4%-UU

I

127

4+*4+** •4+4+4+4+4+ Q***4+*

Q4+*4+4+* I4+****

•4+**** ‘ LU-;+4+4+4+4+ Q •·•***4+* (j RX«I·4+4+·•+4•~~ cc u •-·•·-•

*4+**4+LL: '7 *•

4+**** lu C¤Z ••·~ MN4+4+4+*4+ N•Z•-ea: C:•-·• -~·•4+**4+4+

•-•>•D LU DN DU4+**** ..H·-ZG!. I• dz**4+*4+ 4*-* dd lud *3*-*****4+

n-•ZI-•L!J< •I-— C32****4+

I-DZNZ LOW U•4+4+*4+4+

•-• •·-• ZQ ••-•4+**4+* Z·3G<< LLJ.J ¤~«·-44+*4+4+* •-«•--1 I- ..•>· ·-·••4+4+4+** lud lu• ~•~¤

***4+*•• •LlJ¤:Q ,Q me

·n·4+«•+·¤·4+ ·~UJIO GI uu.:*4+4+4+* •-AGP-I-LL dd •C3

4+**4+*•·O WO O• *0 ·4+*4+4+* .JU• 3‘7 •-Al)

4+*4+** ~·•'7P-Q3 UZ -Z4+*4+**

U ZZZ •• N•*4I·4+·¤·4+ z••-•<u.I mc U-4+*4+** •-*><< ~·• Ljlu A••-• « .*****

Z•~1•_•~ •Z AO an**4+4+4+ ¤:•·-·q;lu• N• •-lm •-•**4+** •I·-•v7•-•G¤. Ulu ~·•~·•

•**4+** V'I<!ZCOO •Z •-•LU•‘• N ·**·l··I·4+ lu'£G7Ud •-•• lJQ•-* «**

*4+ •-* U *7Q. Ut.) •G~·• U4+4+ 4+* Ulu • •Z •'-U!-* Z4+4+r-4+4+ •·-Q•-zu„Q Lu•- ~•¤~ •-*‘*£J** GCZGÜZ JZ •••• ai¥• LL!•¤••¤~ ••e•*4+d** r-• GI-Z Ulu Ze-4-4 ••-•4I··¤·l-•·¤··¤· r-wucac :5.::---Q N,.*4+l/7*4+ d2 lu!-*2 c¤QNluQd -••·~4+* *4+ lu•-•Id+-d •U|-JOh- U***-I- *·I· CDCJU•-•<m dZO¥Zv> Z•*4+ 4+4+ Z'7<lQUZ lu •·UluQ ¤·-••-• “·l·* 4+4+ LU LU G x

I:•_|gd •-•

**lu** ilu 7-•.J•<

|Q••~>· •Q ||**2** IZZ V7 ‘¤' (•r¤l• •¤~Z ¢¤•**l¤•** UJl•D*'-*L°JLL| O- -an-••¤~ •·-••-n '5**I-*4+ I LLGZQ U •-·•<3•·-4 •2 '7•

· **3**I¤-•LL '7•-O D Q-Z•~• •·-•• Z,]

**@** @* GE} Z *•<L|J@ nenn •~•4+*d** O OU-IZ I- -IUJ-II U• •-*Iu

**Q**Il/III3-J ln ddlud luZO NQ

4+*:**ub-u•—¢1..1 lu< z•·-•m m·¤Qu.a

4+*l/5** .luZI-U l/ld LU d •I • Q3** **

LU OlulJ 2 Z -*•·•-· •-•O"7Z*4+ *4+ ¤1‘CDZd •-• l-O OIIOZWIIUN •-•I.u4+* *·I· ZLuZ<d•• I-· •-•-* •-••··•<•-•Z>.J +-34+4+**4+ <.Jd OG D Uv! UJdZ O ZZ*4+***

LU •L.)II Q •-•Z •·-·QdcL•-•C>O Q•-•4+·I·4+4I·4I· Q Q: I cc ..:u.1 ZN •-4- ub-4+***4+ d\u<DLU3 Q Q.! un Z Z****4+

UJILUZIZ 3 Z*-'* dC OO O**4+*4+ dl-—d"'2|-*7 ln •-Q ILO UO Q*4+4+** 4+ 4+4+**4+4+4+ c oo**4+** A N lbs?****4+

*4+*******4+' UUULJUUUUUUUUUUUU

1

128

•OI1 ¢~• M°') ilZ ••

Ü Q2LU ZZ IIO• anU •)-•Z •Uv-•4 MLLJ2 •-•¤¢• phd

Q •Q „Q •2 NOLU ~••Z

. • U<0 ZZ •-•¢I-U im •·~_| •@ •

·-LU •2

§·~O • CD ZLU O MZ •·• _Z Qt I- _ <• O •)-• ¢_ LU O MZ O-O U un!-¤• LOO • •—,¤.•zQ} {Ü •I"}•Q

U2 U O- -IIU» • • 3[| •··••*3 N ¤.·•v3C•L Z U 'Z•|-"'3O• • •—••Z•<|•LU •··• (Ü!-••|¤•

Ox Z U U*··•<O•||•··• • •· Z•¢<'¤¢O•~C! U LU •·••§-I-°··•OI*3 Z .J•*~! •v3•• .D•¤:

•-•···>¢•··• •-•Z··O _¤•Z2¤·• 2UJUNUJ~O2MO*3OO •Zä•IUUOI·--2*: Lu• zh-Z•Z• -•¢"')• QLU•I¤•••-••'§«f1 \,L,|•¤••Z QQ<L/3 •ZIl\•••••-• ZQOD UO!-¤OO••··••·•O •"'3¤Z *3U%-IN•|-•OO"3 ~·• '3 ~•2<>~y-Q••·-••-•• _2UJt-•• <n~•~• \•-•\•-•-·2 DOZOLULUOQ \•·•\••DOoZO•-•<.J¤ZCJ xxxsx2~0P·*3U¢UJ•··•O<¢ -~••-·~·•~•' _"3 ••'1¤.¢IU¤h¤„ G-•|-••-|··•|¤-LZ•|·-I-LU 3 2 <<<<<!c£OZZ-I 222223<•¤•r¤•~··• O-I «J dddßüil-OUJ¢%I Z<ß<OOOOOLUZ¢¤.¤.3LUUZU*U•LLLLLLIL¢UJ

° OQCDOO•·~•t'¤~0N®

1

129

46** . ’1+****·I· _********·It-*** l-I•*«¤· ttäüä ww ‘*·)t·•I- GU-***2GW<I·**•¤•LJZ***

'7<ßüßw xn***¢LL!-LU***LUG G***LD >·G _üääwwmu***Ü°F-

F. ••**4I-ZZ• 1****-|UJUJLL •#§# ZQO m**·I·LDLUG ~¤#**2Uum 0 w***~w:Z w Q***2

Z Z•·~ Q****3G •·D ••'* U**•l·••·•&LU.1 LU•· G ' *7***t/ILUCBG G10 G •****0NGU G•·• •~·I|~**<ZLJ ULU 2 7 A***

Ü xa UJ * •***>Z¢h •G I N*

·I•G LUZ *7LJ O- ~·•ä * Um~ ZZ m*¢/7* •.J! •• . ···~ G*LU*LU<LULL U.»•• •~ ät G*·G*G IG 2-* G *•* U*G*GG G ••

*7..1 *7*LJ*LJ|—LULJ LJN • •~• •# äw Zw z— w am •* *

•I·• •-LJ Z -•G *7*, *•L0 LL ZZ • LUG •*|J„l*L|JZUeG. ••-• GU •··*·I·Z*G!Zt·~ LUX •~ G Q': L,*•··¤•*GD<¢/1 G• *7 LU LJII LU*•··•*LJ-I¢Z G-·~ • Z ‘7·~ Q V*D*1GL|-JZ LJ-4 •J II ||°"• CJ*G*|-LJZG '7• ¤'\~·• ••• •~• LJ*&*Z LU-I ~¤G‘\ •LU•-**7 M•·-•N'* "7*©*•••*>•LDÜ L/7** •'*G•••• ••+ •*3*GG LJ LULU OG-I •~•~•-l.;-J 7*%*1 ••QQ*

*•OLJ GG *7 ‘3ZU.J•·-• u.1••·||LULIJ *7G

* *LULUI-UZ UL.) Z-1l~•|IG LU Z•··*N-IGGLU Z~D***IU2•-• *7 •· GGG3 •~••« OGG ••-•

***I-Z I LU •··•Gu.LULJ2Z •*LJUGLJLJ2 •-I*** LUG ZZ G•-•Z7LU•··• IIZZNIIM GGIII-***LUDh•< *"•G II-I !-LU:-·••-••-••-• I-•LU¢'¤~1‘*7ZLU«l·**•-O

•··•I-•-• '> ZD I! ZD-••··•

•-D**-I·<u.1•-•> Dv'! G GZGIING GZ G0£Zyääxm ¤ZOc¤ u~~¤¥¤ u~~~m¤¤ 7**#w IO xwuv hä »Zz« h***2wGZ mic Z Z~~ Z***LUI¤C•-• G•···•LUG GG G¤¢¤G G:::L3•-U.: WGZG UG LJ¤•¤„G LJ*** GG GG G —**~}# GU* N-·* In***

•-4 •-••-4 •-•**4+LJLJLJLJLJLJLJLJ

130

•·G4*• I-¢~ •• ll

0 | an4* In -•an | •

E " '“• Q- ·°O N P-

U 4* •E I- N

Q Q Id¤¤ • ••

Z I~~ -4* 4*M xl I-

QD 0[JJ • • 0 fdO X XG M

„ Q Man Mm •U x\ xl- NZ I-• I-•• M 30 (• {0 pg*

£I•‘•Z| •I: mm m m••~ UJ|Mu.Il M _NI l/7• •m• •~•• O•NC• NLUGce vs4·I-mm I-¤u.I ZI-•ZI-· •UO <•r¤<• MIQ ¢••¤•£• M•I.J I-I •I*•I •-2 NN N N ·Z• I.LIIf^UJl N 1•·'~ C.•I·-G~ I-r-II @••Q• ••~••· u¤¤¢^L.J¤¤ m

LUIIX WMMIN MQM h•• }- •OLLI l.I.I•NLLI• NUO I•NI• N·IQ F-•|I-I-I I- —0;) ••-••••-I •ZZ •|l\'\•·•••g\‘\0 Q•MQ•\M

U-IO t\|••N•••ZG |·••GNI-m•·N•N •¢\|•—• •(\|}p4•·• \|-I·•\I-•~OI··•

OOIII- \••\•| •FGIZ LU\\\\\•\•-Ind M Q~••~•M~•~• er

Ox ZI•!···I··•I···I··• P-ZI--U-•U*¤„ •-•<<t<<4 41ZZM I-XXII! ZDl-••-• Zxttßtßßä ¢£!*'*OxxG OOCJGGG GLLIZ .¤.Q„O *L.}LLLLU„U•LL*LLxLU

OOQOOO OU°M4*~Of~G O•-I-••-••-••-•«-I N

I

‘ I

l3l

*********32*3I 4

*.

****#* •~

***>Q

***24d***~mWW ·

***¢>N**I*·I•••l.U••¤•Z

***~@FC***¢WUZ***m#w***NZ&l***-|••¤•V7O***O WI***IG¤W***~m

U***

Lu•Z

***~~mW***•Z¢¢***¢OWW***

ZUW***• WL***¤##~

’***W</SZC#** <~z**>4 Z**C C3

***Cd! — l

***•Zu~— .***C4NX C

***2Z<• C C M.

***4#G2W C C H***CMZ C C*

*£x WQ •- Zä

* ~#IU O Q <* *•uw#: Q*G*I UJ • • { °*Z*#WOm& O O*4*QIü¤O ¤ W W M*Q*~»< w • • Q*:*3 4QZ Z z*

*C• ZZ • e • 4*

*ZWC4D W~ ~ ~ C*

*<CZC4 QM • • -{*Z*CC4IO G• 4 4*C* U U Uß ~ M M ~

•*¤*W:# ZM W ¤ W ~ h##*4 W•> ~W W C P C P 0*U*4WWZZ CQ Z D 4 O 4W•*Z*IO424 ZG P U WM U WMM#3* 43 4U M ZM4W 2*4WIl#&*W2<4Z CZ —+~C *l*C4¤* *I!IC— I N 4IO 4IO¤C*

*#DmU Z WN3U WN3UH~* *

4 M ZD ¤ 44 2 44 Z&~W***WCW#x O~O MM CH0M CH* D***#¤:<w ¤WHCNI zmni Z4CmZZ***3 O-ILD P•ZCD•¤*-I3 LUP-43 LLJ•-••-•-••—·•1***&I #W UWZN #3***2UW # 224 ZFC***O4d&Z EMCO DWZ***UW4C* WCIQ U¤W******

C#** 4*** N***

'UUUUUUUUU

II1 I132

*4%**4%* •

*4%*'7*41-*

Z*·¤41·•

*4%* Lu*•I··¤-¤z Z •4%**D IH- •· •~•·~***14- UD U -••-1 ‘

*4%* < Z •-M-**14-1 •UJ|-·•14- --• 1"^•··••***1-••~ ZO Z ~•N4%**-D-~•1|-1J •- O•4%*M-Q-~•CDZ1/'1 O 1·~***2*-9LL.OD D CD•··•-*4%*OZ Z-I Z D-*4%*-ULUO D•• U4 U1M-4%* •4<uJD·- • •·1-··¤·**••uJLuIO~ gg am „-4%**** 11••X~•• Z •-1O 5***"'7•

D LU ~¤-I •

*4%-*•·I•• •LuI .-I 1*1)* M‘****•·•1·••«~-I1 U4 U•·

~*M-*—•L9•-·••··•1·- • •-·• QM-**DZ•••~·• • Q •••-·• :4***114-IM<I•·I nc •-·•~••-O

*M-*D-IUUJ•‘*1- C ~·•D 5D •-4%**-D •·¤:•-•LD O NI •U N4%**UUJ-<~•Z U U1 !"\• M-

x** F-IIJJ O Oh aus**¤lv* •}--• •NI,J fh •~•·~ Q'7 M***10 N- U -•-•-• ¤:• .:***1-1-1••U•··•• •|- • -·•• CN Lu

**1-1••·•v>•-• N •-1N CS~ +

**<UJ-<•·-Z • U U~·- UO N

·I•Q,·I•ZI•~I•-LU><j•¤~ • •1,) vg •¤»M-OM-•-•-J~·-•¤·=t •-• ·-• •·~Z

·~¤ «¤·*1*GO""<I1" LJ N** DC -•~¤·~¤·~¢'\I-I-Q-*1IU -*1441 • •Z •Q

LU• (UO •••\,|,3*·

4l-D •<~• M ,}•-·•

Ze*LI-I*U-1vi2~mO¥N•·-U-4 O5 ·-•--•-JN*2* NUJD W-I U•NL-U-• ¤£• DCOM-*•··•*I·~•Z•·•-I<>• 231cB.-JO O-1 111**1-·4%2U•-·•1··<I CDI- ¥D O~• DDG-·••'~*DM-•···• mUU • •<n•U}Z UD DDD.}-•4%D4%D•DU-1CD •1/7 <OIDu.1 •1 UUU1-U—·*1**71/7UV'1«J•‘•1f1 Lu-I|¢‘¤• ··~D |I|-U*°;‘%§¤„$zm¤"'§ 5*** "° "S """"Z*

U•-„--•-•

• ¥¥>¢¤:u.J*vl*I OVIIOI-• ~••G •-•~·••···••

•••Cy-J

**1-•>~•·-O1-·-D10 c-I¤~•U 5~·•5 LlJ•·~••~r·-4<\1ff11/)\.u

4%*

C1-1 Z (31*42 ZO• Z•··••-•—•~«—•Q\

***O UUO-LUO 1 .IU-lu.: •1O •~•·DDD1I•·•***11-1-U

D J Q. <1-4 •-1DIß •-••·-•N111·•-I***LJZ1LI-|O•14J u.J<14J DN ·•~•OOD•-•u.J***UJ14|•-•ID>-•-• U4 1 IIU ||UUDOD--IIM-** ZD|—·<h->- Z Z DD •·1- DD ZZUUU1-9•-***OLU •-• •-¤ I-D N¤"15DZLLJ~ON•·-••-•»«|I 11|I2•-•***2-Iu.J•·-<UUJ 1- •-••-• NN <•-•DNN ZZ•·•N¤"•u..|«***<uJIZ•-••-•I D Uv'! DI-U12 OIIII-I-1.-J-1•-•4%** •·•~UJ1-I-1-- O •-Z 1-b-~1'¢¤.•-1-1-m5:tL1.1uJLL1uJU***:1 zum cz ..au.• zzrv •-ZZN***<UOu.1u.•<¤ cm ¤.Z -••·-• Z-~•-·•***1-lJ<Z•4Z-IZ D Z*'• 111D D11O***gLU<LU•-UJ< gn •·-•O ¤.¤.O U¤.¤.O45** M- M-*4%*

O*4+* ¢**-1% N*4%*UUUULJUUUUUU

133

N N(xj n·I$ •~ WQ nn I- '••~ ~• 4 .•¤I M Z •nnen}- •-• gf •CÜ*••I/7 I •Z-·Q M • QLux-I O • LL. II...1*-)- CD O • •~ ‘Luv!• LJ I 0*Q•- I M -'I" ~•~,-|l¤¤• Nun • [-• ••-•>¤W 1•(\] • I {Has• •I•¤@ (H •-•sQ

‘ <IIZ U‘\f~•tl\ • •••W•~W LIJI-¢‘I¤|• I- ••* •O

age,] gl-••·LI.J•• •-• —••-d•-•< •W <•GM• LL NLL.••~•h¤•• *~D4< •· g_)•

- M\~•••·~ VIU-II-• •··• Ih •lhI--W•• I-·I-'•MI-· M •~NVI!-•«J¤• Z4NWM I- CDI-G•·•¥C3 •-•Z •¤‘>UJ •· ~i"~„J•-•UI CD•'·*f*ZZ N I-•>•NDM ‘7OU.AW¤-4 • ••·¤·Q• M•I• G: 0u

uni ¢• ¢~ BJQLÜ O Q. •¢~

•¤••¤¤•••~•¤¤• "" Ih ••-••CQ•-••-• M I *•‘!I- N U7U..MIQ-N Q LL)-NLIJ• I- Luv-g:g• • Q• I • • Z\h•*W!-•~ ¤•• *NU•¢/)••U'I •••N•

n•QV7•-A • LhOLL¤:• Q I/5I¤•~¤•¤¤•€\IC••· é LIJ§'* -IM®•~@ •N\'••·l•-JO '·• I··I·•Ol/ISI-•LLI'¤L_)•¢•J

_ •-••I•)•C ~• <•l'GIJ-IQLÖ •• •‘ NNIZ N Z•I¤~•-•CGl¤C3 II •

•N U-! U •-•lu••-·£.!·-·••-•Z•-•.n·•~O* •• • QI-•NM•>-I-LUCZ ~O•¤•|ßL-an •~• gd•-•LU •• •••-••I¤¤

•••~•••-•_|•·¤• • @Z•~Q,,~¢•I'*J•¤d|-¤••••··-••-•¤~‘I'•~·· •~ D•··•• DN~1'•··-•Y~•..J!'¤0~•~•Q•-4 4 ••• QD MI-I*••I•I•U•'··• •wu! •··~U-! ~·· Maß ••·-• •¤; •OZZIUt'*'\••*M rl U-IG • • ('h••••«¤0WW•I *< IJ ISI-W4•¤t •O~••U•-I.I~II•-•• ~ I-·LJZILL;LD¤:U••¤~•LuLU•···••·~·~·••-• •-• • I•~•I-¤:2IJ.Ju.•UO\\~••¤•L.L|• • •><D•4I-IJQ•¢•|„h -NN4 *«-JG WO I.h•'1•••-lIU‘~‘I'•·I···•J•JW*‘*¥O* ZN •-•••Q•LUI-UI·HI·••I!\WWM-UN •M I-Ih •f*'I0~•II-••-lII•|<LuD •-• xNO•·--•• xy-•~•~ •.It'¤|- OIII- xl-·•-Ax!-N- x•¤••·•O>I¢~•Z|-I-JO•-•ZW\\I¤-\\~O\ xx !~•~••4LJ •-IDM •·-•3~¤•~¤•¤•~••-ny-•« __

~mu.•:>u.¤¢2 cczzn-•-•···•-I-• I- I-I- ZUL.)M@•·-•¤.•·-•I·-•-*&•¤¤•4444< 4 << M

I-ZM I-IZZZZ I ZZ DZ•··• ZMMMMM M MM POOMG OOQCDOO C3 OC! u.:ZLJILCJ LJLLLLU„I-I•LL*LL LL.LL*MLL2

·I·. O OOO¢OO O CJ¢

ß *'*¢\I!"^'·n-OI'·• 0* ONN MNNNNN N MM

· Q 134

O

CL •-•••~*%*%* G •E •m%*%** <G •¤w Gm*****

wZ XWF WO***** %4 4Z• •Z•

*****ZXX ~X—

***** GZ ¤I< aIJ·*%***

Z4 w•£ •««****% 4J •UU M13*****

J GZ¤ •g¤•

***%%GW G~m ¤4w•

%%%%* m¤ Z£• mG¤~*****

W w•ß OIJ•#4%%% ~» •wm G•GG*****

4 UGW U*•Z*****

O ZQ% •¢~w

****% FF WU: eva;%***%

W JZ% dQ~F****~I•

0)% LIJ•4 ~•••¤,•

*****U •GG Gmwm

***** wwW G•G a%Q&

**%**mF *Gu• mm•z

*****FZ UWG ewmw

.*****

ww •wm Nkmh*•I•·!l•**

Z !'“¥U) _ LJ•••**·!I·** CLL! U•C•~ ••‘•¢\!•*•

*%***2%•wJ%**

**4LJ ¢'\!_Q@P'• •¤¤••g„§•

%%**

Z wQ•w ~wZw**U*% mm •U&G ~Z~Z .*%~** Z ~¤w4 wet-**F**

mG• Q•G> •X•X**4**

442 •¥J•~<~<~

**F**%G3 MCCN Nimäm

. %%w** FJO JJ•X •&•@«

** **m LL! ‘¥C"!• UJLLi„p•·-eg

** **FCB L}IZ•-I Z•~•0)P•

<l$*LL!** •·% 3••><•·~ —••-U.l •0)**2*% mmm w¤G•~ mmc-G%%~%% hmm ••wG| J~3mJ*%F*%

ZW <LZZO^¥GU~>**3*% W m wL•w•OUOZ&•**O**

£Wwwiw <&Zh|Zww•wM<h*'I•C** LJ)-L) •• 4•••.-qgevgth

**3** 4 LJ LJ •-•O¤•~•~••¢\!><x**w*% J Q m wmmm~X<m** *% ¤•mF**

**w4& 4 *X4ßWv~•• Q

** *% ~F F Jxwzcmmqh w _** ** G<W w 4~%WO<~GZ Z*****

G> wl4JUGmm3 •

*****W m w mu WWGXZG m .

***%% N>F Z wZ· <U M*****

m%< m h¥C J Owc¤**·!0*-I-

.44% F m m %!!\•-••-••-•%**%% <mW 3 www wm Q ·*****

mmh Q m*Z *GhhFF¢%%*%% hw~ x 44w 4wZZZ2m*****

mg G G4! 4Fmmmm***** ZWZ 3 IWF wZ%%%%O%#%*% ~Z< w ~mG

**UUUUUUUUUUUUUU y

1

135

_ CLL:

- hl

, LI.\ UI~ ne• 1-E <C} VICLL1 J I-LU •·~ FD

„ ¤¢ ·· ZLL\••C V7

LL,•( FüCOC

C-1 Zm• CUJLHC *·•LUMUJ I-¤c•·U •-•@@2 CLUC< ZCI.! C

C< UOEG)~¤·-• CD_ Q • C•C I‘ •mu..1 LL:•I- JI-U~1'< •-•1'@C IC •¤. 3CMD .•-1 CJ 1-<•·I-• C <.J1'^C I’ .1CZ •·~ 1--

>- uam 1:LI. 1'I •w < C-• <C*/I .J V7 »C -|•-•U..I X•'• OC G •Z < O•"• OCC I .JU'\LL„ Z •

~·• OCCC * .J•-LL. O „M OCCOC I <~¤•-• • «-1< OCO••. < I•I-· LUQ QG •cc .1 mmm ...1 1.

-O O•OI||| X Z I >- .•• • 4O•¤¤•• •Q||•~•¤~ ( ( U, •••O--! LUOII-••-•¢\1 21. -1 •-I I- CCOZ < I-Qxu Z||•~•-••• •

-1 X Q .4-4«-14 Q 1;,;C<CO *•-Z *22 Z LU ¢ C I-•I-•I--J Q VIA ß•p,,|•-IZCQ ||~·•@~·-><U-I .1 • • • cx LL1+< V! ‘

_ II •I-I-UJ2Q„*·*><<-IUJ.J CCOOCOOOC@\ CC-I r-••-CZZD LlJ¢h<Z¥DI.IJ\¤f'¤I"¥~1'1'*\l£\f¢\@f"I¢"'IO*~u IIC~••-•<•-••-·~Z¤CC!I!3LJZC 1- <E Z~••L„1•1¢M•-·•l.¢\„.1..J¤.•·-•D•-••I-I-I-I-I·•1·¤•I·••·~I··-·I·-1·—< CIILLJ QGMCQ.!-VGCOLUUICPCZZZZZZZZZZZZ m•-¤.| •.|

Z Z<•¤•••••-n•¤••··••··•v—«•-r·n•-nu-•x EC- VIOC CLLJMMMMMCZMMMMMO <C!3I Q.ua UM¤.¤„¤.„¤.¤•¤.¤„¤•Q.¤.¤.LL •-JZ3 LU*·I|·C C C~‘f' IG CBM I"°‘ 0*

OU

136

\ LL\ LL• LU vv• LL; hd·I(· •><*

X< IX •~ ••<I U*·• O LUEG <M •-·• QQ ¤.•-· v.u•-u. • Q-

LU UJW <•-·• I- {JNI •• I-Z Z ">><U GO < W D •·•

• < C16 <nZ• Q ¢_•),.•G LU YU GWCG U •><LU N UJ*"• LULUIMLLI er @6Z •W |--ZI·-•|- G GL')N UG <LL<I< G- ZZCJ •-- 2..1 ¤u.c:Q E mwLL G LUG- Q.•-•|-UG. 6,,}

Z .I6< DI-|••D • LDI-W LUQQ ¢A•- M Z-•··• •LU¤J W W O LUGLU QQZ •··•LUO•·-• • .J•·LL L.: ¤c..:< I- wc:LL Z GG-I XI- W O •·LL:LU LU O•• •··• NW OZM LD UGM •~ c.1Il-JLU • ct-N 6LUI-• an I~•{3I-Z' G GLUG' LU MZW ~·• <3LLL•. LU GZ< — > U•Q U. ZQ<t~·• • g_;•:}G G Z •LU.I— LL N I- •GG•-I ~ G G G N2')- LU WI W I- <'*"•UJ

G U U•• LL WI···• W UZZLU ’ Z •UN I UJ WLLJ M •><LU> ••~ LU ·I~ •-AZX •·~ ZI-U•••°.L° •-• NZI G•-• 4 I ·¤·

L.>•··•• •-· ILS!/H··· LL. L.:••·- U.:I- I I- • •Z•-• -• U.•-•>- 6;} •·-•ZQ Q • LU•>< M •-I-UO • «-•Z•~Q•LU C •·— Q -|LU• < I- <I.U M U-Oc¤•·-•LL • O N ¥G¢.3 G3 WI¤··ZI G 6Z IIILL -4 •-I I-· UGZ G W<U • 4•••")LU 6 GULLJ ·|» LUM <I LLJuJO‘•-•• • \ $2-I <! I!·~NLU •-4 NGLUIINLU I·••"‘I- \ *•I— G I-LL<N <G •*-•~GI LD-LC) \ <LU• Q LL: •C3 vg.: ¢'^ 1I- *I'• \U‘ LUGQGZ ZLUZI- OO LLI>••-4Z --¤~ MGIU.I< LUI•-·C LU u..•u.~¤C31 ZGI- I-0* <ULUZ-I II--JZ •Z •··•G¤•f'¤G• QCZI-< —•··:•·-•u

•- u.:-••-«::¤Z G JUDZEG I- •'**‘• ZMW >•I||WZGGG • WIIGMNF- U II•-• e-¤¤•GL."D*"• LLI•'I-• *IC:1 O' Q„I•···UNGG LU •-•~·•LLi LL •-• W.1LL~•••·* LUZ•-AU-L9 > LLD II LU G••~N-ILLI- IIGO~·•D LLLL OLLZ •GU GG!-•<LULLW ZII II GLL •-• ~OLLI•-4 >•Z‘LUZ Z LLLJ¥•-•x GI-I~LUI.J•-• _| MMI- LLGZLU —•••-• -II/IZ-I G-I Z ~·~•-••-•L9 OLL WMS-- Z< Q Q Qr-Io: u.u.:G-*"GI LUU G U C¢NLU •-••LU U..•U.•..>Z¢ ZgLLJ>I Luv-Z>— u.•-LUQ•··•—-QuZG *II•

*·l·•-·• Q

~0M

UU UUUUUU

137

•Q

G|. 4

7-.LU

- Q

4 M•·~ CJQ •-—U- LJ «Z LU .~··• >Q•~ 0 I-'7 LU Z L• Z LL:•¤• X X •¤•~•• Z U-I ..| ILL •~ • · Q < vsLL _ "5 O 4 > I-LU • Q .-I C2 ..JZ •-• Z ¤. ~·• 3II ~• •@ V7 N 7* L/7•~ Z OG •···¤ * M us"B Q UJ0 Q 4l- G M• „-I Z ·‘• V7•··• C •C Z •—• C3 •··•~·• 'OI U-7- •-• ¢~~·•¢'\7 \ ZZU-! UJII I-LG •-··u.·N• ··-·

•-•QD •·•Z•• UJQB U-I '·•U-* UJ M„-JZ ¤•'7 cc Q LLU-l•‘* 3 ¤„Q•-•L|J Qa-•• ••~

Z |,L¢•¤¤• _;II-.? Zfllr-• LI-O < LU+~•• 4ZZ •'1••I.U LL I OMLLIO > •Q•-• •··• LLD I-u•· Q LLx+D-••

- czUP- |I~'I’LLZ ZLU Z•*•J-J 7- LU 4Z •-•~0UJ•-•LL: ~•Z Lu ••-•<4 M > QQ MZPD LUO I •-•~¤>> O O QQ M ZZ > G I- IIOIIO U'! IU- ~0O G"! äCD•G •··•IIUJ||L|JC3 V7 4•·-·Of'7¤ Q7- LL.Q• 3 -ZJ-JDLI •—• ..1Q ZLLIAZIIO G G••'•«-|4ZZLU •O C] @°" "'*|-UN Z Z OOOZU-ICD U «-|•••D-I ¢'*‘7G>C!|--|*'• O IUBQHzum Q.: ..1< vz ZLAI -7.1 Z4LL<> •··• O OG-3 I- I-•|-7-—I·•

LU U-IL-7*'••>G O LJLU < ZZZZLI. Q M •-••·-•—•-•U. Z LU MMMMLU LU P- Q-¤„&¤.x •—•

~·-• ¢¢¤c~o~0~¤~¤ r~ c~MM NM M 0*UQL.7 UQU

138

N. *

‘Z~••X4• ZV) LD

Z MM m( G••• 1 an

-|·• •-•

•ll• V) •Z• Q ~•• nl•· Z X •

Ih < <t •~·~- *M Z ••• Mg;• an L7*4+*

•*• UJ M ·¤·~¤~ 44-*

UÜ ° U} Ö •*\••••••*«j|•|| U) • 4b •••• gg.

UJ •·~* 4**** *U1 G · N Ü •#** -I·

Z· IM • Ü N'} '}. CJ vi Z

*•-•*-- #

hu M *|/}@* •• ifI- Z X *LU•*Lh•.¤•*< 3 < #3-* •••*cc Z ‘ 2: *.1 ·¤·¤¤¤¤m-¤·LU M Q 41-4||*LLLLM*

_ F- X LU *> # •••·¤·I-• Ä G*

M*•••*I •~ #G•* 41-·•• LL M *<I•*|l|ll|*

M O Z I- •*¤M·¤~ *M 4 Z Z *0*-•Ü:Z>-*

Q • ,,3 •-• •••·* •-¤·<<LL#• Z J x X*

•#JJM·*‘ M D LU Q 4

*~·•#J><C3*• Z Q I * ¤€*UJ<O·I·

OO I- + Q*

4*C‘..IZ#LU0 2* <

• LU*

Qi-*Z D- Q G •

*0* #

-I·- O- m LU ac 4+*4+****MZ 00* Z > • ****Ü·I|··lI•*

"I-O In-! { Q UJQ CDOOQQQD —r-•¤\-UG O-••-C: J Zm ••••·••••

Q.D|*·\!\Y~N~•f'~*·ßII vs •„-• cccmmmmoM -Z I- <LU M OOOM OMNNNNNNNMN MD-•!"!-l•~<!I-*··GJ •-•N•-•|||·~LLI•-•\I¤-·•·-I¤·-l·-I··•·-|-|-

ZMMMMGMMZI M MZ I-I-I--I-H-|··•!·-!·-U-•CD O¤¢¤t¤;¤¢O¤¢¤¢<3 an •·-·•-•-•·-¤:~¤:M•-·<<<<t·<t<~1<<Q L.JQ„Q.Q.Q.U„QQ.J >- ZZZZ~0¤.l-ZZ'•£°Z'ZZZ«‘F.'2I!IG .1MMMMZ

4 GGGGG GGOOOCOCGCDGLU Z ¤„Q.Q.¤„Q LJQ.LLLI„U.LLU.|J•LLLLLL

4•-• M 0* Ih IAQIAOOCOOOF P- 0* ~D -••-•Nt'•‘\·•fLf\~0Y*·F'! 0*

UUU

f

139

*/1{ U.·¤· 1 •

*F •

*cn

#*

I •·I• 3_ •·

*Z Ih·l· •-• •

dl- >< 4 —**4 •-•

* Z G*

•

*•

*{

*{

* *.

*< ·i|•

·lI• Q{ G •·I· I •·{ < N*

-4 ••~ ä Q•-·~·I¤ U.*•* •{* •

¤II• Z*

•¤•0* { •

• •* Z • ·•h* F Ihm•··I· v1 ••I-hä 4*Q-•—I· I •-4 4•-•Q«I• 2 O '

|„;,•* Z •••{ hd •• { X

lI* < I 'II ·l· Z ·I•

•·~·I·<•·II>* ¤•·*

* 4m¢"'$·I· •Z*"** F •<•·Il· Z m ·_|•* KU hn I~•·I· Z •

Q*1LQ••~•-I·• -4•**U·•*

·I·{•I·*••·I•*·I• {•••*•(••'•@@0* •Q •••-••··•m·ü·mQm4I••-·•···•-·I·•-ZI-~•~•—•*—•(•¤••-D-I-*I-·-Jl-• Z<<<{< <•MIZI·I·Z SEND1114+1 1••-QOOO·I·CJ O$LLJZLL|4.LL.*U-V7U.LL1UJ

*·I· {

OGG O O ·$0** N M•-I •-* 1**

140 -

4+4+* •4+** mx**4 _ IQ·§I•·I+·4+

r•*4+4+ ~o·o4+** 0 . |•

***an an • 9Lf\‘

4** •··• N ··~u'\• Z

*4* ~·• X vd Im G*4+* C3 • G •| M)**4+ •··-• •·C¢ M- LLQ**4+ en Lux <!4+4+4+ I" G• •-••~ ·OI UJ**4+ Z GQ nad •• •M4+*4+ LU UZ LQ• LOW •~J4** Z "7W ZN I ~0<

LU *•-I UJe• • Qi4+** U CDI- JU ~O• U*4+* <

•~•• WZ I¤0 W**4+* •-I GO •*•‘I *h VILLI ••~¤••~**Ö B- €* ••I NN ZZ ·•••-¢-4+** vv ZG •-•• I•·

CD•-·• ~~~444 hd WW ••- ••~1• •-um *4}*

4**G •Z Q•d ¢•~ |¤~G 4+**

*44+ LL ZW GO ••I Q Z224+** G U-JZ M- ~O• •·••Z n~•n444 J•· GW •N MG •-•NM*44 I- WO GG NI I-*··• UUU4+*4+ W •\-U UG •• 2+- III4+4+* W G2 •U ~‘I’~1' QLU • • •4*4 ¤:>< dt I- un: •-4-n···•**4+ Z GZ 1-I• • tn n•~¤•~•4+*4+ W G • ~¤•·• Lh• XG ¤~| II

*4+* •·-• •·Z U• •• gu.: «zzzI-I L§~¤•~·-~¤•

**4 UI •·--•ß"I • <I-• ZUJUU4+ 4 < •• •dLI,J~••••-• gg wzzz* *

NUJ ~•QN-·~• Q _ILIJLIJLU4

*M UG NGXIIA WZ I-JJJ

4LL* G •G·•~ UU ••l· W4 \LUWW••~·•~

*LL* LL ••ILJNI •7••~L¤•~ LU •-\\\ZZznnnnnnnnn

4+-* ><•~• «—•-·••~—•¢I G LLU • ~•Z2ZNM

4+W* •-• <!Q•Qn·Q«·-••• Q I,g,Z•¤• <•«„.•„„g_;q__;4+ 4+ cc WQIW•·-•~·¤><•-••-• Q •-•u..1•— u.•c¤<.¤uJ**4+ *

•• ¢z£IZL.Ju: •·xI c I-...1u ¤:ZZZ··~·—4W* <

<•<••••••~ • WI-LU <WLULUZZ4+2* Z ~·•LL-O-••·•-•~0 OO ·-> *J..J...•·-•~4•···•* ILLL

LU-••·-•-•LUII +- LL •-I--!-I-•d•-•

4+-4+ W LLLUQZ--LL•~¤ Z•• ZI Z-~·•—-•UL.> -434 W- •-•¥*><<£QZ-• O•'7 U-JI·••M-44****G* LU P JIWGWX Wv-•• ZUG WG<<<<<

4+M* Z V! <~·•M!JW Z|Ied LUZLL ZGZIZIZ4+Q* LL WU.<WI·-G •"J-W JLU •ZI1II2I4+34 LL W MLL Z •'* LL3 WJG •dLIJ<<<<<4+4/74 n Z WZ *"• |I~OLLZ W Il IIGGUUU4 4 I- •-• I->¢G n-•~QW•-•W LUGZ Z<I|III|||I|* *

U1 In •-•hn4+4+ 3 UQW Lu LR ZZ I-IZ OZ-•¤'\|¢'“~1'*·¢‘

*4+4+ W G •·-4Z U ~DG C-·• Mx N<•«—n—•4+*4 I M JJLU LU •·-G UI- IGLU v-·•LDL9<..9L9L9U4+4* M Q ¤.<Z P- Z MLLI-4*4 G 3 ZW*•• Z G C GI-UUJ G*4+4+ LL W •-MG •··• G U WGG G4*4 4+ 4+* 4**4+ cm4+4+4 ~O~0444 _ -••-• „

4;;**uU_v..>UL.>U ULJLJUU

l4l .

Ä•• -I•J I. T

LD lb+ I_ 1 es'7 "')

th Q• •M G! X .LU sv vZ ZLL u.u. · C2 wu. LL ·LL G ILIJ LU•-• ‘ I-! ¥I- Z •~ II IIM LU Usa- •·~

I "50‘5 ""!..4 C; I--•• • •< G +uJ•¥ ät

Z G Z ZOC¤vLDLL LLv •-J u.1LU• ZX •U.Ou.M L5 I"'JLU•+Lu LUGLULLQ I-••-•uJ'7G„J:t zu-• ‘*

O -•-ZIZ~• LU•·~ Lu •~•-•|LU••-•- M GZ G ZCLUQ IIIILL •-J ZLL~• Z • •·-•Q•-·•¥-I•·-• LU LU:-• .N < ~Ou.1• Uv LUQ G •"!LUOI GD

. *•··*~·•ZU'•IILL ZZ

< Q ||Lu•-•-••—• LU!-•! I- LUG I-Z z '>Q··¤O ZLLLU< •··• Uvß Cl•-D<b oz u zII LU QIILL ‘ G•-•LU•¤~- ,4 •··•">•-• _ ZI-.3 .

~O ¢¤ UJZZZv I O O*·-Q!w LU c ua-‘:>

M ZI-Gan Ousz< UMLU

V C COCh <¤I~•-• •-••-n

UUU

I

142

*4+*4+** M

· *4+* Lu·¤·<¤-·¤· •-*4+% UJ< .*4** IZ**4+ I-•··• •~ •

4+**G••~ N •·~ ··I·** GMM >< ••

4+** GN «-• N4+** MUX ><-

4+**• • g;

**4+ •~ G LD Z#4+* •-•Z Z •-·•4+** ••UJ< LU Z4+4+* Gt- J •·I·„-l•4I· <- I- ··~*4+4+ U!-M •· P4**4+ ZL/]~·• CZ •**4+ ÜN •-O •• F5*4+* 00>< Z ~·•*4+* Q!-U • LU***

<ZZ U 0·i+«¤··I· mv-·• Z Q·l+·¤·* >·CJ ·-• LJ4+%* GEL)- E S4+** LUJ • ••

**4*(AQ!-• LL! es

- ·I··I··¤· LU ex Q ·-•

***•-•!-UM U •'¤•~ _ N**4+ M20 7 •-M 4 ät-

***0 Q. • Ce 0 G 4+

***U<Z 0 MN 0 0 M4+4+-II- UJ M 0>< J·I- 4+ ZZ}- 0 0• Z Z LU

*‘l' 0M ·0 U·• UJ LL; +4+ 4+ •-00 U •m I I N4+M* ‘I-U.!-U • ¤~~·- I-- •~ I- •~ 44+0* U M M •-••-·• s-• v-• 4

*ä*LUOQ (J•~•••)< es ¤• an nn N

* *Mh-!-• •NM• O O O T3 J

*UJ·I· •-4 M N|U·‘· +”+ ' LU4+-4* GLU U0••·-• ' • •- ¢• •··~ - +4*

*P'!-U •••~~• LU J J LU PJ

4+*

G<M •~|I•-4*.9 Z • • Z • • gg,4+Lu* ZZ< U|-Z • Z Z • Z 1* 4*2* (I-I ~•((\lLIJ ••¤~¤• ~• ann-• su pl*•¤·•* QLU f/‘)~•¢J...| ·•~-IQ Q ••~¥Q Q ,4·¤·•·-·¤· ¢.'J¤c•— Q ••- ..1-:: cc xn: og LU*0* Z0< U$•·~•

•$0 0 •!I0 0 •~·•·~·•-·*0* LUOh• Z4+•··•-

Z~•0 0 Z~·•0 0 •·-•N<'¤|-•*1* JSJLÖ LIJJ'··••···• ¤¤•LL|(—) L) ~••LLIg) Q,) ~••~•~••g*Q* I- J<•-•~·• MLUGII II U-IOII II «-e•·«••·-•O*0* LUG u.1UO·-- •·QG·•~ •~ QG- •~*M* VH-LU LUM ZZ•-*00202 0U20’£ IIIG* *

U.|<I 2 Z **||L.)'5~•0~•LI.LJ'7~•0-LL, •~•¤~••|g4+*

Zv-•M •-•l-0 •••NZ'5|I•·• •··••··•7IIN N•·-•LU•·*N¢'^•·~4 ·I» •-•gQ |-•••¤¤• ~•~¤ —••—•>(L,\J>< ••~·•><Ll;X ZD~•~•—Z4+** IILU. DUM UU0 M G M GZNNN--*4+* MOLU 0•··•Z Zzcu. J Zu. J Zn-•>¢><><L'>**4+ LUM0 MJLU •-•-•N•-• Lu LLI•-• LU LU!-IIIIIIZ*4+* I-Q QMS IZ Zn-•N<'¤u.!***

UJQ.\-L D£•-• NII0 BJJJJ***

G<0 M•-•0 J¥G QLL:UJU.JI···4+4+* **** O**4+ G*4+* N*4+*UUUUUUUU

143

ZZZYLGLOLDZ22LULUUJ

LUUJLUII II HZesananiZZZD~•~¤•~¤•I••C}•·-•N¢'¤LuZLJLJLJGCLU

I144

ÖÖÖ • n***

K •—• •K ¤¤• ••· •*·••* • LU C •-• C

***W LL Z -• •-·• _

**·¤» Lu •~ UJ•·¤. W4*** Z X JnZ Q***

*-4 <• LU-•l.U J***

W ZG. ••·•-· CJQ nßh ng·¤··•I·* U Wu.; „-•„„-• Na.

***•|-• ••LUN XLLI

*** Z Q•· QQ• •·Q41-:: O CJX C£CDLU e-AJib •-· ::< CDQZ ><Q**4 I- U-II OI~• ••

***U •<D U•X CDU-I

4** LU L9•-• •·•·~< ZZ**4 ß ZW n•·*$.Z U..!«•4**

••-• u,1• •-••¤ _;--•

**4Q JG ~•m•·-• |~••

***U.J•· Mem •~Z I

***Q• •LD ULU•· GO

4** Zn Q•-• •·C- •·J

***<W QCW -Q•-• •—•W

***M CO •-4U•• •¤.n

***ILLI OJ -*70** UUJN

4}** |·~¤¢ UG N••••-• z••

*** GII-- •·• <.>•·•••·•-• •-·•><q·:

***ZW MQ.U-J L)!-H sauna}- •EM

***JJ •Q •-•LI„L'}W_ LL!¤„Q*·I·* < ev.: ~·•U-•··•Q QUJJ _

* *Q•-• UC: •·-•LumJ Q•>-

* *LUX •• UI-LQ)- UQ•

* *Id •-eG ••J• 'QCLS

*I-4 Zw UL-U n-·O·~ •I2*U* Q •Z••· NN•M QLLJLU nnn*I«U* U-L9 LLI•N ••¢•~• ¢•_; p•••¤••—•

OLD!-• ~•~•-•*LL„* Qua XZM ZZ•··•>< QZ• <<!< ·* *

$,)•h-ns;-~¤•Q,• LJLUX UJUJLU

**· LUUJ 3UWNLU><UJn •J< atßfx

* * ZI- mZQéJ<Q¤'1 MLU-E ¢!<<*LU*

•-•< ••··•J ¥ZJ~• U•LD****24 IJ <t!I>·•U¤.Q•-• •UJ•-• • QLDLD

4%*** MD LU••I3UJ•>< NJW W •-••-••-•*t-* U-IU C!|•UN|@••••• U>£• Lu WWWnnn.*D* I-J <QX<•·•'~•-·••~ •L.)<.'J U ***•-•Nf'¤*O*

LLI< ~·•CD •-•n•-•••··l Q •-•3•·-• g nnn~•~•-¤*x* QU I-U-4 •-•-•N~•• O Umm C •··••-••-••5,Q.¤.*m* UZXm~•Q~•U Q ee gg, ~••.«•.•z};g*3* GQ u.•••*<Q¤z0c mm ·-•~mu4u.:u.•*W*

t-I-· >LULDJUJ!ZZUJ¤J• LUCJW Q UUU!•P-h-* *

LLQZ(¢UJ¤JZQ ZUUJ Z I I I I I I* *

WW C3LL|U.J< •g;....•|| •Z¤£ LU III! IIIIIIII* *

OM UJUJM •-ln •···¢L|J|- ·•~•‘•-·••*nn

* *ULU Z"'!I·- Z I|»·• IIJW LL! -·•N¢'•'5¢lt\~D

***LU!-• D- •·-••-4 U-3 JJ < Q„¤.¤.¤.CL¤„

*** JW D UW OLLZOJJ J XIZZZI·I~*·¤· Q ·-•z •-•u.1•-·~•:<t Q IAJUJLULULLUJ4+** .1.: ct Jus «'•u.•-·m<.J<.J U I-•!·-I··•|-•|····P—**4+ JJ C2 ¤.Z Z J*** << 3 :•-· O Q3 <***‘ UU W •-•Q Q UQ U**—I· -¤·* **4+ ***·II· G**·||· v-¢*4+* M*** ·LJUUULJLJU UUU U

145

~

an‘ I-ZLU2luL2<•|Q_ V!•-nQ«J<6OJ .L'} - AI an

'I. 23 §sW LL!u; Cl-¢&J C24-

- O ZZU- L|J•••

II-LE *3:U-I •~L|„.

•·~6I•LL! •··•·-~I- ••Z

< ¤O‘7U„J~• „•·• •·••ZU.at •··•uJ•U„Q NQ UJLLc "¤¤ZU••-u.•I.! LJ~• 3Q 62 GZQ Mänv. Z•—•u.1< M •-• Lu!-D

ZZZI G ¤--•¤:U Ch LJ!-3l- Z!-Q< OU-JZ V2 LJILU

. OOMNFSF!

UL}

146

**4+4+*4+*4+**4**4+****41- • +-·_ ·~O 1 (Ü*4+* G Q. "‘ 1I I-· •4+*4+'r··• 1.1.1 •· <1-• •-• Q4+** +-• G Q. LUJ •-1

**4+ < ..1 11.1* Z 1- u.***

J G G 1-4LU 4 9*4+* LU • J JI I •**4+ 1 LU G •·-••-

+-4+** Z • ca w**4f Z •••~ •~•·~ Z G V74+** •-• •-nh! N1-• LLJLU 1 UJ4+** < •• •~• II Ü 14+** 1 Z1 LU1 1-+¤·• g)• Ln4+** 0* GO- 20* LUG

;*-*4+ V! JL/1 ev! 1LU 1LU I-*·** 0 G/IG XG G> 0- <***

V0 Q.J 4J U.•-• G44+** V0 LU)- I)- I- •~ ZLU G4+** LU ••· ¤.•· 0-< •·~ <¤- G G·I·** 1 XG LU•~ ••·•L9 •¤·•••~ LL1 LU _***

0* 42 9*0 ZLU ~••-4 LU1 2 ,.14+**

V! tu.: ··~~· •··•Z¤.-• LD LU z

·*** ¤.J *•G J L1;1 4LU I LJ**4+ 1 LUI-• ~¤•Z L/1 GI- G Wm 0* G*4+* < ••· QLU 1•-• .1w C3 V3 cz:*4+* LU GX GJ•~ < ‘ GG LU+— ·~*4+* Z G4 2+-1-• LU2 IJ Z ZG O •-*4+* ** II LU•~• ZG Z)- LL: Z G •**4+ J LUG •¢'-G

**-0 GI0 I 1 G 6*14+** •-• ••-• •~NZ JV'! GJÜ 0* GJ O --•4+*4+ f-D ww •-*•LU Q. C:1w•-• 1J • •-1+** Z• .-1.1.1..1 zum ¤.w ·-

1•·- Q •4+ °·||• G LUG GZLU I ZUJ •- LU3*¢/I4! 2 ..11-n Z-\ 1-1,1, L1.1~•·- r-• • 1O*0/7* 1-• 1,,1,1115 1.1„1><-• •-• I4|·•~ •_1·-LL1 G LUG*LU* U! •••~,.14•~ Z +·--•-• •* ZG LU OG*1* IJ·u.1LDNLL1Z•·-• LU• ~·•~¤ e •-•< • EO

*•/1* w zw ·-•-•<.¤ 1-ww DD1- Z.1 ¤.w -·~<9£•-·•4+*

V! L..JG•Nv7Z Luv! OGV! G! LU •·-1N9-••1|*w* LU D.1I••u.1 I.L;1LU GZG Ju wz •·•w •·-*2* 1 ¤G|UJ•~.1 >+-1 OLU,1 •/73 Lu •-n•—• •1nN*•*·* 0* ~·• <Z•·4LU I-V!1-• •+>- ¤..¤¤ JLU ~••~·-•·-••-49

*0**V! tl! ••~•~•| hn U'! O¤ LU ¥I UJLU 90**-*3* V7 LUG- LAG •-••

*• Q1- ...1.,11-••«•4+Q* .1 LU ¤¤.1•-••··• c.1¢¤ •~••- •-1- D zz 1-1.11

*1*4 1 *1*/0*- QLUJZ LUGG •-·•J 1:00- GL}!-•<J '

*1:1* •-• 1- JLJQLD •·-••·-• ab-•• ~•_• < 3:22::*G* X V! 4DJZ 1-/$>·J' •U7 G 1I Qdlv-•1U ‘*¢/0* 4 LUGGLU •-• ät GG GG LL10- 10-1GB*

.* LU 1 J LULJ ZJ•* Z•-• G G QLLLCD·I•*

LU Z Z 0* ZID OGV'! LUV! IG •-·•LL* *

Z •-• 0-·G •-• G1-G JN- |I~ LUU"1 L/!•-·•*4+* •-• 1- •·-er-1 10 J ww GL.! I*4+* Z D·G¢/5 Z ent/!LL1 Q.•-•U„G•··•LL G*** 1 G •-•Z O ¤.v···•I 1..1,,1V‘!•-• •/!•-• u..1LL1*4+* LU 1 JLU J LU 1- ~• LU IJ*** +- OS Q.! V! 3 V! 0-¥***

UJ D Z•-·• Q. LL.4L/7 U. J G4+** G V! •·-•G LU **J°"••-• LU LLD4+** 4+ 4+ •-•¢¤

4+** · •-•4+***4+*4+**LJGGUUG LJLJLJLJG LJLJLJLJ ·

— _ 147

I-4ZLU •-·•

I'•* LUI- M

4M QUO

O4 O UG CDQ Q Z OI LU I-4 Z I .J LU I- ZI OLu I- an •¤¤•II ··~ I- ·y- an an {

Q an O ‘ IJ,)Z •"‘

"* I-( • ~•• •-••"•

><Z ~• 4 L/DPl X Z •-•4 4 Q IM Z LU I-l-- O ~·¤U) •~ V7 U,

U1 Q QQ ~» 4z kh Q Z4 Q re

4 •Z — 4th Q PC MIJ) L3 OJ I"1;,; ••-• ••/7 anM !•IhN QI-M LDII II ·•UJN QVIS ••-- ZIIII Z• ZU •-•N Q-•~ <Z QZI.) •**• J*‘N

O JGU. DO L9•-·••-• I-/'I••· me-• I„h•-•. hu Z

•¤•—•—• Q_•-••¤n gn}; Q_yq

LL. •-•>'• L/>><>< LU—·~¤• LIJ4 LUII . ‘ "On-·• ><UJ -44 ~·•><>< MM II-Z 4I MIZ LO44 I-LU •~•¤·•LUO ZI- QLIJL7 QSI th!-• •-•—•‘ Zu. <•-·••-u.<¤.¤.u. •·-• •.g9zLuv-• UJI Qv>m¤QuJuJ~ Lu ¤.•-•¤:

MU ~·-—• MI- u.1I/33G CD*"° D Q OX OO?-CZ I-I LL ZI-L- Z I-I-U JJUJZU-I I/73 •···• U.!-4 LU I/TZ OOMLU

ULJLJLJ ULJLJLJ

I

I148

4+*4+**4+***4+***4+***4+4+* ••• • •****4+ • Q!-UQ. •~ •·~***4+* Q QQUJ •·¤•••-4• •

4+********¤_ QDQO ~•••••¤~••••

***4+* U-IIIOU-JC:***4+*

<ZLU ¤.¥7• ·••OC}GO¤„·¤~+I··I··¤··¤· .4 2¤zu. •-•2C:•:::**4+4+* *·•LL-ld CD•J•LL •·•LlJL.>···~c£w**4+** <UC3 L.>CJC§uJ•~ «-••">•-d•·>*4+4+*4+ >Zu.. •IU-Ix! U··~•·-··••*4+*** <LU m•·Z •|- ••-••·~O•-••·~***4+* MLM kJL°}•|-GA •‘•~¤•G•·~•f¢

****4+LUUJ-I ••LLl¢/7Q OC>LU•'•LL·-•*4+*** dU.C¤ NL-LZ3-I UJZZ•··•LLN

4+**** <U•<! LJU••„J>- Zu.: •-LL¥><***4+*

•··•-I ••LuC!¤„• •.I<'st.'J¤c•4I·4+4l>·•+·¤· v¤¤•-• •···•LLLUOI¤- Qu.su„:»·-••·•·~****4+

•··¤• < L.)•·Z•¤. UJ•Z¢-/!••~M**4+** th.-|> •X><|-3 Z·~><O•··•~¤•**4+** >··<<t U<Z¢./äth ~•-•I•J~•·«-•***4+* J1 •Z •Z> t.>~••-CH-~><*4+***

<l-v'} I.uß.g_)•-n• •|-ng •m•

*****ZZ•-• ..||-UZIN ··~¤.O••~3·~

**4+** <I-U ¥•~O>< N3.|•-4,-J-•***4+*

UZ _ UGZ••· •V7CD•-•Q..~•***4+* LL C) 3D •LL•-• ··~LUQIQ.OO***4+*

Ol-U•-• C¤'ZLUI.I„..>< QZ••LU •·Z4+**** .'Z.'|·-· •LU¤LU• LU-•·•-¤•··~Lu*4+***

IA!-& <•OGL9 ZLU•-*~0·-J··*-I4+****

Q G I-LDL) •Z •-I •~·-O-I-•

****4+ CC: I..uZ2¤.LU QXMLQ •I····•** **

IZM ¤Lu•Q-I U-«U·—••··~•/J-- .4+4+ 4+4+ r-<•-• •.JcO•- Z3¤···•-•Z•··•*4+ 4+* LU en <U.I¤3••

-·¢¤x·-•••-•-4+*U** ZO>· u..•I¤.¤. v>•O~N$T¤.*4+2** O-I ut!-•O£ ¢^••~CDLL~·-<."ZZI**4** OI< <¤.m•UJ~<¤¤ULLU•LU**2** 3U-Z •3t/!O5-•'~|Z—••LUZ·*+-4+*)-*4+ I-U-I< .H/%<••| •<•·•LL•-••-••·¤··¤·Q·¤··••· 2 u.1¤2<.'>><CJ·~Lu¤n•2-·—4+* 4+4+ • x u•••··•<•·0cc~•···~ •·l-LN*4+ *4+ V7¥< U+•LL¢hZILU<Q.N~LL• O4I·4l·w·I··¤· 2¤:Lu <...•u.c:o|z•:: ••-•u.•u.:•·~ oc4+*2**

UJ<2.' —•LuLU..J•¤•< •••GLU •C¤2•···• OOQ**•··•** ...|Z•-• UQ¥O¢/7~¤CZl'-*L)Z~O•••~ OCC4+*+-** @3-J Z U-|—••••'·••><¤.€ G?-7•

**3**OLUZ < <!>Z-J•'•><LU•-•<|- O•O

**O**ZZCJ Z 4+><u.I•-·•<CJ~·•!Z'%/I •QII‘ **14+* Q. Z >-LU O ‘<~•LJI'¤¤„UQv~-|Z||•~•-•

**3** UI¤£ LUU.<ULUZOv9>•~~•**•/4**

•·•|-G LU¤€LL4+*4+* Z Z UJZ I|~•L9~·¤4+***

<I-LIM ••• l-•¥O •-•CL•-•><‘ 4+* *‘* Z¤¢<• I- •-• •··• UJw<*4+*** >-<•.uc D umen •-•c:c:24+**** O ZD O •--*2 C•J-JA.4+****

>-•'*I E J-JLU LDODLU4+**4+* ¤’.LU-44* Q Q.<I**4+**

GI LU 3 II-U•··• O**4+**

LL!-<Z W ¤·•xC3 Q4+**** ***4+ *4+*4+*****4+4+******4+***

4+*****4+* **LJULJLJUUUUUUUUUU

149

Q O Pl‘ ht :··~ MC!LL Q ,J• C•C}! •|• Q- LU¢/7 42• Cc. UJZ Cm G:-•MCI IG GU.: •<: :...4l-< -0 Z G5: -2

-MU.: w•· •CJ<• M- (BGN •-•Z •¤. Gl-ZG GU-

-•·Z•-• vw-• Cc: LLI Mw OU.-Q. C-•· Z4 C3- 4GLL:4 ULUZII C30• C.}- 20 4UJ¤.4 •¥•-~L:.: ZU.:Q u:• <Z < ¤..•4:··· LUZII MQ *0 UM<U ZE!-UZ• •-

b-OLL: (DU.: O QGCJO- ww>·· •··• 4 ZZ MLLZZ UC'.'JZ• ZZ· L:. -4 W- •·-• •-•u.: •¢..J •>< Lu-•-• M< 4L:J lu I ¤'1'>< 4—0G •<U LLJZ ••0’3OP· U•·zä'. UJUJG GU.: •·• Z U.: •:,; •·<.'> •Z2 u.:Zm :-0 O:-Mw NGO:-·• :-•><:-•-••-• 4w m=hG•-• w4w</> 45:• Z4 WZ 223:- •·ßZ•· w•~•· LUZ- GX CLZMM •-I•LL CUN ZCDUJ •Z•-• LUZU G• cgcnzw •¢,9z:.u:_·~; „:,·—••~ 4-Z MU lt/>U.:Z U•·•·¤C|··• MZ• o. LU. GZ ZLUI•·-v -•.:.¤•v: G-1'•¤: C-• C.•‘Z|•4 ¤—:u..wu.C cwgg •-•ZLL: UE ·:-U. 4U.:2U„4 UG _

DU- •• 3U-V) ¥L,|,><LU>· •(DZ MI-U. ¤.U.: LL•¤¤••-•• U•·!0• Mz.:•-• •-•3•-· ZG 2:- 4 :><••a2 1.,:2' 4 LUG GC -M:-<t m<>·¤.>< ••Z LUZ UL.: •··¤> •Zu.G• aß_ Q Zug •'£•~ •,: U.: <I¤.•·-•G•·-• UCE>·Z U. < ¤‘\•N Z4 •~ F-LUC •>< •Z

LL ICtM UGX C3-•P· LU•OCn• •-•••-•• UUJP- •c¤• :·-I-mu.: ¢_3t¤GIO:·- um· G- MIZ N5Z•-•

3•·-••·-M G-O••¤. •¢/JCm •-w Cw•·>< wzw <Zuc2: ·..:<:>-5:-• at-•U Cbt/7b Z'-•>•LU zwwz ••m ••5:-

g;,•• ¤;g.:,.g-• •-Ausw • ...1:: wm--w> <t•N•-•Z• <t ZU<Z LL1<D I<L'JZ-•• I-··LL.><G-- £G• u.:•2:u.: MIZ:-· :·-•Z •</:w LuU.•·O4I• TZZL:. Iu•·4 •-:·-<!'D AIJJUJCZ GU.:--4IZ LLJ<!•·• :-·•U„|·- V! U- -LU4G4u.: •>¢><•Gß Z G <lL• >-MW •—•ULIJDCD4 <••oc ZZC -2 -F-LULL: .:•-·•Icc un.: ••- www••

•·~•·I LUGU.: •··•:„U¥Z dt/H-G •«t:·-Z¤.• MGZ .OO 4G:-• ILLU db-•-• Z>· LL G-•¤.•U.::JJ <QWIII: ZOLL: I-Z- ••u.::·- <4|-• UJZDGGI -U4••~•¤~ DIZ •-•·

O<ß•· <D• •O¢/7C¤4•-• :-*1:-•-aN Z:-~• •·-••G UJLUGG M20! :-GZC3:-· <•• •U.:b 9MUI V<<IQ Z3 I•-••··• GIO IIMII <'J¤¢ LL: L34 •-•U.: ¥~1~•‘ Cb•-* UJ G~• ZMBG 42><uJ INI- GZG OG •-•<DI Z O44,.::.:.::-G\ G•··•C IL:. 4U„JM• CJ4 g G4Z¥DL¤L¤- II-I *··Z ’ZZI Z4 <QQZI': •·- :-3:- u.:•—• hr Gr-•:->< •-<t LULJ•·nD•"••|-< LUOUJ I 4 Z4 *'• U V7MG:-022 EM! -4 U.: GM U. 4

Z<•··•M cn 4 G gzcxwr- •-• w· ßwccß 1.:.:::. •.L<x n ßC:m<LJMCLLL -···M•-·•-U 9- :.:.:.:.32'·g•·¤· ;&~·I$·:t··:• ·N··¤·•-• N

G OIn xn

UUUULJ UUUUUU

1u

150

O O¤.• •L.':••u.z&.'> •7Zahucz c:>Zu.¤IQ-Ju.: ••·-4DCC).-I COU-QLJ rh- CLI4•_ •·"51• EZB.Q•ZQ. LLA•E ·Bc¥•E •U4U.1CJ¤0•..u c¤Z•·—C."§-JLuI·- Z•·•·LJCDZ• UJOD ‘•·I •b-• .4LUIM•Lu• LuZB¢LJLLZX •>(••U- •·< QSL--

NLLIOZ c:••L/SL.>LL¤.u@ Gu:•·•·Z•-• OZ.:•-•><><v! Q-•B.U<E• •EOFZ •LL, Qh•

•·U.tZLu¤: CäcbmLU••-•B¢I- LJOZ.•¤:•m •L,;•··•¥C•L|-Q MZ!LJZLUU--I LJ•O3u.aQLu>· •vT•m•c3Q• ~mU-•LDU.*3

Lu-IcOL/7 uu-•• GU-I$•> •LLC-•-• ••EB.• 4LuQ•·• -JI-•C3f\J LU>fOLL L1J&¢A•>< g••

u.Lu LJL/74 ••-J •QGac <¤!»;'LD>< ..1C>• LGu ••·•»•-•• u.sL,>OLL£·~ ¢I····LL.¢/2U.J L.J">•Z'! LU-IU-GE U•Z•·••• czu.1•.u..1•-• <>¢•-•N•·-••-• 4Q¥CH- ~•Q.J><III-• ··• LL.•Z•·•'¤¥ z •-•C:C3•-·••-• OLU < QIZXLU Z•-•~¤QZLuZ U4 ·•-• •-ein-•:••• g+-4 D-Z-4¤~0O Z•-• .I _mr-•Q Ol--J LL -4E UZLJ r-• <IICJ ¤< QuEQ UL.} CDG u..Z

Z •-wc:‘ LLJLU DV7 Q!-O E-4 ZLLJZuu LL•¤:LU

%·N·¢|··II· *·H··||·N-•~O~B __«-A-4

151

1

4+4+* •··*4+* •·~ •4+4+4+ • ·-•

··4+4+4+ t: Q • ·-•

***Lu D•' M ~·•

4+**1 ZG ~·• QD4+4+4+ •-• u.•LL.1 Q~Z

*4+* Ln •Z 1•·~Lu**4+ u.I QD• D-4..14+4+4+ Q ZI}! CD•I·-*4+* Luz UM•***7+ LU

_|•• ••¤••••

***I- LUG •~Lu“•-•

**4+ < •UJ N\Q-*4+4+ •-I I-Z ··•DD*4+4+ D ...I>< ¤.«.,>:I:4+4+4+ Z Luz C9••4+4+4+ D ••U U••~•~4+** LL DZ ••O•-I**4+ 1*-* -·~Lu—•**4+ DI •·42¤.*4+*

• D• ~·••D**4+ V7 UW DOG***

hd •@ L}LU***4+V74+*4+

>- I,'U•~ ••~X•-•4+4+* ..1 DIN -¢I-•

-4+4+4+ < u•>< -Ua.*

4+ Z •Q• N¥CB —4+

*4 MDA ¤~UD•

*4+ UIX G•„-I·'•

4+D* u ••• U—ä*•D•-*4+LL4+ •·-• N4/vw 2+-•I-•·*24+ I UL112 •~• •G D4+*-* <• •(LU C.^•·-••~• ¤.4+ 4+ ZX •-•I.I LUU~O" I

* *>-r-• U•I-• 2•~••-• 4

* *D1 ¤LL• e•~L9• Ö •*•

4+Lu4+ I- UU„Lu L/1G•N •-• rh*2* Z4 •LuI ‘·^LL.1•~—• • U ‘*~4+ •-•I 4>£I-••<Z•-IU D Q.4+4-* I-•I·•·NI•·-Z ¤. I*3*

DU LULu•I •0D•·-• I D4+D* LUZ DC3•."3D•-LIJD3. Z) U4+1* D-• •C".Z•GZ.‘I •·•-I •*$·|+ U-IQ. (kääzl-U~•I„LJ••~l*"$• ••~*3* Lu£ Lu">•|ZU ••-eeug N4+VI* 24 1*CL<••·'• •NI

-°

4+ 4+ Z ~•DO LU•¤•~·•~••|-•|-•I amp} 4*„* DD D-I•Q2~·•L9u.I•~ •LuD •-—••.„ I4

***•-Z I•LD¤„*V><<ZD¤5+-DU <I-Lu ¤.¤.¤. ¤.I-

**4+ I-< ZIO•JIIuLuD~••ID• I--II III JLU**4+ 4 •·-•••<~••1.JU•-•Lu •- UJI-U*•• DDD 4:5:*4+* ZX L'7GLuLI•<U.JZIXD~<•·* QDI- UUU DD**4+ 1-• LU MU- •I~• ••• ••• ••**4+ D1 Z Lu? <¤.¤.L¤DDDDDDDDDC•DD*4+* LLI- P4 I-:tD +--IIO•—n-·•N¢"1~1'•-•L„¢‘~0I~•—•¤:<7~***

Z4 I- •-• •-• LU<D•-••-•-••-••-•-••·••-••-••-••-••-••-•*4+* •-I D Uwe/u DDD**4+

D •-4+2 •••+-+•|-·+-•I···I-•l¤-•I¤-I·-4·-•I·-I-~I-•*4+*

DI/I 1 -I.JLu DDDZZZZZZZZZZZZZ*4+*

(V7 D Q4! <(4•-••¤·••—••··••-••-·••·-••-·•••-4•·¤•••«••-••-••

***Lu< D ILu•·-• UJLULU1111111111111*4+* 1I V7 •·*1D 111¤„¤„.¤.¤.¤•¤.¤„¤..¤..¤.¤„„¤.Q.

*** 4+4+*4+***4+

**4+4+**4+**UUULJUULJ

I

152

LQ ••, ZV? OU '~·¤•·-• ZZ

Q. UJ*"*IO JZ42 Lu- .c:··- FLLII-• 1-G

4 JC]•G LUL.)GG. GZLUD ••G 4GZG I-Q4Z LLJZQQ-ZF-

GV7-~ D4 •£./7••~Q 3: <<~

··~ I wr-- IzxQ •-1 Q,••I • C3 JU-•-4

V5 cc 0 1-w <•.1.><LU • LU •-• @UJ•5-• G Z V7 •¥(D

·-L} LU • LU*'• G•Z ••—• Z LU UV! ¤cLuLu ·¤·M •· Z Z>· CQ.1 ·1•I-‘ LU • •-•J GG!-· il-4 Z LL: •./14 UL)- -N· •Z • Q Z -*70 -1+•'• LU Q •< l'¤•• iv•-• V5 Q U ac UCBZ ·¤·~• V7 G I CI- •Q„**•

*¤. 4 0 • .,13 NZ.1 4+G I Z V7 OO $.542*G • 6/7 II

1- w 4 -0 •-1--12 jf-·~·- Z V5 I ZD U•• äl--•-·• LU O4

-IC} •¥O

*~··~• I- GZ LD I-M UCI-L1*¤.¤„ V7 • • •-·•I •JZ ·N·GO •-• ZL9 O 2)- 4C..‘•*Q• V7 LUZ Z _|-Il-L ·l|·•·••~ Z I!-U UJ XLU LU•Z ·§I·‘••·'• G P-J J •-•Z @(3-*

··-•~• U ·•LL1 L1.! M4 ••Q ·II·GQ •-•~• e bm 4Qu.1 «)(·Q.- M G 1- 4 LLJOZ ·I•

OC:*•-1 Q nu 4 zw cczx -1+LU•• GQ. Z Z 4u„1!.° ·¤•2*OO G LU! V7 O1-1 ~•• •••-•NO LU •G 4 Z4 G •

udunßlßl G._|

Z 1-•Z• Q} QQOOIBOOOOOIIO Z G ¤.LU>~ 0. \N•-·••-•OO•'*ONO•¤¤ ••-•|····LU D Q-J J O IMC! Z \I-·-1-ned-4NNNNN GZZD J XJGJ II 4 4 4 ~•~•O4—••-Z D4G4L|-Z GX!/5 G I-|··••·-1-1-1-1-1-1-1-<Dl.1.11¤·:¤c•·- w .10 U1-••··• •-·•w 44ZZZZZZZZ¤-•M¤„¤„|- E ~•· LU J IMLU J ZZ1¤¤••-••¤·•1¤¤••-••~·••·¤••-• Z Q, V7 CZ ßh-g} J MMxcsxccrxczoccccb C1 c u. .1 ZG :141.1.1 < GCQ•Q.¤„¢LQ„Q.¤•Q„Q LJ LL •-• LU LUZ LLZZ L.! LLLL· *·||·

O WOO O•·*•—• _ •-•«-e

ULJU LJLJLJLJLJ

153

'N- Q*

nnN- I-N- I < °N- Q 1N- Q LU •·~N- LU ...1 •N- LU Lu N- _

.*

1 UN- LL L,) •. N- < •·

N- IhN- LL •N- O N- M*

•-•N- QN- UJ >• •N- LU I--N- ct ~··• ätN- (.9 LJN· LU O •N- Q ..1 •·N- LU Ih«I· > •N LL M VN- O •-I

aaaaaaaaß Q••••••••* • _

N-•N-·I-N-N-N-N-N-N- (/1 N- •N•*N-*N-N•N-N-N- Z ‘

N- C I·-'N-••••••••* •-• Z••••••••~*P" LU •

lßlf\I\1I·I'\\1'\I!*L¢\l.I\·Il- •·-• I •••••••••·1I- Q LL1 thQQQQQCBQQN- Z LJ •

LLU•U„LLU„U•lLLL* O < M••••••••·)t Q_; ,-1••••••••* Q, Q

N- vv •II II II II II II II II N- ..1 u-• •

ät < Qaaa 4} •-•

*•-•NM< N- I--•~•~·-I<·1t

•-• N-<I•LL1¤„¤„¤.¤.I•·•N- Z •1¤•..1ZZZ£•JUJN- •-·• • •LI„1LL1•*•OGCD<QN- LL 4*QQPUUUQQN • •-«

ät Q •

*I •

N-N-N-N-N-N-N-N-N- QN-N-N-N-N·N-N-N-N-••••D•l•*

* * *V•l••h•••• • • •

C9QQQQQQO• • • •NNNNNNNNLG Ln Ih In -P-•I-•I-I-|·•P-1··-I-I-- I- I- I·-••~¤•i~¤••&1é~•~¤• t snI··I-I-I-I-I-•-I-1- h-·-I-· I-Z<<<<<<·<<<•~<•<••~<¤¢111111111N·1 1N-1I-QOOOGGOGOON-Q O OLUZiLLI•LLLLLLLLIJ•LLLI.‘·?i·-LLI·‘VLLZL1.1L1J

N-OOOOOOOQO O Q ONM~‘|"I-¤~0f~QO‘Q •·-• N Mq-|•¤4•l•¤¤¤I•¤¤I•-lu-I-UX N N N

e

154

*4+**4+*4+**4+**4*4 •

·4+** X444 •-•*4+* M***

I-4+** <4+** Z·4+**4+**

V7**4+ I/I4+** < I4+** Z4+***4+* I-4*4 Z ··~4+** LU O4+** X I**4+ LU Ct**4+ •.J •·

*** LU O**4+ LU4** I- Z

-444 Z • --4**4+ I- Z O M*4+* Ln • I M**4 •-• LU cz M4+** U1 O • - M4** Z O •·~ M* * O LJ •"‘ M •·~* *· LJ I • N O4+ *

• ~3 M LU‘¤•Ü""¤‘ LU V7 er N Z*€* I V} LU N •*2* I- < O N Z4+07* Z O fü •4+<* U. • Q m u;4+$I4|• O L'3•- E · • O* *

•·N • 4+ O4 *•~ L9! •- •~ Q*UJ* M ZO ~D O Z Z

*2* ~• UJ• ~• O ~• •*-•* O -JI-L9 O LD VI*I-*·

LUIO• O Z L/I*3* In v<Lu•- • LUO<*O* I- I--•Z•-• OO .-JOI*¢* Z < _•- LUII LUO•*O* LU ZOOLD Z-•

*•O

*D*I I/7*LUZO•O O•-N- ·4+!/3* LU <-IZLULU-•• LL.lOZ\I

* * -.4 £<-•.JZII•·• ZO~·•·-LU* *

U-I LU'-/ILU •‘7-•LU •OON¢/I* *

UJ¢I/I •-4 mj •-4•I~¤v;**4+ LL! Z <ZIIOv/IZ ||O¢<3<*4+* I- *·•I-IO-•N<•-•LUZ|I II II LU**4* < I•·••-• •··• -•ZI-3 •'••~•'•.„I34** ..4 Duwmc ZZO-•Nm..sZZ*** 3 C]-**2-•O C3-•!\‘\~¤•—•~¤•<•-x4+** Z QS-I..ILLl•-•O Uh-•··*<.’BLDLDLJI-34+**

P5 C¤¤.<I Z ZI·•O·••··¤··¤· CJ 3Zu.1•-O OO czwz*4* U. w•·-•¤:¤¤ oc uccw**4+ _4+**. OO O4** N-4 m*4+4+ •-••-• •-44+**UUOUULJ

u

‘ 155

H1***ti}!***·¤·*·u·***

_*·l|·****

•\

*** NN***

•·•

***rn-•

***••

16** ·—••-•*41-* ••***‘ NM .ÖÜ-Ö ••

***-••-•

***•~•·

*-1%* •-ard ,***·I·** ••*** . -••-·•

***••· _

*** MN***

••·*·l•<|I• würd •

***•• X -

***-•«-• re***••~ •• N -·~

***Q NM 1- — .1***\U •• < an***2 •-••-• I cg ‘*

*• -•·'Ü *2 •• th r•

**• r•—• cn G ·¤ -*z*UJ •• € G •

*UJ*G •·d·-• I •··¤·*¢/7-{PQ ••

Z L-*U7*U MN .1 LL1·~m*<*Z- ·-•• <t ZIZLUV:*

*•s1 •-••-ard Q O P-"§<* *(/äé ••• G Q •Z*UJ*¤/1 ~D•-lwü 4 •·~•~LL1||*Z*<• ~·•••· 4.9 Z ZG•-n•-*•-•*I1I•~LUNt"^ LU • -7*1-*•IGG\ 1-- IC~0LU•X•<I·D·l-LD<UJO•·~ Z 1- ••··•LULU•-ü*O*~¤•~•Z¥~0 LU •··••~•ZG•-•*I'd*Z • • I- ¢•‘*||UJ•Zq/)

*g*LU¢¤O•»¤ V5 Z¤u.¤c: •-mu.Q «|»v;*u,4•·••.« rn • •-•Q•··•|g<•-•LU*V!*v)4Z~0X V7 ~0LL1• Q•4!I D ·* ·I·<<~·•~•LU Z •'1LUGZ OZ* * LU!/1L9G C9 •··•-ZLHIIU. Zr-·•*

·l·LLJ¤¢¢/7 Z U ||U.1••-·••-·••-• mp ‘***2 <Z•-• LUG Z***•-1-2:: LU •:G·¤G GLLLLI***1-•-• •-•N .1 L.>~·•¤ L.J•··•I>*·l·*DUww1.U c¤ G5: Zzil-*·I•D•¤•*·ZL.9 E ~‘1'|!LL Qu-ng·¤·**N..1.1u.:u.: u.1 -•·1•-« Z1-D***¤¤¤.<!Z1·-· 4/1 U12!-G***DZU.1•-•Z V1 G QUJZ*-I··I·m-•NG•··~ ·< G GNU.:*** **** G G*** LO 4***

•-e rd***ULJU LJUU

156

**·¤·*7********

IL***

O*·H·****

W*** W**7** ¢*** X**4+***

w{*50 I*·Il·* I-·

-******

O*7*** I-*{*«¤··¤~•I· •-••v·••«•• •-·• _4**

-an

***0 O 4

***Q I Z*4%* < Qi LL

***•• 4**{ O G I

·»·l··l• Z Lu·•·

*** < Z esO *

•-•*** I·•l¤• LU •* * ZZ Z' •• •·•

* *LULU O rd · un

*{ II LU ~·• - W

*Q·¤· wu.: c C3 In*w*

-J-J O I-

4*¤•* ww U x Z Z*§* Z • ~·• II*3* Iw •-

Q an °*•J* UI V7 •-·• Z •-·•* *

<!·• I/9 •· LU •

*{ LU ( ~0 ,.| •-·•

*II·UJ* LL z" *·• UJ •-*2* ILO •·N LU

*V7

LÖI O an I/7*|-··* I ZO ¤3 0 Z 4*3* WO w~ U 0 ~·• Z*O* V70 -II-Z 0 O

4w w|O• 0 I -*m* II-LI ~•4w- • Qt -0*3* x O~·•Z•-0 GQ

*Z*V7•|I• LULL w •~• LUII •-• ••

* *I ILGOU Z- |~D">Lu

·I· ·I· hu. £·§•.uzg••1 S•-Z

* * O 3-IZww•-•• w •··•w•

*** LL .J<~·•„J2||•···•Z•||0

***..|w wWw •"'>—•w •U\'BQ•¤¤•l,,|J

**•I· 4w wxv! •-• W3 •-•II U~·•3*** Ix Z <Z||NWZ ||V7thZ Z _***

LD •-•|-ZO•··•tf\<•-•tIJZ<tt‘•|II-I„•·-•w ~·|·**

wtü I-•-• ¤ -Z}-··3 !•··•-••••|-3

***..0-Q3UQm-• ZZ~1'LL ZZZ

***3 CJ•··•*ZInO C'.'3¤···•In<O C.‘•-ex·¤·-lI·* ¤.I c:.•..•u..•«·-•Q U!-•-•I0 Ut-3

***ZU Q¤..<Z Z Zl-0

***O4 3Zw•-•O OO OwZ

*·•I··u· uw v>•-czccs IJQ uczu.1***41-** N•-·• mq-***

thln Ihtn**4} •·-4-• •-••-4

***UUUUUUU

:

. 157

{ffes-¤··M· • •·M··II··¤·

•·~ •·<2

{fü •LLs •-A ¥•***

Ü-Q ih 02{f{ •JCD 0** -1:-•{4+* LU0 Z-: O.:{fü QI Lu0 IZ**45 • •• .|~O 00fff ¥*• <0 LU~• OZ{fl- 00 I-·Q 0LU ••«··¤·«:•· .:2 Luz': --0 QQ{Ö'! 0 Q• •-:0 0LL:{{{ IV7 0v/> 00 ZZ{{f ••-n •V> MI LU0{ff <<·•• -•0 0LU·I··l•ü LUI··- IZN 0** 02 •·~ff'} I"" ¢L•X ¤¢•··! · *20 '5{ff I- -JIL* 00 O I-UC! 0{ff LU <LL.•~I Of": 0 .JI-U •-•4** V7 0LU>< 0~• 0 LUZ 0·)|»** •:_7 •¥• •LU•~ Q •>< 3;ff{ 0< 000 ••0m

ll I-Z 0{üü Z0 QLUZ •·*O~¤• •~ -10 .1{ü{ •-•LL| 00LU -•0N 1 LIJ0 O{-II•{ GG C70.! G1>< 0 02 IIJLJP gjbb •-• •|••****

(X 0"'Bb •¤~•~ an Q2 <ü{{ Q•-• N500 ·•~G¢'¤ Q ct0 I-fff G 00• •-•LU~•• CJLU LL:{fl- II- •·GZ *0-Z•-• LU OG Qfff 04 NZ•-• ON •>< V7 QQ C-ll•{f •-•2I 0<.J LU0O0 ..| 00 +{fü LU 002 Z•LU•~ UJ MZ-{{f JV': 0-••-:0 ••·~Z•-• 00 1{ff >-Ln 00Z Or-•><~·• • 00 • —{{-II- (LU 010 LU~•Z0 Q NQ :-•

f f GZ 000 2****2 LU 02 -·{ { IL 0-JLU ~•0>£LU I-· 00 V5{0* >-LL <CZ L/700..: an •-dw V2{LU{ mv-• I-I• u5•~.JI-· LU 00:,5 <I{G{ 9- U.J•LU•¤~<•··*0• I3 00< E{If ><•/5 Q0Z'NI0I•'• 0 0Z•·~ {·§·<{ hn 000é 0G ••-4 U4 Z••N 4{0* ¤:LU <0O ·-LU-se I{ { I-I LLJ@UJ*GZ~O@ II-LL0 OG{ { <|-• q;2ZILu-•0• Ln I-•LULU•-e LU-JfLU{ Z LU <LU><IZ00••• 0 •·-• Q>¢>< Z<I*2* ZI ~••Z(0•0•-O O •~•••Q 00·I·•-•{

O¤•·~ Q0•·~•0·~·~0 GQ I-• •-•<LUtDu.:•—•::fh•{ ZU-!-• LUZ0 LU-·••-•N LUO •·• U.:0ZZ||**{Bf •-• ¤.LUZGZ•~•~• Z! •¢CLU01*5LU{Of G01-/7 Z-I•-•{><<00O•O LL CI<0•J•·• 03{gf ZI-U•-• <LUI-III-LIOZLU•·•|| r-: Lu••1!·•l|L¤•-·•Z·*c¤·¤· <v¤I Q <~·-¤:I•-•ZIl·~ •¤··— •-f—~··•-·{Bf 0DP- LlJIL<LUZ0‘?"7LU >< < •··*0f-fwf LU QIL •-* 00 •-• 03: O Zal- ·I· LUV7|-• 2 Luz I•L¤•·-•Z :1 ¤.¥ r~Q Qer 4l·

I·-·<•-• I-ZD •-•~¤—-•-u.: L- z ·-«Q u

*f I- I-• •-• L-: •¤•0|¤-•D ¢I <„J{ f ><0 0 UG:/3 0 ZZ Z 0.1 0{** V7•-•LU G •¤•*Z ~OCD Q:-• •-eq Qffü S10 uf .J•-Ju.: •-•C5 0I- V': -0{ff MI-•Z Q G4! Z Z-II-·I|··I· ¤<< 3 xu-: CJ Q cz LL.{{4+ LLZQ V7 •··•¤.i0 0 0 0 *1{·!l·{ ff ff IL {{

*4+* IHC ¤'¤{{{~O~O N*·l··¤· -••·-• •-•

{f{{00000000 000

‘ e

158

UJ .3Z•-•I-ZCJLLZLJ•-•&

DCFDZUJZLIJ¢LLA

ON•·¤•

159

•ä•I·* ••~•* •{·•I•ä •-¢N n LL?·I··¤··I•

• ~··• -— >4+** •LL _ MLL.6••··•• ¢~..;{ää O-\L• L,JZ·•~~••¤~ q, QQ{ä{ xl!-IZ •~¤••-OL]-FW LL. GV?{·I··||· Gx-•··~>< •LL.~• LU I•«••··l··ll• G9 On.: ··-•4~oLu•-• 0 L-{ä·I~ LUZ uLUZn ~·•Z-GX LuLuZ4+*4+ cc: •C30¤. N¤•LU•* :::2-

ää-l· ¤:*··• ¢LCDZ£ ULUQ-•~ Z:-{{{ OP- IU•Lu •nCJ•-••-• 4 ZQ·I··I»·¤· 4 O1"H·• -···~U~·-~• U.-CLLJ{ät Z-I U•z• -••-·•£'Q.l·- O·-••···•V>>-·l•{ •-43 nz nt- ~·•~·• nQQ. < IO{{{ Z MBO- •-•Q•·~C§3 I ¤.¤<—I!·{{ Qt!. U-:Lu>< UO-••e.n ¥•<•··—·¤··u··¤• ¤¤ nOZ< -2 -—> mocen{{4+ IH- NI•£ •·~Lum-••• •U')}LiJ*•** P' LJ*'-U13 •-•n-•~••~ F-!-LJZC{·l|·{ UJU •£.‘§Z** •·-LUQ.-4 ¤.LJG{++4+ Z- -4-•Ln O*•-·•¤0~• DG:-•W{**4+ P- ULLOn I.LI~•G •·LD Lh¤:'3•-• ‘{{{ Z< nLLLULL Z<.'JU·~Z >&Lu{{·II· CH- LJLUZLL•~ ~·•Z">•···•LU ZI-·l'I•·I> WV) •LL-XLUM lJL|4•¤•-4 nu.: v-•·¤··I·{ I Lu•£c:•-· n.J•··~O't- •-·>¤{{{ ¤.LU ..|><n•en •~LL.•¤nn ¤.•-•u.1Lu{·I•{ <> ¥<>·LL-C Nnu.I·‘•- D;-•-Q{äü ‘¢I•·• UILLLL-4 n-Z•-••··• e/74u.Z¤|•«|•* [L- ;ß,¤¤m)• amd nene Qgr-••-n .·I~*·I· ZU mLuQO• OZ~•OL9¤. UJQL/1{äelb .CUJ •LnC3 •N LL4-•I·-·LU•-·•Z Q.!-•C:**4+ •-LL 4¤I¤.>< ZLU¤.ZLnu.1 e,u•-et-{*·¤· 3U- 0-—C3•Cn n-4D><GI·~ •-• ez{{{ LULU LuZuO•-• Out!/7Z'..J• enw C{äh Z ®LUZ•>< LUUQ~•G•* IC-JLU nn•-•¤.• Z3•¥ •N u.:r-LU.:4+ 4+ u.;I 4LDZOI~ ef!}-·~Q•~n 2 CDI{ { Ih- LU2••c. v':n•-•-J--•u.1 •-eb-Zn{2* I-, c:u..H-UOD L/:··~•3~·•Z •-M4{D-} LL <.JQ•en·~4-«MI¤.~••- 4IZ·§·|-{ ent.? •LuCJLD>NZ-•~• nLU><•-• II-U*••{3* Z ..1•u•···•| •4¤•—C:4—-• uv!{Luäß LIZ LU}-Zv5LDC3•~Lu¤¢~D-II¢¤t O 4 UJQ{Zi- OC U¤.nC3Z •Gc£CJ~•O<.'>!··- O LLJÜQLLJ{ { LL-*·• UZDCJ.JuJIu14CDL.'3•~en l- m· { { xl- 4¢Ac¤CD-||Z•U ••~</SQ

- LL. OO*Wä LI-IS ~•QI nb-(na ••~•-••,,| Lu Qßp-I-{Zä Q-«| Z••¤. I~••O•-l•'••¤l •••~>· Z Lu en QH'!-•{ O OI··enu.a•..u Lu~·•¤1~•N•-•• •- O UZ•··· LU·I·•·•{ LU!/I I--4<-¢7¤2'I¤Z.-:·-·L.L..~•-·•~ !-·· G Z•—•OLU Z{gä Z 3LLJ<-4~{XuJ¤.U-ULLFH C •-IZCD n{ { •-•Lu LLIQZ¢3!·--4ZUILUZLL„~·I- • O Zn: •-•{¤¢{ I-I Z <-UOLL-•·-•LUNZ LL.: • ZU-Lw!-·· II·|I·¤¤* DI- LULI-<U nI¤><3 -4 •·*

•··-b-•-en•·-•

*3* D LU ' ¤¢LL • C3 •CI| LSLU ZD{mi- cz!-U Z U-IZ U IIZ Lußcnz O{ { mz •-• I-zB GI-I-G cc en ~¤{ { 3*-• I- •-• •-• ¤'1||~·-Z-I LLJLUD- •·*·¤··u·{ ent 3 umen Luk- Den LJ-|@Z•·-e{{{ cz O •-•·¤·Z ‘.L‘zLuC2¤.. I LL. c ‘·¤··u··¤» en!-Lv nc ....•..sLu u6::•..•uLu L-•-u.z cu*4* •-·•·- m ¤.4¤Z I-CJ-• en-·u.4{ä{ II-U D Ztuv-• ZUI •—D•·-I·¤··I·-I· •-CD en •-•¤;c: •-Z3 42en•-—ää{ {ä{{ -{·lI·-¤··•I—¤I·äää{{·I·ät-{·I·‘ {ää ·UULJUUUU UUUUUU

.160

G• C•Q u.a•¥• ZU,. •GZ ° -•LL. I--I•-• Z•··• G.·-• C-I •~ ¤:•·· 3•-• IZ ¤. LLIVI nn•-• •G Z ‘ •~ I- OG. LDZ LU • LLJ-1 •

Q •• I- an- Q4 I- ·0 O0 • ·Il· Z -1*

OU.! LL. O Lu-n Lu•~. IZ LL LU GO ON Lu• LL1 I •-• •·It- •·U-I G U I-cc Qvl- GZ •

< CAQI- Z• *9 LU D O..1 L-L10 Z E! Il-LI OLLI ..1UJ • I LJD UJZ CJ GI- •~• •X LU I" < M·II· I-Z Z O Q- U··~

-l• •· Z -1O •·4 LULJ I- NI-- CZ Z U-III LJLL1 ••"* D U.! > •G Q2 C LJ , •-•>- ul

hd Oé° ESIE E Ü {3** 1 °cg OG • L3 LUG LJQ• UC va - at LLC •mm •L.: vs LU LLZ LU•x mt 4 > Lu- C-I~•I- U• I •~ O 2 Q!·•--1 •C •» *9 IJ C G LUO U•~Ll1 NG Lu • Z O U IUJ ZD•-IO Q2 C •-• Q Z I-I-· LUG~•* ll er uu a- UJ

*UC LI. I- NI I il- ::0. I-4O--• UL/7 'I LL. 4 I I- • ZG. I-·l--· •~4 •Z Lu at O • 43 •'•LL-II-G. UI-·~G.UJ ¥ Lu O •··~ O • ccJO •·•N!II 0II I- • O •··• L/II-• •-«•·LLJ0 4LI.><OI- Lu-. •-• -4 N I- 4/IG! 4Q+ I-LL•U 2*1 • LUZQ •u.z+¤• lJJI,LI•¤|••*• ••

Z • • \ Z -1 GI•••-1 G¥><..|O -••-·• Q I--dy-- \ ILUICD LLS4 ‘•—•~·• •••LIJ• Zlle L/I (3-|~L9 \ LL.•··•I •-•~•& €LULDLJ0 .•"1¥ I •I-••-•-• I-• • I-•00 LUOZLJLLI •-• CLI.! CL Z I- I-!-/7 >·Un II ¢zCu.»<• IIN-ID 4 z3I--4 mw: LLI-LJ~·~ <U-1- •-•~GOZLU x OOZZIG. LI-JO •-•>•--• -•"9I-·|->·•-• •-•I*·•D I -1LäIJ•-•GtCJLL„ LLIZC! OG:~·¤~• I- ULL.+-I I-Z Z I/7I|Q¢OI···•-·• >LI.LL OI-I-LLI4 Lu-•C~¤Q Z•-• CD G.!-LJ¤•LI.¢/7 •-•LL. I-IG.G.DI >OG•-•O OI- I- LL1Z~• O I-•-VI --IDDZX GO! UZLL. 3 --D Z UI-LLJ 4L/ILfI••• IIIO O-• Lu LLIOLL. LLI u.1</II LLUQ>I--1 -J~·•I0 U Z -1I-3*** LL. O •···•

Z-I -1 Q •-• ILUJUO4 4u. Z Z I u.1IUL} U•··• LU •-• 3 I-va0 LLI vsLU IL!-LUQ •··•··•'Z

·II··I·Q Ne-• •—• _~0 •0~O•-4 -•-I

ULJU UUUULJ

161 .

O O"> '3Z• •Z••L§ •• |••(j02 1.90 @02-LLJLU •LL1 ÖLLIUJ ‘ZJ GZ LAZJ G•F- G• G•·F~ L-u.1• ILL1 •1.u•2¤. L1.1z F-Z¤„ ca•Z •• _J•Z

Luuu.1 LQO LLIQJLIJ Q21- zu.1 QZL- QL-•• LLJZ ••-•• (IF- JX GIF-•• LIJI ct-- LuLUX •·• GLUX QG< F-U GG< .GI JZ UG! F-LJLD UJF! •LJL9 ••~ U)I-• GI 1'•‘1Z•-• G D•¢h •• L,)•Lh U. IV50 QUJ •¢/)• ZMU, GO NWUL •-n I-(1-L GG L.><LL. • (Iu.1 GU •ILLI G I•¢! UZ •-••¤*1 LU F-LL|• •• L,JLLI• ZGI-L MG •Gu. X cz •••GU- um UGLL •·~ x L: .4LJ!-H •I •LJU-I *1 • 1- <*10‘N• LU‘1G • G U >•• LJ;/)•~ _)••

hn Q Lu Q4

I-LQ. •L/1N ZI-L@ ~• Z > JLLO •-•<>< ULLG ät • N F-LUG-•U!I• GU-|0·~ G G 1- 4+ ML.L.•¢•••-• ¢¤LL•¤< J Lu *2 4+ G•¤.F•UU-X ••G„I•• Ü Z LL! ·* V7XQLA•LL.• (XQLA GI • I L-· G<•G<U-LG F-<•G LI-III LL. LLJ •~-N \:GJ1—·>¢2 LL1£C!.„1 2- LL. L.>• 1-1LL* •·~Q„•>·UJ •UJ ¢!3@•·>• •"7 LU <•'• -%-1-4+ U-ILL.1L'J •GLLJ.,.| ¤L!.1L§• •-•• g ,,11-1 L,|„L.u•~ :3••-•N•GF··

<••-•NZ11•-• • Q.- 1.L.¤:•·-• .,1G1-/¤X<!G• LUGLAX •·7-1.1.1 L1. LAG LU·F•.• 4¤Q•¤-1L.1O ¤<L:¤••-• LL.: LL. •-· occwc >IJ••·•¤t">• (IJ-LIINLLZ LU G3 @1+:3+ -·1.¤CD><< ~Z —-LuO><•··•!~L1.4•·-Lu.1 g LU o z-..4.1 L-•••~•ä•¤• |-•••• •-•¥h¤•j ev ZZ QQ••-•<< QtL‘&|···1·· J UG@F-•-• ZZ LL: •··• GG-*->> GZLLJ*@<JZ LLJ2uJ@Y~G G-• > LL1 GGIIGIIG LALuc4:ICJC': >L14c::-1c L.41- .1 Lu: •Q•-11LLz11Luc‘:1..1-1v>>cIZ¤¤:..1.4m Z ¤ L.¤•·- c• -:.1:11UJG> G UJG>Q QLLLA Z ||OG•·-•J<ZZLu.1 .4 ¤ L.1•-· <L-· u.111~1·—-<>•-•¤-JOJ LUJ J IUJ GJNG>0F-J-L-1( LA< GJ UG J< ZUSIU JU 2( <>G G@3F-U-! LUU LAG >0G UUJ Z ·Fly" cl-I

_ Zt!LL-- LL1@LLL-1L|J••‘ ¤¢G4+** 4+4+ 4+4+-I- N•-• Ohh ~1'•-lud . N

V UUUU

162

4 C 44

-•·-• 44 F- 4

4 I < 44 Lu Qt 44 L'} LU ··~44 Q -! -4•••*

LU UJ**_ N 4 > U 4_ • 4 Z U -4ät 4 G < -4nn

*L) LD'!}•~ X 4 0*N < 4 O 4 M4••··• Z 4 F- •-•4

In L') 4 Q4ru 4 U'! •*• M 4 Z >~ -4cb •~ 4 D I- 4Q. •·~·~ 4 •-• •-• 44an •-ul

*P- LJ

*IJ.! -4 • 4 < G -4I ~¤ ät 4 cc ..J -4!·• I--

4 Lu LU U144 o. >< 4 I- > •4Q 3 ( 4 •—• M4M Z 4 -·•4U.! Q L9 4 IJ. O4LU I I- •II~ Q •*M

-M 4 4 -4nu hä •

*1

*—

-·~•·~ 4 Lu F- 44 'C3 Q-·•- F · N 4 :23 Z 4

Z LU •*I 4G- X 4 D Z -4I- •·~Q¤. -

4 Z U.; u‘\4Lu AQQ X

*L) 0*. I N4Q < 4 < Q4 ‘4D-• z 4 • ..1 ·-•-¤·

X 4..I- & 4 • Q. Q4C! F-LU-• LU 4 N M -44 .JO- • 4 • •-• -4I !J.!4Q. ••- 4 Q C 43 OMG •··• 4 LL. 44LU 45 •• • 4 • 4Z <+·~ ät 4 • 4 4}¤••~•—• er*

•*I- >• IJJ•-•- X 4 Il • ••|{~Z Q Qeü < 4 U. #43 Q••I-• Z 4 LU•••• •·-n4G •~ LI.J\¤.•·-• ¤. 4 Z-CJ -4Q •·-• Z•eD• LU 4 •-v4 • •·)|•• ~.• •~•I/7OO • 4 F- Q 4I- Q. •"*II>~!'•-• X 4 • 4• cs II*I| · u.•• ab ·¤· •-¤· «••‘·u·OGGG G •-••·-••·-I-!-UJF- ZOG • -M- --(\j•-•|'¤‘\•-• ~•¤•ZZ3,,| •Y~•II\ • •-• ••·

_ O O¤.~·••-·•··•ZLuIJJ •··• am m••.n mmI-F-I-•!·-• Z ~0O¤.q:g•-eq,} OOG!II····!-UJ\|·-• I- I- I-I-•ZZZZ < NOO¤.¤.F-+-•I·|\!!*^~OI!\ätZZD~•-• ~• -•

~·--••-••-·•-••—• ZI-·I •-••-•Z•-··•- I- I- I-F-xxxat-

O OHIO-!-I-·I···IA"s¤t¤•-·•<4·~<<I <•-<<Q.¤.¤.¤. •·-• Q UI- ZZZZ~0¤.¤.!·-ZI•Z Z-ZIG O-••··••-••·-·• _Zx¤:4x 0:4::::::Q. Z¤;¢¢¢O OGO4O O OOG IJJ¤.Q.¤.£.CJ ULLU..:IJ- IJ..§IJ..I.!.4G · LOLPIO O G OG~0 ~¤ ·-• N M <!·¤'\N

IJUU

e

l63·

W .LL;d •E- •WZ •Q •Z UN‘ F-! O>< 4*4 •-•$2 Q•

_ •WW_ WU WZhd • 'hr •

N•QU, .•C

2•••( •¢ • _l**•* IHW •

4*2 •-•D O 'I • ·Id •X4Z W

Q

Z MLu •-•Z •

•~LU¤¤~• *•_J•

WUJW ‘WWW W*•LLI••~W•Z ••*It\•¤¤•U'\WWI-I-·!-*~r soWi- O-•ZW4 <•¤¢WZ INDWu ct•§-Q·¤·¤ ¤c¤u.:ZWU„U3|„L.U•¢u.sW W WC O

~0 _f~

164

4%** •·lI·4I·* ~ Mx*4* •• 4 Fm*4%* • «-• ••**4% LU G -••-00ö** IQ •LU cb- |• •**4% I-•UJ UZ Z•-• *U‘\ 2·¤•··I•··•I en •• u.1• 1.n•. •4%** ¤¢3W OLU -10 IM48-** G •-• OZ LU- •I Inn Q4%** LLUJ 2* •LU M• Z N4%** QI- LL!O' •~O *0 LIJ X4+** >< •-• ••.u •-CJ ~¤| Z •·¤··I··¤ -.4 GZ •U ••· cu «·-•4%**

1...JUJ ZX MZ IOIA •-I ><·>•··II··I· I-•-•¤:• ua: -„• g IJJ •

***<3OQ —I•· O- • LD,*'** 2 LLLU MJU Qt-• 0* LL Z4%** •LUQ *2 CJ* I0 O LU**4% W¥OZ I-*··• CJM *• „J

öl-} chO 4 A2 U- NN l'• I-*4%* LU-|W¤'3 LlJ•· •·¤J-I • I-·~ •·4%** ZQW QLIJ •-OM•~1' UZ O*4%} LLIUJO •·O -•CD-~‘I‘• ZG •·4%** U.•ZZ OO- ·~UNI0 LU•—• Z**4% *'* LL¢ ¤¢U ¤*•‘7><•·I ..|r-• •*4%* I- LL Q2 U••·0•· 4 U**4% V70!-•U7 @• •¢-•~ •¢\| @> Zöl··Il· ••~|-LU UQ •-0MN| LLJ-4 •-rö-¤·••· U-tN•h•-• •¢'¤

•··•LU-••• · Zu Z-II>·l•4I· >•-• U MZ --2-·•~f<!· cccu •ö*-lf P-•u‘\LU•-• U* ON_•>< I 3O LU*4%* I·• It! •ch- LUUO•• LL OQ*Q c.>•I-I- ~ch~ Z•LU•-L¤• LU! Q4%** LUCL 4 U-(X ••-Z•··•|L•‘\ CQ U*4%*

LL Z2 •I• Q•-•><¤••• LL -5**·|$ LLLUQ •-••-I LU~•2<.'>~1‘-4' U.; •*4%* LUILLI.'7 ULLX Z-I-'ZI • Ich OO4%

*I- Z •LL• -•c,:¥u.J••-A I-•-• czO41- Q Lu4LIJ•-• ULULD ch•O..J•-·•• ch Q

* ö ICDLDG. •¥Z ch••~..JI·~IIh LULU Q2 .4%*** I- 42 <•u.J•~<-•O•*I ZI ULL1*4* LU¢< I-!-U-IN2*I‘*L'\* •··•!-· *I*I* LLLUOO LLIOI-I •O •«-••«1' O 2 MI- ‘*¥* OWI- O·O •O·‘*LU•--~i'I OO cdu- U*

Q -WO •UC? •0ZOC@•• OO Luc ••~

* *V) Z <3*IUJ~••u ••-Ind QÖ I" NO ~*LU-II- LUQ•.J< LU•Z|ZU¤•·~x| Q• UJN U*2* 3C]-I !¥•••4••••¤-•·~ •O O ••

-I--·¤· .•3:':>v> <¤.J-Q-••-• •~¤ G¤n ct •-G*9-*

<!-I-Lm •.„.JZ u..¤•-«•-·•N• u.;II··~ CLL: UI-U*3* >LLJ 4 P-OQ€¢Z'••~•-•0 Z•~$ I··•|- *-••·¤·O# Z>-Z <I2-Ii·><<C3U~·- »c •··>• ¤. an*Z* I-U I JIUJGZX LL&••*• ••-• U.J •€ GZ*Q* I<4LU ät 4~•¢2•-•LU ZII-•~• Z WI U•··•*3* I-I-¢I IJJIL-<LUZO *"7-•¥LU • OU Z-J*ch* LUCJI- LU ¤¢U• Z •*' LLO3 •··• U LUZ*

l- LIJQQ. 2 LUZ °"• |IOLL.IZ II ZC «-JO* *

ZI2Q •-• I-·¥Q •-•0LUO•-•UJZ UH- Z·I· ·l· •-•>¢•.uI·- I- ~•·-• ct -ZI!-2 ..1 .1-*4+* I¤¢•- 3 Uwch LU Ih ZZO •¢ LJ

4%**:::4 O O -•-l·Z U 0G Or-F LU 4LL*4+* LuZ<Lu oc ..1.Jus Lu •-ec: UI--4 ..11.1. c.:~·-• ·

*4%*I-3 O O ¤.<2 I- 2 .-Ju.:

*** LULUWO 3 2LU•-• 2 G GQ 4M*-II} ¤2<I< In •-•¤:O ¤·• O QQ U-*** ** *4%

*_ *4%* 0°·¤4%** -Ö~¤·II··I·u· •-••-•4 4%**

UUUUUUUUU UUUU

165

•ZGCJLU*'•l•

LU|•< I1G-! I-CZD LLDu u.,LL.4 GGLL] •~¤~•~

{L) ZI- ¢~•¤~•~C< NNNl-LU •-·•.J *4}*C1 P-·D ***II·Z{ {AQ g•¤••••Z.! Z22UJU GG ~¤•¤•~¤•

12 u., •-•Ns·•‘!<•-• LU Quo3 41 IIILOG < GGGP---4 - LU OGGZG csv.!} GGGLULL 42 • • •{ •¤• -nu-nu-4UJLU V!] ~¤•~•~•.-II * UD -·•| IILU}- 2 <-I — 2***~·- Z-I -Z22QUJ O Qc LD¤•~•~• • Q4d Z ULL ZOUO an GZD LU 4 u.:ZzZ anCLL „.J •-LU .4LULULU LU 2*ULU I- GI I--J...!-I Z LUU441 x I- xn.uu.1•.u LL 1%*•••LLJ

* LU •-\\\ IL CZ I-•_GI Z ILU 2•-*·~

—-• C3 LLJ•-·• ~·•~NN hx ~•Z2.'Z -•·~- I- **•··•LU <·I··l|·* C 4eee Z22 V7 Z 2G-·I LU·H~·l|~·N· ¢/7LL LUUUO eee LULU • 7•<I- • 1*** •-•U4 1222 NMM • I')LU •LUI 4222 U1! 4LULULL: OGG G I-••··~U4GVit-

•!|·--•-•>LU ·N•.|..J.| +0** LU •-•~·•ZZ

Iueßß •¤•••¢¢\j('h Q1 •~}-•Q••L- •••¢•¢~Q •¤~••~[|l„L|‘••¤¤• _MZ ZUUG <|·- Zeee Z22 2 ZGLUG H>•IU ~•·l•·l·l» 2 ~·l··l•·I•

~·•~·•·-• < • •·~G•-•.-I-|•-I G44< 4 G·<<< •··••••N G ~0LU• U*•< CIII

‘CIII GGG 2 •'7lJ-JOIZG IIII MI! XIII 4+*-I~ G •-•••ZU*I|LL<LU LU<4< <l-Z LU4<< 4<4 • HLU Ov-Ihre!-•I IIUUU LUGO HUGO III LUG1ß <HH|I ZZ•·• 4HHH III LU 7C"'9C<C X•·•*•·~C ••-•UJI··• I-·~** 4<4 I U-Gwu. Z-emma .:.44 z‘:·-•~¢~nu.<.¤u:L9 •— c:ZLU <~•~•~·• 2 1 <~•-••·••··•I| IIII ¢!}HU·-•-G UOUULU CGI-U UUOU *** LU •··4'>*·•—I V7 Zlul- G~1'•-¤~0 .4LU -| Z'•¤• Zeee Q Q<I LU <¢ LUUUU I GP" CI LUd IILLU viGLL GLU4 V7LLC ULGLU <

UUUU GUUUU GGG

I

166

O _ .

LLLLLUät .D

O2

LU NQ 45Z 45< I-CD 4• Lu·— Q

··~ .4 Q ·¤·4 I I- 4•¤• ~¤ Z I-•~G es •··• V Lul-+ I ¤¤4an an LU ~nLLI*5 *5 M \Oh • Q ¤~*•··•

~ I- *54Qhv an {Ö •}¤•Q! ac •·-cw _

D Q Q _ ~•¢'DZ4 4 Z c/I45u.1Q c < cncII I <¤••II II X ZGan •¤ hd +••'•"! '5 Q ·•~NO• ‘• I- *5~·••-• •¤• < G•\•e ~• Z Qu-•••~•-bt ¥ -*5GQ Q cn Z>c••404 V5 LUQ•-•

OQQLL U-I I4~•4I I•-• Z I-·Q¤* ~·• UJ LL I+ —cn Q LL •*•Il

u. 4 Zu. •-• Q-••-• LU LU•¤• I- •-• *5LU L/7 +••

QD ·=c•-acZZ U-I G•¤O~•Lu-• > u.z•-42; •LL•·- •-· Z|I+ u. u.ZLLLLJ I-LJ •·* I~•! DLJ Z LU ||N•·~• CBZQ•-·•LU LL WQIILL. Z-•LU _

2l-D LL -·•¥.v-·• LUI-5:LLJZZ Lu •-• zzzQ•-• QQ Q•-•¤cU5- Z •-•Q Gu--Z':Z U. ZI-Q

O CD O CDUJZU LL Q Ucttu

45O OO N•—eQ ¤Z>?‘ GQ•-• •-••-• •-••-•

LJUU

167

***• •

***an • LU*Ö* < • •*• •·~ C LuII•·II-Ö I- u.t•-

•-• c 3· II-*Ö Lu •fZ>< LL ~U•~ C'I|·*-II- cn I-•< LL•¤. • QL: •-•

II-II-* I ¤.UZ I LLJ-Z • •Z ZII-ÖÖ ät DZL9 LL-ILU LL ILLL6 I-II-ÖÖ M I/I-••···•••·~·I·-

LL• LL..I U-II-Ö* < DIL/1 •~•·~<.'>•· LLIVI LLII- LuII-Ö* Z •·••· -IN•-••~ LLV7 LL• I-Ö·I*·II· Z! I-LULL -••*/7N •LLI •¤.II--II··II· ua ..1cLL MI-LIQ• U ><:: Z·¤··II-II- Z t.ucLu <..:Z...Iu.s •¢.: <u.• c·II··lt-II- ccc: ~—-cZ ccc II- IhÖÜÖ LU •Z• •~>(•~•• CDM 0•.• ZZÖÖ* I Q••LL -•<-•>< I-Q. LUX Q.*Ö* I- czft/ItL•·~ -Z-•<•·• U •·<I

<*ÖII· LLJu.I QSI M·I•··I··II- u. >> cc I·II·** C3 U£•·I.n ~•u.I•-IM •-I zw-• ZII·*-II- ••·c.c •-··•c•./-I-- u..1I- Lum 53II-·II··I· • m•.u¤..• •--I.: •m L;4 •• •• I-II-ÖÖ M UC3C?>• ~•‘•CD•C MM OG ··~· 3*ÖÖ • •-G•·•~ -ICD•·•-I-I QLLI Z• •—• LLI**4% NU¤.N UO-•„„>· LLI- tut')~ Z·|I·ÖÖ M U‘70>< •Z•·-•LL•· *··• •-I•···• I-'II'*<Il‘ D •••• •~LU •LL.•'• J UJI/7 G. LI.!I•·Il··II· I- •-•u.c,--I •-I•NLLIM exw •c 7: I*Ö·II• U ULL•>¢_ ••~~•x~• GI OJ In I-*Ö* LU •Lu¢.'J• O-IU •N CI- MCS Q 'II- II- > UU.-I- Lu-Z•·~>< Z CJ• I ILII- II- ••I/tn. 20-•-•• LL CQ. ··~ OÖ Ö Q L-LIXQZ -22-•- UJQ QLLI •·-«

It- II- < .1<.Iv> •„„;u.1•u.m I •¤ U •*I•* Q ¥!IG> •.I^LL~ I·-I- t"^.I G; LLÖUÖ J LJ¤.•• •••LLI-•LLJ•·-I M LJC •-• LLII-!-I-I* ZJLLI¤.L9 N••O>< Q4 •• II- Lu...1 ¤3•LuZ •·•~¤•• CJQ NC'? ^ MÖM* < •C¤I..U LL:•-~•-••- I UI-IJ ··~•II- II- c <c-I...I T:-LLI•·•-4 I-4/I ••Z- N

*Ö CJ- I-IO!-·-·• ~I—¤~·•~·- I-u•··• •-·••I·- * M·I|·U-1* ZN U.IuJ••N U-!¤-OQ.I- IE! ULu• II- CD*2* •-• Q•'„I&| .t'„"JUQ& I- •2M I- I-**·•II- Luth •<.9Z£G MI-/IZOD 2** LLI•I·~ „J U*I'·* > <Z•LU• UC.2••</1 I3 ..IUL/I Lu LU*3* •-•• LLILIJGI-*:**2 ••~¤~> VI ¥ZC Q >ÖOII I-0-·cc•JLL¤•IC'.!¤’J•~-•~• I• U--I II-*M* U <U.IZI-<LI.I ••-I ••••• Q.O IDI> < UJ{vg}- LLILLI ~¤• -•Z•• •¢•nQ.,•-I (LU C•• I- L)Ö Ö LLI I- ••-*I‘ܤ•G¤• MZ •I.LI¢\I LU y,·|-VIII- LLI-• Q QQ~•¤•LU •L.9 I*'•

<C3>< Q GÖ II- LIJ< Lu ÖLU<QC3•'•Z 22 LUO•CJ~• LL ·*

Ö Q > -IZU-JMO•-ILU OM MU-•Lu\Ö*Ö Lu M <~•MOU~•-I I-LLI <5I><2•-I JÖ*Ö IUJ u.H/I<O'5GI·• II- -•-• <ÖÖ* I-UJ Lu MIA U- LLILU I- •-III I>•

***L/I Z <Z ZG U tI•·~ QDA Ö-ÖÖ LLI~¤• •-• I-EO LIJ I-••-•LLI •-Lu

ÖÖÖ Z I- •-• -• LLILLI > -2 U12*Ö* •-·•• D UQIA IQ LI. O¤.Z LLIM·II-ÖÖ IC. G •-*2 I- Mc-• MOII-II-Ö MG M -I•-ILLI I- ...I NOI- LL*II·* LUI CC Q.<Z MI/I ...I Z LLI·I·ÖÖ I-I-• 3 I'ZLu•·-• OD < O O IV?Iii 2; "’ I °"°‘° I *"" ° „° ° *°°". II- II- II- II-*Ö•II- .* * Q41-** I-**4+ N$1-**UUULJUUU ULJUU UUUU .

I

~ 168

2"}~•

_ Q.DG·|I·N

_ •~'7••¤•nn •·I•I-·-I .LUC* -GO- WLß~• Q•I··- I-+G• U3

aß |*5*0 •~•> hl

|¤¤•* en~•••• U,L/I"} ·LLm• LLI<•-·• U,. _Z·• Ieg) an++ •—•

OLLI ~·•LU! LL

OZG LLGG •·I·- I-ULUQ•···•t/1 GZGIIII LUII••·1u.: D-•·-•Q x Z•-•II IIQD •·•~• ·•···•LLIC*|··• I-u.I.u „

¢NI/5Zu.2CDGC3!-UZZGI-O unc--¤:NIAQ II-DZF-DD DWZ-Q LJQCLIJ

* O G0* Q

. N N

169 _

4+**4+** N ·—*4+* 4+4+4+4+ •·•

4+**4+ ¤.. • v1 U**4+ X ··~

|*"•LL LU4+** V5 LU ~0 Q CD LA*4+* •-n I- •~• ••• M4‘ \4+4+4+ • .1 — ¤.•—•.uu. I-4+** Z LL. LU 4+ Q.4UCJ LL4+4+* CJ LL U 4+ 4QCt4+4+4+ •·• LU U CZ -4*4+* I- O 4 LULULLO N***

4 O ·•~ •N :1 hd •

4+4+4+ I- *5 •-•-

4+ -I-4*···· N**4+ •-• Z - Ln 4+ U M*4+* U • Q. ~•· U ZLUQLU**4+ X CJ Z ..1 LU -•¤/IZM LL4+4+4+ u.• u.: u.: LU en 34*- O*** Z I" U \ Z4 C**4+

u.1 • • U I OUQ Z4+** ät I- ¤~ 4 E •-•LULL1UJ C4+4+4+ 4 Z -4 • I-EMI •-• .*4+*

3 3 ~• •·~ • 4 UJI- I- '*** 0 CJ LL ~1‘ • M¢¤O .4***

I U LL ~·• ° N LU•-•2! M**4+

I- Z LU „J • -.„I~1"¢h•··4 LU4+**

M • G UJ Ln LUOZ .-I4+*

4 ln • Q •·-• UMCDC5 LU4+ 4+ LU vv -‘ Q Q U UI-U U4+ 4+ 4 •··• 4 • 4> •··• U4++-* LU Z • -• • mm.1 4•*U* I • M •~ LU •-•¤. Z*LU* I- LU UCM v4Q Q. ZG*>* Q UJÖU L/7 <u.1I-4 4-•*0* >• O Q UI •··~ GICDZ I-* * CD •~ U OZLU •-••-vi GU _4+

*'7 ULUU Z LU>CJ•···• GU-I*LU* Q•G • HIQ O I-•"> 4M4+24+ LL:• ¤. •+-4 •-· I-C: Z

·-*•-* In -• I •·•• • I- IO WQ*5* 3 4+

‘»3••~Ma-- ( ;;yL/7Q•~ I-

* * 4 -· UN -ONG-‘M •··•-44+- U-I*¤4|· U •I g UU

--1.;.;•.u< LLJ<*M* Z UID Z•-IUI I·•.| •·~I- Mn LLU*t¤* M LU• GCLULU ZLU• U LUX LL-•*3* CD * UI•‘*UI-LIUU DU •O~·- •-JC) LUI-*\/7* I·• I UIO••UU Qu ¢~U-IQ M

* *U 44u.l-·~ 44 U4 - NULU >~LU

* *LU II ~•~•Z•-•••~•• Z |*UUJ I->

* * > +— ·U ZZ*4M •·•4+4+4+ ·~ U¤¤0..1•„-•y~ •-•.1·» QQL.1 u. >LLJ4+4+4+ Q u. u1-»u1u1•·-U.„ +1.u* •-•~•LUU-I <>4+**

4 U. >-IZUZ-I-I I-U• I--I-LAILL 7 MN*** O LU 0<•~•U3LULU ZU• 4U\+-O Z Uh-**4+ UI 0 I-U4/74GUUO 34th MI-UZ •

*··•4+** U LUMIA UUUII O•·I- UJMIL/'ILLI •·-4 LLH/I*** UI Z 42244+- UC>• ..1-• LULL! II CCD*** 4 -•I-IO~••· 2 Zcx LUOZZM '7 30-. **4+ Q I"•*•'• ***00 3 |I*"*-• U °"•*"'•¢-'7 UI4+·¤··1•· Q :u<¤¤usQ< GLLI- I- um I-us ca Qu.:4+** Z D-•*ZILU Un-•ZI-4 4+-Z Q G ZI4+** M...J.ILU-•M Z DZ! 4Luv‘! N -•|·-•4+4+4+ LU c¤¤.<Z QCJ-oc U-|•··•>V3UJ*4+* I 3ZLLI•-•LL ZUMO IM•·-44I CD OZ4+4•·4¤· I- w•·-•¤:Q•-• LUZ¤.LL •-—¤.¢.¤z•- Q 1-•-*** **** C4+** O4+4+4+ •-4*4+*QQQQQQQQ UUUUUUU UUUU

170

Q•WOgn I\Ä N

X *1Ü ÜCL G.Z Z-G LuU I-*

-5Ä”

I- *1Z •3 nn

OO ~·•Qä äO Z~• <O L:.J•J 2I!-U IZ I-LJ ··~W-• U •-•IN ·•< ~¤I-•• ¤—C>II u. A

N 1 •·~ OLI-··~m ••Z LULU•¤OI| MXU.J~• ZG*1 •~ •--Zc. GO•II••Z Nu.: •£ u.1••-•¤-•-•LU•• IIO LLILL ZOII•·•*•ZQ„ XOZI-•*•LIJ •II‘7~¤•|-ULU•Z U~·- D •·••*• LLDO UJLLO7 OZ Nr-•OLLZOSI!-·•··••··*|ILL z•-•u.s—-•~··Mu.1•-•u.¤U•-• NZ•-• UJI-D LLNOI-D1 cb zzou. Z22IIIL ZO O•¤NLUO O•-ßI•··• LLIO LJ!-NGO L}I—D

Z ZI-OOO DU-FZUO UQCUJ

OO OO•··•O MN

· NN NN

171 .

4+***4+4+ •**4+ ¤.•**4+ ••\,L4f„§ • •4+** In S.!-UGZ •·~ •~

**4+•-• 2ZG..JLU •·-•• ••-4

**4+ G GGG.-! ~••·~·~-·*4+* wtu wU•I-·• Ne-4 •-•w

w***

L/}|¤~ •71• L)—••~•Z •-44+** LU< G•Z¤. *@•'•Q.LLJ L- 1*4+* ZG M>£•Z •G-•C3-J I/><***

ILS. CUGOLU •·-•Z••·I·-· w***

ILD O-IUJI-· ~•LUM••• LUG*4+* •·-• wCJZ• -·••—••-1- ZLU**4+ I¤•I•• •I•!···· LJ-LLI~·••·-4 ILI·I·** WG I'Ü•I.IJg• ••-IBG~.• gw

***Z wu-ZX ·*~~•G1•¤.. •-•I.LI**4+ LU •IL •< O‘0U•~}I I-g4+*4+ II/I NLJOI LUZ'5•-4LU wu.*4+4+

+-•-• QLLLUL3 ZLU ••••-• LU*4+4+ •·•·Z•-·•·..J•·~L.‘>• Luca:

4+**P-- -·•><><w QLUG•·••~

I**4+ ••-• w<!Z•· LU•LUwN 4-LU**4+ IJJ •Z •·u. Z•·~ZG• dä*'l•* 1 g„)B•L,)LL¤~ ~v••¢ •„JlU4+4+* :>• ••LI-JZUJM LJ-0::2 ••·-*4+* y-• |_u•·•-ng)- •h•I.U•••••·~ gw4•·4+·¤— ox .4¤z un ·~¤.Z•~><•-• ILD4+4+4+ DG >cC‘••u.c ~D><•-•<~•· LUZ3** M-J wZLUU•.I •wI-ZM ac**

I-Q :}LU¤LU>- •~L.uQ~•¤.g9+-·· 9-*4+4+ WI w•GO•-GZ •¥u.:•-w ¤•-·4+ 4+ • •L9w •I- I•U~•-GGwG

I--*

4+ LU <ZZSS. ZI„uM.-|.J•..| _ZG4+ * IZ 4••UJ•C§ •_|••QC•~)• nnen*¢* P*!¤| UJ-IGGV, G¥G„I••·•4• -*4* www •> ww}? •·~~•- Qu.:-px-u..•·¤· ILG ••::¤.• Z:Q·—•-•LL·- Luz*2* Qu; ,4+-••QN ~•¤:Q•-••g•- I-•¤•«l••¤¤•* Q! U.:¤,Lh•>< I/1••~••(\}L|,,|)•— Q_p•*,,14+ I/7G LJ3wC3*• w-•·~LL.~•1S. Q:4; QQ4+

*ww <Cz$.’OXNI¤•lUZ•w M4+LU* >· • •·•••-••| •..ImLL•-··-•> w4+24+ www (9**-LL/lUJQ¢•L1J~«•SZ•«• Q •-«•*•-* <Z•-• I-U-|I&.¤1I•0L.‘|G•~•:„I.•·~ G LU*|-* Z<V7 MI-UI-I-|.„.J•-•IIUUMN·LLf*\ >·<>*34+ < >- <G>¢C>+-|2<c:)••-•IIJ~• an •-•,„|

4+CJ* G.;-

<••C)I1J•ON LU ¤:O*M* MLL|< M ~•O¢~LJZ~0•>< 2 l-V)*$* (ZZ < UJ•¤~I•v••¤~• ld <• •

1*3*I„u•-•< lu wZ~·••·~><U.x•··••-• 5- Z S. Z4+v»4+ 2:: 2 4+><<·-¤<c>—·m u.1u.• •

*4+ •·••MI-IJ •'• •JIUJ•-ZGB.- • IAIP- •-•

4+*

LIUJI ..1 <~•MI'¤¤•L.JG•-4 LU wl-V7 II* *

I-•-u.!IL<LJI-U!IO>< .-I LU •-«

* *<LU LU MU. • •·~ ZZLU «-•

**4+ Gt- Z Luz \ u,v·-•Z +•-•

**4+w D •·-• I-··:¢O Gt- \ LL •-• GN4+4+4+ Z>•C I- •··• •·-• ||-·•-•—- •·-•G!- ¤¤···•

4+4+4+ zGL9 3 www P- I- I-LU Z*4+4+ C3<G G •·-4+2 ZLU}-< w¤¢>- IICI4+4+4+ u.•-UC: cz ..1.1u.• *::.42: Lux zo4+** MMM G ¢..<£ Gr-••-·•M LUI-··LU4•·4+·¤· UJLJI 3 ZLU- L.>I¤:CJ 2-1>***

S.<4- w •·-MG 23S.LL I-•<LU*4+*

4+4+*4+ *4+*4+4+*4+* ···•4+*4+4+4+4+4+**LJULJUUUUU UUULJLJ

I« 11

172

Q•-• Q. I-A LU •~Q I- NO • • {In4+ LL

-4|··• LL N I-N u; •-1 .1 •

4+ C1 LH LU an4+ •· Q I-I- "> •*

,4.1 Z Q. < 3LU • I- LAQ Q LU Lu LU~• LU I Q MÜ Z I- -•an •« ( \ nn I-4 I- Q

- O ZI- Z - LL •-•LU 3 LU '7 Z MQ Q LU ~¤• •-• AIC LJ LG I- •CC Z -• A QCQ •· - D LU •Q • vv x , Ln Z LLLQN :1 CI Q >< LL•\ 4 I- U Z LU-·I- E U

-• cz+-I • LU ‘§ G"•LU LL! > • Q 3

·-•-C Q •- I OI '•'* Ü C nr • Z• A•-‘ U < Ln LU C2•-• C¥I•¤I -3 Q Ln M LU L/1-• Ü-• • .J < Ce Z •-• ‘

¥ I-G- A Z I-• •LU ~•• V) LL XLJ LUG CD > + + LL CDO G+ LJ *"* LU •- LU I-OI -•I··'• • I- COM •-• M ULUII •--• .1 U OU-ICD ~·• •· LuZ-• •-•- LU Lu CCZI···~ LL LL >•'! G~•A U IL OCC•L/I LL LL Q•"°• LLIOO LJ LL LUG ••"‘II LU LU I- LUII-• ZIIII 4 LU ZCCIILU C8 ¥ Z Z7-LU ••-•·~ ~• ••II"!M\UII ~·• LU •

gg; Gl!-ll-! L- Lu •-IQ- QD- LU Z I- '•-•NLLZ II~¤•-• U I |III•-•L^I·-ZI- > LU • III-u.••-•L1LJ-••··I-•LL1u.: I- •¤¤•LU~••U·v!•-~·•LU.1 U OCCCC-•-•¥I·-D AQ.D> • MLLLQ I-LLDO 4 mu-•N•-•M•-1

ZZCDDZCZ1 LU• OOLL ZLLZL/1 .1 CE- O-~0LhLn~·• I-LL UN-LUQ OLU-·• A I-I-|••I·-·I—I-CUI--•C>•-.1 4LL LOLAMQ UMI--I L/I ZZZZZZ0Z Z-I ..1LU Z-J •··• •-••-•••••-••-••~¤•OO D4 DM O C14 Q MMMMMMDUC UU Z• Q UL)

LU AAAAAACM .CW ILL*'* I-

N-4 C LH CI-P- ~¤ U* Ch•-an-1 •-• Ln LhUUUU UUU

» v

173

• 4+. Q. 4;-U1 •2 4+Z LLLU 4+•··• LLI- 4+(LU U.I•

*MI LLX ·• 4+I-I-• •< N 4+V1 LU XI • 4+Z3 <U X 4+GWG II-! ~n 4+‘ ZG; ät/7 X 4+4 • < 4+Lu: •·0 Z 4+• I/!U1U C5• LD 4+CJ LUDUJ OLD •-• 4+O U1 I- 2*··* U1 4+I +/7+- LLJL/I •

*I- LUOZ •Q- 4+UJ MZQ (-Ben] li

*•

2 I- U1 ZC! •• 4+ •· ‘men: U-|• X 4+ Ng -• •-Q. „JQ. •.• 4; •

M N U.! 4 LUu.| >< 4+ m4 4+ II-C: •¤ < 4+ u.2 ~l· I---•'I CD.! 2 4+ •·3 I·- Z MCD U 4+ ~LU ..1 I-U O O • •- 4+

· Z LU Z•I- OG U1 4+ IIG *-ll/ÜZALJUJ • 4+Lu 4+- 2ZuJ •2·~ •·~ 4+ LUI <•·—~·~ :;::2 r¤•I·-· N 4+ 2. .I- I-~••···• Ls-J2 QLU• • 4+ •-•

u.JQ..- I-*"*LU •ZM X 4+ I-' 2 QQQ. UJXI N•I- ~·• 4+C3 ·-oc: ¤<•·- uvm >< 4+M \4+C6 2 •ZCD 4 4+5,;, -+-• Q Z -4-•-J Z 4+··--J- I-LU-• UZ>· Q 4+Z •-•\,U•··• I •·•• 5,;,; ·§•

_ Q ~•[§~• Q!-•L/} UJUJG] •*•-• +-·I·Q. LU •·-• JQX ·•~ 4+

I- Q.l¤0 ..10 XO••-·• 4+4 :•• ,,•¤:•- Uu•-• • 4+X ü-;,;,; Q-•-• QQ m•• J 4+ ·,,5 In-ne LUU1 •LU<.'J >< 4+•~ LU •-—•0 U1M< <¤Z 4 4+In Q •-•+•-•• •-• LUDUJ I

*-U ~•Q.-• QU1 MU-I Q. 4+LL 4 CID•· +-2I/4 <">I-· LU 4+U. -V500 U<LU ~• • 4+LU Q |I>~f•-I LU U I- X 4+M Z ··~II >¤-KU U LU• 4+ 4+ll < •·-••-+-I-LU LLZCJ Lu O-- ZQO • ••¤~ ~¤•+-ZZ: •-••M > J •NU\ •-• •·•-• m M-·•-••-Z LUI-CL u. UJLU •—• \•t\ U1~• LU CQ.MM•-• Z Q.! QOOIII·-I-LU\I- +-0 -• 00Q.Q.I- •-•>·Z ..I «I·~u\u\«¤m;4zz;•« •.•P- Z I-MO .J I-I •-••···•ZI-+— I-•-• O DUJ•-4 4 IIZI-l-·I·-I-LQMM-44-4U U O>I·• U I- ZZZZOQQ.!-22•2••O MU-JD Q•-••·-••—«•-• ZMM*M•.I Q •-I ZMMMMC3 OOG4+O*uu DI-Q u.4cL¤.¤.¤.c:: uu.u.·¤·u.> wdr/4 4+4+ 4+ 4+CD LHLÜC CJC: ~¤ •··• N~0

UUU UUUUU

174 _ ·

Q at en ‘nn ·|• LUP { M •( ·l• In •M { U1 -LU auf ·J •{ I •LU ·|t—It 13 •U { Z mU •l *•• •< •«l· >< ¢

LO'} ( •-|•l Z G{ M·|t •

ul} •Gl {•·I· ·I·>· •{ {

I-· { LU {*'* {{ Z AU { ¤• •G •{ I- •J •·I· NUJ ml •> •·I· QM{ LL•·-I{ · •

Gl ••{ Z·It •* •-• .{ 4 • _I-• {Ü M °• ’Z ·I· •·- an .LU •{ vi •Z •·{ 4*LU m{ Z •-•U •·I· G Q4 M{ Z •nl •¤¢* hl •Q. Gl ><ch •{ 4•-¤ •·lt I {G {

{{* {

* *•

•{ fn •• •{ Z M 'U- ~1'{ LU •··•Q r-•{ £ •

Q p*@gy•¤••O Q*Q_jQ .

G {{LU*{{ ‘{ {{l{ {Q Il*•LUQ¢•• ••{ •Z ••m mmlm•¤m{I-· P-•|-{P-t••|·-·( ;•¤•*•« GI- I-I-{O- I-•Z· <•~<<·|•·¢! <!•·¢Z•zx‘·••·Z INGM{MM·lt¢ QC•I-GO GG{G Ga)!-UZ -LLZU-U•{U.U7U„U„¤CLU

{ { { ·|tG GG G GM ~1"m ~0 N A

175

„ Ö******ÖÖ·ÖÜÖ******ÖÖÖ*°Ö***-lv·||·** ••

***J**Ö V3

ÖÖÖ Q*** ¤. •~_*** V7 •\Ö**

O\***

Q - N•

·l·*·l|·Z• V-••

*** 4..4 •G

*** va xz·I•*·I• <¤ ••• •·3

LL¤„ CD •GÖ*Ö GW LL LL*ÖÖ Q. Z K**·I· V)-I •-• . <u4*4+* ..I •· .4¤¤**Ü -I< G 3

.***

•-JU Lu ••~ LDZ' ÖÖÖ < 2 G Z<***

U• X LL •-•U

***«-• I Z- cn

* *•^ • •·•

Z an

* *·-•U Q •- mc u.

Ö Ö II-! G G •¤••-• LL*LLI* U E CB I- LUÖ>Ö ..„I• • I XD K*-IÖ Lh C2 • •-•-I •·*G·lI· •Z LU O KG G*¢/7* ZG Z LL: •-vi G3* *

O-• • Z < ZÖ Ö P•!l•• LL • IC] •Ö Ö I-•'• LL••· OZ Z OÖLU-I- •-•G LUN LULIJ ¥• Lu*2* GZ KI ZI • 2*•··•* ZCJ •Q XD- • •*t-Ö GU LL• Z O O*3* U LLI•·~ ••··~ N U4 .*¤* Q wga mc w z*KÖ G< ¥<• LL • ><*G: (G ~·•~••G•~ LL|•G\ Z*3 Q.4 LU u4•-• xuawx •*IA* .4 >®Z••

~·•Zt'¤~•• LL* *

I-- -J-I•><tL <• I-· LLÖ Ö I-Z G-IILL LL I-< U4

* *mau m<-Lu QQZI ¤- ac

* *K3 u.•u..¤c ¤.~•4.•-•¤: Du. -'*·I·* •-·•G •.u¤¢LL O¢nZ¤cO hn-• .4

*** LLLU Z LuZI• —•¤.u. vv cn***

vv •·-•l·-:¢GG-J-- C5 cn · ·*** zum •-·•- •···•LL.J Z ß.**Ü I3 3U®v‘!2<LL Lu v>ZÖ*Ö .|-V7 G•-•*Z•-•U•-• K*** K-1.-ILLI .43•I·Ö·l• KK ¤¤.<Z O-Il-·G***

GG 3$LU•-• ||<U4Z**Ü

LI-LL L/$••••KQ •••UKL£4 -*Ö* *Ü** G**4+~**-I• M

****Ü

UUUUUUU

176

**4% "*4%**4%*****4%***** 44%****4% ·•~

***•·•

**4% •·*4%* •·~*** *74%*4% •*4%* D*4%* Z4%**

-4%** Q**4% Q ‘4%*4% <***

•4%** •-44%** •4%*4% •·~4%** Z4%** *7 ·*4%* •4%** - ¥**4% •-•**4% an*4%* Q***4 - Q·|··** < ·*'I%*•¤ •4%**CD D4% *I„L Z C 4*

*2 I ¢C ~• CJ‘ ·l·L|„*£ N I- I-·|-Q4%• O ·~*¤.4I·Z C Q- CmI"• V)! (§~•

4% *< •- *7 V U) I-4% *C •-·•O I •· •·~C£·¤·u.I*-I ••g3 -4 ICQ*2*•·

•·-•'7 ';•-·%·I-• Can·u·•-•*¤O D •|··~ 'QZ •··••-••-• •·~Q¤*I-*QU•„ Z IND••~·•II* 7•*D*<Z • I4-IDXQ I··I+ •C||*@*e•¤••~ ¥Z 'QZ Z~•@••• •-4*¤¢*<••-• • •-•~•-• Q<7+¥¥ +••·~*Q*LL2• ¥• O OCI-||Q\• •-•7 Zus"!*D*Q•< 7•-•'7C+><><«| <|·•·¥¢h UJtu~„•_;•*V:*¤•ZC¤I·• • O << O! ·•• II IIDDC ••-·•* *Gh•.I•• "7III| •IZI II IIQII ZZQ +4% 4% <-•I·—

~ Q ZG nu ¥¤¢~••-•<V>2u.¤c4% *LUCCC ¥7O II II II-•-•|¤·•%·~<v5¤•7%-I-• --D***2.JQQ •-• LLII ZZII QZII4%**•-n •<¤/lv! CZ ¥¥DLLg GO u.Q•-4 LU***I·-x c¢M•·-•m•-·•"3I•-• UUI/7•-•<%-•C.7D·••4%4%:¤u.1¤¤¤¤¤¤•.u zu.zz***C10***L!JQ QZ•-•¤:***¤¢LU-1.1-IUJC U•··•I-D***Q!·•<<I<I- Zh**4%DZU.JLLILUZ Qu.:***</Dv-·•¢¤i¢•·-• Cc!****4%* CC C C**4%

•-•N M er**4%**4%gut.}

177

QZ

A LU

v· I

178

Zää**4i-

iii:4+****·I·4+**4+****4+4+**4+**4+***4+**4+***4+ ·**4+**4+41-4+4+ '4+4+**4+***4+4+***4+4+*4+*4+*4+·4+**4+*4+ *4+**

•-·•4+** •*4+* * _4+** * _ ¤¤ ‘4+*4+ •-• -4*4+* • _

-4+** * ab. ii ·I••'* @* •

*4+c¤ A! •-•*•J*• ~•• •

*V¤*2 E-·•**¢!J*• •+ M

*¤.*Z •-I2 • ·*{h*§ •~• an (4+ *4 *Q x «l '4+ *G ZG} • ~¤•

*LLI*„-I * •4•··• CJ

*2*- •···• 2 4\ + cf: ~*•-•*¤ ~• „J -|* 2 4*|·-4+Q G • •~ ~•+- •~ •· • .*34+4 • m 22 C3 22 O U-4+¤4+-· * .J •-I CDI Q•-I co •*;*...4 •-• • •—• 4 X--• 4 2*·¤*|/)2• < II ••~ Z II \ .4*3*-¤D•4 JZ! 22¥ I! 2* ~·•*¢/I*¤„ZQ|•· • -•"°«J-J-• •

~••··•-J! >-·I• *4/7 •..J •~m •·O ~·-G3 -••-40 ~·*¤„

* *4~·-I-ät--•Z+I+-~• Z+I¢¤¥><

**UJC‘•¤C3• •··• O |I+•-•

~·-4***Z.J¤Q¥||22¥Q!I 22>¢|I¤¤•„n,**4+** 4W vv Lu¤:Z I u.:**4++-% c¢¥|| II II *D:£ II II II*'• AD4+4+*2Ju.•m®u.1 IIXZ ll Ztll-JZZ*4+*¤£D**L¤O24¤¤ "’·-C

!!4¤:— 4•·-•cc4+**¢Lu-J-tuJ•—••J„.J•J•·—¤‘:I-—N>¢.J.J.•c¤I-LJ+-D*4|·*¤3+·-<<I- Z 2+-G**4I-DZLULUZO OC Ol-IJZ***4/1•·•xct•-•¤ UO UQZUJ**4+4+** CD O**4+ . •-4 N4+***4+* -uuu

179.

*4+***4+*4+**4+* .*4+****

_ _**4+*****4+**4+**4+4+**4+****4+*******4+* -4+**4+**4+**4+***4+**4+*4+4+***4+4+********4+*** nen4+**)- ° ‘ · •-ANM***U .**4+2 G _ +4-+4+**--• N**4+• Z -••-• •-nn*

*>' • Q ~••n•~••4+ *I/7 •-• +•- 4-+ XXX '4+ 4+• Q. www*)-•I-X Z G X)- •- 4+4+4+*Q„*U • LD UU X <<<I4+X*Z I •·~ ZZ n www*(*|¤¤4 • Z1-I F-Qld nn an an4+•/'»*•

>- ¤:• 4+* X •-• --4-++4+ 4+X •-• GO -•·~ an -• -•*

*07 • I-LU -4--4 4+ O X ><•·~··~··~4+u.s4+• >< Lu• +4- < Q V7 vv-wnzm*Z*<<•··• ¤<)- ZZ an 4+ Z 4+*-•*U‘Jv‘>• U II O < Qt <!4-4-+*+-·*•-•·)- -2 •·•~·- 4- •··· V7 D V!*:*2ng; cg.; |- nnn*¤*~••-dz G• IIII ^ O 4- Lu Q4·—«—•~•*G4+>-~·••-•ZQQ >-X)- U d • >->·>·{¤3*¤.>-•¤CGZ X)- -·-•UU

·~ Z•-Vätnt/I•< hin! ~¤•22 an •¤¤• ••~ Qi*¢A*<•U|··'G• ‘*••‘~Z>··•-••·• In •·•••|II|||{ *v'J-ZLu •-4 GO•·<n •~¤•>- Q Q.)-* *

•·••·-•ß•• •••··• 4-+ Q •-4*/I •-4Iv>•••·~•

*·¤·u.1-••-co +—+- ll •• • •-•NM«l·*4+ZXnGu.:lu -I-III X)- ZGIIII +··+tIII-¤·4I·<¤·•-nm ••• •• ne-••-•u.1 --•..u LU,.) +4·+u.14+**+- ¢UJ X X)-*·•> D Q•n•~D •Zn•- 5·l+**3GU..I.J<U•··••·•UU -•l|||ZZQ nz nnnnz4+·l+{G{c>•mZ Zzcn •-•¤g:::c—•nz1•c—«•-n*4+-l+&„JLuZ-•·•|||!n•—•-•>-X>·I-3 ¤'¤>·+- m>->->->·!-*4+*¤J<•·-~• ~··

•••~·-vv-·••·-•Z•··•••~·•• l/7Z~·••-I mmmcnz**4+DI-UZ|4.LLt1,X)·LI•tLO OLIJ ILO DLLLCD U

4+4+* O G G G G·I+·¤·4+ ·-• N M Q an4+4+*4+**QUU

180

ZctDO-C)LIJZ ·xu.!

· . 181

4+** •~**4+ ~i’4+**‘ **4+ +***#1+* •-•

· , {-«l·*~•

4+*-* >-***

M ·4+***·I·4l•4+ -·~**4+ ~7'

*****4+ +4-4+** ‘

**4+ •-•~•4+** ><*4+* 4-V)**4+**4+ n-•+**4+ •···-·I··l-ät >···~41-** MM*** , **4+* · ••~·4•·¤··¤»·b •-•«¤·4I-4+- --•4***)*

+_••

***U >·***Z_

-•V'I

****-4° O _ -•*

·|·**• N ><-43··u··u·_>· Z -••-•. mm***w

• O4+*-*• -4 I- +4- •- 4-4-***X

Q >·***0

Z O ><>- #-4 •- •·••-***2 ~ O OU -• •·-•

•-·•-4+ 4+-#*4 Z •‘• Z2 >• ~• ~•X4 -[·• • •-• n-••-• M >- >·L'7·¤·•-·•#>< >· • ·I··¤· N- va M*O*¢-0Q•·-4 O -'•··~ -'•• 4+ 4++4I»C3* •$.'• LL.: n-lv-4 >< Q

-Q -·)|·v)*ZLU>< • 4-+ •-·• 4- •-• ~¤ •-•·~

·¤·4+~·••-•-·• >- ZZ

--• —·N

*4+-Ol/7• U I I X 'D X O x4I·Z**•·>· Z -•~·- M •-• m •-• M4-

•-• • 3 •-•xozhzgII! + O 4- O W4-*¤•*g~••-• ZQ X>• 0 0 • ~•

·||•L,1*M>-• ¢Z ><>- QUU _ Q ZQ>·4+g: WX 34 •-••-4 SIZZ •- I •·~ •IZ¢/7*

Z•U Ol-• "•‘•ZLLJ•·•#·• ZU-I •·*|-U'}·I·u„*0•·~ZOQuJ•·-• 0Q ••·- ¤. -0 •3- an ¤.•-··-*

*•-••—••-•OO¢• •••-40*5+4- Z'. th ¤-•M -42%/9N*

*|-— •O •*'•C!4-I-• LU •• •

**L.!><•-• •OOLU •J•J|II|><>~ I- ZOIIII I-+||I|+ · '

***2MQ •• •• •-••~UJM uu.! LU.,} UJ

*4+*3 Qt IILUX ><>-•-•Q D Q••-•QD nir-•¤..•-e3***LL¤I.LJ|I .JU**-400 IIIIIZIIZO IZ Z~·•Z4+** *0 Q•Z ZZOLLJ •-• ¢IIOLI.I•-•ZllCLU>¢**•***•J-JLlJ|-£2""|!|I•¤••¤•·-•|·-X>-•·••-·I) fühl- U'\|·-M|-***<<+-OU-|~·•~• ~·•-• v)•-•·-•ZO|-•||~· MZ~¤¤4 V7 Z***LULtJZC3|-I„t„IJ„X>-LLLLO OOLU LLO OQQO O*U4+** 4 O O O O O·K··lI··¤· •-• N M 4* nn4+** .**4+LJULJ

182

MZLu .P-

MO-I) ·Q!-CQLUZWMUJO~0

183

·¤·«l•··II· •·~

***• -0

***•LS "‘ Ü" •

***•ZLLI •-• In·II··I··II·<D•--J •~ Z n***•·C]I···• I'¤•- _***0LLI• ee: Q***02Q 0-40 0*·lI··I•I•I 1•• C5***UJu.ILL! CM-e

**U-IUJI •~OU-X M

*·**-IZ¤¢ I'•‘\0U-In •***UJ><• -7Ge N*-lI··II·•ZI- Q••I'¤ u, _·\|·*·l·0•¢/I Zee-, ••·I··II·4I·c:¤Z> OG-•·-• •***024 L.JLU-><

- ***0***Q•·ZQ•· II**·I-U20 •~•¤•·~*·l•*••• •-400*-*_ Q***¤-UJ|··• ~•UJ •~• Q***20l/1 MZ~L9***002 U><•-•Z

***L.JL.J•··• •£-LU e •***•£Z ••~•Q.J •··• •***I‘¤•G

-4>¢C7I-• —- M***kJVI• -¤--•0•• Q_ q***•¢/ILL

ON-I•~•- _ C P-***N<LL LUI.JC···••·* O LL***UILU Z•I~·•-•

*•

**·*••G••'• OOQ f¤¤~•***•-OU-• O••*•• •I

<•··•***U'LLQ LLI~·•~¤••LU +--II***•U-I0

Z••*•·••·-•I- •·~Q

**<¥O ~UL9•• •~ ¤·•0G

**LU•• L/!••Ne rn -„-Q

*U„*¤tU-IQ I/Iee—-«-I U- e Q~*••·•*<0Cl -<•-••-•L.J~·• Q •-• C7^•*0* •·0•·

N£~•-ZQ • Z ..I •<0•-•I 0 0 Q I¤¤•~·-PG*UJ*I-U"'>•· 0•-|•UOZ1 CD U 0 .IQ-•

·Il•IJ*L) •Ze •G1‘Z••I • O U„JG•

·II· ·lt·I.:>c•·-•¢\IILl-I<tl-I-I··~•~ I- ·•~ • OQ•• ‘

**<0.|><|Z•·••-••-4 U.: N e • Ole

*I,|„l*~¤•_|Z•( ••~- •~¤ Z an I-I U)Q ~•• Z O-•—-C3*•-•*•-•IZ>< UJ•-~·•~•I/7 LU I Q 0 •--00

*I-*O <¤Z.I¢U-*3 I 0 G •—• ¤Q•Z*3*2 *><LIJZO-J UJ I- QG• I- IIIII-••*0*%-U -•-IZUUJOQ Z •— •·Lu·~ •-• •·~-••·*1*4-J <~·•U-IUO •-• U- NI- ••Z•-·• G •-·••-OLG*0*

LLIU-<U„II• I- O *-J -••-• Z —--•—II·•·I·3·I·u..I 1LL • *L¤ -•-•G 0 I-I-In-*l/7*2

U-IZ I- In I-0 Qll • U VII/I I-*

*•-• I-•¥0 ..| I- -4* ZI-0 3ZI-<t·II· -I·I- ~·• •-• U-I Z ILINCDNQ < .I ..I•-ZI*

*3 Uwe/I 0 < 0~••<<LJOUJ < Q2!-•C¢***0 •-*2 O••

I--\\*\•~Q1'•-• GU10 '

***1 -J-JLU II0 I/I -••-•N•-I0~O I- QU-***0 Q<Z 0< Z I|l|l|I|< •-I

***3ZU-|•·• GJLLI 0 O-INMUJ0 Z

****/7•-10 Z1 U <<<<10 •··•

*** *** ***·¤··¤··II· c-1+** •-I

. *** . InUUU S-JUL} UUU

I

„ 184

I >~ N...4 -4 ><• LL: Z •

· G L/IQ Q •-•· LU ¤•U ><•-4 LU< G •·

··~•

Z--44- LU L9 Q- LL.

G< LAI I- Z Z LL.•-•LJ U < LU Lu u.:I- LU:-• .4 -4 I- ¥(LU F- • PI-C un? Z * LL LUD I-• d 0 LL CJ ·¤.•- LU C3 -•· LL: GIL/7 GZ U. LUG 0 UQD LU-·• GLU •· *2UZ dt L/4 GZ '2 •·

•-··¤, »—• ¤..2•~ Z L3QLU V7UJ "'SUJ

- -LUZ 4.:44- an LZ Q G••~ LU-0 au; th L9- LU GLh ¤„I- Q LU -0 Z Z

O L/7: >' Z GU-I • _U•iQ G -4G LL GZ I-

-•- Id ZI- LL IX Z L9LL LD · •·~ G •-• LU! G Z• •-•• C3 • L- •• Q U,}• ILU I I-• V7 GU U -4

> nt •LJ ZZ Z LU|| Q:-4

-I-LU Lu Lu•-1 • •

GG O '3> _ I -4I Ln GLU um L.: Oc 6- u.x• L7 cgZ

-Z I-- •LL4 < C3•-• G • Z ¤~ GG Z OI-• LUU-I LU •-Z O dG • U

mit Z cc-·• u C41.2 LU •• DI- • Q. Z GI GCN• LU Q *··• U- GGLJ’It'* LU• G LULU -.4 •G LJ •• GG G IV7 G ‘Z MCE "SZN

O LU LJ I-D G G UZ •LUU, •- Zt/2 E _ Z •• ¤.I*

LL <D • oc!/7 Z-

Nu. ZI--a•~ U M CJ-• LU ULL OO LJ• V2 LA LL I Ln -LU GL-7·••mu-• < I- L- •-n •-ng •••-•·<

II V7 x dZ va L.2 . -..4 LL:LU <L/7 • LUG •‘• >- • LULU •dII- ZV} L9 I·-G 'G .4 < IUG<•·--4 < Z ZU < LL4 -•LJU.4-•••~ 4-Lu GI LU DZ• • Z cc • I-·< ••···M -G LU -4 G LU O < < L/7 ~• <• I-• GF- LU LJ V7 LL4 ~•• •- •|·-ZZ

I- „-I- ZZ " OD • d I- IA LUL.J*·•¥LL LU- DLU G <G < < >• -4LU-4

GO .4l-• LU LUG Z U4 I -4 •>Z-4-4-• .¢/7 Q. v2I-I·-I-I Z ät < OG-4

LUNI- U4- I •-•Z OO-4 •··• Z 4- Z4_ :90*** IV! D **2 II IIZ -4 -4 < --I•·•LJZ I-• I--Z -.4I- I-dG I-I-CD -4 LL. -4-•|-< G -4 2¤„•-4 ZZZ <• < •-• Z u.4<tLL.4-ZZ >·¤ -ILI-4 D •·- DD- LU L2 •·-• -4c.2•-··Z-ct -4 -4G Q!-U< OC} mu G U •-•GdG ZLL <II Udd UULL GZ Z LU I*LJ¤-LL G*" UP- •-<LU •-•Z•-• L4-G *U—J Q I!G NO G 40

UUUU UUUUU UUUU ULJU

185

{ß .UJ«-ILU•~ U

N U ‘X <f

O•-I * QX *7 Z• an <•L3 C'.!Z it- VILU •~ W

·_} es hdP *7 I-• • neO *"° U9 U Q an

G U') •I ••~LU v'9* LU •-·•Z <7 > •~~••

G Zn! huhuLU ·{|-I-· Z •·¢/1z mm LU •-D0 (Z I ~¤••«I•~

O I•··•I--

L/>¤••·~LU -Z - mo•-• GZ *7G <+~•_ G>< •$I· • 2-I-Z •-·•* G \•-wm Z• ~·‘7 Z N-3 LL;U {L• 3 —Il·O-I IZ LL•··• •·· O —Il··II·¤- I-•·-• Lu- •·~ LL• I-NOZ • ¥L/9 ~• LU .JI+ *• ct ~¤<-/I CL' LUI LU•~·~ OLU O +< Z czr-· Q•·-e•··• ·G P *2 LU << ·I•—•~¤ •G U v-•·l{• P C3 *{·-{·- OQ Lu UQ | ¤• •••¢/H/7 • LUZ > ¤.< * {-O ~•Z2 VI •• OZ+ •-·• m•-• |„|_•-ee-• ee p-•

O G LULU - ~• 3• u..1£Z at! •-J *Z OO O •{| LL Q. O-I OOP + VI •LU• ,4 •-•¤~ LU G• I|·I{·~·• LU||¢/I {-• LU I- I-

ZO |{•-• O -Z *O* 2*3 Z Qt Z •lll LU ‘7~• LUII O •-•<•··• •¥•J 3 3 OO•-4* > Q. 3* VILU '·'I|<

v-•~•¤• G G GU‘\•-•<\J{IP •‘* OZ Z•-• P I'•‘*I{ {IPO U LU U•-•—• •- NLU •·-•~··· ZZ mv-•-Lu>¢¢n•ILu- ¤·: ••·•PI-{-•

Q. U ~0I-- {-LL LUG 3~••-#3 Z*3II •-• ~·ZZZLLOI LU ZLL Zct .„J¤„-•ZO•-•¥Z{- ch G•-•r··••·-••-4-·•1.u u. G Gu: wu. ¤G¤.•·-•Mz-••·-·z u.: Gccntct~OP LL G UO U OOOPOOOP3 G ZQAO.Q LU <¢/7 Z ZG --ZG .12 GG GG P LLLUG Z ¤.G UG U"* Z •'•

rt 4/>•···•~G •··•|'- Q';

~ LL G< Q.·I>

* O O ON •-• M~O ~0 ~D

UUU UUUU UUU

186

45 G*

nn$1- I-

. 45€

{ M45 U-3 -··41- -3 •{ LU {45 U ·45 U •45 < ••{ In{ •45 45 M4} •-n45 G·¤·

•

*3- •

45 P-{ —— ·¤·{ ~ LJ{Q Q Q •45 N .J •45

• UJ W45 GQ > •{ LL m _·¤· • •-4{ • G*

•

-45 II { •

. "‘·*, -• 45 Lu _I-

*Q. 45 I 2O 45 •-• lu •O 45 P- E •• { Lu UN•'~ 45 U •

•-• { < nnU { ,,1 -•G. 45 CL GQ 45 I/I •

.•*

hd Q•- 45 C3un

* *~••*O 45 45• 45 •

Q- { • •·UJ• 45 LI- ~7'ZOO { • •··••¢•-I { Q ••

•-|*

• •' OOOIII-I-LL3 { G-4¢'H•¤-••¤•ZZD

*-••-Z { { ·|· ae-I¤I-P-OMM-• I- •

~• •

ZZZU"N¤„¤•I·• J •-• • • ••-·••··••··• ZLLu„Iu..=\l¤ UN Ln UNMMMC3 GP-•O-I\I-• I- I- I-·

· cs-::0-I- 3- 3- I-ZZ|I3<<••< <•-<¤¢UJI- 2:-2-!I•1°OQMM4PC£•¤L·I5MI-•O

ZCG'IPG*C CDUJZu.1u.u.*u. u..Zu.¤cu4

45 45 45O UNO O O OIh -• N M ¢

187 .

4+4+* . •*4+*

n‘I‘\4+4+* ]¢'¤*4+4+ L2 ••4+4+4+ 2 ~O·O***4* Ill |• V •4+4+4+ Q •~ • •I¤ Z ·-••··II·-1+ Z

~•~ In• •

*4+4+ •-• >< •-I ]t¤-1+4+4+ IL •~

~·-•| I- ·~**4+ I-I •O f'¤• Z N

4+** Z •·X •—•· •~~Q LU X*4+4+ I-I LU• •-••—„ ~0l@(5 ~••¤¤4 •• LU •-I

4+ Q* C32 ¢.9• L¤II'\ ..I ><4+4+* LIJN UI-U ZN ] LU •4+4+4+ IAO "7-J IU•-• •· L3*6** DIA •+- JU ~0• IL Z*4+4+ L'>• LUZ I~¤ Q LU*4+* LLI• •G ••-I •• J aaa4*** SQ. G9 af NN IO )- aaa4+4+4+ DG •-¤•• |•• +··•·~ • NNN4+4+* GW ZIU •,•~ •s7' {SZ G 4+*****

Ü": {Hui ~"• •***gg if Luv-! Z aaa

*41** X¢ LDLU Q~0 •I JP •· ZZZ*4+* •-IG ZZ ¢¥~• ~0• < LJ ---•«4+** M LU•· QIU •·N Q) Z •·-INN

***+-LU -40 GQ N] LU-• •·-• LJULJ

4+** <|-U LULU UG •• ZM E III«¤·4I··l· Zw •Z •w ~·1·~1· ¤:I-I-I • • •• _4+**

•-• Q>< •·~Z _| GQ ua •-I•-••-•

#4+4+ V5 xt •-•• • L1. C3 ~··-•-**4+ In G•

--Lßb LUM CD--] I]

-¤·*I· LU • Qu M-I |I.ngg***ZM Q2 Q• •• L], •5~••ZZZ

LLJ*

*ILO- MZ *~•M| •· IL/7 QZLQLDIJ

4+*

I-IQ Q• •·*UJ~• ••¤¤4 ]¤-•+¤I ;!U;ZZZ4+ 4+ U-LU •LI.J ~••QN•-•• In C...ILUIULu4+ 4+ w> NQ NOXIIJN LULU CT.}!-...I.J„J·¤·I·-··••· w¤··~ ww••• zI wxl-uu.1w-4+<* LUQ •·UN •‘>·-I!\• •·-·•|- •·*\\\Z

*¥* WG Q•Ga•4a¤•\1'| G mg UQZZZN

* *I-.! •Q •·O~•~D•-I•• O LUG •(—•—„«-4__;

4+ 4+ L.) <C¤II.U-I-•><•-I•—4 Q I- NU-I¢.9L9L94+·¤·u.I·I• LL|•-I u.1zIzw<.¤•\I G LLJN wocZZZ*4+2* LI„< z•<•••-* • Q •<LULIJI-UZ4+•-•* ILQ <IL-O•~*•-Io GG ‘ ct «-•*..|..I...I~·•{II-* LUG -IL LU•·-••··~I-·• LU!] QLU U•*|·-I-h~«-I*3* Z •·~|-¤¢¤Z••~•0~0 2* I-I-· ••2~·-~·-U4+G* LU <X4+><<Q2~• G•·7 Q. v"I~··•4+*4+4+*M4+ ILU Z -III-UGIUX LU-I•· LU •< GQ<<<<

·*ß* I-) X <~·•MI-ILU Zllv-• Z I/II UGIZZZ*3* •-·• LUIL<LU]-Q •~'!~•I.U • OU ZZZZZZ*I/5* L/H- LU MIL 2 •·‘ ILD •-I Q LULU<<<<

*4+ LULJ 2 I.UZ •··• ||~0ILZ II ZG ...I|IL.'§L.9<3<.D

4+*

I-UJ •-• I-XG •-~0LU•-•LUZ LUI- <IIII|l'II4+ 4+ <LI• I- •-I •·-• M -IX!-3 -1 ..I!Z****«¤··I•·-1+ ..1u. D www LU Lß Zzc ·¤: ..1::-•~m~1··***

DUJ O ***2 (3 ÖÖ @***2 UJ €<•••~•~•—•4+*4+ E M •-ILJLIJ I.U •··*Q IJ]--I -ILI-• QOLDLSOLB4+*4]- MI-U cz; ¤.<Z I- Z am·¤··II··•I· CDI 3 im- 2 O CJCJ <¤c·¤··l+-u·

u.•-· w •-¤:C: •- Q wc I.:—•· ·‘4+***

4+4+ 4+4+*4+ I ~OIt‘\~¤··I·«¤· oo·||·*·]]· «-••-I _**4+LJLJLJULJULJ v UULJU

1

188

Ä•·~ .1-| Ii‘L'} L3<I• I ” ~

Q 1•· ') ZLL Q• •L], Qu-• •-• 'LU er _•••Z ZU. LI.• Q 11.161. LL. .

O ILU LUX ~ PZ Z••• Z"· II IIg u„1LL|•••••~ anF- I'>O'J *5I-• • OZ O U.1••~• •-n

21 äthlßg ngZZ • Z ZO-•LDLI. LI.° —•••• Q L1.1 • X|U.QLL.MM LU I~OLI.1•LI.1 LLIOLIJU.

_ UL) O I-•·•-•LL10..IZ Z•··•·I··I¤ Z *-***22- LU·-- < ‘*¢•IIL1.1••-• en QZZ Q ZOLUO IIU. -1 ZLLee Z

• •~•Q•·••,|•···• Lu gun-n•-•N D ~bu.¤• LJ- LuUL) • •"5LLIOZ OD*1* •"‘••'2.’U‘IILL. ZZ<< ..1 IILL1••-••-••-• Lu)-• _IZ •| LUO PZZ D WDWG ZLLLU ”(4 U. L.)-O Ol-LDGL') OZ LJ ZII II LU QIILL O•·-UJ-•- .1 -•1•-•

ZF-Z3 .I¤~0 O UJZZZO Qu-ngww LU ¤ un-:¢/7 ZPO

I/I OLUZ< LJ¢LL1

O OOO CON•-• •-•«-n

UULJ

jTHE EFFECTS OF EARTHQUAKE EXCITATIONS

ON RETICULATED DOMES

David A. Uliana(ABSTRACT)

Comparisons were made on the behavior of two full-sized

reticulated domes subjected to uniform static loads only and

uniform static loads with earthquake excitations. Space

truss elements were used in the dome models. The stiffnesse

matrix of the space truss element allows for the nonlinear

strain-displacement behavior and the stress-strain behavior

of the material is modeled with a bilinear approximation.

The nonlinear solution technique is the Newton-Raphson meth-

~ od while the direct integration technique is the Newmark-

Beta method.The joint displacements for the static and the dynamic

analyses were compared for both domes along with the axial

stresses in all members. The percentage increases in the

”axial stresses of the dynamic analyses as compared to those

of the static analyses were determined.

The reticulated domes used in the study were found to betcapable of withstanding the earthquake excitations when sub-

jected to various uniform loads without failure. ·