THE STRUCTURAL MECHANICS BEHAVIOR OF SEALED …

THE STRUCTURAL MECHANICS BEHAVIOR OF

SEALED INSULATING GLASS UNITS

by

JON BAXTER ANDERSON, B.S in C.E.

A DISSERTATION

IN

CIVIL ENGINEERING

Submitted to the Graduate Faculty of Texas Tech University in

Partial Fulfillment of the Requirements for

the Degree of

DOCTOR OF PHILOSOPHY

May, 1985

^'"^^ { ^ ACKNOWLEDGEMENTS

Support of research work used as background for this document was

provided by the Glass Research and Testing Laboratory of Texas Tech

University and the National Science Foundation (NSF Grant CEE-

8118214). Any opinions, findings, and conclusions or recommendations

expressed in this publication are those of the author and do not

necessarily reflect the views of the National Science Foundation.

I want to thank the members of my committee for their assistance,

and a particular thank you to the Department of Civil Engineering,

Texas Tech University and Department Chairman E.W. Kiesling for his

patience and support.

n

TABLE OF CONTENTS

Paae

ACKNOWLEDGMENTS i i

ABSTRACT vi

LIST OF TABLES viii

LIST OF FIGURES ix

I. INTRODUCTION 1

II. DISCUSSION OF INDUSTRY RESPONSE TO HIGH DEMAND 4

III. THE RESEARCH QUESTION 12

IV. THE RESEARCH PLAN 17

Mode 1 s 17

Global Model 18

Local Model 21

Sealant Model 23

Other Models 23

Component Behavior 24

Gl ass 24

Sealants 24

Spacers 25

Corner Effects 25

i i i

Exercise of Models and Applications of Investigations 26

V. INSULATING GLASS UNIT RESPONSE MODELS 27

Global Model 27

Local Model 28

Spacer Model 33

Corner Effects Model 37

VI. MATERIAL PROPERTIES 40

Gl ass 40

Spacers 40

Sealants 41

Analysis 42

Method 42

Verification 50

Results 50

Application 53

Work in Progress 57

VII. PARAMETRIC STUDIES 58

Selection of Reference Evaluation Condition 58

Evaluations of Seal Details 61

Parametric Studies 67


IV

VIII. DISCUSSION OF BEHAVIOR PREDICTED BY MODELS 89

Parametric Evaluations 89

Split and Welded Spacers 89

Geometric Studies 90

Effect of Sealant Depth ..." 91

Effect of Spacer Aspect Ratio 91


Potential Additional Model Applications 96

Conclusions 98

Recommendations for Future Efforts 110

LIST OF REFERENCES 112

APPENDICES

A. LISTING OF SEALANT STRESS-STRAIN PROGRAM 114

B. TABLES OF ORDERED STRESSES 141

ABSTRACT

Aesthetically pleasing, glass sheathed buildings and insulating

glass (IG) units have formed a combination that is at once attractive

and efficient. The use of IG units has increased in all types of

buildings construction. Typical IG units consist of two glass plates

separated by a perimeter spacer of aluminum. The perimeter is then

coated with a polymer sealant which seals the air between the glass

plates and holds the unit together. Until recently, most IG units

were designed on an experimental basis, primarily by improving the

polymer seals that seal the unit and hold it together. Computational

tools for examining IG units on a structural mechanics basis were not

available. This document introduces a series of working and proposed

models designed to meet this need.

An examination of the need for research and development in the IG

unit field is followed by a discussion of "global" and "local" models

designed to examine IG unit behavior from a structural mechanics

standpoint. The global model considers the response of the entire IG

unit, while the local model focuses on smaller segments of the unit

within the seal detail. Specifically, the local model examines the

complex response of the boundary of the unit where the materials

making up the unit seal (aluminum, glass, sealant) are in contact.

Engineering properties of glass and aluminum are well defined,

but those of sealants are dependent on polymer type, strain rate and

vi

st ress r e l a x a t i o n . A method fo r f i n d i n g the engineering proper t ies of

polymer sealants i s presented.

F i n a l l y , the loca l model i s exercised in a s e r i e s o f pa rame t r i c

s t u d i e s which examine the e f f e c t on component s t r esses caused by

changes in environmental c o n d i t i o n s , s e a l a n t modulus, spacer cross

s e c t i o n , d e p t h o f p e r i m e t e r s e a l a n t , and spacer aspect r a t i o .

Po ten t ia l add i t i ona l uses o f the l o c a l model are d i scussed . These

d i s c u s s i o n s i n c l u d e the e f f e c t and modeling method fo r inc lud ing the

IG u n i t mounting system such as a mechanical or d ry neoprene gasket

and a polymer " s t r u c t u r a l " sea l .

v n

LIST OF TABLES

Table Page

1 SUMMARY OF LARGEST STRESSES FOR SCENARIOS USING 150 PSI SEALANT MODULUS 63

2 SUMMARY OF LARGEST STRESSES FOR SCENARIOS USING 250 PSI SEALANT MODULUS 65

3 SUMMARY OF LARGEST STRESSES FOR GEOMETRIC STUDIES 74

4 SUMMARY OF LARGEST STRESSES FOR SEALANT DEPTH STUDIES 76

5 SUMMARY OF LARGEST STRESSES FOR SPACER ASPECT RATIO STUDIES 84

6 SUMMARY OF LARGEST STRESSES FOR CORNER EFFECTS MODEL 87

7 CHANGE IN MAXIMUM PRINCIPAL STRESS DUE TO SPACER GEOMETRY CHANGE 92

vm

LIST OF FIGURES

Figure Page

1 TYPICAL SUPPLY DEMAND CURVE 5

2 SALES OF INSULATING GLASS 1972-1980 (BAR GRAPH) AND BUILDING CONSTRUCTION 1972-1980 (LINE GRAPH) ... 8

3 TYPICAL IG UNIT 14

4 IG UNIT MODEL WITH SIMPLY SUPPORTED PLATE ASSUMPTION 19

5 PROPOSED MINOR-VALLABHAN IG UNIT MODEL 20

6 LOCAL MODEL SHOWING INPUT PARAMETERS AT "CUT" SECTION 22

7 CROSS-SECTION OF IG UNIT AT TOP CENTER SHOWING LOCATION OF LOCAL MODEL 29

8 LOCAL MODEL DISCRETIZATION 30

9 LOCATION AND POSITIVE DIRECTION OF LOCAL MODEL ELEMENT STRESS 32

10 SPACER MODEL FOR ONE EDGE OF IG UNIT 34

11 SEALANT DEFORMATION AND SPACER DISPLACEMENT CAUSED BY ROTATION OF IG UNIT GLASS PLATES 36

12 DETAIL OF IG UNIT CORNER SHOWING VERTICAL SPACER PORTION AND CORNER EFFECTS MODEL TO STUDY THE EFFECT OF THIS VERTICAL SPACER PORTION 39

13 CASTING THE STRESS-RELAXATION TEST SAMPLE 44

14 STRAINING DEVICE ATTACHED TO STRESS-RELAXATION

TEST SAMPLE 44

15 AN INSTRUMENTED STEEL POST 45

16 RECORDING OF RELAXATION DATA 45

17 SAMPLE GRAPHIC OUTPUT FROM SEALANT COMPUTER PROGRAM 48

TX

Figure Page

18 INSTRON TEST SAMPLE 51

19 PREDICTED AND TESTED STRESS-STRAIN RESULTS FOR "PRO-SEAL" SEALANT 52

20 VERTICAL PLATE WITH TOP AND BOTTOM SEALANT SUPPORTS i 54

21 MODULUS VS. ELONGATION RATE FOR "PRO-SEAL"

SEALANT AT VARIOUS STRAIN RATES 56

22 CIRCULAR SHAPED SPACER DISCRETIZATION 69

23 TRIANGULAR SHAPED SPACER DISCRETIZATION 70

24 TRAPEZIOD SHAPED SPACER DISCRETIZATION 71

25 INVERTED "T" SHAPED SPACER DISCRETIZATION 72

26 "STANDARD" SPACER DISCRETIZATION 73

27 ASPECT RATIO TEST SQUARE (DATUM) SPACER 79

28 ASPECT RATIO TEST 3/8 IN. BY 1/2 IN. SPACER 80



31 ASPECT RATIO TEST, THIN STRIP BY 1/2 IN. SPACER .... 83

32 EFFECT OF SEALANT DEPTH ON IG UNIT COMPONENT STRESSES 93

33 EFFECT OF SPACER ASPECT RATIO ON IG UNIT COMPONENT STRESSES 95

34 EFFECT ON MAXIMUM PRINCIPAL IG UNIT COMPONENT STRESSES DUE TO CHANGE IN SEALANT MODULUS 97

35 PROPOSED LOCAL MODEL FOR MECHANICALLY RESTRAINED IG UNITS 99

36 PROPOSED LOCAL MODEL FOR GASKET RESTRAINED IG UNITS 100

X

Figure Page

37 PROPOSED LOCAL MODEL FOR POLYMER MOUNTED IG UNITS 101

38 UN-DEFORMED AND DEFORMED LOCAL MODEL CROSS-SECTION FOR SCENARIO I SPLIT SPACER 103

39 UN-DEFORMED AND DEFORMED LOCAL MODEL CROSS-SECTION FOR SCENARIO II SPLIT SPACER 104

40 UN-DEFORMED AND DEFORMED LOCAL MODEL CROSS-SECTION FOR SCENARIO I WELDED SPACER 105

41 UN-DEFORMED AND DEFORMED LOCAL MODEL CROSS-SECTION FOR SCENARIO II WELDED SPACER 106

42 UN-DEFORMED AND DEFORMED LOCAL MODEL CROSS-SECTION FOR SCENARIO III 107

43 UN-DEFORMED AND DEFORMED LOCAL MODEL CROSS-SECTION FOR SCENARIO IV 108

44 UN-DEFORMED AND DEFORMED LOCAL MODEL FOR CIRCULAR SPACER WITH SCENARIO IV ENVIRONMENTAL CONDITIONS 109

XT

CHAPTER I

INTRODUCTION

The oil crisis of 1973 ended an era of plentiful, inexpensive

energy. Large, powerful, energy-inefficient automobiles were replaced

by smaller, more efficient ones. Buildings constructed for low

initial cost, assuming cheap energy, experienced a change in which

energy costs became a major yearly operational expense. Particularly

vulnerable to increased energy costs were high rise, glass curtain

wall towers with monolithic glazing. These buildings were both

aesthetically pleasing and had low initial cost, but were dependent on

cheap energy for heating and cooling. Following the oil embargo,

architects experimented with various methods of making buildings more

energy efficient. These methods included reducing the number of

windows to few or none, designing sun shading as part of the

structure, and increasing insulation. These solutions increased the

initial building cost in order to save money (energy dollars) in the

long term. Larger initial costs and life cycle costing increased

investment recovery times. Reduction of initial cost and investment

recovery time, while maintaining energy efficiency, became a new goal

in building construction.

A possible method for reaching this goal involved use of

insulating glass (IG) units. The attractive and low cost glass towers

could be retained with a relatively small increase in cost if IG

units were employed in the glass curtain wall. When this approach

proved successful, not only for new construction but as a retrofit for

1

existing buildings, the demand for IG units increased. The demand

was sufficiently large that entry into the marketplace by many

new IG unit manufacturers was accomplished with minimal amounts

of testing or research and development. If IG units were tested at

all, they were evaluated from a seal durability standpoint, to ensure

their integrity as a sealed unit, rather than as a structural system.

The general objective of the research reported herein is the

development of mathematical models to describe the behavior of the IG

unit as a structural system, using the principles of structural

mechanics. The models are used to characterize the behavior of

representative IG units under loading and environmental conditions

that may be expected in service. Specifically, the investigations

reported herein include the following:

1. Structural mechanics behavior of materials used in making

an IG unit, with particular emphasis on engineering

properties for the sealants.

2. Structural mechanics behavior of glass plates within the

IG unit in response to environmentally induced loadings:

wind pressure, barometric pressure change, and temperature

change.

3. S t r u c t u r a l mechan ics behav io r a t a boundary s e c t i o n

( inc ludes the spacer and s e a l a n t d e t a i l ) l o ca ted a t the

top edge cen te r l i ne of an IG u n i t .

4. O v e r a l l spacer behav io r d u r i n g temperature and pressure

changes.

5. The effects of rigid spacer corners on the behavior of a

boundary section near the corner of the IG unit.

Results of these investigations provide useful insights into the

material properties and structural mechanics responses of IG units to

environmental conditions in which they are expected to perform. The

investigations provide the following results:

1. Comparisons of behavior for IG units with different seal

details.

2. An evaluation of the impact on the market for insulating

glass produced by high energy demand and increased energy

costs.

3. An assessment of additional investigations made possible

by the availability of the models and methods developed

herein.

CHAPTER II

DISCUSSION OF INDUSTRY RESPONSE TO HIGH DEMAND

The increased requirement for IG units was essentially the result

of two related causes of high demand. First was energy demand.

Second was a demand for products designed to reduce energy use when

prices for energy increased. Energy demand was high because increased

energy use to produce goods and services was perceived as improving

the quality of life. The low cost of energy prior to 1973 allowed

goods and services to be provided at a relatively low cost. For

example, the initial cost of new buildings was low since provisions

for energy conservation were not included. If the buildings were

energy inefficient the energy demand could be increased for a very

small increase in variable costs. Energy demand was large enough that

the United States could not provide sufficient energy to meet the

demand. The remainder was imported, mainly in the form of petroleum,

from other oil producing countries. Even with imports, prices for

energy remained low. The oil embargo of 1973 was essentially a

created shortage for political gain. In this country, however, the

demand remained high. The result was classic supply-demand response.

This shortage constituted a "change in supply," as opposed to "a

change in the quantity supplied," which had the effect of shifting the

supply curve to the left while maintaining its position relative to

the price axis (Ref. Fig. 1). Demand did not change, however. This

caused a new equilibrium point to be established at a higher price.

Energy prices became four to five times higher. Since the amount of

0)

to

u o

On

D

>«1

0 rH D D4 c a ro 3

pC W U

• ^S . • » • " ' ^ ^

a U (U

•H & )^ (0 Oi 4J

V4 E 0 D ^

•H W U

Xi 0 •H V< rH 0 •^ IW

> 1

•H

o o o z

a I

>-—J Q-Q .

0 0

I—I O->-

OH

o

aoTJd

imported energy curtailed was approximately thirty percent of total

demand, the large rise in price demonstrated the very steep slope

of the demand curve. The steep slope of the demand curve implies

that demand was nearly constant and was due to the lifestyle in place,

in the United States, at the time of the embargo. Typical responses

to shortages are conservation and rationing.

This classic response of supply-demand was to be relatively short

term. Because of the embargo, conservation measures were instituted.

Some of the conservation measures included changing heating/cooling

thermostats to marginal comfort levels, forming carpools, lowering

highway speed limits and apportioning gasoline to suppliers. The need

for long term measures of lowering consumer energy costs was apparent.

One long term measure was to improve the energy efficiency of

buildings. This improvement meant retrofitting existing buildings

with a means of energy conservation, as well as making new

construction as energy efficient as possible. One measure that met

both the retrofit and new construction energy conservation criteria

was the installation of IG units.

Meeting this energy conservation need with IG units caused an

increase in demand for the units. This second cause of high demand is

the result of an effort to ameliorate the financial burden of a price

increase due to a shortage (change in supply) of another product that

has few or no substitutes. The bar graph of Figure 1 shows the

results of a survey taken in 1982 giving sales of IG units in millions

of square feet from 1972 to 1980 (AAMA, MIR, 1973-1981). As a com

parative measure construction trends in millions of constant 1972

7

d o l l a r s are shown as a l i n e graph f o r the same years on Figure 2 (U.S.

Bureau of the Census, 1982). Sales increased d u r i n g the 1973 energy

c r i s i s and the year a f t e r . The year 1974 witnessed a severe dec l ine

in new c o n s t r u c t i o n , y e t i n 1975 IG u n i t sa les remained c o n s t a n t ,

perhaps i n d i c a t i n g a move to r e t r o f i t e x i s t i n g bu i l d i ngs . A f te r 1975,

sales of IG u n i t continued to increase u n t i l a s l i g h t decl ine occurred

i n 1980 . T h i s i n c r e a s e i n demand had the s h o r t term e f f e c t o f

increas ing pr ices f o r the u n i t s . An inc reased p r i c e prompted more

manu fac tu re r s t o e n t e r the IG u n i t manufacturing f i e l d . Entry i n t o

the market f o r IG un i t s meant a qu i ck s t a r t - u p i n o rde r t o compete

w i th producers already in the marketplace.

Methods o f e n t e r i n g t h e m a r k e t p l a c e from a manu fac tu r i ng

standpoint e n t a i l product development, t e s t i n g , and f i n a l l y marke t i ng

the product . Entry i n t o a high demand market of ten precludes the time

n e c e s s a r y f o r p r o d u c t d e v e l o p m e n t and t e s t i n g ; t h u s , e n t r y i s

accomplished by copying designs or by s imp l y b u i l d i n g a p roduc t and

marketing i t . In the case of bu i l d ing a product and marketing i t , the

development phase i s usua l ly accomplished in the f i e l d through t r i a l

and e r r o r . This process o f ten involves f a i l u r e s and l i t i g a t i o n . This

approach cons t i t u t es a v a l i d product development method i f the demand

i s h igh enough t o assure t h a t i n i t i a l p r o f i t s are s u f f i c i e n t t o

r e c o v e r i n i t i a l i n v e s t m e n t . The company may t h e n l e a v e t h e

marke tp l ace or p r o v i d e monies to cover l i t i g a t i o n and, p o s s i b l y ,

replacement cos ts . The primary de t r imen t t o t h i s method i s l oss o f

consumer c o n f i d e n c e d u r i n g t h e t r i a l and e r r o r phase o f the

development.

8

Building Construction

Sales of Insulating Glass Units

b

cr en

o

c o

•H

400--

300-

m Q)

tH (0 cn CQ CQ (13

rH

C •H 4J 03

iH D CO C H

200-

100-

$100

$90

$80

$70

$60

CO

u

o Q

CN

4J

c (T3 +J CO c o u u-i O en c o

•H

2

G 0

o

3

CQ

<^ o u

•H 3 C3

YEARS

FIGURE 2. SALES OF INSULATING GLASS 1972-1980 (BAR GRAPH) AND BUILDING CONSTRUCTION 1972-1980 (LINE GRAPH)

The advantages of the trial and error method are the small lead

times for market entry, low investment cost for plant and equipment,

and low product development costs. Even if a high demand market entry

competed on the basis of price, the overall higher price for the

product due to the high demand would'provide a large early return on

the low investment costs. This is an obvious advantage.

The disadvantages of trial and error entry into the marketplace

are the potential for high litigation costs, loss of consumer

confidence and replacement costs in the event of product failure.

Entry into the marketplace with the intention of maintaining

product position and consumer confidence would require a reasonably

long lead time for product development. This research and development

phase usually consists of design, making prototypes, and testing until

some predetermined criteria are met. During this development time the

market is developed and, when a reliable product is obtained, sales

begin. Research and development does not end with the initiation of

sales. It usually continues during the market life of the product and

contributes to product improvement and reduced manufacturing costs.

Improving the product gives it a sales edge in consumer perceived

quality, which in turn enhances consumer confidence. Product

improvement and reduced manufacturing costs combine to improve the

company market share and margin over the long run. In contrast, the

continuing product development program of the trial and error method

consists of revisions to solve failure problems. Results are

increased manufacturing costs without significant product improvement.

10

Advantages of the product research and development method are

consumer confidence, a potentially larger market share, long term

return on investment and reduced production, litigation and

replacement costs. These advantages result primarily in providing a

more reliable product at a lower manufacturing cost.

Disadvantages of the product research and development method are

the high initial costs and lead times before marketing the product and

lower profits due to extended investment recovery time. The high

initial costs are due to investments for plant and equipment and

personnel costs for the product development phase. These costs

provide no return on investment during the product development time,

thus increasing the time required for investment recovery and reducing

short term profits. Profits could be larger over the long term for

the product research and development method; however, an examination

of opportunity costs would be required to verify this.

Entry into a high demand market would probably be predicated on

an expectation of high profits. This expectation would prompt most

entrants to select the trial and error method for a rapid return on

investment, unless an evaluation indicated that the demand for the

product would extend over the long term and an ongoing enterprise was

the goal of the investors. The long term demand for IG units is

probably going to be constant, as a minimum, given the popularity of

buildings with glass sheathing and the continued need for energy

conservation measures in years to come.

There are examples of companies entering the IG unit market

using, essentially, the trial and error method. Rapidly developed and

11

marketed units began to have service problems within a few years. In

many cases litigation was initiated. Settlement conditions sometimes

required that the company's units be replaced by the product of

another manufacturer. Eventually, the original IG unit manufacturer

sold out. In these examples, profits 'from a high demand product were

apparently not sufficient to absorb the costs of trial and error entry

into the marketplace.

Capturing a market segment is difficult at best. Maintaining

that segment requires consumer confidence in the product. Consumer

confidence is a must if the product demand and company survival is

expected to be long term and is expected to increase during continued

construction recovery.

IG unit markets are well established. Entry into the market at

this time would require a consumer perceived quality improved product.

Maintenance of an established market segment requires meeting customer

expectations of product improvement and cost reduction over time.

Market entry or maintenance can best be achieved by an active research

and development program and not through the trial-error-litigation

cycle.

What new methods can be a p p l i e d t o meet c u r r e n t consumer

c o n f i d e n c e c r i t e r i a ? The answer t o t h i s q u e s t i o n r e q u i r e s an

i n v e s t i g a t i o n of the research quest ion.

CHAPTER III

THE RESEARCH QUESTION

Glazing in construction in many parts of the United States has

consisted, until relatively recently, of monolithic glass plates.

Typically, rectangular glass plates of constant thickness are set in

some type of restraining frame. The glass plates are designed to

resist the effects of pressures (representing wind pressure) acting

normal to the surface of the plate. A mathematical model for

analyzing this type of plate and associated loading was presented by

Navier (Timoshenko, 1959) in 1820. This analysis method provided

adequate results for simply-supported rectangular plates with uniform

pressure loadings and small deflections. When large deflections

occur, membrane forces come into play and the Navier solution no

longer applies. The approach used most often in the solution of large

deflections of rectangular plates was advanced by Levy in 1949

(Timoshenko, 1959). This solution, which was formulated for steel

panels on ships, assumed an isotropic, homogeneous material, and

boundary conditions which forced edges of the plate to remain straight

during loading. When Levy's solution was applied to glass plates

the results were not always in agreement with experimental data

(Al-Tayyib, 1980). Recent research produced more modern methods of

solving glass plate problems (Al-Tayyib, 1980; Moore, 1980; Vallabhan

and Wang, 1981; Vallabhan and Ku, 1983). These newer solution methods

gave proper attention to glass plate boundary conditions and led to

better correlations between results from mathematical models and

12

13

experiments (Linden, et al., 1983; Behr, et al., 1985). The simply

supported assumption used with monolithic glass plates has been

adequate in studies accomplished prior to this time. Most glazing

support systems allow sufficient rotation and in-plane translations of

the edges of the plate to make valid the assumption that the plate is

simply supported.

IG units are constructed as two glass plates separated by a fixed

distance and enclosing an air space (Ref. Fig. 3 ) . The units are

considered "sealed." Trapped air is kept dry by a desiccant, thus

enhancing insulating qualities of the unit while keeping the inner

surfaces of the glass plate free of condensed moisture. Starting from

the outside of the unit, the glass surfaces are numbered one through

four. These surface designations are used to specify locations of

coatings that may be applied to the glass.

When the unit is sealed at the factory, the enclosed air is at a

specific temperature and barometric pressure. Changes in temperature

and barometric pressure, and the application of induced pressure when

the unit is in service, produce pressure changes in the sealed air

space. Analysis methods which characterize glass plate behavior may be

applied to individual glass plates within the IG unit. To use these

methods, pressure differences across each plate must be determined.

Determination of these pressures is in itself a complex problem. For

example, a wind pressure on the outer glass plate of an IG unit causes

a deflection of that plate. Deflection of the outer glass plate

alters the pressure condition in the sealed airspace. This pressure

change, in turn, produces a pressure on the inner glass plate. Hence,

14

SECONDARY SEAL

OUTER GLASS PLATE

INNER GLASS PLATE

PRIMARY SEAL

SURFACE DESIGNATIONS

FIGURE 3. TYPICAL IG UNIT

15

determination of pressures across individual glass plates becomes an

interaction problem involving relationships between deflections in

both glass plates and the pressure in the sealed airspace. In the

case of an IG unit the net pressure across the outer glass plate

depends on the wind pressure, the piêssure inside the sealed unit

(which, in turn, depends on temperature and barometric pressure

changes), the change of pressure in the sealed airspace caused by the

deflection of the outer glass plate, and the resistance to pressure

change presented by the inner glass plate. Since the purpose of IG

units is to help maintain a temperature difference across the unit,

the two glass plates will be at different temperatures most of the

time. Due to this difference and the thermal expansion properties of

the glass, the relative sizes of the outer and inner glass plates will

vary, depending on temperature differences in the two plates. This

relative expansion will have an effect on the perimeter of the unit

where the various unit components (glass, spacer, sealant) are in

contact. The complexity of the IG unit in a structural mechanics

context does not end there. IG units are constructed of components

with different material properties. Each material responds to changes

in temperature and pressure according to its individual properties.

Each material also responds to displacements of adjacent materials at

component interfaces. Response of the IG unit due to these loads and

displacements include both primary (global) and secondary (local)

effects. These effects must be described by theoretical models.

Components at the boundary of the IG unit usually consist of two

types of materials. A metal spacer separates the glass plates. A

16

sealant (or sealants) around the edges o f the u n i t sea ls a i r i n and

m o i s t u r e ou t w h i l e ac t i ng as the s t r u c t u r a l component tha t binds the

u n i t together . Excessive stresses on the spacer could cause permanent

l o c a l d e f o r m a t i o n s o f t h e s p a c e r w h i c h w o u l d , i n t u r n , p l a c e

a d d i t i o n a l s t r e s s e s on the s e a l a n t . Local sea lan t f a i l u r e , i n

adhesion or c o h e s i o n , cou ld pe rm i t mo i s tu re and a i r t o c i r c u l a t e

i n t e r i o r t o the IG u n i t , r educ ing i n s u l a t i n g q u a l i t i e s and v isua l

aes the t i cs . Extensive sealant f a i l u r e s would r e s u l t in s e p a r a t i o n o f

the glass p la tes from the u n i t .

S t resses i n these boundary mater ia ls (spacer and sealant) r e s u l t

p r i m a r i l y f rom edge mot ions o f the g lass p l a t e s . Hence, t h e s e

stresses are e s s e n t i a l l y "secondary" s t resses. Special ized models are

needed to examine these boundary s t resses.

The c o m p l e x i t i e s o f IG u n i t b e h a v i o r desc r i bed above are

representa t i ve of the IG u n i t as i t i s manufac tu red , t h a t i s , as a

s t a n d - a l o n e u n i t . When IG un i t s are i n s t a l l e d , most g laz ing systems

app l y c l a m p i n g and o t h e r f o r c e s t o t h e u n i t s , a d d i n g t o t h e

d i f f i c u l t i e s o f d e s c r i b i n g t h e i r b e h a v i o r . A " t y p i c a l " IG u n i t

support system i s d i f f i c u l t t o d e f i n e . Many are custom-made f o r a

p a r t i c u l a r s t ruc tu re and o f f - t h e - s h e l f systems vary from manufacturer

to manufacturer. This s i t u a t i o n compounds the problem of de f i n ing the

forces placed on the IG u n i t by the g laz ing system.

Development of models t ha t def ine the response of the complex IG

u n i t system i s the focus of t h i s document. Primary emphasis i s on IG

un i t s as stand-alone u n i t s . Discussions fo r i n c l u d i n g c o n s i d e r a t i o n

of support cond i t ions as fu tu re endeavors are also inc luded.

CHAPTER IV

THE RESEARCH PLAN

Describing the structural mechanics behavior of IG units requires

several theoretical models. Each model represents a portion of the

total response that is of interest. Some of these models have been

developed fully; for others, formulations are offered that are based

on empirical factors yet to be determined. The research plan consists

of model formulation, the development of material properties for use

in the models, and demonstration of model use in describing the

structural mechanics behavior of IG units.

Models

The first step in the research plan addresses the response of an

IG unit as an integrated system. The unit is modeled as two

monolithic rectangular glass plates separated by an air space. Each

glass plate is considered to be simply supported around its perimeter,

with in-plane motion permitted. Units are also considered sealed

around their perimeters. Pressure differences between the sealed

airspace and the atmosphere on each side of the unit must be

considered. Unit response is based on pressure differences across the

glass plates. Unit response is measured in terms of bending stress,

membrane stress and displacement for the glass plates. This type of

response is "global," and addresses primary effects. Secondary

effects, such as edge distortion and support behavior, are neglected.

17

18

In the second part of the research plan, discrete portions of the

IG unit are examined to establish behaviors between components making

up the IG unit. The responses addressed in these discrete models

involve mostly secondary effects resulting from interactions between

IG unit components where they are in coritact at the perimeter of the

unit. These discrete models address the structural mechanics behavior

of individual components in the seal detail.

Global Model

This theoretical model representing the response of the IG unit

as an integrated structural unit is called the "global" model. The

global model provides information on the rectangular glass plates that

make up the majority of the material in the unit (Ref. Fig. 4 ) .

Rectangular plate theory provides the principal solution methods for

the global model.

A difficulty arises in properly defining support conditions for

the glass plates. Most rectangular plate solutions assume simply-

supported (non-yielding) conditions on their boundary. Glass plates

in an IG unit are supported by sealants; thus, the rectangular glass

plate is supported by elastic (yielding) boundary supports. Further,

the entire IG unit may be supported by dry neoprene gaskets or a

structural (liquid) seal (Ref. Fig. 5 ) . The inclusion of these

conditions in the global model has been proposed by Minor and

Vallabhan (1984) and is left for future efforts. All glass plate

solutions in this report are considered simply supported.

19

INNER GLASS PLATE

Surface designations

X

Spacer assumed rigid

Pressures acting on unit surfaces

OUTER GLASS PLATE

FIGURE 4. IG UNIT MODEL WITH SIMPLY SUPPORTED PLATE ASSUMPTION

20

-wv-

INNER GLASS PLATE

SURFACE DESIGNATIONS

Gasket or structural seal

'WArm Sealant response modelled by spring

3 2

jyVW

\

OUTER GLASS PLATE

Spacer assumed rigid

^ 1 ' ^2* 3' pressures acting on the unit surfaces.

FIGURE 5. PROPOSED MINOR-VALLABHAN IG UNIT MODEL

21

Local Model

Determination of local response within the combination of

components at the boundary, and determination of individual material

stresses and strains, requires a different, complementary approach.

The approach taken is referred to as the "local model" (Ref. Fig. 6).

The local model is capable of describing secondary stresses in the

boundary components at a single cross-section at the edge of the IG

unit. Modeling this response requires an analysis method that uses

individual material properties to calculate component responses to

various imposed loadings and or displacements. Because of the variety

of components, each with its constituent material, the finite element

method of modeling was considered the most viable for the local model.

Modeling of an entire cross-section of an IG unit by the finite

element method would be costly. Further, responses obtained for

various components at the boundary would not be descriptive at a scale

necessary for proper evaluation. Even if the centerline of the IG

unit were considered as a line of symmetry, the element size necessary

for efficient modeling would lead to excessively long computer

solution times. To overcome the difficulties of scale and solution

time, a small cross-section focused on the seal detail itself was

selected (Ref. Fig. 6). This approach had advantages in increasing

element size and reducing the number of elements. Difficulties are

encountered in representing stresses and displacements at the point

where the local model is sectioned to remove it from the global model.

This difficulty was solved by imposing boundary variables from the

22

I—

0 0

UJ

<: Q-

e3 I—•

o 3 : oo

o

o

U3

UJ

23

global model at the cut section. Boundary values impose the same

stresses at the boundary of the local model as those found by the

global model solution for the same location. Displacements and

rotations from the global model are imposed at the local model cut

line in a manner that produces proper bending stresses. Membrane

stresses are matched by imposing concentrated loads at appropriate

nodes in the local model (Ref. Fig. 6).

Sealant Model

Establishing sealant properties for use within the finite-element

oriented, local model also presents difficulties. The polymer sealants

used have moduli of elasticity that can vary with time, temperature,

strain rate, type of polymer, and for some, degree of elongation.

Because of the influence of these variables on material properties,

moduli or stress-strain data for various sealants are not widely

published. Thus, it was necessary to develop a method which could

provide necessary properties for use in the local model. A method for

obtaining the required properties of sealants in IG units is presented

in Chapter VI.

Other Models

IG unit behavior that is examined herein includes glass stresses

and displacements, and sealant and spacer response to service loads.

The global and local theoretical models provide most of the required

data. However, methods for modeling special types of spacer response

(e.g.f spacer migration) and complex corner effects are also addressed

24

as part of the research plan. Testing to establish empirical

variables will be necessary before these models can be used to

describe behavior of these specific segments of IG units.

Component Behavior

Glass

Glass plate response is obtained using nonlinear plate theory

(Vallabhan and Wang, 1981). Behavior that is examined includes glass

stresses from lateral pressures on the surface of the glass plates

which are simply supported. Since IG units are made up of two glass

plates separated by a sealed air space, the response of one plate with

respect to deflections of the plate opposite the sealed air space are

examined. Rectangular glass plate response to lateral pressures has

been studied extensively in recent years. Several methods of solution

are available (Al-Tayyib, 1980; Moore, 1980; Vallabhan and Wang, 1981;

Vallabhan and Ku, 1983).

Sealants

Factors influencing the behavior of the IG unit sealants are

different from those influencing the behavior of the IG unit glass

plates. The sealants seldom experience the environmental parameters

that act on the glass. Forces on the sealant are generated, in

general, by the glass plates as they respond to temperature and

pressure. Except for the direct forces across the seal detail induced

by the difference in pressure between the inside and outside of the

sealed unit, factors affecting sealant response are in the form of

25

displacements caused by the reaction of the glass plates to lateral

pressure. Because of this, the majority of sealant responses are

modeled on the basis of strain. Commonly, sealant behavior is modeled

on the basis of time and a specified strain rate (Ferry, 1980). Input

to the local model requires knowledge of sealant response to strain.

Sealant data obtained from the models are normal and shear stresses

calculated at the center of each element.

Spacers

Spacer response on a global level is a facet of IG unit behavior

that is examined by the global model. Spacers respond to glass

motions induced by temperature change and to lateral pressures induced

by forces transmitted by the sealants. Sealants not only transmit

forces, but also they restrain spacer motion induced by expansion

caused by temperature changes. Preparation of a response model for

the spacer requires consideration of effects of these various forces

and restraints. These effects include axial loading (buckling),

lateral loads (beam action), elastic supports, and end moments for

some common spacer types. Information desired from the model is

primarily displacement of the spacer within the restraining effects of

the parallel glass plates.

Corner Effects

Because many spacer styles have rigid corners (corner keys or

formed corners) the ability of the spacer to deflect in concert

with other materials is limited. This limitation r,ay cause material

26

stresses uncommon to other locations on the perimeter of the IG units.

An attempt to model this complex area with horizontal and vertical

local (cross-section) models is offered as part of the research plan.

These local models combine information from the corner grids of the

global model with additional boundary restraints in the finite element

solution (local model) to simulate the effects of the rigid spacer

corner. Expected information from this model includes displacements

and normal and shear stresses for the various materials.

Exercise of Models and Applications of Investigations

All modeled responses from the local model are based upon

linearly elastic material action only. Failure criteria must be

applied to computer results. A decision on the part of the data

interpreter must be made as to whether failure has occurred.

The final part of the research plan involves exercise of the

models to obtain information on the structural mechanics behavior of

IG units.

In format ion provided by the models ou t l ined in t h i s research plan

con t r i bu te s i g n i f i c a n t l y to the understanding of s t r u c t u r a l mechanics

response o f IG u n i t s . Imp lementa t ion o f t h i s research p rov ides

r e s u l t s t ha t can be used as a base f o r d e s i g n i n g more e f f i c i e n t and

s t r u c t u r a l l y r e l i a b l e IG u n i t s . Eventual uses include spacer c ross-

sect ion op t im i za t i on , general u n i t des ign methods, and d e t e r m i n i n g

e f f e c t s of cu r ta i n wal l r e s t r a i n t systems on the IG u n i t s .

CHAPTER V

INSULATING GLASS UNIT RESPONSE MODELS

Global Model

The global model characterizes the behavior of two individual

rectangular glass plates that are joined by a spacer along their

perimeters, enclosing a sealed air space. Lateral pressures used in

the determination of stresses and displacements in the glass plates

are the change in pressure across each glass plate brought about by

the effects of pressure within the sealed air space and pressure

changes that occur interior and exterior to the IG unit. Pressure

changes across each plate are determined by numerical methods from

imposed wind pressures, barometric pressure changes and temperatures.

This analysis method takes into account the nonlinear response of the

thin glass plates. Input parameters include changes in barometric

pressure or imposed wind pressures external to surfaces of the plates.

Pressure differences across each plate are found by an iteration

process which estimates displacements in the plates, computes changes

in volume of the sealed airspace and compares the resulting estimated

pressure with that calculated by Boyle's law. The analysis method was

first presented by Solvason (1974); Chou and Vallabhan (1985) offer a

refined analysis.

Pressure differences across glass plates obtained from the above

analysis are then put into a finite difference solved rectangular

plate program as lateral pressures (Vallabhan and Wang, 1981). Output

includes membrane and bending stresses and displacements at each node

27

28

in the finite difference discretization. Details of the method of

solution can be found in Vallabhan and Wang (1981).

Local Model

Interactions among components at the IG unit boundary are modeled

by the local model. Cross-sections normal to the edge of the IG unit

are taken at points along the boundary where the necessary input

information, from the local model, can be determined. Discretization

of the cross-section into rectangular elements prepares the model for

finite element solution (Ref. Fig. 7 ) . A typical detailed

discretization is shown in Figure 8. Discretization is purposely

coarse to reduce computer time. Each glass plate is divided down the

center in order that moments in the plate can be simulated and

membrane stress, in the form of applied concentrated forces, can be

applied along the central nodes. Bending in the spacer cross-section

was assumed small because of the small spacer thickness. Hence,

spacer discretization consists of single elements across the thickness

of the spacer material. Bending in the sealant is assumed negligible

because of relatively low sealant modulus. Sealant elements are also

single elements across their thickness.

Solution of the local model depends on correctly describing the

input variables. As mentioned above, the local model cross-section

does not extend to the center of symmetry of the IG unit plate; hence,

parameters necessary to provide similar stresses at the "cut" section

on the local model and the corresponding point on the global mo

del must be provided as input to the local model. Variables chosen

29

SECONDARY SEAL

GLASS PLATE

PRIMARY SEAL

SPACER

A & B are lines where Local Model is cut from Global Model. These lines are also the location of local model input from the global model. A

AIR SPACE

FIGURE 7. CROSS-SECTION OF IG UNIT AT TOP CENTER SHOWING LOCATION OF LOCAL MODEL

30

FIGURE 8. LOCAL MODEL DISCRETIZATION

31

to provide proper s i m i l i t u d e are d isp lacements and r o t a t i o n s a t the

c r o s s - s e c t i o n c u t l i n e ( t o r e p r e s e n t the bending s t r e s s e s ) and

concentrated loads at the nodes ( t o represent membrane s t r e s s e s ) . To

check the accuracy of t h i s s imu la t ion , moments from a loca l model run

(w i th temperature e f f ec t s omi t ted) , we're compared to moments f rom the

g l o b a l model a t the l o c a t i o n o f the l o c a l model cu t sec t ion . The

g lobal model moment was 8.3 i n . / l b s and l o c a l model moment f rom the

c u t s e c t i o n i n p u t was 7.9 i n . / l b s , a d i f f e r e n c e o f less than f i v e

p e r c e n t . Th is d i f f e r e n c e i s deemed a c c e p t a b l e , c o n s i d e r i n g t h e

r e l a t i v e l y coarse d i s c r e t i z a t i o n .

Temperature displacements ca lcu la ted in advance also may be input

at the " c u t " l i n e . With these displacements and loads appl ied to the

c ross-sec t ion the model i s solved by the method of f i n i t e elements.

Outputs produced f rom the l o c a l model are normal and s h e a r

s t r e s s e s f o r each e lement i n the d i s c r e t i z a t i o n . S t resses are

provided f o r the center of each element and are or iented to the Y and

Z axes o f t h e i n p u t c o o r d i n a t e sys tem ( R e f . F i g . 9 ) . S t ress

d i r e c t i o n s shown in Figure 9 are p o s i t i v e . L inea r , e l a s t i c response

i s assumed f o r a l l m a t e r i a l s i n the f i n i t e element r o u t i n e used.

M a t e r i a l t ype and s t r e s s e s are examined f o r each e l e m e n t and a

judgment made (based on knowledge of mater ia l p roper t ies ) to determine

i f the e lement has reached an e l a s t i c or f a i l u r e s t ress cond i t i on .

Based on t h i s judgment, po ten t i a l problem areas can be i d e n t i f i e d .

32

o ^ a *

CO

CO O (0 Vi Qi

0) CL >

t ^ *

• *

c o E .2 0

00

UJ

a: 00

A 2 O 00 N

UJ

UJ a o

o o

o z o I —

UJ

Q:

o

oo o Q.

a

•a: o

N < O o

cjs

UJ

cu

33

Spacer Model

Spacers used in IG un i t s can be examined by a proposed separa te

model. One segment of the spacer i s modeled as a beam-column on

e l a s t i c foundat ion w i th the exception tha t the springs s imulat ing the

e l a s t i c f o u n d a t i o n are changed t o Maxwell models (Ref . F i g . 1 0 ) .

R e f e r r i n g t o F i g u r e 10 , v a r i o u s l oad ings are generated by the

fo l l ow ing cond i t i ons :

1. The a x i a l l o a d i s g e n e r a t e d by c o n s i d e r i n g t h e

d i f f e r e n c e i n the c o e f f i c i e n t s o f thermal expansion

between g lass and aluminum, and by c o n s i d e r i n g the

r e s t r a i n i n g e f f e c t o f the s e a l a n t on the aluminum

expansion r e l a t i v e to glass expansion.

2. Normal, or beam, loading w i l l come from pressure w i t h i n

the u n i t , caused by temperature or barometr ic p ressure

change, or both.

3. Maxwe l l model e l a s t i c f o u n d a t i o n parameters are

determined from the r es t r a i n i ng e f f e c t o f the s e a l a n t

on the spacer i n the l a t e r a l , or normal d i r e c t i o n .

These parameters are t y p i c a l l y found by expe r imen ta l

means.

4. Moment intensity at the end of the spacer segment will

depend on the material properties of the spacer, the

rigidity of the spacer corners and the rotation at the

segment ends caused by the axial and normal loading.

34

4J c n HD

H C fO fO 0 m 4J

c >i 4J QJ 0 -H U E C S D

"U u C 0) c

•H U -t-l rtJ ^

TJ Q44J rtJ to -H

M 5^ C 0)

&>-H U C 4J D

•H CQ to T: -H m C 0] 0) (D 0 U

OQ ^ 0 4

TJ ^ i 0 S rQ U

4J c fO c

H 0 (TJ - H 0) CQ CQ CQ C CQ

C

0 •p

(D D

TJ -P

O

C rH fO

•H

CQ 0 TJ 0) 0) -P fO U 0 ro

C C E ro 0)

H CQ O (U

• H CQ <W (0 X CD - H O4

»< M T J CQ

0

CD Q

O

UJ O O

a.

UJ

O

35

One additional piece of information input to the spacer model is

an initial displacement at the center (if any) obtained from the

cross-section (local) model. This displacement is caused by the slope

of the glass at the spacer due to edge rotation pinching the spacer

from above or below (Ref. Fig. 11).

Once the various materials properties related parameters have

been determined, spacer response can be found from solution of the

equation:

where:

V = displacement of beam (spacer) in y-direction

u = displacement of beam (spacer) in x-direction

k = spring stiffness

c = damping constant

g = normal load on beam

E = modulus of elasticity of beam.

I = moment of inertia of beam cross-section

P = axial loading

Equation (1) can be solved numerically by finite element or

finite difference techniques. Solution of Equation (1) is left to

future efforts. When a solution of Equation (1) is obtained, various

loadings may be examined to determine if spacer bow can be described

using this model.

36

FIGURE 11. SEALANT DEFORMATION AND SPACER DISPLACEMENT CAUSED BY ROTATION OF IG UNIT GLASS PLATES

37

Corner Ef fects Model

Examination o f c r o s s - s e c t i o n s , s i m i l a r t o those desc r ibed i n

Figures 7 and 8, near the corners of the IG un i t present an add i t iona l

cons idera t ion . Spacer corners are of ten r i g i d , and the res is tance

of the spacer segment o r thogona l t o iihe c r o s s - s e c t i o n needs t o be

taken i n t o account.

Near the edge of the u n i t the displacements and ro ta t ions of the

glass p la tes are smaller than those near the center of an edge because

of the p l a t e response near the c o r n e r s . A p r imary e f f e c t a t the

co rne r i s the d i f f e r e n c e i n p l a t e size due to thermal expansion (or

c o n t r a c t i o n ) . A one-dimensional steady s t a t e heat f l ow a n a l y s i s a t

t h e c e n t e r o f t h e u n i t and a t t h e space r r e v e a l s t h a t l a r g e

temperature d i f f e r e n c e s between the g lass p l a t e s are not uncommon

d u r i n g usua l ' mid-summer or m i d - w i n t e r days. The assumpt ion made

throughout these analyses is tha t the inner (room) a i r temperature i s

a constant 70°F due to a i r cond i t i on ing . Heat f low at the boundary of

the u n i t shows the spacer to maintain a temperature nearer tha t of the

outs ide glass p l a t e , and the spacer and outer glass p la te are assumed

t o m a i n t a i n t h e i r r e l a t i v e p o s i t i o n s d u r i n g t h e r m a l e x p a n s i o n .

Expansion o f the o u t e r g lass p l a t e and spacer whi le the inner glass

p la te remains constant w i l l cause add i t iona l st ress in the components

due t o t h e l a c k o f f l e x i b i l i t y o f t h e s p a c e r a t t h e c o r n e r .

A d d i t i o n a l s t i f f n e s s o f t h e s p a c e r a t t h e c o r n e r , due t o t h e

orthogonal spacer segment at tached, i s represented by add i t iona l nodes

attached to the spacer in the c ross -sec t ion . These nodes are assigned

38

the modulus of the spacer material and restrain its motion accordingly

(Ref. Fig. 12).

Various temperature and geometry combinations can be examined to

determine if the additional stiffness of the spacer at the corner

creates stress changes in the materials as compared to the local model

which is at the centerline of one of the sides of the unit.

The above four models used singly and in combination provide a

better understanding of the primary and secondary stress and

displacement responses of IG units.

39

iV«»i«i«.$(S«9«9i>999$«9».'«IC«fiQ»>«»$«NN;

V v ^

Oi

c

CO I

CO D CC

•goo = s§ O C ^

^ •*- ^

< «£

LU Q

o CO I -o LU LL U . LU

CL m

cc oo o — a . 31

o o C_ H -OO o

UJ - J u . <C lJ_

i< o UJ CO

- J < UJ CO > CL <

S CL CL

CO - I < O K GC UJ >

O Q

3 OO O = o oo h-

CC _J UJ UJ z : 2 : Q O Q: o •—' o 2 : I— o Q:

00 o \— \— CL.

Z UJ Q^ => U . UJ

u. o cs UJ <c t—I Q .

Q : 0 0 U. UJ o z —i

en ea: -J o <_) i-M CJ t—I •a: h -I— Q Q : UJ Z UJ Q < : >

CM

UJ a:

CHAPTER VI

MATERIAL PROPERTIES

Glass

The rectangular glass plates within an IG unit constitute the

majority of the material in the unit; hence, their behavior has a

significant effect on the behavior of the entire unit. In the global

model the behavior of individual glass plates is determined from thin

rectangular plate theory (Vallabhan and Wang, 1981). Behaviors of the

local and corner effects models are influenced by the structural

mechanics properties of constituent materials.

Glass is a brittle material whose stress-strain properties remain

essentially linear until fracture (Shand, 1984). Stress-strain

properties of glass exhibit only a slight temperature dependence. For

the range of service temperatures considered in this document (-40°F

to IIO^'F) these effects are neglected. Since glass exhibits

essentially a linear stress-strain relationship. Young's modulus

is taken as constant within a range of 10 to 10.5x10 psi.

Most theoretical models use a Young's modulus of glass of 10x10

psi. The coefficient of thermal expansion of glass is taken to be

4x10"în./in./°F.

Spacers

The two most common spacer materials are steel and aluminum.

Both of these materials behave linearly within their elastic ranges.

Since the models described in this chapter consider only elastic

40

41

response, elastic moduli were considered sufficient for use as stress-

strain information. Young's modulus of aluminum used in the models is

10x10 psi. Aluminum properties are taken as representative values

(Birdsall, 1965). The coefficient of thermal expansion for the spacer

material used in the models is 13.x10~^ in./in./°F for aluminum

(Birdsall, 1965). Steel spacers are not used as part of this effort.

Each glass and aluminum component is assumed to be at or near a

constant temperature throughout the component; hence, each component

expands uniformly. This assumption eliminates the presence of thermal

stresses due to temperature differences within a single glass or

aluminum component.

Sealants

Sea lan ts used i n IG u n i t s i n c l u d e p o l y s u l f i d e s , s i l i cones and

hot-mel t b u t y l s . Others, such as polystyrene, are being t r i e d at t h i s

w r i t i n g . The only sealant tested f o r use herein as a r e p r e s e n t a t i v e

s e a l a n t i s " P r o - S e a l " sealant , a po l ysu l f i de . Mechanical proper t ies

o f t h i s s e a l a n t are used i n the models addressed he re i n because

i n f o r m a t i o n r e q u i r e d by the models i s a v a i l a b l e on l y from special

sealant t es ts described in t h i s chapter. Propert ies of other sealants

may be employed in these models when comparable m a t e r i a l p r o p e r t i e s

become a v a i l a b l e .

Mechanical p roper t ies of other sealants used in IG un i ts are not

r e a d i l y ava i l ab l e . A l i t e r a t u r e review y i e l d e d very l i t t l e data on

polymers tha t could be used in the t heo re t i ca l models. Hence, i t was

necessary t o deve lop a method f o r g e n e r a t i n g s e a l a n t m a t e r i a l

42

p roper t i es . A semi-empi r ica l method t o f i n d the r e q u i r e d m a t e r i a l

p r o p e r t i e s o f polymer sealants f o r use in the theo re t i ca l models was

developed.

Analysis.

Important parameters which a f f ec t the s t r e s s - s t r a i n behav ior o f

polymers are tempera tu re , s t r a i n ra te , time dependency of stress and

polymer t y p e . A s e t o f e m p i r i c a l l y based r e l a t i o n s h i p s t h a t

c h a r a c t e r i z e polymer response f o r s p e c i f i c combinat ions o f these

parameters c o n t a i n s numerous cu rves . Perhaps t h i s o b s e r v a t i o n

explains the absence of published engineering data on polymers.

Whi le master curves can be constructed to al low fo r temperature

in polymers t h a t undergo s t r e s s - r e l a x a t i o n ( W i l l i a m s , Lande l , and

Fe r r y , 1955) , a procedure to cor rec t a general polymer s t r es s - s t r a i n

curve f o r the spec i f ied fac to rs ( tempera tu re , s t r a i n r a t e , and t ime

dependency o f s t r e s s ) was not found i n a review of the l i t e r a t u r e .

Polymer s e a l a n t s t r e s s - s t r a i n i n f o r m a t i o n f o r a s p e c i f i c s e t o f

f a c t o r s i s needed f o r the prev ious ly mentioned theo re t i ca l models, A

new approach, described below, addresses t h i s problem and p rov ides

t h i s i n fo rmat ion .

Method

S t ress - re laxa t ion proper t ies of a polymer sealant are obtained by

a s imp le t e s t . S t ress - re laxa t ion proper t ies are converted to s t r ess -

s t r a i n re la t i onsh ips f o r the t e s t temperature. The conversion method

has been coded f o r computer so lu t i on and resu l t s are presented in

43

g raph i c and t a b u l a r fo rms . A l i s t i n g o f the program appears i n

Appendix A.

S t r e s s - r e l a x a t i o n t e s t i n g i s done by cas t i ng a sealant sample

between two aluminum bars (Ref. F ig . 13). A s t r e t c h i n g dev ice sepa

rates the bars, thus impart ing a f i xed elongat ion to the sealant (Ref.

F ig . 14). Instrumented steel posts maintain the separation of the bars

a f t e r the s t r e t c h i n g dev ice i s removed (Ref. F ig . 15). Compressive

s t r a i n on the s teel posts, induced by the s t r e t c h e d polymer, i s r e

corded over t ime to p rov i de s t r e s s - r e l a x a t i o n data fo r the sealant

(Ref. F ig . 16). The polymer sample size i s 1/2 x 1/2 x 2 i n . ; i t i s

elongated 25 percent or 1/8 i n . in the 1/2 i n . d i r e c t i o n . This sample

c o n f i g u r a t i o n min imizes the Poisson e f f ec t as a percentage of t o t a l

area. Tensi le s t r e s s i n the sample i s c a l c u l a t e d on the bas is of

o r i g i n a l c r o s s - s e c t i o n a l area. Dimensions of the instrumented steel

posts are 1/16 x 1/8 x 5/8 i n . S t ra in gages are mounted on oppos i t e

s ides o f each s t e e l post (Ref. F ig . 15). Compressive s t r a i n on each

post i s taken as the average of the recorded opposite side s t ra ins to

compensate f o r bending in tKe posts. Stra ins are recorded at d iscre te

t imes over an 180 hour i n t e r v a l (Ref . F i g . 16). Steel post s t r a i n

data are used to ca lcu la te stress in the polymer as a funct ion of time

by c o n v e n t i o n a l methods. D i s c r e t e p o i n t s f r om t h e a n a l o g d a t a

d e s c r i b e the s t r e s s - r e l a x a t i o n behav io r f o r the polymer s e a l a n t

tes ted .

Stress re laxa t ion data from the sealant t e s t are conver ted

to s t r e s s - s t r a i n re la t i onsh ips using Equation ( 2 ) , and a computer

44

FIGURE 13. CASTING THE STRESS-RELAXATION TEST SAMPLE

FIGURE 14. STRAINING DEVICE ATTACHED TO STRESS-RELAXATION TEST SAMPLE

45

FIGURE 15. AN INSTRUMENTED STEEL POST

FIGURE 16. RECORDING OF RELAXATION DATA

46

program. Equation (2), from Nielsen (1962), calculates stress as a

function of strain.

a(e) = Eê + K xHdnx) (1-e""/^") d I m (2) '-00

where:

a = tensile stress in psi

e = strain

E = rubbery flow modulus in psi

K =

T =

strain rate in inches per hour

relaxation time, hours

H(InT) = increment of distribution of relaxation times

Evaluation of Equation 2 within the computer program begins by

input of the discrete stress-time values from the experimental test

into the program. A polynomial (first to sixth order) or exponential

curve is fit to the discrete points by the program. The distribution

of relaxation times (H[ln(T)]) is obtained from the fitted curve using

a second order numerical differentiation routine (Ketter and Prawel,

1969) and Andrews' Second Order Method (Andrews, 1952; Tobolsky,

1960), represented by Equation (3).

H.a(^) -1

77303 dEr(t) dlogt + 0.109 dÊr(t)

dlogt^ (3)

where: -'t = T -'t = T

Ho (T) = distribution of relaxation time ordinate for time 2a^

Er = relaxation modulus

H ( T ) = H(lnT) for single relaxation times (Tobolsky, 1960)

47

At specif ied increments of t ime, e longat ion is converted to s t r a i n

through Equation (4) from the theory of rubber e l as t i c i t y (Treolar,

1958).

z = 1/3 (^r (4)

where:

L = initial length of material 0 L = final length of material

Change in strain is divided by the time increment to obtain

strain rate. With this information the program evaluates Equation (2)

using a linear numerical Lagrangian integration routine (Ketter and

Prawel, 1969) to obtain a stress from each incremental value of

strain. Increments of I m = 0.1 combined with strain increments of

0.01 provide sufficient accuracy while maintaining program run time at

acceptable levels. Stress as a function of strain can be evaluated,

by the program, up to elongations of approximately 300 percent

(strains of approximately 100 percent).

Figure 17 contains a sample of the computer generated output.

Experimental points and the fitted curve vs. log time are shown in the

upper left quadrant. The curve fit shown is exponential and becomes

asymptotic near the rubbery flow modulus. Data points grouped near

the 28 psi stress and the 100 hour time indicate that this sealant

exhibits a rubbery flow modulus; hence, the curve should have zero

slope past these points. Averaging the stress values of these grouped

points and dividing the result by the fixed strain produced tne

48

UJ

/^ H (/> Q.

(/J 3 -J D a o 3;

- U J

<s

en

UJCJOXOCnOr-'^ —OOLOCMCDCDO TTcococoeocjcMcu oxocn

lUt-

s o

<:

o

OC9C9 OC3G C9QOOOC9 •^•^CKOcncncvJcvjcvj 0(0<n

s

o

o

W

UJ UJ> H 3

I /-> > 7)

1 3

(9

0.:= >-'M V ) 0 (/)Q. UJ QC< • - ) -I /5<

Q

f

f

• ^

3 -

: -0)

^ j a .

O (S

lOOLO(SLOOtJ)Sl/}(SLOOU)<S r-r-<OU3L0WTTC0CnCU<M U)

o

a.

0 0

IS <s

U}<SU)aL0C3U>aU)<9l/}SL0(S

49

rubbery flow modulus value used in Equation (1). Modulus vs. log time

is obtained by dividing fitted curve values by the fixed strain from

the simplified stress-relaxation test and the result is shown in the

upper right quadrant of Figure 17. A plot-of the distribution of

relaxation times is given in the lower left quadrant and stress as a

function of strain for the temperature of the simplified stress-

relaxation test and the specified strain rate is in the lower right

quadrant of Figure 17.

Other equations that convert stress relaxation data to stress-

strain relationships, for polymers, were considered. One such

equation is reported by Ferry (1980):

a(t) = k H(l-e"^/'') d Inx + E kt (5) V _oo

and has a constant value for the distribution of relaxation times (H).

Another equation, also from Ferry (1980), is of the Duhamel integral

type.

a(t) = k E(t-T) dx •'o

(6)

These equations f i n d st ress as a func t ion of t ime and can r e a d i l y be

conver ted t o s t r e s s - s t r a i n by mu l t i p l y i ng the time axis values by the

s t r a i n r a t e , K. Equat ion (2 ) was chosen f o r t h e s t r e s s - s t r a i n

conversion because i t re la tes stress d i r e c t l y to s t r a i n . S t ra in i s a

mo re common parameter in a structural mechanics system than time.

50

V e r i f i c a t i o n

V e r i f i c a t i o n of the s t r ess - re l axa t i on , s t r e s s - s t r a i n convers ion

program was conducted on a two -pa r t po l ysu l f i de base sealant, brand

name " P r o - S e a l . " A p o r t i o n o f the mixed sea lan t was cas t i n the

s t r e s s - r e l a x a t i o n dev i ce desc r i bed above and the remainder cas t

between glass p lates coated wi th re lease agent . Samples were cured

fo r two days at room temperature. Bone shaped tes t pieces were cut

from the sealant cast between the glass plates (Ref. F ig . 18). These

bone shaped t e s t specimens were to be used to check the accuracy o f

the program generated s t r e s s - s t r a i n informat ion which used data from

the sealant in the s t ress - re laxa t i on d e v i c e . Four bone shaped t e s t

p ieces were cu t w i t h gage lengths of 4.32, 2.9, 1.8 and 1.8 inches.

An Inst ron t e s t i n g machine provided force-deformat ion i n f o r m a t i o n f o r

a constant e longat ion ra te of two inches per minute on the bone shaped

t e s t p i e c e s . C o n v e r s i o n o f f o r c e de fo rma t ion t o s t r e s s - s t r a i n

in format ion f o r the t e s t pieces used the same p r i n c i p l e s as used i n

the computer program. S t r e s s - r e l a x a t i o n data from the t e s t device

were input to the program and resu l t s generated. Inst ron and program

resu l t s are p l o t t ed f o r comparison in Figure 19.

Results

P r e d i c t e d va lues f rom the s t r e s s - r e l a x a t i o n tes ts var ied less

than ten percent from t e s t values obtained from the I n s t r o n t e s t s on

the 2 .9 i n . and 1.8 i n . gage l e n g t h samples and are approximately

cen t ra l to the range of Ins t ron values up to s t r a i n s o f approx

i m a t e l y 0 .8 (Ref . F i g . 19). Var ia t ions between predicted and tested

51

FIGURE 18. INSTRON TEST SAMPLE

52

H

04

CQ CQ Q) U •P

cn

200

150

100

50

o|

/ •

a / •

/

P / z? / . ' / >

a//

d J 1 y

/ / / •''y

I/// j /i S t r e s s vs

p - ^ P r e d i c t e d and

f \

i / i /

/j^ ^ y / z / jm *

yf »" mi ^ T t *

/ i *

f / / ^^^ / / •

/ / / / / /

/ if

0 4 . 3 2 " GL

a 2 .90" GL • 1 .80" GL • 1 .80" GL

— P r e d i c t e d

S t r a i n Sample T e s t s

i 1

0 .5 1 .0

S t r a i n ( I n . / I n . )

1 .5

FIGURE 19. PREDICTED AND TESTED STRESS-STRAIN RESULTS FOR "PRO-SEAL" SEALANT

53

stress-strain data suggest that the prediction curve may not be

accurate above strains of 100 percent (Ref. Fig. 19).

Application

Most polymer strain rates in IG units can be determined from the

controlling motions of the more massive and stiffer glass and spacer

materials. Thermal expansion and displacement-rotation response to

pressure for the glass and spacer materials tend to control the

deformation response of the polymer. Estimation of times required for

these motions provides elongation rates that can be entered into the

program to provide polymer stress-strain data for the specific polymer

being examined.

One application where polymer response is not dependent on

motions of the stiffer materials is the case of a vertical plate

attached top and bottom by a polymer sealant/adhesive (Ref. Fig. 20).

The example considered is a weightless, rigid rectangular plate

supported along the top and bottom by the "Pro-Seal" sealant that was

tested. (This is not a recommendation for using this sealant in this

manner. However, since it is the only sealant tested using the above

method, it is used in the example.) Lateral loading on the plate is

an assumed 50 psf lasting three seconds. Plate height is 60 inches

and a one inch wide strip is used for calculation. Polymer supports

are 1/4 of an inch high by 1/8 of an inch thick. Using symmetry, half

of the plate height is used in the computations.

Describing the response of this system, using the principles

presented in this paper, requires assuming a polymer modulus. An

54

Rigid, Sealant Support weightless rectangular plate

1/4' (6.35 mm)

FIGURE 20. VERTICAL PLATE WITH TOP AND BOTTOM SEALANT SUPPORTS

55

assumed modulus value can be selected from the modulus vs. time plot

generated by the program. Using this modulus value and the applied

load, an elongation of the polymer support is obtained. Dividing this

elongation by load duration gives an elongation rate that is entered

into the program and results generated. A new modulus value is

obtained from the generated stress-strain information. In this

instance the new modulus is 184 psi. Using the new modulus a new

elongation rate is calculated, entered into the program and the

process repeated.

After the first iteration in this example there was practically

no change in the modulus value in subsequent iterations. This

occurrence led to the examination of modulus variations for various

elongation rates. Several program runs were made using different

elongation rates and the results of modulus vs. elongation rate are

shown in Figure 21. Polymer stress-strain plots are often nonlinear

and the modulus vs. elongation rate is also shown for various strains

in Figure 21.

Elongation rates for the example are in the 10 inches per hour to

100 inches per hour range. Modulus vs. elongation rate varies less

that one psi in this range; hence, the rapid convergence of the

modulus value. Figure 21 is an important tool for determining the

material response of the polymer when elongation rates must be

estimated.

56

c •f-4

fO u AJ CO

1^ o o i H

c •m rtJ ^ JJ

c/:

i n a r-i

o o fN4

o H

o •

o o

r o

13

c 'M (tJ u 4J cn 0 ^

in CN

c • i H

^ }^ JJ

w 0 ^

O i n

c •f-4

03 5-1 +J cn

i n

r

r H

o (

o

o a: H

O

r-i

o O O O

o

u

o

c

Q 4J (C a c o -.J

c 0

rH

_ j < UJ oo

•a: UJ oo

I o a: Q.

o

cn oo

Z UJ o t— ^ <: I— Q: •a: o z z • - • o <c _ j cn UJ I—

oo •

oo oo =» :z) o oo •—' - J -sC

o O I—

UJ cn C3

(ISd) sninpow

57

Work in Progress

Equation (2) does not consider variations in the stress-strain

properties due to changes in temperature. These variations are

presently being incorporated into the program using the method

presented by Smith (1956). Other improvements include a technique to

input a sketched curve directly into the program by digitizing (thus

eliminating the need for a curve fit), reading strain data directly

into the program for conversion to stress, and incorporation of a

fracture criterion to predict adhesive and cohesive failure.

CHAPTER V I I

PARAMETRIC STUDIES

As stated i n Chapter IV, the primary purpose of t h i s research is

t o deve lop models which can be used t o character ize the s t r u c t u r a l

mechanics behavior of IG u n i t s . Use of the models and t h e i r behavior

are demonst ra ted by pa rame t r i c s tud ies . Local models (described in

Chapter V) are used to examine mater ia l stresses and e f fec ts on these

s t r e s s e s i n d u c e d by s e l e c t e d a l t e r a t i o n s i n spacer and s e a l a n t

geometries and mater ia l p r o p e r t i e s . St resses examined are maximum

s t r e s s e s i n l o c a l models f o r each m a t e r i a l con ta ined in the u n i t .

M a t e r i a l s used i n the s p e c i f i c examples presented are l i m i t e d t o

g l a s s , aluminum spacer , and a po l ysu l f i de sealant . IG un i ts are not

l im i t ed to these mater ia ls , however. Any number o f m a t e r i a l s may be

s p e c i f i e d and each m a t e r i a l can be d e f i n e d as hav ing i so t r op i c or

a n i s o t r o p i c p r o p e r t i e s . A n i s o t r o p i c p r o p e r t i e s a re l i m i t e d t o

orthogonal planes in the elements.

Select ion of Reference Evaluation Condit ion

E s t a b l i s h i n g a re fe rence point or "datum" f o r use in evaluat ing

resu l t s of parametric studies i s an essent ia l f i r s t step. Cond i t i ons

used t o e s t a b l i s h t h i s datum a re r e f e r r e d t o as " S c e n a r i o s . "

Scenar ios are c o n s t r u c t e d i n o rder t o d e f i n e se ts o f " r easonab l y

expected extreme cond i t i ons " which may create s i g n i f i c a n t stresses in

component m a t e r i a l s . Reasonably expected extreme c o n d i t i o n s are

58

59

defined as environmental conditions that an IG unit could experience

at some location within the continental United States during the span

of a year. Each set of conditions which are combined to form a

Scenario may not occur at the same location during the year, however.

Conditions from each Scenario are input'to the local model and results

are generated. Output from each Scenario is examined to determine

which set of conditions produced the largest stresses in the spacer

and sealant. Glass stresses are not considered as a basis for

determining the reasonably expected extreme conditions since they are

best described by the global model. In addition, glass stresses from

local model Scenarios were found to be small when compared to expected

failure stresses of glass.

Conditions for each Scenario are given as follows:

Scenario I. Assumes the IG unit is assembled and sealed at

mean sea level (MSL) at a temperature of 70°F. The unit is

transported to an installation site at an elevation of 6000

ft above MSL, thus causing a corresponding barometric

pressure decrease of three psi exterior to the unit. After

installation, the temperature exterior to the unit rises to

110°F. Finally, a positive (inward acting) wind pressure of

35 psf is applied to the unit.

Scenario II. The same as Scenario I except a negative

(outward acting) wind pressure of 25 psf is experienced

outside of the outer glass plate.

60

Scenario III. Assumes the IG unit is assembled at an

elevation of 6000 ft above MSL and is then transported to

sea level for installation, thus subjecting the unit to an

exterior barometric pressure increase of three psi. After

installation temperature exterior to the unit decreases to

-40°F. A positive wind pressure of 35 psf is experienced

outside of the outer glass plate.

Scenario IV. Same as Scenario III except a 25 psf negative

wind pressure is experienced outside of the outer glass

plate.

In each scenario the unit is assumed to be in an installed

configuration and the temperature interior to the unit is maintained

at a constant temperature of 70°F by an air conditioning system.

Individual glass plates of the IG units are first analyzed using

the global model for overall responses to pressure. Pressures acting

across each glass plate are obtained using one of the methods for

analyzing pressure differences across glass plates in IG units (Chou

and Vallabhan, 1985; Solvason, 1974). In addition, dimensional

changes in the outer glass plate caused by temperature are calculated.

Thermal expansion is determined using the entire height (or width) of

the outer glass plate as it is assumed that the IG unit is resting on

a setting block and that all dimensional changes are referenced to the

bottom of the unit. Displacements and rotations obtained from the

global models and thermal displacements obtained as noted above are

input to the local model and resulting stresses in the elements are

61

calculated. This procedure is followed for each Scenario and the

results compared. Comparisons are based on the maximum tensile

stresses in the aluminum spacer and in the sealant. Glass stresses

were examined and found not to be a criteria; hence, they are not used

as a criteria on determining the datum condition.

Evaluations of Seal Details

Local model runs are based on an IG unit that is 67 inches high

by 59 inches wide. Each glass plate is 0.,250 in. thick and the

insulating air space is 0.500 in. wide. Assumed glass modulus is

10x10 psi. Datum conditions are obtained using a 1/2x1/2 in. spacer

that is cold formed from 0.022 in. thick aluminum. Spacers are

constructed so that the cold forming seam faces the sealed airspace of

the IG unit. Spacer seams are occasionally welded. When the seam is

welded it is assumed to act as a continuous cross-section in the local

model. When spacer seams are not welded, they are referred to as

"split" spacers. Aluminum spacer material is assumed to have a

modulus of 10x10 psi and a yield strength of 10,000 psi. Spacer

lengths are 1/4 in. less than the dimensions of the glass, leaving a

1/8 in. channel around the perimeter of the IG unit that is filled

with sealant. This structural seal is called the secondary seal.

Secondary seals not only seal the perimeter of the units but hold the

unit together. Local models considered herein have an optional

"primary" seal that coats the vertical sides of the spacer. This seal

is assumed to be 1/32 in. thick and coats the entire vertical side of

the aluminum spacer.

62

As presented in Chapter VI, sealant moduli are strain rate

dependent. Deciding on a sealant modulus value presented some

difficulty because of the time dependence of values for sealant

modulus. Selecting a definite sealant modulus would require the

assumption of a specific and possibly transient set of loading

conditions. Effects of loading (and strain) rate are examined by

selecting the upper and lower bound sealant modulus values from

Chapter VI and running a set of local model Scenarios for each bound

of the sealant modulus. In this manner upper and lower bounds on

response stresses can be determined and differences evaluated.

Sealant moduli selected are 250 psi for the upper bound and 150 psi

for the lower bound. Resulting largest stresses for the various

Scenarios are found in Tables 1 and 2. Primary and secondary sealants

are usually different polymers. In this document they are the same,

since Chapter VI results are based on the single polymer tested.

Scenarios III and IV were not applied to the split spacer. The

reason for this is that these Scenarios caused inward deflection of

the two glass plates (toward each other), thus placing the inward

portion of the split spacer in compression along the central portion

of each side of the IG unit. A "master-slave" routine, which

prohibits element crossing, is not included for the element type used

in the finite element program. Since element crossing would occur at

the location of the split in Scenarios III and IV, the results were

not realistic and are not considered.

Stresses ordered by magnitude and material type for the various

spacer-scenario combinations are shown in Appendix B. A summary of

63

•9: PLd SSPL6 j8:;no o: paLLddc eunssBjd 6uLq.oe pjPMt no j.sd 92 t^daoxe j j j OLJBUBDS ^^ ^'^^S—suoL:n.puo3 [B:Û9QJUOJLAU3 A I OLJPUQDS^

•eq- Ld SSBL6 jeq.no eqc o: pei-LddB j.sd g£ J.0 ejnssejd puLM 6UL:^DIB pjPMUj -J^Q^ ^^ peuLBt uieuj SL ejn^^Bjadiue: J0LJ9ÛL SLJ-qM jjjOfr- 0^ saseajoep ajn^Bjedmat^ JOLJ9:^X3 '^Lun eqi O: J0LJ9:^Xe 9SB9wlD9p 9 jnSS9Jd DLj:^9llJ0JBq LSd £ SULSnCO L9A9L B9S UB9m 0^ p9q.wôdsul J: ^LUp "doOZ ^L 9jn:^pj9duj9:^ U9LJM -JS ^ 9AoqB -^^j. 0009 :ê p9 [e9S pUC p9LqUJ9SSB t^LUn—SUOLtîpUOQ L P : ^ U 9 1 U U 0 J L A U 3 m 0LJeU9DSg

•9^B[d sse[6 j9^no o: p9L[ddB j.sd g^ ô 9jnss9jd puLM 5uLq.Di? pjCM^no :^d90x9 * i 0Ljeu9Ds SP 9iijes—suoi^^Lpuo^ LP:Û9UJU0JLAU3 I I 0LjeU9DS3

•9q.B[d SSPL6 j9:^no o^ p9LLddB j.sd 99 ^0 9jnss9ad puLM 6uLq.DB pjeMUi '^^Qi %^ p9ULnuLPiu SL 9jn:;Bj9duj9:^ J0LJ9: UL 9[LL|M jÔLL ^^ S9SM 9jn:^BJ9dui9:^ J0LJ9:;X3 '^^lun gq: o^ J0LJ9q.X9 9SP9J09P 9jnSS9jd 0Ljq.9UJ0JBq LSd £ 6ULSnBD U0L^BA9[9 QQQQ o: p9q.jodsuBj:^ t Lup 'doOL s|. 9jn:^Bj9duj9:^ u9qM ( isw) L9A9L e9S 'uceuj "^^ p9[e9S puB p9Lqm9SSB :n.un—suoL:;Lpu03 L'^Û9UJUOJLAU3 I OLJBU9DS^

21 2

21 I

8^ S9

99 I

9e 21 59 n 62 I 9e

3-DOT

r"e£-ri62-0'L2LZl-

L'tl-rZ99-e'esoe-9*1-9*826-S'OSS-

9*9frfr-r£L88-

z*o-2 > 8 2 -Z'tSl-

Z*8-6'L2t-i'OZSV-

"dUIOQ

s(22S) [6UU0| UO

9S I

- SS

62 2 9e

9S 99 9£

2L 2

52 99 9£

2L 2 LZ

s'ooT

8*01 8*9L6 O'OetEL

9'1 0*2U 0*SL£2

Z'n 6 "5801 8*£^*2

e*£69 9'0Z.Z8

6*t rzzt E*Z69£

f OL Z*9C9 e'OLBZ

•suaj_

t^38Jtp-2

21

55

21 IE 55

E2 55

95 LE U

2 1 6t

95 OS

g-ooT

3dAI SS3aiS

5't^-E'2iL-0*EL82l'

8'OE-6*55-Z*06W-

r9E5l-

f O l -fr'8Z-2*806Z-

E'L-0'8E-S"S2Z-

f 8 l -Z'8fr-0*£Li5-

•doioj

s(US) ! [CUUO(j U0|

95 LE

- 11

62 E2 LI

95 LE

2L EL 55

52 LE

2 1 E l 92

9*301

6*12 S*2EL 0'L69ll

9*L E'O* 9*6622

L*2E 6*E^ t*8^frL

2*M 0*8E 6*0998

O'Ll t*2E 9* ELE

Z'ZZ Z'ZZ 2'S8E8

*SU8J_

SSP19 unu{.ajn[v

ssPLS uinu|.ufn[y

SSBL9

ss«L9 uinu).uini y

[BMB BW

(j83VdS P8P[8M)

.AI

(jsDeds P8P18M) ,111

(.jsseds P8P18M)

(j83eds f»Pl»*)

(j83VdS

(jd3«ds Ûds)

OMvuao^

smncow INVIV3S isd OSL ONisn soiyvN3DS yod S3ss3yis iS39yvi JO Ayvwwns

L 3navi

http://jeq.no

64

TABLE 1—Continued

STRESS nPE

Pos.

406.2 156.7

160.0 164.5

1.9

584.5 152.0

229.7 85.9

3.8

304.0 38.3

5.3

556.1 113.3 26.2

Shear Stress (S12)5

Loc.^

26 65

27 65 29

n 65

44 66 43

55 58 51

45 14 51

Neg.

-273.0 -149.2 -10.5

-206.9 -138.6

-369.8 -159.9

-17.4

-328.4 -30.7 -0.1

-324.0 -124.7

-705.9 -121.5

Loc.^

32 66 55

36 66

45 66 46

55 42 29

44 23

11 23

Maximum Principal Stress (SMAX)

Tens.

3411.0 637.9 29.0

3713.0 474.2

11.3

8779.0 694.8 54.5

2492.0 1092.7

32.7

2315.3 712.0

3.0

13469.0 917.7 42.7

Loc.°

26 2

12

36 66 25

54 2

12

36 66 56

36 2

29

36 1

56

CompJ

-1483.2 -44.6 -2.5

-17.0 -2.2 -0.4

-2251.9 ^ 4 . 3 -0.4

-379.6 -4.2 -0.5

-886.9 -36.2 -13.6

-2979.6 -51.3 -32.8

Loc.^

44 50 25

19 2

37

36 50 28

55 7

37

54 16 12

54 21 12

Minimum Principal Stress (SMIN)

Tens.

1972.9 12.3 4.6

958.3 11.9 4.6

2074.6 32.9 24.0

768.1 18.9 13.6

651.3 9.2 0.3

3441.5 32.1 0.7

locj

25 13 12

36 21 25

54 13 12

36 16 56

11 50 28

36 30 28

Comp.

-5750.4 -422.4

-25.1

-756.2 -358.9

-2 .3

-S839.9 -447.4

-25.1

-1629.4 -928.7

-3 .5

-3096.8 -664.3

-30.9

-12816.0 -900.6

-75.0

Loc.«

44 1

56

34 65 12

36 1

56

55 65 38

54

12

55 2

12

5See Figure 9 for orientation and positive directions of stresses

within element.

^See Figure 8.

65

M ; , .„

y

•9:^PLd SSCL6 j9:^no o: p9LLddP 9 jnss9Jd 5 U L ; D P pjPMino i s d 92 :^d9DX9 I I I 0Meu9Ds se 9iues—suoL^LpuoQ LûgujuojLAU3 AI OLjeugos^

'B%T9[6 sse[6 j9: ;no 9 q ; o: p9Lidde i s d 9e :ô 9 j n s s 9 j d puLM BuLtôe pjPMUi - j ôz ^B p9ULnuLBiu sL 9jn:^Bj9dui9:; JOLJSÛL 9LLMM JÔt^- 0% S9SBajD9p 9jntêJ9dllJ9:^ J0LJ9:;X3 -^^Lun 9u:^ O: J 0 U 9 : ^ X 9 9SB9JD9p 9 j n s S 9 j d DLj:^9UJ0Jeq LSd £ SULSneo I 9 A 9 I B 9 S UP9UJ

o:^ p9 :^ jodsuB j : t :^Lun -JÔZ SL 9jn:êj9dm9:^ uai M isw Âoqe -tî QOOQ : B p9[e9s pue p9LquJ9SSB c^Lun—suoL:^Lpuo3 L^Û9iuuoj LAU3 m O M e u g o g .

•9:^PLd SSBL6 j9:^no 0:; p9LLddB ^sd 93 ^0 9 j n s s 9 j d puiM 6UL:^DP pjPM:^no t;d9DX9 ' I OLJPU90S SP 9UJPS —SUOLttLpuOQ [ BCÛaUJUOj L AU3 H 0LjeU9DS3

'9:ê[d sse[6 j9:^no o: p9L[ddB j.sd 9e i o 9 j n s s 9 j d puLM 5UL: ;DP puPMui - J ^ Q Z ^^ p9ULe:ûLBm SL 9jn:^Bj9duj9:^ jOLjs^ÛL 9LLMM j ^ O L L 0^ S9SLJ 9jnt^PJ9diu9:^ J0LJ9^X3 "^Lun 9q:^ o:^ J0LJ9^X9 9SP9JD9P 9 jnSS9 jd DLJ^SUiOJeq LSd £ SULSnCD U 0 L : ^ B A 9 I 9 0009 o: p9:^jodsuej:^ :^Lun 'doOl SL 9jn:^Bj9duj9:^ u9qM ( i s ^ ) 1^'^B[ P 9 S 'UP9IU

: B p9Le9S pup p9[qiiJ9SSP :n.un—suoLt^LpuoQ [B:Û9UJUOJLAU3 I OLJPU9DS^

21 2

21 I

8E 59 frE

95 I 9E

21 59

62 I 9E

9*301

E * E ^ 9*2E6-0*25Etl-

1*61-t*9t9-6*Ef9E-

8*2-9*92Ll-l *W5-

5*2- • 1*59*^ 9*9W6-

f L-l'ZLZ-E*E28-

8*01-5 * * 2 ^ 2*MES-

•duio3

95 t

- 9E

62 59 9E

95 99 9E

21 2 *5

52 99 9E

21 2 LZ

9*301

^*8 2*6E6 0*925tt

Z'i I'lZL I'LiSZ

6*02 0*5821 2*Z892

l*2E E*02A E*S586

Z*9 8*L25 9*886E

8*01 i'9t9 t'62L2

•SU8J_

s(22S) ss8j^s

2L El 55

21 LE 55

8E E2 55

95 LE LL

21 6t St

52 OS n

5-DO-]

1

3 d A l S53UIS

8*96-9*6^-0*L5LVl-

2 * 8 t -2*19-2*9L82-

l*E-0*L2-2**E9L-

2 * ^ V'Ll' 5*2288-

8*2-L'LZ-t'OLi-

5*22-l*L5-8*2999-

•dUIOQ

95 LE 11

82 ZZ LI

95 LE

n 21 EL 55

52 LE

Zl zt 92

9*301

8'SL 6'2EL O'ZOOEL

2*2 rzt 6'95SZ

9'Lt 0*t8 1*5151

S'U Z*Et 1*0856

2*51 2*8E 6*82EE

t'VZ 1*52 9'ilH

•suej^

s ( l L S ) s s a j ^ S [euuorg UO 1.^08.41. p>;^

ssPLD

3up[e82 ssPLS

iunu(.iun[y

ûe[e8^ S"LS

uinu),uiniy

ÛP CS SSS19

uinuLun^y

sspts uinu iun y

ÛCIV8£ ssPLD

uinu ttin y

[BMS^BK

papiaM) .AI

(j83SdS P8P18M)

£ l l f

(jsoeds papIa")

(j838dS P8PI»M)

(jascds ; H d s )

(jaseds

0I.JVU33S

smnaow INVIV3S isd 0S2 aoj oiyvN3DS AS S3ss3yis iS39yvi 30 Ayvwwns

Z 318V1

r-Pv.- .. = — .

66

TABLE 2—Continued

STRESS nPE

Pos.

431.4 156.7

173.3 167.5

2.1

679.3 156.2

245.5 94.1 3.9

342.3 35.5

5.9

614.3 109.4 28.5

Shear Stress (S12)2

Loc.s

26 65

27 65 29

11 65

44 66 43

55 58 51

27 14 51

Neg.

-312.4 -149.2 -12.0

-223.0 -135.6

-390.8 -155.6 -18.9

-397.1 -33.1 -0.1

-334.4 -130.8

-329.7 -130.4

Loc.^

32 66 56

36 66

45 66 46

55 42 29

44 23

11 23

Majclmua Principal Stress (SMAX)

Tens.

9443.8 647.6 31.2

4005.5 555.6 15.4

9905.8 722.0 71.8

2707.3 1292.0

48.0

2603.6 733.6

4.2

14567.0 940.2 40.5

Loc.s

26 2

12

36 66 25

54 2

12

36 66 56

11 65 43

36 1

56

Comp.

-1668.1 -47.3

-4 .0

-21.7 -3 .7 -0.6

-2447.9 -40.5

^ . 3

-406.3 ^ . 4 -1.0

-1092.5 -40.1 -19.0

-3412.0 -54.5 -42.3

Loc '

44 50 25

19 50 37

36 50 28

55 7

37

54 16 12

54 16 12

Ml

Tens.

2217.3 18.8 4.0

1057.2 14.1 6.4

2398.9 39.6 31.9

828.7 24.3 20.5

765.9 8.4 0.5

3730.3 30.5 1.2

nlmun Stress

Loc.°

26 13 12

36 21 25

54 13 12

10 16 56

n 47 28

36 30 28

Principal (SMIN)

Comp,

-6696.4 -425.0

-28.9

-825.5 -435.9

-3.3

-9575.1 -466.0 -22.1

-1762.6 -1126.6

-6.3

-3660.7 -647.3 -43.2

-14367.0 -935.7 -97.2

Loc.'

44 1

25

34 65 12

36 1

56

55 65 38

54 1

12

54 2

12

^See Figure 9 for o r i e n t a t i o n and pos i t i ve d i rec t ions of stresses within element.

^See Figure 8.

67

largest stresses for the various component materials and Scenarios are

given in Tables 1 and 2. From these tables of ordered stresses,

Scenario IV with a welded spacer is chosen as the reasonably expected

extreme conditions for reasons which follow.

Parametric Studies

An examination of Tables 1 and 2 led to the selection of Scenario

IV with a sealant modulus of 150 psi as the datum condition for

subsequent parametric studies. This decision is based on the large

spacer stress results in this Scenario. Tensile sealant stresses are

also considered significant. Scenario IV with the 150 psi sealant

modulus has the largest tensile sealant stresses with the exception of

Scenario I (welded spacer). Neither Scenario sealant stress,

regardless of modulus, was near the assumed adhesion or cohesion

failure stress of 200 psi. Because of these low stresses Scenario IV

with the 150 psi sealant modulus was considered acceptable as a datum

condition for sealant stresses as well. The 150 psi sealant modulus

for Scenario IV was chosen because in this Scenario the maximum

tensile stresses for the sealant decreased for the 250 psi sealant

modulus while compressive sealant stresses increased. Due to the low

sealant modulus, compressive sealant failure is considered unlikely.

Once Scenario IV conditions for the local model were chosen as a

reference point or datum, the next step was to vary other parameters

to determine their effects on spacer and sealant stresses. Spacer

geometry is varied first. Basic geometric shapes of spacers are

examined using the input of Scenario IV. Shapes chosen are a circle.

68

triangle, and trapezoid. Two other shapes are considered: an invert

ed "T" shaped spacer and an idealized spacer shape meant to resemble

many spacers used in IG units at this time (Ref. Figs. 22-26). As

spacer geometry changed, the sealant is assumed to fill the space

outside of the spacer around the pertmeter of the IG unit. Sealant

geometry was changed also to ensure that the unit is sealed against

vapor penetration and for structural integrity. In many of the spacer

configurations a primary seal, as such, could not be defined. This

fact is not expected to affect results because the same polymer

properties are assumed for both primary and secondary seals in the

models. Aluminum spacer material of 0.022 in. thickness remained the

same throughout the parametric studies. Comparisons of the largest

spacer and sealant stresses for the parametric studies using Scenario

IV as are shown in Table 3.

Effects of sealant depth on spacer and sealant stresses are

examined using Scenario IV input and the square welded spacer.

Sealant depth is varied from 1/16 in. to 1/2 in. with the 1/8 in.

sealant depth of Scenario IV used as datum. Above the 1/8 in. sealant

depth, the depth of sealant is varied in 1/8 in. increments to 1/2 in.

the 1/2 in. square welded spacer dimensions are held constant (except

for spacer locations below the top of the IG unit) during variation of

sealant depth. Results of the depth of sealant tests using the local

model are compared in Table 4. These results are discussed in Chapter

VIII.

69

FIGURE 22. CIRCULAR SHAPED SPACER DISCRETIZATION

70

FIGURE 23. TRIANGULAR SHAPED SPACER DISCRETIZATION

71

FIGURE 24. TRAPEZOID SHAPED SPACER DISCRETIZATION

72

FIGURE 25. INVERTED "T" SHAPED SPACER DISCRETIZATION

73

FIGURE 26. "STANDARD" SPACER DISCRETIZATION

74

'92 9Jn6Lj 999g

•92 9 j n 6 L j 9995

•t72 9 j n 6 L j 999^

•£2 9 j n 6 L j 999£

' l l 9 j n 6 L j 999^

•9:^P[d SSCL6 j9q.n0 9i q. o: p9LLddB j.sd 93 ^0 9 j n s s 9 j d puLw SuL^ôe pjeM^^ng "JoOZ ^^ p9ULe:ÛLeuj SL 9jn:^Bj9duj9:^ J 0 L J 9 ^ U L 9LLqM j ^ j O t ' " 0^ S9se9«iD9p 9Jn:êJ9duj9:^ j 0 L J 9 : ; x 3 "t^Lun ^\\'\ O:; J0LJ9^X9 9Se9JD9p 9jnSS9jd DLJ^9m0JCq LSd £ SULSnPO L9A9L B9S o:; p9q.J0dsuBj:^ :H.un "JoOZ SL 9jn:^BJ9duj9^ U9L|M 19^^ 9AoqB "\^ 0009 : P p9[B9S pUC p9[qLU9SSB ^LUn SUOL^LpuOQ [P: U911JU0J LAU3 /\ I 0LJPU909^

z\ 2 E5

21 2 51

Et 2 LZ

2L 2 t5

9t 2 •5

21 2 t5

e'Do-i

8*9L-t*9^8-5*8Lt^

6*t2-t*EE8-E*5fr52-

0*E-

t*fr0L2-

0*11-f L t e -t*82L2-

9*221-2*f96-E*Z2ZE-

E*EE-Z*Z68-0*Z8Z2l-

•dui03 g

95 L OL

89 I 59

52 I 9E

52 I 01

02 Ll OL

95 L 9E

•00-]

E*8 9'L2Z 9*frL2

5*6 8*099 l*WZ2

Z*Z L*S0Z 9*E502

5*9 2'09Z Z*28LL

6*11 2*E9Z 6*E9Z2

8*0L 8'9L6 O'OEtEl

•suej^

^(22S) ssaj:^s l«uuo|g uo;.^38j).p-2

2L 9 1

ts 02 ZZ ZL

2L OS ZZ

2L El 55

21 EL LZ

21 El 55

e*=°1

•

3<iU S53211S

o*ot-9*851-5*ESS-

8'Z-t*82 l -1**822-

9*22-8*89-f L 0 2 2 -

2*9E-Z*8E-2*6E0E-

6*95-B*t9-Z*2L9E-

5*frZ-Z'ZL-0*EL82l-

•duio^

95 05 OL

89 tE t9

62 Z5 frE

62 Z5 Ll

95 LE l l

95 IZ l l

g-oo-i

2*61 E'Ztl 9*99E

Z*02 5*501 t*ELt2

2*El 2*801 8*ZEt2

8*11 Z'LL 0"ZL92

rLi 9*5t 0*9E5E

6*L2 5*2El 0*L69ll

•SU9_L

^(LLS) ssaj t j s [euuofj uoLq.oaj|.p-;,

ss?L9 uinuiuin[^

SSPL9

ssBLS uinu).iun[v

SSPL9 uinuLiun[y

SSBL5

SSP19 iunu).uin[y

lB|.ja:jBK

s ^ P J ^ D

s^t^^^S J. . .

^8i6u«Mi

gpiozad6jj[

2„pj«pire^S,.

(uin^vp) ajvnb^

i(^"dui AI oMVuao^)

adaqs 0). j^Mtoac)

S3ianis Diyi3wo39 yod S3SS3yis iS39yv"i JO Ayvwwns

e 3navi

http://j9q.n0

75

TABLE 3—-Continued

STRESS TYPE

Pos.

566.1 113.3 26.2

377.3 113.4 18.4

627.8 96.6 14.1

532.5 124.2 18.5

110.7 76.0 21.2

143.5 231.5

6.8

Shear Stress (S12)7

Loc.3

45 14 51

45 14 17

55 58 56

55 14 12

66 22 68

18 14 56

Neg.

-705.9 -121.5

-1313.3 -112.3

-527.3 -122.3

-1233.3 -100.6

-0.9

-101.6 -44.9

0.9

-169.4 -216.0

Loc.3

11 23

27 57

26 57

27 57 56

n 23 63

10 57

Maximum Principal Stress (SMAX)7

Tens.

13469.0 917.7 42.7

3536.8 763.6 30.7

2713.9 760.8 17.6

2903.0 705.3

17.8

2765.4 661.6 37.0

1 476.2 721.8 22.4

Loc.8

36 1

56

11 1

56

n 1

56

34 1

29

65 1

68

10 1

56

Comp.

-2979.6 -51.3 -32.3

-1113.4 -16.3 -18.6

-731.1 -28.3 -5.2

-1083.0 -37.7 -2.8

-648.0 -63.2 -15.9

-196.7 -35.3 -15.3

Loc.'

54 21 12

27 22 12

26 22 12

32 15 43

17 72 12

54 15 12

Mil

Tens.

3441.6 32.1 0.7

876.2 15.4 5.7

751.2 23.9 2.2

1178.2 59.5 1.5

701.3 10.2 0.9

104.9 55.3

5.0

nimum Stress

Loc.9

36 30 28

11 50 25

11 47 25

34 58 25

65 57 37

10 31 56

Principal (SMIN)'

Comp.

-12316.0 -900.5

-75.0

-4302.7 -966.3

-63.8

-3204.4 -943.3

-41.9

-2849.1 -901.4 -32.7

-2546.0 -834.6

-64.2

-598.1 -378.6 -41.4

locJ

55 2

i2

27 2

12

55 2

12

27 2

12

15 2

12

54 2

12

" See Figure 9 for orientation and positive directions of stresses within element.

^Stress locations: For "standard" see Figure 26. For trapezoid see Figure ^4. For triangle see Figure 23. For "T" shape see Figure 25. For circle see Figure 22.

76

ii.i

'S9LJBA l^^d9p :|.UeLB9S 9[Ll^M ^ UB^ SUOO SULeUJ9wl S U 0 L : ^ B D 0 [ ^ U 9 U J 9 [ 9 9AL^B[9y 'SUOLq-POOL :).U911J9[9 JOJ. g 9 J n 5 L j 0 ^ J 9 j . 9 y c

•:).U9lil9[9 ULLj ^LM

S9ss9ji^s ^0 suoLq.D9j.Lp 9AL:;Lsod puB uoL^c:û9LJo Jo^ 6 9-«n6Lj 999

•9:^BLd S S B L B -i9q.no gq^ o: p9L[ddB j.sd 93 j.o 9jnss9Jd puLM 6UL:^DB

pJBMq.no "JeOZ ^'5 p9ULB:ÛLBUJ SL 9jn:;BJ9dUJ9:^ J0LJ9:ÛL 9LLL|M j p O f r -oq. S9SB9J39P 9jn:^BJ9dm9q. j o L j 9 q . x 3 •tn.un 9LJ:^ O:; j0LJ9q.x9 9SB9JD9p

9 j n s s 9 j d DLjq.9UJ0JBq Lsd £ SuLsnBO [ 9 A 9 [ B9S oq. p9q. jodsuBj:^ '^\-^0

•JoOZ SJ- 9jn:^BJ9diu9:^ U9I^M "191 9AoqB •q.j. 0009 ^ ^ p9[B9s puB p9LqiiJ9ssB :^LUn SUOL^LpUOQ [ B:Û91UU0 J L AU3 y\I 0LJBU9D9 :^ndUL / \ I 0 I . J B U 9 D 9 0 ^ p9 : ^D9PqnS 9 J 9 M S[9p0UJ q ^ d 9 p q.UB[B9S [ [ B *Uin^Bp 9 q ^ Lj^LM s v ^

21 2

21 2

21 2

ts 2 1 2

2 1 2 ^5

£-00-1

6*8E-2*50Ll-0*91621-

L'LZ-O'LZOL-0*80lEl-

Z'SE-Z'BfrOl-0*Z9LEL-

Z'ZZ-Z*Z68-0*Z8Z2l-

9*EE-9*Efr0l-0*860El-

•dlUOQ

95 59 9E

95 I 9E

95 I 9E

95 I 9E

95 I 9E

£*301

9 * 5

retB 0*Zt6Ll

f 8 Z*66Z 0*lfrL2l

O'Ol l'28Z 0 '9Lm

8*01 8*916 O'OEITEL

Z'Zi 5*08Z 0*0t6El

•suaj^

z(22S) ss*J^S isuuo^ uo;.ôaj|.p-2

21 91 55

21 El 55

21 EL 55

21 El 55

21 12 55

j-oo-i

3 d U SSiUiS

8*98-0*89-0*fr9E2t-

2**8-2*t'9-0*6E92l-

Z*6Z-9*69-0*L90El-

f frZ-Z'ZL-0*E1821-

C*5Z-6*9Z-0*SL2El-

•duioo J

95 Z Ll

95 OE l l

95 OE LL

95 LE Ll

95 IE l l

•00-]

E*OL t*Sf 0*L*2Ll

t*9l E*8t O'OLtLl

0*02 2*GZ 0*21611

6*L2 S*2El 0*L69Ll

0*52 5*5L2 0*19021

•suaj^

ed lS) ssaj^s [BuuoN uoj.^Daj|.p-x

ûp[pas ssPLS

uinu(.uin[y

ÛBi»as ss^LS

unu(.iDni y

:>up[aes

umu ttin y

ûsi»as ss»L9

iunuûn[v

tûBlBas SSBL9

iunu).iun[^

l«Lja^«W

..2/L

..8/E

nt/ l

(nmâp) ..8/1

..9L/1

M daQ ûc[ea^

S3ianis Hid3a I N V I V 3 S yod S3SS3yis is39yvi dO Ayvwwns

t 318V1

http://suoLq.D9j.Lp

http://-i9q.no

http://pJBMq.no

TABLE 4—Continued

77

STRESS TYPE

Pos.

590.7 138.5 28.2

566.1 113.3 26.2

564.3 118,0 26.8

566.5 122.4 62.7

529.9 129.4 25.7

Shear Stress (SI 2)2

Loc.3

45 31 46

45 14 51

45 14 46

45 14 20

52 14 51

Neg.

-718.4 -109.2

-0.3

-705.9 -121.5

-743.2 -123.9

-754.2 -122.1

-762.7 -129.6

Loc.3

11 23 35

11 23

11 23

11 23

11 57

Maximum Stress

Tens.

13981.0 781.2 46.8

13469.0 917.76 42.7

13456.0 783.0 34.2

12171.0 800.7 38.9

11980.0 850.6 32.9

Loc.3

36 1

56

36 1

56

36 1

56

36 1 56

36 65 56

Principal (SMAX)2

Comp.

-3036.3 -73.3 -33.0

-2979.6 -51.3 -32.8

-3098.1 -54.2 -25.2

-3154.6 -60.7 -37,3

-3146.0 -67.8 -19.7

Loc.3

55 21 56

54 21 12

54 16 12

54 16 12

54 16 17

M1

Tens.

3596.6 35.4 1.2

3441.6 32.1 0.7

3379.9 37.3

3087.5 31.2

3047.8 27.8

nimura Principal Stress (SMIN)2

Loc.^

36 47 28

36 30 28

36 30

11 30

n 50

Comp.

-13216.0 -1046.6

-75.6

-12816.0 -908.6 -75.0

-13130.0 -1051.7

-80.3

-13124.0 -1074,4

-84.6

-12933.0 -1109.0

-t7.0

Loc.^

55 2 12

55 2 12

54 2 12

54 2 12

54 2 17

78

The local model is also effective in examining stresses in spacer

and sealant when the aspect ratio (ratio of height to width) of the

spacer is reduced in 1/8 in. increments and each position is examined

using the local model and the Scenario IV inputs. The final spacer

shape is a flat strip of aluminum 0.044' inches in height and 1/2 in.,

wide. A width of 1/2 in. is maintained while height is varied (Ref.

Figs. 27-31). Comparisons of spacer and sealant stresses under these

changes are given in Table 5. These results are also discussed in

Chapter VIII.

Corner Effects Model

A single corner effects model evaluation examined spacer sealant

stresses for modified Scenario IV conditions. Corner effects were ex

amined on a local cross-section sufficiently close to the vertical

edge of the unit that glass plate displacements and rotations could be

neglected. For Scenario IV, dimensional changes caused by thermal ef

fects are the primary distorting influences at the corner. In addi

tion to the elimination of plate rotations, modifications to the local

model include an added vertical restraint to the spacer. This

additional restraint simulates the restraining effects of the vertical

portion of the spacer on horizontal spacer cross-section motions.

Also considered is the difference in thermal expansion between the

outer glass plate, inner glass plate* and vertical portion of the

spacer due to the difference in coefficients of thermal expansion

between aluminum and glass. In Scenario IV the spacer contracts a

larger distance than the outer glass plate, causing a larger extension

79

38 37 28 29

FIGURE 27. ASPECT RATIO TEST SQUARE (DATUM) SPACER

80

36 35

FIGURE 28. ASPECT RATIO TEST 3/8 IN. BY 1/2 IN. SPACER

81


82

32 31


83

30 28

FIGURE 31. ASPECT RATIO TEST, THIN STRIP BY 1/2 IN. SPACER

84

'l£ ejn6Lj aes ,,2/L X d.Lj S -'OJ 'Oe 9Jn6LJ 99S „2/LX„8/L - Oj •62 ajnS.Lj eas „2/LX,.^/L JOJ

•82 ajn6Lj aas „2/Lx..8/e - oj V 2 9Jn6Lj aas .,2/Lx.,2/L -»0j

:SUOL:;BDO-|

•ûaiuaâ uLqq.LM sassaj:^s ô suoLtôauLp aALC^Lsod pue uoupûa.LJo JOj. 6 sjnS.Lj aa^ ^

•a: i?[d sse[6 jat^no aq^ o: paL[ddB j.sd 92 j.o a-inssajd puLM 6uLq.DP pjBMi no "JoOZ ^^ pauLeq-ULBiu SL ajnt^Bjaduja:^ j0Lja:ûL aL.LLjM j^ôfr-o: saseauoap ajn:^Bjadiua:^ JOLWIS^^B '^Lun aq^ o: jOLjat^xa aseajoap ajnssajd OLjiâujojeq Lsd £ BuLsnco [aAa^ eas ULBUJ O: paq.wiodsuBjq. ^LUp 'JoO^ SL ajnt^Bjaduja:^ uaqM ig^j aAoqe -q.^ 0009 "^^ pateas puc pa[qujassB ^LUf]—suotq-LpuoQ L^Û9"J"o-»!-AU3 /yj OLueuaos ri^nduL / \ i OLjeuaos o: paôapqns ajaM sâpouj OLC^BJ : oadse jaoeds [ [ B »ujn: Bp aq:; q LM sy ^

Zl 2 Z2

ZL 6E 2

91 2 ZZ

t l 2 62

21 2 ^5

.-OCT

6*9-l*6EB-0*1-

6*9-9*E0E-0*8^8-

9*61-l 'ZlfL-E*2EZl-

8*SE-9*EE6-5 * 5 0 2 ^

Z'ZZ" Z*Z68-0*Z8Z2l-

•diuo^ J

62 L L2

LZ I 61

I ZZ

LZ I

95 I 9E

•00-)

Z*5 6*969 E*l

Z't 5*00Z L*WE

5*21 Z*E5B 0*V69L

O'frL 5*5EZ t*ZE8E

8*01 8*916 C'OEKl

•suaj^

2(225) ssaj^s leuuofj uo(.ôdj|.p-2

Zl ZZ L2

Zl SE ZZ

91 6 ZZ

81 12

21 El 55

g-oo-i

3dJU. SS3dIS

E*9l-8*89-t*2l-

t*9l-8*05-S'LOL-

L'n-Z'iZL-

6'ZS-8*E0l-9*229E-

5*tZ-E*2Z-0*EL82l

62 91 LZ

52 6 OE

n LZ

ZZ 5t ZV

95 LE

- L l

2 * L L t*E9 8*5

2*EL 2*221 6*16

8*52 t*EZ E*666

1*62 t* l6 6*900t

6*L2 5*2El 0*L69Ll

z d L S ) ssaa:^s [auuofj uo(.ôaj),p-;^

ûBiaas SSPL9

iimu|.iun[

ûcisaj

û»lBas SSPL9

ÛBipas ss»LS

uinuj.iun[y

ûc[aa3 ssBLD

uinu|.uin[y

[KHa^sW

..2/L y

..2/IX..8/1

„Z/lû1f/i

,.2/l^„8/E

(uin^cp) . .2/l^.2/l

32 s ja39d£

S3ianis oiivy lOBdSv asDVds yod s3SS3yis isaoyvi do Ayvwwns

9 3"iavi

TABLE S—Continued

85

STRESS TYPE

Pos.

566.1 113.3 26.2

285.3 143.3 15.0

362.4 131.8 11.1

88.2 241.7

5.7

3.1 232.4

2.5

Shear Stress (S12)2

Loc.^

45 14 51

20 9

27

43 18 25

38 7

25

25 8

18

Neg.

-705.9 -121.5

-292.0 -133.9

-139.5 -133.1

-38.5 -80.8

-51.5 -0.3 -1.2

Loc.^

11 23

42 54

40 45

23 42

36 21 17

Maximum Principal Stress (SMAX)'2

Tens.

13469.0 917.7 42.7

4034.8 737.4 38.4

1695.2 845.8 29.9

306.3 701.1 16.1

5.0 697.5

11.2

Loc. Cotnp.

36 -2979.6 1 -51.3

56 -32.8

42 -900.7 1 -37.4

49 -2.4

32 -401.9 1 -31.3

44 -2.7

19 -97.1 1 -16.2

25 -6.6

22 — 1 -11.7

29 -6.7

Loc.

54 21 12

29 47 41

23 10 34

23 46 17

2 17

'11

Tens.

3441.6 32.1 0.7

950.3 19.1 5.0

359.3 51.8 7.6

88.0 19.9 3.2

24.4 5.7

nimum Stress

Loc.^

36 30 28

42 45 22

32 49 44

30 16 37

16 29

Principal ; (SMIN)2

Comp.

-12816.0 -900.6

-75 .0

-4209.2 -934.3

-63.3

-1734.6 -742.9 -46.5

-306.8 -848.9 -16.7

-12.4 -840.0 -16.4

Loc.

55 2

12

29 2

14

23 2 3

39 7

17

21 2

17

86

in the connecting sealant. The spacer and outer glass plate were not

assumed to be at the same temperature. A one dimensional, steady

state, heat flow analysis gave the average temperature of the outer

glass plate at -67.35**F, while the spacer was warmer at +15'*F. Even

with this temperature difference the aluminum spacer contracted a

larger amount than the outer glass plate. For example, in Scenario IV

the outer glass plate decreased in height 0.0296 in. from the resting

block to the top of the IG unit while the vertical portion of the

spacer decreased in height 0.0483 in. Unlike the outer glass plate,

the spacer is assumed to contract half the total distance from top and

bottom. A comparison was made between the corner effects model and

the center line Scenario IV to determine if the presence of the

vertical spacer caused stresses in the IG unit components to be

appreciably different from those obtained from the centerline local

model. Largest stresses for the IG unit components, in the corner

effects model, are compared to the local model Scenario IV, as shown

in Table 6. The information in this table is discussed in Chapter

VIII.

87

L.

'l_l ajn5Lj aas—SUOL:^BDOL ssaj^^g^

•:ûauja[a uiq LM sassawiq.s j.o suoL:).Daj ip aALq.Lsod puc uoLq.eq.uaLjo joj . 5 ajnS.Lj aag-

•^[uo paL^ddB /\i OLJBuaos luojj. saBueqo aunq-Bjaduiaj ^

•a^PLd sse[6 jat^no aq^ o: paLLddp j.sd g2 J.0 ajnssajd puLM 5UL^DP pwiBMq.nQ "JoOZ '^^ pauLPq.uLBiii SL ajn^^Bjadmaq. j0Ljaq.UL a[LqM jpO^" ^^ sascauoap ajnq.Bjadiuaq. joLjaq.x3 •q.Lun aq^ o: joLjaq.xa ascauoap ajnssa-id DLj:).aujojpq Lsd £ 6uLsnB0 [aAa^ cas ULBUI o:; pa:;jodsupj^ %\.u[\ '^ÔL !- 9-»n:^Bjadiijaq. uaqM -]$ j aAoqp ' ^ j . 0009 ^B pa[Bas puB paLqiuassB t^Lup—suoLc^tpuoQ LBûaujuojLAU3 ^j OLjeuaDg,

21 59 t5

21 2 t5

t,'=*°1

t 'E l -E*25Z-l*LE29-

Z'ZZ-L'LSd-O'LBLZi-

•dlUOQ

95 99 OL

95 I 9E

^•00-]

rti 2*209 0*0068

8*01 8*916 O'OEfrEl

•SUB^

£(22S) ssaj^s [BUUOf uo.L^DaJ^p-2

21 EL 55

21 El 55

^•Do-i

3dAi ssaais

f O E -5'OOt-9"9L5^

5*tZ-E'2Z-0*EL82l-

•diuoo ^

95 LE l l

9 5 LE Ll

•DOI

t*62 6*921 0*5E95L

6*12 5*2El 0'L69ll

•sua_L

E ( I L S ) ssaj^s [Buuoi uo;.^3aj|.p-;^

SSPL9 uinu;.iun[y

tvuBiaas SSBL9

uinu|.uin[y

l»l.je^BK

ziapoK s^3©ii3 jaiuo^

lAI o^jBuao^

lapoK

i3aow S1D33J3 y3Naoo yoj S3SS3yis iS39yvi 30 Ayvwwns

9 3"igvi

88

TABLE 6—Continued

STRESS TYPE

Pos.

566.1 113.3 26.2

1147.4 477.9

7.4

Shear Stress (S12)3

Loc."*

45 14 51

27 31 25

Neg.

-705.9 -121.5

-857.6 -142.3 -14.3

Loc.**

11 23

11 23 43

Maximum Stress

Tens.

13469.0 917.2 42.7

15714.0 604.3 37.8

Loc."

36 1

56

11 66 56

Principal (SMAX)3

Comp.

-2979.6 -51.3 -32.8

-1334.4 -47.4 -12.0

Loc.**

54 21 12

54 21 12

M1

Tens.

3441.6 32.3 0.7

6300.2 15.3 5.9

nimum Principal Stress (SMIN)3

Loc."*

36 30 28

11 30 56

Comp.

-]2816.0 -900.6 -75.0

-6318.7 -752.5 -31.4

Loc.-

55 2 12

54 65 12

CHAPTER VIII

DISCUSSION OF BEHAVIOR PREDICTED BY MODELS

Parametric Evaluations

Data generated using the local model are analyzed to determine if

any of the sealant-spacer combinations has an adverse effect on the

magnitude of stresses at the boundary of the unit. Data are examined

to evaluate the effects of having the spacer split or welded, and to

establish extreme conditions. Data generated from geometric studies

are examined to establish effects of changing the shape of the spacer

cross-section. Sealant depth and spacer height changes are also

evaluated. Finally, results of an evaluation using the corner model

run are compared to a Scenario IV centerline local model to determine

if the stiffening effect of the vertical portion of the spacer at the

corner significantly increases the IG unit component stresses at a

corner. Scenario IV is the local model input used on all parametric

studies except the corner model.

Split and Welded Spacers

Selection of datum input conditions to the local model is

accomplished using the Scenarios of Chapter VII. Two spacer types are

used in this analysis to determine the reasonably expected extreme

conditions. These spacers are referred to as split and welded.

Additionally the welded spacers are referred to as solid in the tables

of ordered stresses in Appendix 3. Both are cold formed and have

89

90

essentially the same geometry. The preferred type of spacer is

difficult to determine from the data generated from the several

Scenarios. Examination of the data in Tables 1 and 2 shows that, for

Scenario I, solid spacer stresses are generally larger than stresses

in the split spacer. Scenario II data "indicate stresses in the split

and solid spacers that make it difficult to state that stresses in one

of the spacers are generally larger or smaller. If sealant stresses

are considered, they are larger for the solid spacer in both Scenario

I and Scenario II. Based on this observation the split spacer would

seem to carry a small advantage.

Scenarios III and IV address conditions which involve the solid

spacer only. Conditions in Scenarios III and IV cause deflections of

the glass plates toward each other, producing compression of the

spacer in the central region of each side of the IG unit. Subsequent

element crossing at the seam in the finite element solution of the

local model in Scenarios III and IV do not give results that are

considered reliable. Hence, split spacer evaluations using Scenarios

III and IV were eliminated from the evaluation.

Geometric Studies

Stress changes in the local model are examined for varying

geometric spacer cross-sections. Cross-sections used are described in

Chapter VII (Ref. Figs. 22-26 and Table 3). The datum cross-section

is the square spacer and Scenario IV input (reasonably expected

extreme condition) is used on all geometric studies. In general, all

spacer cross-sections produced relatively large stress reductions in

91

the spacer material relative to the square spacer. With the exception

of the S22 (Ref. Table 3) sealant stress in the detail with the

standard spacer, all sealant stresses are reduced slightly. The

square spacer is the least efficient cross-section in terms of spacer

and sealant stresses (Ref. Table 7).

Effect of Sealant Depth

Results of evaluations with different sealant depths are given in

Table 4. Starting with a datum depth of 1/8 in. the maximum tensile

stresses in the sealant and spacer materials decrease slightly with

increasing sealant depth. The largest compressive stresses in the

spacer material tend to remain constant while increasing in the

sealant material. This trend continues until sealant stresses

decrease at a sealant depth of 1/2 in. The largest tensile and

compressive glass stresses increase with increasing sealant depth,

indicating that more of the secondary stresses on the boundary of the

seal detail are carried by the glass as sealant depth increases. As

can be seen from the plots of maximum material stress (Ref. Fig. 32),

stresses in the materials remain constant with increased sealant depth

for practical purposes. Depth of sealant has little effect on

secondary material stresses at the boundary of an IG unit.

Effect of Spacer Aspect Ratio

Examination of the effect of spacer aspect ratio was accomplished

by keeping the width of the square spacer constant while decreasing

the height in 1/8 in. increments. Four runs were made with the

local model using Scenario IV input conditions. Largest tensile and

TABLE 7

CHANGE IN MAXIMUM PRINCIPAL STRESS DUE TO SPACER GEOMETRY CHANGE

92

Geometric Shape

Square (datum)

"Standard"

Trapezoid

Triangle

"T" Shaped

Circle

Material

Aluminum Glass Sealant






Datum Maximum Principal Stress

Tens.

13447.0 777.8 42.7

13447.0 777.8 42.7

13447.0 777.3 42.7

13447.0 777.8 42.7

13447.0 777.8 42.7

13447.0 777.8 42.7

Loc.

36 1

56

36 1

56

36 1

56

36 1 56

36 1

56

36 1

56

STRESS TYPE

Maximum Principal Stress w/Geometric

Change

Tans.

13447.0 771.8 42.7

3536.8 763.6 30.7

2713.9 760.8 17.5

2903.0 705.3 17.8

2765.4 661.6 37.0

476.2 721.3 22.4

Loc.

36 1

56

11 1 56

11 1

56

34 1

29

65 1

68

10 1

56

Percent Decrease

—

73.3 1.3

28.1

79.3 2.2 58.3

78.4 9.3 58.3

79.4 14,9 13.3

95.5 7.2

47.5

93

uoTsuaji uoTssejduioo

CO CO

CO CO <D

CO

CO CO 0 w ^« CO • *

c CO • • M

CO o CO

^ ^ i «

a ® TD ^^ c CO CO <D

CO

ii -o

o o CO

a CO

ISd/ssajq-g

(speapuriH) ISd/ss3j:;s

/. • • .

>:• C-: I.-.

in ID

^spuBsnoiii) i s d / s s 3 j : ; s

t3

a. LU a

to h- LU Z 00 < 00 -J LU <: a: LU I— oo oo

o o LU a. LL. S LL. O LU <_>

CVJ OO

94

compressive stresses from Table 4 are plotted in Figure 33. The

largest tensile and compressive stresses decrease in all three

materials as spacer height decreases from the square configuration.

Spacer and sealant stresses decrease rapidly as the spacer becomes

thinner while glass stresses remain essentially constant. Since part

of the spacer function is to hold desiccant, there is a limit to the

amount of reduction in spacer height that can be accepted. Generally,

as spacer height decreases secondary stresses in the spacer and

sealant materials, at the IG unit boundary, decrease.

Corner Effects Model

Results of analyses employing the corner effects model are

compared with results from using Scenario IV with the local model as

shown in Table 6. Except for an increase in spacer stress, the

effects of vertical spacer restraint are not as severe as may be

expected. The probable reason for this is the small force required to

elongate the spacer. This small force is due to the small cross-

sectional area (0.044 sq. in.) and comparatively long length (67 in,).

Elongation of the spacer occurs more readily than may be expected.

The corner effects model may be used further to examine how stresses

are affected by changes in spacer material and material thickness.

Examination of effects of changing sealant modulus upon IG unit

component stresses is accomplished by performing a local model

analysis using an upper and a lower bound for the sealant modulus.

These modulus values are found in Chapter VI. Moduli selected are 250

psi for the upper bound and 150 psi for the lower. These two values

95

uoTsuaj, uoTssajdmoo

CO CO

k. ^« CO CO CO

CO CO o ^

CO CO 0 k.

CO

CO CO CO ^^

^ M

J ? w

O CO a

CO

/

dTj:^S

ISd/ssajq-s

dTJ:^S

("spsjpunHT ISd/sse j :^s

dTj^S

o o

cn

Q. OO <a: 00

LU cn </i LU oo O LU <: Q: Q. ^— oo oo

o z

o o LU a .

Lu O LU O

ro CO

(spuesnoqi) ISd/ssej:^s

96

for sealant modulus were used with each of the six Scenarios in

Chapter VII. Results are presented in Tables 1 and 2. The effect on

IG unit stresses is that component stresses increased slightly

(approximately 10%) when the 250 psi sealant modulus was included in

the local model. Since sealant modulus'is dependent on strain rate,

these results indicate that IG unit component stresses may be higher

for short duration loads on the IG unit (e.g., a wind gust). Effects

of sealant modulus on maximum principal stresses for the IG unit

component materials, for the six Scenarios, are shown in Figure 34.

Potential Additional Model Applications

Motions of the boundary portion of an IG unit, as represented by

the local model, are controlled by motions of the two glass plates

which are the most massive amount of material in an IG unit.

Secondary stresses at the boundary are the controlling stresses for

the spacer and sealant materials in the IG unit. Based on these facts

the local model can be used to define an optimum spacer cross-section

that would minimize spacer and sealant stresses at the boundary. In

this same context an optimum (minimum) amount of spacer and sealant

material can be determined. As an example, by considering the outcome

of the geometric and spacer aspect ratio studies, a good starting

point for optimization might be a circular (elliptic) spacer cross-

section with a minimum practical height. Considerations of desiccant

amount and required sealant bonding area will determine practical

spacer diameters for given IG unit sizes. Use of output from the

97

Scenario

I - Split

II - Split

M l - Solid u ^ II - Solid

III - Solid

IV - Solid

Stress - PSI (Thousands) 4 6 8 10 '12 14

i I

I - Split

II - Split

S I - Solid

O II - Solid

III - Solid

IV - Solid

_Stress - PSI 30

I - Split

II - Split

5 I - Solid

< II - Solid cn

III - Solid

IV - Solid

FIGURE 34.

Sealant Modulus

150 PSI

250 PSI

EFFECT ON MAXIMUM PRINCIPAL 16 UNIT COMPONENT STRESSES DUE TO CHANGE IN SEALANT MODULUS

98

local model will reveal changes in secondary stresses as the spacer

cross-section is modified.

Local models also can be used to estimate the effect on secondary

stresses at the boundary due to changes in unit response caused by

installation method. Effects of mechanically restrained IG unit

systems may be included in the local model as spring forces at the

location of the gasket (Ref. Fig. 35). An assumed clamping force of

ten pounds per lineal inch (or other values obtained from a global

model of the same system) can be placed at the appropriate node as a

concentrated load and the gasket response can be modeled as a spring

at the same node. Effects of details using dry neoprene gaskets may

be represented by including the gasket in the finite element

discretization (Ref. Fig. 36).

Recent developments in glazing systems attach the IG units to the

building structure by a polymer (usually silicone). Secondary

boundary stresses of this type of installation also could be

determined by application of local model techniques (Ref. Fig. 37).

Conclusions

These newly developed local models do not have a base of prior

methods of analysis for use in making comparisons. However, local

model responses are compatible with intuitive expectations.

Generally, stresses are largest in the sealant and spacer materials

when caused by racking motions resulting from thermal expansion.

These stresses arise primarily from the attempt of the spacer to

rotate in order to compensate for the height differences between the

99

(0 o ^^ CO

^^•i 3 E • • I H

(0 ^ c CO

on

st

u

• ® 0) c o

resp

^^ O) ® c ^

^ CO

a CO CO a

n

O ^

«

n

m:^î^!m^^;^^m^^msm:

^ M ^

-WH^

n A ^

CO to

«

5S^}SSS^SSSSSSSSSSSS^:SSSSSS?SSS3^ /

/ - 0 ^ Jo to •»

«

9 IO

4 CM

e

rvW4

r -CO-Ui

->w-^

^^SSJSSSSSSi^SiSSSS^SSSSS^^

Si^SSiSSSSSiSSJiS^S^^

oo

o

o LU

<: cn h-oo LU

cn >-

O

O

o

oo o CL

o a.

in CO

cn

100

DISCRETIZED GASKET^

MOUNTING FRAME

FIGURE 36. PROPOSED LOCAL MODEL FOR GASKET RESTRAINED IG UNITS

101

Seals included in discretization, mounting system assumed rigid.

MOUNTING SYSTEM

ATTACHMENT SEAL

FIGURE 3 7 . PROPOSED LOCAL MODEL FOR POLYMER MOUNTED IG UNITS

102

glass plates. Wind induced pressures can increase or decrease these

stresses, depending on the direction of rotation of the boundary

caused by the wind. Visual interpretations of the above effects can

be seen in the computer generated un-deformed and deformed cross-

sections of Figures 38-43. These cross-sections are provided by the

local model results.

Geometric studies indicate that spacer cross-section affects the

intensity of secondary stresses in the glass, sealant, and spacer. A

square spacer cross-section may be desirable from a fabrication

standpoint, but it is the most highly stressed component of all the

cross-sections examined. Sealant and spacer material stresses are

reduced in the "standard," "T," trapezoidal and triangular spacer

crossOsection due to increased amounts of sealant. Thin strips of

sealant between the vertical sides of the square spacer and the glass

plates do not provide sufficient volumes of material to permit large

displacements of the glass plates without causing large unit

displacements of the sealant sealant material, thus placing greater

forces on the spacer. The above mentioned spacer shapes have larger

amounts of low modulus sealant material surrounding them. More

sealant material makes smaller unit displacements for the same overall

displacements caused by the glass plates; hence, spacer and sealant

stresses are smaller. Additionally, the circular cross-section spacer

reduces stresses by rotating in response to the thermal expansion

induced racking motions (Ref. Fig. 44).

103

SCENARIO I Environmental ConditiorxS. IG unit is assembled and sealed at mean sea level(MSL) when temperature is 70**F. Unit is transported to 6000 ft above MSL causing a barometric pressure decrease of 3 psi exterior to the unit. Exterior temperature rises to 110 °F while interior temperature OS le st a TO^T by air conditioning. A 35 psf inward acting pressure is applied to the outer glass plate.

FTRllRF 38 UN-DEFORMED AND DEFORMED LOCAL MODEL FIGURE 38. UN ^ ^ ^ jQ pQ SCEMARIO I SPLIT SPACER

104

SCENARIO II Environmental Conditions. IG unit is assembled and sealed at mean sea level (MSL) when temperature is 70°F. Unit is transported to 6000 ft above MSL causing a barometric pressure decrease of 3psi exterior to the unit. Exterior temperature rises to 110**? while interior temperat: is kept at 70*F by air conditioning. A 25 psf outward acting pressure is applied to the outer glass plate.

FIGURE 39. UN-DEFORMED AND DEFORMED LOCAL MODEL CROSS-SECTION FOR SCENARIO II SPLIT SPACER

105

SCENARIO I Environmental Conditions. IG unit is assembled and sealed at mean sea level(MSL) when temperature is 70**F. Unit is transported to 6000 ft above MSL causing a barometric pressure decrease of 3 psi exterior to the unit. Exterior temperature rises to 110 "F while interior temperature OS le^st a 70*'F by air conditioning. A 35 psf inward acting pressure is applied to the outer glass plate.

1 • 1 — \ — 1 . I--

1

1

i 1

FIGURE 40. UN-DEFORMED AND DEFORMED LOCAL MODEL CROSS-SECTION FOR SCENARIO III SPLIT SPACER

106

SCENARIO II Environmental Conditions. IG is assembled and when temperature to 6000 ft above decrease of 3psi

unit (MSL) sea level

is transported sealed at mean is 70''F. Unit MSL causing a barometric pressure exterior to the unit. Exterior

temperature rises to 110*F while interior temperature is kept at 70*'F by air conditioning. A 25 psf outward acting pressure is applied to the outer glass plate.

CrrjH

"^^^

FIGURE 41 UN-DEFORMED AND DEFORMED LOCAL MODEL CROSS-SECTION FOR SCENARIO II WELDED SPACER

107 SCENARIO III Environmental Conditions IG Unit is assembled and sealed at 6 000 ft above MSL when temperature is 70*F. Unit is transported to sea

causing a 3psi barometric pressure increase to the unit. Exterior temperature drops

level exterior to -40°F while interior temperature is kept at 70''F by air conditioning. A 35 psf inward acting pressure is applied tc the outer"glass plate.

j

1

1

1

FIGURE 42. UN-DEFORMED AND DEFORMED LOCAL MODEL CROSS-SECTION FOR SCENARIO III

108

SCENARIO IV Environmental Conditions. IG unit is assembled and sealed at 6000 ft above MSL when temperature is 70° F. Unit is transported to sea level causing a 3 psi barometric pressure increase exterior to the unit. Exterior temperature drops to -40** F while interior temperature is kept at 70° F by air conditioning. A 25 psf outward acting pressure is applied to the outer glass plate.

L=

•

k >•

r

»

FIGURE 43. UNDEFORMED AND DEFORMED LOCAL MODEL CROSS-SECTION FOR SCENARIO IV

109

FIGURE 44. UN-DEFORMED AND DEFORMED LOCAL MODEL FOR CIRCULAR SPACER WITH SCENARIO IV ENVIRONMENTAL CONDITIONS

no

Reducing the spacer height while holding spacer width constant

also has the effect of reducing stresses in sealant and spacer

materials. Most spacer stresses are due to geometric distortion of

rectangular cross-sections. As the length of spacer adjacent to the

glass decreases, the force transmitted by the thin strip of sealant

also decreases, and spacer distortion decreases.

Sealant depth, according to the models, does not have significant

effects on spacer and sealant stresses. Tensile glass stresses

increase slightly at a sealant depth of 1/2 inch.

Corner model evaluations indicate that stress results are lower

than may have been expected. Spacer length and small cross-sectional

area allowed greater flexibility of restraint at the corner.

Recommendations for Future Efforts

Development of the local model is directed toward achieving

better understanding of the secondary forces at the boundary of an IG

unit. Since this is a new area of investigation, the accuracy of the

models needs to be confirmed by a program of testing.

Prior to the testing program, the spacer model of Chapter V needs

to be solved. Methods of solution and a proposed equation are also

presented in Chapter V. Once the spacer response model is developed,

it can be tested in the same program mentioned above.

Sealant response, as presented in this document, does not take

into account changes in sealant response due to temperature. These

changes can be included using the procedure presented by Smith (Smith,

1952). A fracture criterion that can predict adhesive or cohesive

Ill

failure in the sealants needs to be incorporated in the model. Using

the local model to examine glazing systems such as the clamped,

gasket, and polymer mounted systems to develop safe and efficient

glass curtain walls is strongly suggested. This model can handle

effectively the stresses involved in these systems that have been

elusive in past efforts.

When a testing program has proven the global and local models to

be accurate indicators of the structural mechanics response of IG

units, they can be used in forming a reliable design method for IG

units and their attachment systems.

LIST OF REFERENCES

Al -Tayy ib , A H . , 1980: " G e o m e t r i c a l l y N o n l i n e a r A n a l y s i s of Rectangular Glass Plates by the Finite Element Method," Inst i tute for Acr^#PB81-8439f ' "" ^ ^ "" Universi ty, Lubbock, Texas. May (NTIS

Andrews, R D . , 1952: "Correlation of'Dynamic and Static Measurements on Rubberlike Mater ials," Industrial and Engineering Chemistry. Vol . 44, No. 4. pp. 707-715. ^

A r c h i t e c t u r a l Aluminum Manufacturers Associat ion, MIR-1973-1981: Industry S ta t is t ica l Review and Forecast.

Behr, R.A., Minor, J .E . , Linden, M.P. and Vallabhan, C.V.G. , 1985: Laminated Glass Units Under Uniform Lateral Pressure," ASCE Journal

of Structural Engineering. Vol. I l l , No. 5, Paper No. 197261

Birdsal l , G.W., Ed., 1965: The Aluminum Data Book. Reynolds Metals Co., Richmond, Virg in ia .

Chou, G.D. and Vallabhan, C.V.G., 1985: "The Behavior of Insulating Glass Units Under Latera l Pressure," Glass Research and T e s t i n g L a b o r a t o r y , Texas Tech U n i v e r s i t y , Lubbock, Texas ( repor t in preparation).

Ferry, J .D . , 1980: Viscoelastic Properties of Polymers. 3rd Ed., John Wiley and Sons, Inc . , New York.

Ketter, R.L. and Prawel, S.P., 1969: Modern Methods of Engineering Computation, McGraw-Hill Book Company, New York.

Linden, M.P. , Minor, J . E . , Behr, R.A. and Vallabhan, C.V.G., 1984: "Evaluation of Lateral ly Loaded Laminated Glass Units by Theory and E x p e r i m e n t , " Glass Research and Test ing Laboratory, Texas Tech University, Lubbock, Texas (NTIS Ace. #PB84-216423).

Moore, D.M., 1980: "Proposed Method for Determin ing the Glass Thickness of Rectangular Glass Solar Panels Subjected to Uniform Normal Pressure Loads," JPL P u b l i c a t i o n 8 0 - 3 4 , Je t P r o p u l s i o n Laboratory, Pasadena, Cal i fornia, October.

N ie lsen , L .E . , 1962: Mechanical Propert ies of Polymers, 1st Ed., McGraw-Hill, New York, New York.

Shand, E.B. and McLellan, G.W., 1984: Glass Engineering Handbook, 3rd Ed., McGraw-Hill, New York, New York.

112

113

Smith, T .L . , 1956: "Viscoelastic Behavior of Polysiobutylene Under Constant Rates of E longat ion ," Journal of Polymer Science. Vol. 20, No. 94.

Solvason, K.R., 1974: "Pressures and Stresses in Sealed Double G l a z i n g U n i t s , " T e c h n i c a l Paper No. 423, Div is ion of Bui lding Research, National Research Council of Canada, Ottawa, August.

Timoshenko, S. and Woinowsky-Krieger, $ . , 1959: Theory of Plates and Shells, McGraw-Hill Book Co., New York, New York.

Tobolsky, A.V. , 1960: Properties and Structure of Polymers. 1st Ed.. John Wiley and Sons, Inc . , New York, New York.

Treloar, L.R.G., 1958: The Physics of Rubber E l a s t i c i t y . 2nd Ed. , Clarendon Press, Oxford.

U.S. Bureau of the Census, 1982: Stat is t ica l Abstract of the United States (1982-83, 103rd Ed.) Washington, D.C.

Val labhan, C.V.G. and Ku, F-Y, 1983: " N o n l i n e a r A n a l y s i s of Rectangular Glass Plates by Galerkin Method," Inst i tute for Disaster Research, Texas Tech University Lubbock, Texas.

Vallabhan, C.V.G. and Minor, J . E . , 1984: "Experimental ly V e r i f i e d Theore t ica l Analysis of Thin Glass Plates," Preprints, Conference on Computational Methods and Experimental Methods (June 27-July 2, 1984, on board the Queen E l i z a b e t h I I ) , I n t e r n a t i o n a l Soc ie ty for Computational Methods in Engineering, Southampton, England.

Vallabhan, C.V.G. and Wang, B. Y - T . . 1981: "Nonlinear Analysis of Rectangular Glass Plates by Finite Difference Method," Inst i tute for Disaster Research, Texas Tech University, Lubbock, Texas, June (NTIS Ace. #PB82-172552).

Wi l l i ams, M . I . , Landel, R.F. and Ferry , J . D . , 1955: "Temperature Dependence of Relaxation Mechanisms in Amorphous Polymers and Other Glass Forming Liquids," Journal of the American Chemical Society, Vol. 77, No. 14.

APPENDIX A

LISTING OF SEALANT STRESS-STRAIN PROGRAM

114

115

<r

ID O Ci

2 :

2: <I

: ^ ^ —i —^

:— ~- — 3 — ^ 2:' 3 :i « X

<r w x: -

•c ^ i : i : 2 : L_ Li

- — ^ •_•• ^ < : ; -^ ^ ^ ^ ^ - « * < • . * % • : . ^

2: 3

^ 1:1 Zi i^ "21 J- 'j^Z.'!^ IZCiL; ' IZ iii 21 - J ' . - < - - • . - ^ -^ -^ -y • - , — < , ^ - ' T ' • -

^ r j x ^ i n o rsaDr> --> .~v - ^ . - - ^ -^S.

r j ^ j r\i r--j ^\ r-i ^ j "^ ••« ^ " - :. M r - 4 r •<! ;:••< i: •< ^ >• "^ .;~ 'C .-• — r . - " ' - ^ . •

t >^"^ - « ^

116

Ci <:

<z ij. :D

r ^ ,::. X

Q: <r 2: 2:

2: >- LLi <: 2:

s

_ C

2: ~ c

C 3 2 _= >- c

-2:pz:p:::Lij2:2:2:z:3Lj_j2:3^ 2:pzp2ip2:z::i:2:2: 2:2:2:— = •~^ -- T ^ '- "2' < T :'.-' :"< :'r ;'r "T^ ^"7" '• • 'r^ "^ f^. •"< ^»" "- T*' •"--• "^ '** " ^ .'- -'- ."- -"< '< ;*< ' ^ ^

O |\ r3 > O —; <?- -JT T <7 U ii

- ^ '-s /«^

; n '-« •••

l i ^ " ^ 1 ' ^ -^ "J -r <r ^ >< -: cs t; ^ \ >v N ::::

117

-

3 <C ^

<r — n <r Lii

2 : H-.

•z. .— cn UJ : - r-t 

^, ^ 1 * ^ 1

— s

«« — I

•

- 5 :

» •

• ^ ^

— '•—'

'•^ s '<

a.

^ ?<-:

f O l

i J j

;— c

««

: ^ i

X,-^ < >>

i \ »<-: '—' <r

». 2 • •

»rt » o

—'

;21 • ^ " *

>—

•- — • •

N^ • « ^

• — '

^•: •'O "^ f^ fT\ <' ^ - . n^ ' S M ^ • ^ •

K^ ^_^ ^ ~ ' ^ ' < - N ^•^ ^ "Tr 'Vw - ^ v _ _ ^

Ti '•<-: ^ 2^ •^

'> 0 'y- ^ y- '>

118

<z -— H

! - X

o x 2 X

— s r-i X i - i "^ ^^ '^"^ fT\ ^^ fn ^m* -^^ ^ -^^ '"^ •^*

n X

3 2 .*0

2

>C 2 3

X ^ X

rs. s

;—

1 - *

• — •

:r:

^

.> X

2

—*• •^ "^ —y -^ fr\ •^ - f •^ -rr ' ^ K ^ II « ^ B ^ S B ^ ^ V H ^ ^ ^ 'TaB * <

X - i _^

• 7 ' :". ^ ^

^ 2 : : :

2; r ;^ 3; — 2J ,-\

3 ^ - 2 3 : ^ 2 2 — — - _ X - Q . 2 - ^ Q : ^ X - 7 - • : • " - ' 2 : ^ - ' : ' - ' —^ . ' - ' : • —•

0 0 0 0 0 0 *o <?" jj"; -"O ! \ O:D >- o - r-4 !- T L": >c " c: :N

*»< > 0 "^^ *<^ *< : ***• V ^ »•*-. < N < S <

•<r <r

119

•- o

<: <L

X

^ ci ^ in LL. •• CD r-i

2 0 i -• • r^ 3 • • 3

2 2 ^ ^ : ,: -" "^

2 -=i 2 «

«?• — T <r

<Z >-' T- •?- * ii ^ !i <Z ^ Ci —' li _J i - ! W ^ ^ ifi i— i— X X ?— 3 ^ ! — *-i ii ii ii :-^ ii —( ^ T i ii

i j J 2 i Z i 3 L L ! 3 > - ^ — _ J _ J ^ i — . . B . - ^ - - - , 2 : 3 i 7 ^ 2 2 : 2 u _ ! : i : ; l . X - j : i - ^ X i J I i ^ X T - . : : ^ : - . ^ — Ii i jJ ^ Ci r—i r-i i—! 2 0^ 3 2 ijJ 3 ""^ UJ Li_ !.:_ 3 - ^ L_J 3 ^^ '"-' • ~' f"* i : C : _ ^ - i i = i L _ - . U . L ^ - r 2 u . C J ^ Z r^-—- ! ^ C r - 2 3 ^ X X > - - ^

0 0 0 0 0 0 0 Ll 0 0 0 r i ^ > 0 O O O O O O O O O O O

o ^ r-j r« "c- iji sG »c i \ 3 cs cs C"- cs o -- r-i r; T iii v: -s 3 ^- o

120

• X

2 i i i—i — •/'

•rt X T rH -rt -2;

; ; ^ Ii X ^ X ^ ^ ^ X X C ^ ^

3 iZ 3 2 3 2 uI iH <i: 2 2 iX uI y ^ *-v .^x ^^ " ^ ^ - ^ -^^ ^ x "X f ^ . /^ -<—s •S_-' ^^ - • • . • ^ ^ '-—' -"-X s . ' - ^ .^ ' ^ i ' K^ ' * • •«•/• ' - . ^

•^ ^ i"N "^ rv x r- TN fs. ^ r . -N, 3

'T~ *• *— "^ ^ ^ 2 -^ -^ ^ ' ^

\ ^- -" r-^ ^ X X i^ r-! |j^

3 3 2 2 ir 3 iZ L i •-• ^ X > :

r,'i .-'; -v^ c- o —• "y

^ r i 3 »• — X X Ui ^ -3 CS -O O O -

X

2 C 2 C 2 C

<r Ii u l ii i: <-» -i - ^

2 _^

— X

X >: iz

T-* T-- — X ii ^

v - w v x i : : ^ ! ! ::i i i x - ^ x x

^ X r - 3 ^ X ^ 3 - ^ X i - ^ 3 ^ X - ^ - ; - ^ X - ^ - i 2 u . L ^ X 2 2 ^ ^ < : U . C 2 0 i > GD > O ^ •~i ! ^ ^ i i l vc i \ 3 0^ O ^ r-i . , m r; ro r* r* '^ ?o ^ ^ ^ <r <r T ^ 'T ^r T iii L1 Ji

O O O O O O O O O O O O O O <r J i <; r-x 3 CN o -^ r-i r : ^ iî <; ^ u l i i l i j l -1 iT! i i l <; ^ ' ^ ^ ^ <; >C >C

121

X

< • r—

— X

X — X

X ^

^ >:

X -

X = - >c i-! X

X o

^ >i

X o

^ X

X o

>^ -r-

X —: :-; X r-! ^ ^ 2 X— —

« k * ^C ^ " M ^

3 ""C ''*• £ Si Gu ~ î 2 »• 2 »>

rr: •'-^ m -^ ^^ —y -y "c.

-V — . • X T-; - X — X — ^ - ^

3 2i r ; »> _L: 3 2 ; 3 »• C-i -U 3 S; ^ L i i 3 2 ^ - 3 2

2 2 ! r ! > - ' 3 2 2 ^ . r ; 3 2

Ci ii X - ^ X

. J - i - ^ ^C- »>^ - ^

<—N ^ " N . •<"*. ^''"S > " ^ ^W' w ^ > ^ ' "—' - ^ ^

^ ^ ; -x; - ^ ; j j

2 3 2 2 3 3 2

. '•V .-->. ^ i -^ - - ^ y ^ • - X ^ " ^ ^ " N > ^ -"X

N ^ - W ^ ^ •'W' X^^ > ^ ^ ^ ^ > • • •«-• -'•m^

^ Li"; ^ r^H CD i> o — r.i rn ' ^ ^ " ^ ^ " ^ " ^ ^ " ^ * ~ ^ ^ ^ • ' * ' s < ^ • < % ' <

3 2 3

O

>«- "«-\ •«- :

^ X

X ^

122

X

Si ^

^ X

<r

i—: X

X -^

X

<?• ^

^ : X

X ->

^ X

X ^

i - ' X

X

X

X ^

•r-. X

X - -

!—! X

i ^ X

X

^ X

- : X

1- r \ as K

:-! X X

X o N-C! i i l

x-' 2 X r-t ^

N ^ * • • • i - ; j

r^rt > ^ V ^ "^.

•<r fv r^

s. ><

•«-' 2 >-' 2 2 X ^ ^ X - i — ^

O • * — 3 O • * — 3 3 T O ^ 3 1 ^ O ^ 3 3 .i i ~ : •. •< > j ^ 4 , <

•<•> r—: -<^ »• •»* O ""^ •!"* -lil " -•* O •'^' r—• -"O *• • • -•* *•• X T^ : x ^ • • X I 4 > s -r-S • • X ^ r x - ^ —i ^

• ^ 2 r0 3 > 0 - r t 2 r 0 3 - 0 - r ^ 2 r r ; 3 3 3 k U J 3 3 i ; r - i » ' L J 3 C S ; C 2 i r - i » - L L l 3 2 i 3 3 X 3

•' : : ; 2 *' i j j - i _ 2 * LL- . ^ 2 r—!

• - C n 2 2 h > ^ 3 i Z 2 h - - ' C n 2 2 2 L J 2

>- =

r^ X

• • X

• ^ :-• "T

-^ ':: . V i j j ; ^ j j ^ 2 :'r' • - : ; ; • • " . ' ; ^ ;: .'.-' • = i • ! "<^ ' : •

IN •<-; Si

>— X:L —i

.- ;•;

•?r --' • \

i j j

:_; <r 2 1 - ^

>— X ' . • •

-y

3 * • • ' - •

- •_ ; ^

2 2

-^V. .'•>» > " v - ^ ^ i " S • ' • ^ ^ ^ ^ " ^ • " ' ^ > ^ \ ' " X i.'-S --V . ^* . >•-»» --—V .<•%. y -N .*-%. . ^ N

-D —! r-i 'o - 3 -0 r\ 3 cs -o T-i r-i m -sr ji v: .-v 3 r - r •=?- " ^ -c- -C «^ <T ^ T « • L;l L l 3 L-l u l . 1 3 ^1 - 1 L l

< ^ - >C ^? C ^ 'O <i S)

o o NC \ X.-1 -r:

123

X

<r *

<r «

3 2 3

<r — ^

o -••• U 7 U ^

^ — T-t • • ^ . r^ • • X

X^ - r _

-^ Z-iX rx 3 r-i ^ s -i X

2 L ii — 2 'O 3 iV ; ; Ô X - - :^: ~~;

~ ~ 3 ^ ~ ^ ^

^ ^ J: s; ft^. n\ r" : (î : .:

3 2 2 i2 ro

C -^ 2

i . 5— i— rv <r 3 2 2 ro ^

2 3 — -^ <: X

^ . — • 3 3 2 _J

^ 2 - ^ ' 3 -

'-i X 3 ^ - i 3 •T

3 i 3 2 — V ^ « - _

2 2 2 ^ ~ ^ — C

• ' "^ • ' • ^ r ^ . '^N > ^ s j ^ - * . ./-N

:"-i "^ •^ Ll >C r\ 3 'X r \ fN >s 3 3 3

> o -» :"i i-o <r 3 O^ >» CS C* C."~-

• < - • < • J - 4 . s

124

<:

<£

O "

-^ i \

^ 2

X

2 2 ? -

^ j ^ r-i X

H LI 512 3 2 2 2

<r

-C 2 T-i Tvi X X i— T-i

<:

! ~1 ^ •ri X

sD —

vj-;

a <r T-! 3 Ul

2 3 — ^ <I X

^ C< i- X

» ' 3 * » O r ^ i •<T-^"^ ' x i— -r^ - • T-i r-< X '•-- — "-O 3 vi 2 - : — X

^ i! "~ ^ '» 3 3 2 U 2 »

•i , •!

^ Ll --0

C-^. Ci Ci

;N 3 CN O O

^ < ^ < N -4

- < . < ^ <

1 -Si ^ ' • s . - -^ . « " \ - " ^ >^». •^^ s-^ s-^ '^.^ ^w' -«• w -

—! ? i r* *T j " ^ N'J X ^ O ««<*i " -^ .-H-^ - O ! i-i-^ *<-:

r.: '-.: . r • ^ : r-.l - : ^

2 3 2 -^ -C ^

-r --'

125

<L

—'• : V

 J ! - ! - w

i— ! \

^ X 3

._ .*- 2 2 "- 3

Ll = r-i i \ L l C^ " • • - » •* • - o r-i r-i '^ is. ^ —i ^ *•

ro 3 3 3 >0 2 f^ f^ ^ : ^ ; f^: ; ^ : r*.j ; '

2 2 ' " - X

r, X

3 < : 3 2 2 2 2 ? 0

i \ ><^. : -*:

U -

2 — i

r - -rn 3

• ^ ^ 2 ;

•—! '>— 2

;'< ^

r-T

U -

X

* •

<; N '4

m>.

i \ ><j

3

2 L

•

U -

N -<

• . •—

r . >

•^

rt^

2 ! — •

' ? ^

3

X T - "

»> • '

hC-.

> »«<*,

rx — '<: 3 — ^ r—•

2 H-« Ci

T - !

. Si

> 2 • - ^

r-t

' X

2 3 2 2 2 3 - i C X 2 2 2 2 2 —•

o o o o o o o o o o o o o o o o o c - o o o o o o o o o o o o o o o o o 3 > O —i r-i 'O <r ul vC i\ 3 > O r- ?-i r: <r Ll >C i" 3 CS O ^ T-i r; T 3 >0 x 3 0 O - Ti ri *- T 3 ul Ll ul Ll 3 13 ul Ll L;1 >C -0 -^ ''C "O •>i -^^ --' ^•j -î Ci Ci Ci C-i Ci Ci Ci "i Ct ri r-- --i Ci C-i C<

^ x! -C xj <; N X i \ ="\ >v i \ X X rx rs 3 3 3 3

126

. s

Ci

>0

CJ

3 '^ r-i X 3 B. 2 oi t-i ro 3 ^ 3 •«?

2 3 1 -^ <: X Ci 2 UJ u_ - i 2

•XJ r - 3

r\ i—

* • T-! iT; >C ;-! 3

— o 3 >0

D-

f^

^^ X - _ i

. s

a>

rv 'O . - ^ i

2

2 2 ; : i : I ;

^ L l SD ^^

•^ : 1^.1 ^ . : -•*•,, r ^ . ; r ^ . ' r ^ . j

2 i--H X

iZ 2 2 2

O O - i r-i > cs

s; -c T-! 3

i-( -•» •>-!rox rs.— T- •• -T-iro ^ 3 o 2 - i ^ ro 3 <= 2 -^ Si r i LU 3 " Si 1-f S; r-i Uu 3 3

i - : » ' _ 3 2 i u u ii r -<» .— 3 2 2

2 • - ro ' 3 -^ 2 iz ! - ro 3 3 ' i : ^ X 3 L l " - H 3 > G ^ : : i : - i X a j > C ^ 3 3

2 2 - i

O O ro <r

•Ii 2

N-D [N. 3 D- CS CS

X 2

2 i :

> o > o

"" 2 6 2 -3— "" 2 3 2 i Z 2 2 2 2 J - i . J : ^ < Z X 2 2 2 2 - ^ J^--,-^.— : : • :'r^ i : ^ ^ : ' < ^ : • • • : : ; : ' : V : ""^ :*-' • ' - ' '-^

.--^ . - •

< V < N < ;. " i V •«

*<«^ .*-% > ^ ---s . ^^N > - x ^^w ^ • s ^ ^ ^ f^K -"^v y-*. -""X .-^s. y - ^ X ^ ^ N • ' • s . -""^ S « ^ > • • N ^ N ^ S ^ \ ^ N ^ >W^ N«^ > ^ % • x ^ ^p*- ' ' ^ ^ N_^ \ ^ "w** >—^ > - •

^ r-i ro ^ iji s: N 3 ?> o -* r-i ro <r Ll -xi > 3 c -> ^ \.y s^y - s ^ _ ^ •«^ . ' . ^ > _ ; - r ^ - H — r —- T ^ - ^ ^ — — ^ ^ —

l>rt '<^ i«rt >«r ><-. >«-i v ~ "M-! N ^ ««-i »<^ >«-. ««-i >«^ N-t >*> .N-. "St-- K-^

127

* « X

as . s

X

O X tr 3

<-x

X T - :

.> X

r—( • «

N j

^ *< > •

: ^ <

•' - ' ^ , - '

• —

7 — :

! ; >.

r - i

rf^

2 •-^ 3 3

—: 3 fi:

-r-i

— 2 i

? H

2 i — *

•

-r-! 3 Gi

• — !

3 GJ

• •

Sl: ^ • '~S.

-H >>.

- ^ • ^

N * ^

= = f^^*" > ^ ^

» k

X V—^

r-J

«

-••

•r-*

*« •x5 s *4

»w

; \ ro 3

«« -H -^ SJ

3 2 > — ;

^^

• •

1-'.

3 1 ^ !

f r s

2 r H

II ^

• «

-r-i f

- C :

<< ro >-n ui •-• 2 2 2 — ro _ i ^ i^ X 3

-^ ^ 2 - ^ .^ ^«JS^ S^ ^ « 4 B ' ^ B rf^M • ^ B

3 3 •—: r-f I—1 •—i

3^ r 5 ;

i ~

iz i — : • - •

^^ i^^

—•

r— X T . ; fl^rf

2

"^ :* ;

(— 2 : • - T

• - • l ^ B

u_

3 0 TV. *s ; • ^ ^ s -4

a>

•— r\ 2 ^ --^CSJ .- * • ^ v

'*: >—

--

^ —

r ^

i — f

a f r ^ • •

2 ^ • ; — • • « •

3 X 3 •<:

':— -UJ

C -<r X 2 2 2 2 2 2 2 —•

; • . . ^ ^ ^ 2 | * • • - ' ' ^ :*-^ ; ' < : 'r^ •'•< '-^ :'•

>-x. y ^ .*"», > ^ -^"S ^ ~ \ / ^ - - ^ . ^«^ >->\ >•»,

N_^ y ^ N ^ ^ > • • N—^ > » ^ ^ ^ >—/ ^ ^ ^^.^ > • •

—a ?*.» r<^ •«• I:": vTl ^ "r: rv^ ^ __• ^ . « ^ 1 . . ^ ( *^ - -fc ( ,•%_ I ^ 1 ^ 1 ^ 1 ^ . s ^^r „ '< , • • . *< X '< •- » -S s ' , 4 . •< •* < . , . ^

K^ *«-: * o ?«« N * ^ o H ^ ^rt !v- -^ *^

2 UJ 2 3 2 -- C ! \ 3 C > - O — i r - i ^ ^ 3 -' ^1 ^ ro ^ i-o "" -^ ^ "-r <r -:" "T »«-: >1--. IH-; ><^ >.^ •><- »r> f-O x-^ K > >»~ "<^ * 0

2 3 — 2 r^ <: X ~ r

y - s > ^ - * % * ' ' ^ . y ' ^ >-N. * ^ .--^^ - - ^ > ^ ^ * > • • N ^ > . * • - S ^ - - • w ' ^ ^ S w * S ^ '

i \ 3 C s o - ! r> ro«r3 C" T •T 3 ': ul Ll 3 -1 *<-i ""O V- -.- s o .-v^ hO •<-•. "v .

128

•^

• ) « •

s ••! i 2

- - N

• •

SD s 4

• - » .

r H ! \

3 'O w Si

. ^ V .

1* ?*?

iil <r 2 LU '

•—

•»^ -r-^ v

• «.»

<r -^ i \ ^-' rOiXi

4 9 ^

2 » t : ; %• •

2 ii *— -3

=

—' ««

^ s -<

as

i \ ><; S i

< . s

- ^ -r-i x . '

Wi^ 4 . S

s

• ^ If

3 s

• «

T H

- ^ S i

• •

T H

— S i

*-x

«* x ;

»> rx ro S;

T- t

; 'H

•—

r H

Ox LiJ - ^ •y

^ >" s^-i N-^

C^ - ^ - > T - (

• N - " ^

ro ! \ ^

2 UJ T 1 —

^x.

• —

^x.

!—! i H

o ^ '4

jNx

- ^

>c •sr;

2 ULi 2 >—

x-^ ' » • ' • _ "v

Qx

ro 2 LU "T !—

Ci

x ^

- ^ ^ x

e

4 . S

. ^ s

i H

• ^ i ^

4 » >

a

%-< !i '— s

• •

T H

3 S i

T H

*« SD V '«

Bo

rx ro S i

4 . S

X ^

•r-! >^ •-*U

«». (1

s ^

t :

••J J

S

• •

- H

3 Si

-^x

* • SD s -<

.« fS. 'O 3

* —

ro '-s

r-i -^

2 »•-

! "0

% 4 r ^

rx <T "O

; • *

2 2 -j _J 2 2 iz Z 2 r-i - * 3 - ! - — — 3 3 2 2 2 2 2 r-i >- 3 X

:': 3 i ^ ^ -y 'r: ...^ —. -y r?^ ;_; _ ; :": •"• :"• :": •*• —; UL. 5 i i

X

2

>0 ! \ 3 CS o o o o o o o o o o o o o o o — r-i ro <r iil >c !-x 3 ch o TH r- •<•,

Ll -o sD >c >c xo --c >o >c "x r^ !x r\ ; *o "o ro "o ro f*

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 . o — r-i 'O <r ul xi i\ 3 > o — <r

•Ns

f^.

• ; ^

r -l KS

N*-"^

rx v*

i \ rN s o

•J>^

> s

»4-!

0^ rx so so >* »< v" so so so ô •«*. so so so

129

^

"T >my

&

^

:n.

^

J i -!- *

i ^ 2

r-i iSi

5f ^

— ^

* ^

rn SJ 3 >C

^ 3 r-i * "*^ L l

r-i •b « « • « Sk

V *< ? hiM

^ ^ - ^ T - ! <»*

"Z **^ ^ '^^

•-i -J^ T —

s,- ^ xQ w x; ^-'

^x • >x rH -r^ i

^ f -H - rH • ^ < 5 ' » 2 ; r - ^ ' 3 = S i 3 3 S ; -^

•* ' 4

2 2 2 2

O O O O ' J ^ <r L l O C? CN c>

' — ; • < : .

-i j pv ::;5 :•> -^ TH : •< rr- - ^ u l x j C 2 c-« > o o o o o o o —: .-<-: •''-<-• - r *?• * - - ^ <r T «T

2 2 2 2 2 2 ri " ^ -"-^ ; - ; • .•':^ ."< i"-' r~^ •• i - _ ^ I

^ " ^ . ^ S . /I»"V y - V . 4 ^ > , ^l*K , < ^ > " ^ 4<—lb - ^ _4» S ^ \ ^ ^ > . ^ S,^ > , ^ > . ^ •S-*' >_/• N«^ " ^ ^ >«.^

-^ ^w- - ^ -. •< . ^>r w ^ X-; ^ -J.^ ^^ v. ^^

H H 3 — - - 3 2 2 X _

2 3

X, V

- < X < X < 4 \ 4 <« <

' r < r - < ? - < r < r ' r < r - ^ < T « r < r ^ ^ ' < r - ^ < r < r - ^ < r

130

X ,

cs rs

-3«T

<»s x ^ -x^ y ^

— • « •

•^ >^ s <».

<as r 4 * ^ -XX L i

;::: ' -?- « • »

•if

^ o

• » - - ^

^ o ^ rs - L l

* > -• « •

3

O ^

4 , . « *

x ^ ^ ^ ^ ^ > ^

• ^ r H

r-i ^

X -4

fx *? ^^ '"^ T-i

X ;

^ —

•«^ x-x

;;X —

r-i *

• * - -

< • ' ^ i ^ • C-i •

2 ; 2 i S i - rH

r-i — i: • pxs

rs 3 - ro *- 3 3

^ r 3 - ! - i - i - 3 2 2 2 2 >-' 3 X i-

2 ri

;~j i r H • « ^ » 3 3 ' « ' 3

— 2 2 2 2 2 ri

0 0 0 rH Ci "O

0 : 0 . ' s o

- - T «r <• '=' •«'

. " • ^ - - ^ - " S ^ " ^ - ' • ^ . ^ V . ' " N . ^ ^ > » ^ < ^ , * ^ . / ^ ^—S, .^-Vi

< ^ • "^ >«'^ r v ••*^: ? ^ ' ^ ^ ^ ^ : ^ : ' ' < ^ r-^ : . "* -. ' ^ > <

" v ^ V ^ * « ^ h O »^r-i » 0 < - * ^ ^ < ^ « » « ^ ^ . ^ ^ i ^ ^ . ^ * . f . \ » ^ : *. •, x» "v„ x_, - . " ^ , ^,..

r- T <?• <r <T <r

s: rs 3 3» o — -i -o - 1 - 1 _1 u~ >C ^0 ^ x

131

• !

3 X

• X rs

<Z X

• "N

T

2 !^ uu •' "^

-*~ f— '• •

t" in •-^ i s < •xX > ^

C^ .x-x

* w y x -xx

rH rH

'îmi - ^ ^

ii j — •^ 3 r"~t •

>•** — » ir^ H-i

.-—s

V -4

rs •T

2

• ^ >^

•«r 3

• H

^w —

^-x

T H

x.^

X ^ ^ . X

f

•• ' rH * iil

•

r-^

^\,

x^ rH

• — ^

•

o -^ "^

^^

!—»

. X

2

• ;^

i «^

13 ^^

/ ~ s

r H

^ x

l2i *« ro • 1 ^ .

j — 2 i — i

r^

;*•-

z> • •

ro •ro Si

i —

2 H T

_"- ;*;

O'

3 u_

. ; i

> H

_.--x f—"»

>~. ! — •

x ^

r—

m • •

><-; M^

««

— 2 •r—1

.--'' _"-

i—!

1—

X

-^

I

2 j—i

>— = « •

x ^

5x rs ••r 3 2 • — i

^^

>— 2 !—< ."w'

;-.

as

X -% " 4

i H

as

<z u ;

S b

X s -4

rH ».

— 2 •—! . • - •

-.

r ^^ • ^

•

; — r

ri •-*• r~

—. ; .

^^

• - w ^

—-!

^ , .

• •

» "^

> k

T-T

^^ * •

V . ^

*. .^ • - , ^

"T

-r^.

IZI r — •

"^

»— 2 ; i — '

-^ '.

^ >.

X i ^

» b

Lw

<r » s

X ^

3 b

• I

•C 3 k

X x " ^

. t

: _: <^ ^^ _*

•

•

N - i ^

-^ "^

^

U . ^

5—

X - ; ! —^

— i

* •

"C -_ ;

» b

> x

ro f^'.

'— •T>'

• r ^

.-- -.

T—:

^ . .• ;

! Zl —' -^

• *

^ . M

^ • ^

=

•r^

: f^;

— 33 '—« .".X

- •

> b

X --~^ -^ s

.^ 2^ — s^

:

T-^.

,,: ^ :

— m —1

." ^ _*.

r-^

^ . ' ^ t

i —

33 ^^ •• .*.

r ^

• ^

>—*. - ^ !> Xv

<r __|,: 2 ; H - •

xnl

:

r H

*— ^ 1

— -—-.-- .-.

s

a :%

• b

X cc •

c 2 ( — •

* 1 ^ ' ^

, :

• ^

-"^r

'— 2 -

• _ * •

.-.

D-

:,_ U ~

T H

}: • — ^

^ • <

."- ••

— U. O- j i i 3 HH - i rH

O ^ u'

o •'•• --> < ; >o sD

Ll 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 Os o —i r-i ro - ul s: rs 3 Ox o •— r-i sD -x; rs fs. >>. v >x rs fs -"X rx ' v 3 3 3

-i -i ro -^ o o o ^ i i l -x ^

3 CN ^ CN 0-s x NT ^ - r V ^ -r

132

x^ \ xO

2 ' ^ * 4iT —I : " -

^ •-' X X . ^ ^ *

x_^ s 4 r H as

2 s o

^ Z> rH 3> -•Si z> cn TH • • • • ^ ^ • • ^ ^ ^"^

*<^ N ^ >— "<* ^ . . ^

i UJ • * O

:> -!- ri ^

! - ! ^ \ : ^ : f * i * . 4

•sO 1^1 fî _ ^ : ^ i _ ^ : ^

^~ 2 2 —4 X ^ ^ 2

2 2 ^

2 2 — 2 U . - 2 : : ^ X 2 E ! i ^ _ _

x,.^ S^^ >,^' v ^ > ^ > • • > - /

i i U - X i C ^ X i i l i n i i ^ X :; >o r-i _:

Hr "** : : 2 ~ ~ ^ - ~ : " • " " " ' '

; J X j • X ; j j ••>s ' - ^ ^ ^ •J** - x ^ ^ <

rvs > C- 0» CN O O O •r- -rr -^ -sr <?" Ll Lfi Ll

o o o o o o o c o rH r-i ro 'T Ll NO r 3 CN o — r-i ro «r Ll

> < * W -s < r-i c-\ c "•: t^. -T'

133

^ x ».

<: X

3 X

LJ X

»b s

3 X 3 <: 3 " — - X

2 X

2 » 2 2

i I>

>-< ^ • • ^ ^

< ^ • *

*« ><

uLi

2 • — -

i —

•

«« -•-x

3 •^

; ^ 2 !—i

X 1 3 =

a a

 S2 ». =

<i: <r 3 r—^ Mmm

»s i-H

3*

3 i —

as

-^ as

• —

•

* •

^ ul

'^

z u_:

^ • ^

• ' , '

*<'. ».

X S s

rrj - ^ .-n

2 »• — X

— • ^ —

X 2 ^ 2 2 U_ J_ U_

1 3 " ^ — ! 3 S : 3 3 3 ^ 3

-^ 2 3 ;^ ; - 2 2 2

• ^ L-l- XJ Nx "i C i -r^ -~^ •—'. X^ ,-X <-x ^-s

i ^ ^ ul -O i x 3 CN O r • •' T -:- — -rr -r- «?• ;

i ; >,-^ ^ *. < . . X Px X. X, :v c; c- o — Ci

1 Ll ^ ^ X-

134

s r

<Z «•• LU X

o -

X

LU X

2 ~ H-f «

<r . * • :

>^ e

cn • -= <z c:: « • O^ as

O •> X T H X *?• - <

3 X

 r-i - O 2 O 2

3 ro :*: ^ ^ -lî !î ^.^ r" ;

- ^ s -4' ^ 3

as xc-

3 <s 3 ri 2 3 2 - •• —^ as rH r s - :

3 X 3 ro 3 3 3 3 3 3 — <? —•• 3 3 3 'î ^ : "S: ^

^ ^ _, ^ rx

_ ^

Ll ul >o > cc; o- o — xC X i x : '«.

j j j >«i ^_J T r ^ ^ " g ; — — : ; ^ : ' • ' - I " ,"?' • - ' • 'r' .•':' " ^ "r' ^ "-'

O -1—; •• .j N^ ^ •-; v.- ^x -- ^ ~x ''^ 1 ~. 1 so «T T^ ^r '— •~-.r: ^ X s 4 : ^ XC i4 , X ^ ; X . . ^ ^ X . ^ ^ ^ ^ » 4 > X ^ X X _ ; ; T ^

—'•^—' -^ — - r H •— — r—. ^ - i ' - . ; T ' "î r-i r< r i T i ~^ r ; c--

o

135

r-i

1-. 2

; t - * i

- • • 1

LiJ

•', •' <r

/"X

x ^

•^x

•^ • w

r H • ^

» b

2

fO S;

2

^

i H

:!

-x^

?~"

»<

; « i

r—f i i l

- s . ^

i = i l >

ro ro ><•> so.

^. » ^ .

o _

»—

r H

j :

T H

i " ^

ro S i

2 2 3 2 u . u i : 3 X U J i - i < : i - i 2 3 2 U J ^ i = i i : ^ U _ i - i L ^ i - ^ 2

I > - i Z> _ 3

o ro — ro o cs "o ro -CN ^ S; rH Si '*r

rs ;: —!

2 3 2 -UJ r-i 3 - 2 3 2 uJ Ci 3

!l !i — !; •— t—I 4-^ i-H

3 O 'H —

i-i U- :_ 3 2 -_

• ^ U J S 3 3 C N O ^ : ' - i r o - c " u i > G r s 3 C N O - ^ r ' r o c - ^ ~ t N < X < - . < - . « » < •4 . i r ^ s o s o ».x

X V. <

S s

ii ii 2 : 2 ^

2 r -i : -^ X

— ---! ro ^

\

r-i

ro vD

\ ' — rH i s i

. w -o : ^ • x ? ^ : 1

x ^ - ^ •

•T- 'O ro _j — _ j ^^ - ^ s o s o .-<

3 <; '^ TO "O 'O

•^ -^ •<;

2 ^ 'O

Z> O i -

3 -Jt r — ro r-i

i i r-i •iH •<-<' i i

!i s ^ •••••

z> ro

Li •<;

. • -T 3

o - 2: !S Ch X —i ^-' O U. 3 - r • * 3 •• •Jit ;o:- •- ^ 3 <; ro 3 3 uu r-i c-i - ^ • • 2 ^ as • • fc

- i . ^-^ r— as r x r H r s

»<-• s<^ r^. -^^ M^ •""• ^'^

- _ i ! t r o — i i i * ^ >-J Li iu_ i s O 3

- * ^ ^ ^ ^ . . . ^ y ^ ^ * ^

O O

• c - <?•

O O O O O O O O O o o o o o o o o o o o p o c o o -iro^Li^crs30ô-r.ro'ru^>o;s^C)^^^.^^^-^>^

136

<r -r-

T 2 ?— LiJ

* 2 *r :—

_ ! i s \ ab - ^

L 1 2 i . r H i j j a.

\ 2 O

3 'T xT x .^ V,'

2

2 r-

O 2 • b ^ ^

ro -3

o^" ^'^ Ukd T—! ^ ^ : . ^ „ ^

— 3 H- - n - 3 - ^ 2 —

_ ri ^ -p 3 —: ^ <r r-i rH

•^^ —. T T T i j i S ^ x T c " ' ¥ >':u.x • ^ • « - 3 3 i : u j - ^ : i : u _ u _ < r

• v o - ^ x i ! < r ' ^ i : i ^ : : i _ u _ 3 3 ; 5 u U ^ i J i U _ 3 3 U _ 2 ^

; : i I > ! - X O ^ I ^ ^

. ^ ^ 4 ^ ^ . ^ - V . - ^ ' >^^ N„«i' . ^ N - ^

:rs 3 D>- O •s i \ s . 3

4-X . . ^ , ^

o <r L"

^ .*-x >-x x ^ >-^ . 1 ^ -i-x .'-X .0^ .'"s .-s. . ^ _ j r^.: »«4 - ^ -^.^ -.^^ ^ ^ x ^ -.^^ > . • . ^ •»_> x ^ s ,^ 7~r , ^

r^ o^ n-> r ,. r s ^x x^ -v "v, -X ' v *>v "> ._* .—

^ ul -C

X

i-i •<J -r-. •^ 2 ^

:> r-r 2 ^ ^

2 • ^

i x,* k_ —J ""x i— f— ^ ^"~ r H x ^ •—

• % ^ ••••-. -se-•NT: r».: :"- >^ ."< r \ '-^

— -; _ .r

; _ j

*<^.' t^ ^'

• . —

X • - •

->-

O --; 'T

W ^

It

^^ , s 4

•—

. 4 ^ .

s '4

^r

^ ' : ^^ •^H*

—

N - ^ -

S O

<r

'•.jj i^ i/l

4Mi^ •val^ • " ? " t .

•C u ^ t

T x i i ' i l i ' ^ i i X M LU UJ L U 2

^ Z^ ^ ^ :• r -r- i . .—: r^ • • : .-. .-. 2 ' :_. ; ! ,"• '^ • : i—; •-• 2 : •"'• 3 Li. !— Cs. 2 U_ ^ i '—' O" 3 ^ 3 ^ 3

S5 • X w CN o ^ r-i ^n -r- ul <• *r <r -cr «r 3 ul - v i i, -. n->

CN O ;=-; xT? >o >c -c >c <:- x! -(:! "s "X

~< -o <r 3 -•X - S X , -X

137

\ z>

• ili

2 3

* O U l —•

.— 3 2 3 — 2

• -"^•^ ^ ^ - U - O ^Jl -ri '<r 3 r H 0 3 3 3 - < 2 0 3 ~ ^ < -• '^ CI.; iil TH f— UU. i—, LU "— -^ 3 CZ, 3 -— •O " ' 3 ili U_ X

r-< rH 3 •rH <r -.c -3 1 3 3 i O 2 3 3 3 —i —i 3 3 — = •C • S ^ O i i i ' S s ? — r H - — 2 T - S 2 2 3 r H 2 r H 2 ~ i S X — •— 3 T - i 3 - r - _ :

- f - * 0 I— U-ii:. 2 ^ 2 I » - 3 2 I j 2 L i » « 2 3 J : : U . X 2 - d ~ » ^ . = i " ^ E - « Z > • O - ^ 3 i _ ^ L U r H » r H a 3 3 U J « r - < " 2 — i - C C L U s T - ^ ' r H * rH • • ' " • ' — - ^ 2 •'• 2 _ i - : • • ••• O 2 r—i i l i 2 • • i • • O 2 - ^ 3 rH _ ; 2 ••• • • ! • • >^ 3

S i S ; -^-r" r H a 0 3 S J 3 - S ; - ' - ! = •^^= O S ; 3 S j r H a — l a - ^ a O S i 3 S i 3 S ; » • — : 3 >- C i — • u i i 2 i i i 2 3 - U J 2 - U J 2 i — 2 i j J 2 3 2 L U 2 r — 2 U J 2 u L i 2 3 2 u U 2 L U 2 r i L U • ' - ' • 3 2 X Z > r - i : > : - ^ Z > i - i Z > i - i - H O - — M O ; - ! ^ Z > - i I > ! - ( - . ^ • - . 3 > - ^ ! ^ . : J :

: l . i > : 3 2 2 C ^ 2 U . ^ - < 2 ; i 2 U _ ' 3 U . 2 - j _ ^ i : ^ 2 c Z 3 u l 2 i i ~ 2 Z Z ^ i l 2 i ^ 2 Q l 3 2 3 I • S ^ ' S ^ >—• > i ^ V i - ' > . • N . ^ - . . . ^ • . . . • ' ^ . ^ > B > - ^ . X S _ X - ^ g ? N ^ - . . ^ N ^ ^ > ^ S , ^ N . ^ - ^ « ^ N ^ ^ > , ^ < , ^ ^ ^ ^ ^ . ^ ^ . , ^ , . . ^ , , „ ^ ^ y,^ 4,^^^ S „ ^ ^ > , ^ S ^ ^ ^ ^ ^

3 0 o rH r-i ro <r Ll <! !\ 3 0^ o rH r-i ro • iil >o rs -3 0 o ^ r-i rs T Ll >c 3 0-- o -rH r i -i : : - ! : - ; '. " ^ "r-^ : . ~ }•- :- m • ^ • • : L l - < 5 S 2 > C > C v C > 0 - > C - 0 •. i \ 'x, - N fs Nx 3 3 3 3

!>«

\ T - r

-_ b ^ M

» b

"^ \ T- t

;•; » b

y * ^

4 ^ ^ . ;

<-• : . ^ b ^ •- 4 " S B ^

'O • .-^S

>^ i \

4 - X

jm, ;

s *4

SD

a

. ^ }— X . X

2 2 ~ ] - 'b.f J

Zl

-^^ r\ i"^

.J .J

-1 r*:^

^ J 3 J

^^ ^ n ^ M

-^

—• : ; • *

f

- - X

—^

r: O.: ^ ^ 4 s f

»• -c

4 ^

•—i x,^

-o . s

^ 4 - X

. ^ -»

•

r H

- * i i l

•

o _

;.".

: j « :

b ^

* -^ * • : • * :

* .^ ""-^ ab

.-^N, • 'w ' - ' " V

""^ W >

«

^ J « J ,

•

. ^ -•-

• ^ ^^ Na^ 3 Z

>- - ] ! - 2

• • r j •••

^ - ^ 1 ^ !"e:

^ ~ . . ^ —' .4U. ^ ^ -£— • ^ - M X _ d_l ;:-! '-s = •• ; j j •11 Ll_: LLI 3 ^ = — ^s' U J 3 *

3 - r - < 0 2 2 3—^_• — i— \ w 2 •— >— Ns *• r-i

rH i - 2 rH C-i 3 • .". r i ^ 2 ^ ^ - H :'; * ^ i-î

•rx, fft, ' ! -— ! >—! " ii ^ S i »• ~ i - ~ r- w ro !- Ci >-i ro — r-i r-i ri — ri — - : 2 U : 2 0 i : ^ u J 2 ? - 3 0 i . u U 2 — U J 3 U J r - r - 2 3 2

J ii Si

• 2 O r-i LU i ^ 2 — J *; ^~ ^ <

^ ^ ^ v r^-

S 2 Z> 3 3 ^ I> • ii iui ii O ^ X ii L i !! Z>

L: i i . ^C .—: .»« >- X => O

r-.i -O "T 3 >G ^^ 3 CN O rH X 4 > < N •«

O T L l >C "s 3 CN O rH r i •o '< . ' 4 ' ' H 4 b < - '4 *o »< «o -o

X . ^ S ^ - - s ^ , - %.«,»• > « • S..** Nw"* N - ^ N ^ ' S . ^ N ^ * • » - • > . * i '

^ 3 x j r v . 3 C N O - ' ^ r i N : ! T L I X : * o ^ r o * o •o 'OT '« r<r<v 'T ' * r -<?"

S x

* 3

138

r— u ^ U ,-- H -"T -^l ^ .s \ O W^ ii i ^ H * ^^ »s 2 ; O j — i i l ! »• 2 Tvj " 3 i-H T - r-i • ^ • ^ a. ». X - ^ O rH rH

a

o b. 4

2 ^ 4

X <2:

2 2

\ i - : :

¥ X ii

• ^ / •S^ U .; rf- s o .v^

~4 U ; «»• JU - _ : ^ LU r H " J ~

3 * 3 2 3 • 3 r H 2 2 N . 2 - 3 3'«»> - 3 » - " ~ 3 U : 0 » > 2 j— C 2 ^ \ r ' " ; 2 3 r - H 2 3 — • —-e^ , . . .s —

• - i 3 0 3 * • - ] T 1 C 2 2 0 - 3 3 2 ^ JiS 2 - J ^ r i 3 L i - f c a . r - i i H r O « r H 3 » » a . . a fcas^r-a . ^ s . , X • •

3 2 0 0 i t — L i . M i i - i - O i-^-r^ O — ii — f i ! 3 * - iO 3 5 3 L U 2 0 U l i i i 2 — O 3 U J 2 : — L U 2 U i 2 = ' ' 2 — ' 3 i z — U i 2 L i J 2 ^ Z > > - i ! i i i i i Z > r - X i i iJi i ! Z > i - < X I > — Z > ^ il u : i ^ X U : i i ^ X O - ^

i : > 2 < Z 2 ; j » i £ i r u l 2 i J . 2 C 2 i u _ d 2 i i i l 2 2 U _ 2 ! i Z 2 L ^ u l 2 ^ X U _ 2 2 3

xo fs 3 CN o ^ r-i ro <r ul >c rx 3 CN o r o r o ' ^ r o ^ T - c ^ ^ « r « r - 9 - ^ T L i

• S - " ^ >^^ .^N . ' - ^ > ^ - < ^ ^ ^ *^S ^ > ^^ --"^ - ^ -••^ >^b • • S-iK* ^ ^ '^-^ > ^ "»•• X ^ > • • ^^^ > , • N ^ *^<» • • ^ > • • X ^

s '• *•<% «•• ' -^ xj*: 'Xs ;*r ^v "^^ _ ^ "*.; " o -c* ' •"* • " >C xl >0 <: *C ^ ^

r-i

o r-i ^ -^ CS rH rH

• r ^ r H

2 3 I > 3

3 • s

"~

3

.--

S y ^ V N . ^

<-

T ^

O •i-

—; I t

- ,

. ^ s s

•x^ u l

-

;— X • ; •

2

4 - X

< ; . x » ^

> " x

Ci 3

'-H

^^ rx

% < •

j ;

~''

r • ^ T ^

:. -4

^^ fgt

Lli ^ f ^ t

— >**.

| > ^ • ^

T - ^

^^

. " - ' •

• • •

^

4^-S

D^

H *4

^^ 3 ;

3 C j -w '

—

o r H

CN

r H

x ^

• ^ 3

i t

4

^x. x.^

V ^4

CN

r ^

r— X L;-t

2

4 ^

• S O

X s

2 . " - 4

3 : •— LU ~

\^ T ^

L.

2 UJ

-'^

; ."* • ^ .

^ O 2 U.O

o ro : : : i _ l *<l

•cro -"T ? ^ UJ ^ "

2 2 2 ii ¥

- ' 3 ^ 2 *-N , •• ro 2: -J - -

i— ro •• X •o ro <L

rH :^ uU 2

3 2 3 — Li il. — ii > r—. •J' •--' . ^ • • : • _ ; ^ . ^ - ' S^.4

2

o -^ r-i r o ^ 3 s : > x 3 C N o - ^ I 7< 7ii

ii s\ ^ ^ C . . _ . --s.

Ul '^ ¥ X ii

4-X ^ 4 ^ ^-S

s-* >.y x„» ~-^

-C- % 3 •> ri -".i Ci c<

L

139

2

fO — Lil <»' s 3 3 ?s • - ^ ^•. 2 O 2 -Ki-

"^ u J S s ^

-1

on i— — « — • • ' • • r- i •—

*^ --4 s 4 ^ ^

_U 3 ? - 2 3 U J 2 0 L : _ i _ J 2 i - 0 3 L J 2 I > i : i < I X i - ^ O - ^ i i i V i i Z v i - i X i i i i l i i O - i - i 3 3 i i : U J U _ X 3 i i : r O 3 f 0 3 i i : L U ' 0 3 ! ^ 3 i J : : 3 L ^ - i 2 ^ < I 2 : U . i _ U . ; : i _ 2 U . 2 3 U - 3 2 U -

U.; T - ^

H-^

M —

•^

ul

\ ^^ r^

»o r^.

Sb

o • *

, : » • <

—»

~ ZZ 32 •

«« ^ '4 • ^ ^

^^ frx\

.^x x . ^

as

r H • •

^ . 1 s 4

^

2 X " 1 - ^ . " 1 3 a as

r i • • ^ ' ^ ^ ^ '•> '4

. - ^ t " ^ l

3 ^^ Zl m

*« s "4 ^ • ^

^^ f ^ t

— T

f^.

_ - -cn

i ^ ;"

2 UJ _;

r^

^

.,_<

2

2

^ X •• o

f^\ !%t

L U 2 U u 2 » 2 - 3 2 - ^ - Z > - H X ^ ^ ^ 7 - i i i L i i ^ - i X ^ ii i - i X ^ i : 3 U :

4"" -" ^ ^^ ' ^ ^ ^ ; ^ ^ \ ^ \ / ^ ^ ^ ^ ^ ^ \ -""N .#"v >•% >-s . -N, . ^ >*s, y"v >-N -b* >*> .-—V ./•N. y ^ ^s, y^k > >. >-^ 1^^ >-b, .^v ,< v S^^ x _ ^ > , . • > • • >—' •«*• > • • N - ^ N_^ "^.^ b^,^ N , ^ ^ ^ . ^ ^ s ^ ^ . ^^^ .^^^ 1^^^ „ ^ ^ „ ^ ^ ^ , ^ ^ ^^^^ . ^ , ^ ^ , , ^^ .^^^ 1,^^ . ^ ,,,_^ .. ^ ^ . ^ ^ ,„^^ .^^^ , , ^^

! \ CD CS o ^ r.1 ' ^ ^ LO ^ r \ c^ CS o 'T-? "> r^ ^ Li"; sD i \ E 0^ o -^ r-." ** ^ u": - r rv z ; cs o • " ---

140

. - J ^

- * ^ ^ ^ B ,

* l -

2 <Z

LU < £ -

i—i

2 <L X

£ * <r i—

<L , »_ ^ • ^

u J

2 <E 4 ^ X

•LU , • ,

H—

• * 2

ro

asUJ O i - i ;i i - o •ro • -»s ». ro

D • • O 3 i i i s '< _ • - '• 'i X •<

rTL-: !«l ! ; ^1

i=i • » 2 a a X •

I!

Li.1 i-ii czL 2:4—•' X i—<•

3 - . I > ^ < r X 5 C ^ . 7 ^ i 7 i U - _ 2 S 2 i = i

2 u l 2 u l ^ Z 2 - U . Ul-ulî^ . U _ 3 5 u _

X C 3 0 0 0 0 0 0 o o o o o o o o 4 ^ _. c«.- r; «r ul >c is 3 CN o rH r-i ro <r O O O O O O O O O O O ^ — r H - ^ - :

II M^

APPENDIX B

TABLES OF ORDERED STRESSES

141

142

OaOERED STRESSES SCENARIO-! ( : ? L I T SP»CE» I - . I ' - ?S : Z^MA-.r -nCULJS

r-*»OR»i STRESS

3 3 * 9 . 2 0 1 6 2 3 . 1 0 1 3 1 7 . 4 0

7 0 7 . 4 7 3 3 « . S 7

• 5 . 9 1 3 9 . 4 0 2 3 . 2 9 2 3 . I S 2 2 . 4 1 ia.32 1 9 . 2 6 1 9 . 1 6 I 4 . d l 1 4 . 3 2 1 4 . 2 7 1 3 . 2 1 1 1 . 7 7 1 0 . 9 7 1 0 . 9 2 1 0 . 6 1 1 0 . 4 1 1 0 . 2 3

7 . 3 1 6 . 4 0 9 . « 0 4 . 1 1 3 . « « 3 . 6 6 3 . 9 9 2 . 5 9 2 . 2 4 1 . 7 * 0 . 4 3 0 . 3 3 O . l S 0 . 0 8 0 . 0 1

- 0 . 2 2 - 0 . 3 4 - 1 . 4 3 - 2 . 7 3 - 3 . 6 6 - 4 . 1 9 - 4 , 3 7 - 9 . 2 0 - 9 . 7 3 - 7 . 4 9 - « . 0 7 - 9 . 9 8

- 1 9 . 9 § - i a . 0 3 - 1 S . 4 2 - 1 9 . 3 1 - 2 3 . 0 2 - 2 3 . 3 9 - 2 6 . 4 9 - 2 8 . 8 2 - 3 9 . 9 2 - 4 2 . 4 1 - 4 8 . 7 1

- 2 1 6 . 0 3 - 9 3 4 . 6 1 - 7 9 6 . 7 9

- 1 9 3 3 . 6 0 - 9 7 1 7 . 0 0

HAT. «i»». LOC.

26 27 4 5 11 18 3 2 3 4 12 13 4 2 4 3 39 17 16 38 2 1 4 1 2 2 5 4 1 4

2 99 60 19 4 0 66 37 69 62 61

6 20 46 39

9 1 9

93 4 S

3 3 4 7

3 • 8 2 3 28

7 64 63 51 29 2 9 5 6 2 4 10 9 8 30 9 7 31 49 9 0 52 55 36 19 44

Z-NCRM STRESS

7 8 1 0 . 8 0 1998.AO 1 5 2 1 . 6 0

6 3 6 . 7 3 4 6 1 . 4 1 2 9 9 . 0 9 2 7 1 . 5 9 2 2 8 . 0 1 1 8 9 . 2 8 1 9 4 . 5 8 1 4 4 . 6 7 1 3 4 . 4 1 1 2 3 . 3 4 9 9 . 6 4 8 3 . 1 2 7 6 . 0 6 4 6 . 0 > 4 4 . 7 2 3 6 . 1 6 : 3 . 0 6 2 6 . 4 1 2 3 . 4 9 2 1 . 8 5 2 0 . 9 7 1 8 . 8 9 1 1 . 3 9 1 0 . 3 8

a .62 8 . 5 9 3 . 2 0 7 . 9 9 6 . 7 7 3 . 5 7 2 . 9 7 0 . 9 1 0 . 4 6 0 . 1 4

- 0 . 1 5 - 0 . 9 1 - 2 . 8 3 -3 . -33 - 3 . 0 8 - 4 . 8 4 - 4 . 2 7 - 8 . 5 9 - 8 . 6 9 - 8 . 9 4

- 3 2 . 4 1 - 4 2 . 7 8 - 6 3 . 2 4 - 6 6 . 0 2 - 8 9 . 3 9

- 1 0 1 . 9 1 - 1 3 0 . 6 6 - 1 4 6 . 4 9 - 1 9 4 . 7 0 - 1 7 4 . 2 6 - 1 7 9 . 9 5 - 1 9 1 . 6 3 - 2 0 7 . 3 1 - 2 1 1 . 8 9 - 3 0 1 . 2 6 - 4 2 1 . 9 1

- 1 4 7 1 . 6 0 - 2 1 0 3 . 3 0 - 4 5 2 0 . 4 0

" » T . SHEAR -îT. LCC. STJ>«SS MUM. LJC

2 7 4 0 6 . 1 9 2 26 26 3 7 7 . 8 8 2 44 34 1 5 6 . 6 7 I M

2 1 4 2 . 5 3 2 zr 3 1 2 7 . 6 9 I 57 6 1 1 5 . 8 6 I 63

11 4 1 . 0 8 1 61 66 6 0 . 4 2 I 59 63 5 1 . 5 6 2 13 62 4 7 . 2 7 I '*l 1 ' 4 1 . 2 3 2 54

7 3 2 . 7 9 I 23 59 2 1 . 9 7 I <.a 58 2 1 . 9 5 I 39 13 1 6 . 8 3 1 49 4 9 1 5 . 2 9 I S3 48 1 4 . 5 1 I *7 14 1 2 . 3 6 I 13 10 3 . 2 3 1 30 15 5 . 3 2 I 21 13 0 . 4 3 2 9 22 O.Ol 2 53 16 - 0 . 6 5 I 15 23 - 1 . 2 4 3 35 41 - 1 . 2 4 3 33 53 - 1 . 1 7 3 37 12 - 3 . 3 3 3 28 21 - 4 . 5 3 I 22 31 - 7 . 6 2 1 16 43 - 9 . 9 9 3 38 38 - 9 . 3 9 3 29 17 - 9 . 4 3 3 29 4 0 - 9 . 6 4 3 43 37 - 9 . 9 1 3 ZZ 2 0 - 9 . 9 2 3 46 4 6 - 1 0 . 2 5 3 51 33 - 1 0 . 2 9 3 17 35 - 1 0 . 3 4 3 12

9 - 1 0 . 5 0 3 ?6 30 - 1 3 . 3 4 I 5 2 4 - 1 3 . 7 7 1 I 28 - 1 4 . 3 3 I 7 51 - 1 5 . 5 7 1 40 25 - 1 9 . 0 1 : 3 56 - 2 0 . 7 5 1 *2 2 9 - 2 1 . 5 0 1 4 39 - 2 6 . 1 3 1 3 42 - 2 6 . 5 6 1 2

8 - 2 7 . 3 5 1 i 54 - 3 5 . 5 6 I 31 4 7 - 3 9 . 4 7 1 24 52 - 4 0 . 0 2 I 14 50 - 5 3 . 4 6 1 60 57 - 6 1 . 3 6 2 36 45 - 7 3 . 9 4 I 62 60 - 1 0 8 . 5 3 I 64 61 - 1 0 9 . 8 2 I 53

5 - 1 2 9 . 2 6 2 52 44 - 1 4 9 . 1 6 I 66 65 - 1 5 4 . 7 5 2 *5 55 - 1 7 1 . 5 0 2 18

4 - 1 8 3 . 2 9 2 55 1 - 2 1 2 . 2 9 2 11

4 4 - 2 2 3 . 7 5 2 19 32 - 2 7 3 . 0 1 2 34 36 - 2 7 3 . 0 4 2 32

^ - 1 1 . : ? 7 8 1 4 . I J 1 5 ? : . 7 0 i : 3 4 . . ' o

7 9 3 . 77 ;>37.fl6 * « 2 . 1 3 «-2'. .*5 3 0 2 . 9 3

2 4 2 . 7 9 1 4 4 . 7 7 1 6 3 . 4 9 1 6 4 . 0 0 1 4 0 . 5 7 1 3 5 . 9 6

iT.ZZ e':.35 7 8 . fcl 7 1 . 2 6 4 6 . OZ 6 3 . 3 9 5 7 . 7 3 5 4 . 2 9 • 3 . 4 6 4 2 . 7 4 3 7 . 2 6 3 5 . 0 0 2 9 . 3 f l 2 9 . 3 3 Zo.li

za.f'i 2 8 . 2 2 2 3 . 0 8 2 7 . 3 4 2 4 . 7 2 2 6 . 0 4 2 5 . 0 4 2 4 . 5 2 2 2 . 0 7 - '0 .7T 2 0 . 7 3 1 7 . - e i.Z.O') 1 1 . 51 1 1 . 3 0 1 1 . 0 4

6 . 7 6 3 . 1 6

1 . 3 3 : . 3 i 0.3 2 0.60 3 . 4 4 0 .24

- 0 . 2 5 - 0 . 6 7 - 1 . 9 2 - 2 . 2 7 - 2 . 5 3 -5 .311

- 4 4 . 6 3 - 1 2 9 . 0 9 - ' = i 5 . 7 3

• 1 4 3 8 . 2 0

• * T . -•u>«. LOC.

*5 11

2 3

• 4 66

6 63 '.2 '.9 ^9 59

7 " i«

32 ^ • » 14 10 4 | 57 *9 23 *4 13 61 *2 « 4 2 4 12 3 9 15 31 16 6 0 22 * 3 17 38 -.0 21

S

' 3 « 6 17 51 35

5 4

33 1

4 7 9

30 29 5 6 2 9 25 52 50 55 •!6 4*

' I • ; . J R IN. •«» r S T R E S S

i ' ;72 , 161<»,

185. 12, 10 I

< 4

2. 1

0 - 0 , - I . - I , - 2 . - 3 ,

- 7 -*, -«

- 1 0 - 1 2 - 1 3 - 1 5 ,

- 17 -21

-n. - 2 5 , -26 - 2 6 , -29 - 3 1 , - 3 9 - 4 * , - 5 1 - 5 2 - 5 5 - C s

- e l , - 6 0 -« , - 8 1 , - • • ' .

- I C 5 , - 1 6 2 - 1 7 0 , - 1 7 6 - 2 0 5 - 2 1 7 - 2 4 1 - 2 9 0 , - 2 9 5 - 3 0 2 - * 2 2 - 4 1 7

- 1 9 5 7 - 2 1 3 7 - 4 5 2 1 -'^750

. ao , 2 9 . 3 2 .ZZ . 5 3 .-.0 .29 . »2 . ^» .50 , 70

•7 f

,C5 , - l ,15

17 l l » l 43 28 60 36 34 56 44 16 62 63 98 91 36 76 il 52 •5 07 22 38 76 47 38 22 7 i 58 09 19 60 72 94 66 52 "56 67 21 38 65 •3 78 36

,42 •n] 50 - 0

, VI

26 27 11 13 22 16

2 15 21 12 43

37

53 17

i 35 33 18

3 7

29 20 46 40 "•i 34 ; 4 99 51 39 s'O 25 «6 62 23 30 41 42 49 24 10

9 31 63 •>«

47 «4 58 50 45 60

2 61 57 b 4 45 52

«> I

55 19 32 3b

Material Information

Material No. 1 2 3

Material Type Glass Aluminum Sealant

143

Y-*«OR« n« STRESS N<J

3 U 7 . 6 0 2 1 1 7 1 . 0 0 2

9 7 4 . 4 0 2 6 1 6 . 1 7 2 1 5 9 . 6 0 2 1 4 4 . 3 9 2 1 4 2 . 7 6 2 1 3 6 . 1 2 2 6 3 . 3 1 2 3 2 . 4 3 I 2 4 . 5 9 2 1 6 . 5 4 I 1 4 . 2 7 1 1 4 . 3 4 I

1 3 . 1 0 1 1 3 . 0 5 1 1 1 . 1 1 1 1 1 . 0 2 3 1 0 . 5 9 1 1 0 . 2 6 1 1 0 . 1 9 I

9 . 1 7 I 7 . 3 9 3 7 . 2 4 3 6 . 5 9 3 9 . 9 3 3 9 . 7 5 1 4 . 9 4 1 4 . 7 9 3 4 . 0 7 I 3 . 8 6 1 3 . 5 8 1 3 . 1 9 3 2 . 3 2 1 1 . 9 9 2 1 . 5 2 1 1 . 4 8 1 1 . 2 8 1 1 . 0 8 1 3 . 9 7 3 0 . 8 6 1 3 . - . 3 3 3 . 2 0 1 3 . 1 6 I 0 . 0 4 2 3 . 0 1 2

- 0 . 0 3 3 - 0 . 3 1 3 - 0 . 4 1 3 - 0 . 6 3 1 - 1 - 2 9 3 - 2 . 1 9 1 - 2 . 3 3 1 - 3 . 0 6 1 - 3 . 7 0 i - 4 . 7 9 I - 6 , 6 2 2 - 7 . 2 8 1 - 9 . 4 8 1

-13.ao 1 - 1 6 . 2 7 I - 2 0 . 7 7 1 - 3 5 . 1 1 1 - 3 8 . 0 1 1

- 2 S 9 . J 5 : - 7 2 5 . 4 8 2

WffbvrfbKCW

T . N . L O C .

4 4 2 6 3 6 2 7 5 2 3 4 3 2 59 18 3 1 1 1 2 1 2 2 4 2 3 0

6 0

4 1

25 6 6 1 4

5 9

1 3

2 0

4 6

5 1

4 3

1 6

9 6

2 9

6 2

6 9

1 9

1 7

6 1

5 4

5

3 9

4 0

6

2 8

4 7

3 8

1

3

9

5 3

3 3

3 5

3 7

4

1 2

2

2 4

4 8

7

9

1 0

6 4

6 3

2 3

5 7

5 8

5 0

4 9

19 4 5

i i K c u e s i

l-HOHM STRESS

3 6 9 7 . 3 0 1 9 7 0 . 7 0

6 3 7 . 0 0 4 3 2 . 7 4 3 1 4 . 3 4 2 0 4 . 3 7 1 7 9 . 0 1 1 7 8 . 4 8 1 4 1 . 5 6 1 0 6 . 4 1 1 3 0 . 9 8

7 2 . 9 9 5 4 . 9 1 4 9 . 0 0 4 4 . 5 6 4 1 . 4 8 4 0 . 9 6 2 8 . 9 7 2 1 . 7 7 2 0 . 3 6 1 7 . 1 3 1 1 . 7 3 1 0 . 9 1 1 0 . 0 4

8 . 5 3 4 . 8 7 3 . 3 1 2 . 8 6 2 . 5 8 2 . 3 4 2 . 1 0 2 . 0 9 2 . 0 9 1 . 9 2 1 . 6 7 1 . 4 9 1 . 4 1 O.Tr-0 . 4 5 0 . 2 0 0 . 1 4

- 0 . 2 2 - 0 . 2 7 - 0 . 4 6 - 0 . 4 6 - 0 . 6 7 - 2 . 9 6

- 1 0 . 9 3 - 1 1 . 2 2 - 1 1 . 5 9 - 1 2 . 0 9 - 2 0 . 5 2 - 3 1 . 6 6 - 4 4 . 4 0 - 5 1 . 7 0 - 5 6 . 4 9 - 9 7 . 9 4 - 7 3 . 6 0

- 1 0 2 . 7 7 - 1 3 1 . 6 8 - 1 3 8 . 0 7 - 1 6 0 . 8 8 - 2 1 3 . 0 0 - 2 4 7 . 0 6 - 2 8 4 . 2 4 - 7 5 4 . 3 4

kEHARI

H A T .

mm.

2 2 2 1 1 I 1 2 1 1 1

1 I

2

1 1

1 9

2 2

1

2

Q - I I (

L O C .

3 6 2 7 4 4 6 6 6 3 62

1 2 6

4 5

5 9 3

13 16 5 5

2 1

5 8

2 4 4 9 4 9

1 1

5 2

1 0

3 0

4 8

2 9

2 0

4 6

5 1

4 3

2 9

4 2

5 3

5 6 4 1

4 7

1 7

3 9

2 8

3 5

3 3

9

• 0

3 3

3 7

1 2

5 0

5 7

3 1

5 4

1 8

1 9

2 3

2 2

1 5

1 4

6 0

7

6

3

6 1

2

6 4

3 2

6 5

3 4

spi iT spscrs 1 - I T H i ; 1

IMEAR >««T. STRESS MUM. L : C .

1 6 4 . 5 3 1 6 0 . 0 0 1 3 2 . 7 2 1 2 6 . 1 1

3 9 . 4 7 8 4 . 9 0 6 9 . 9 9 6 6 . 4 4

4 5 . 0 2 4 0 . 3 3 39. -"S 3 8 . 4 0 3 7 . 5 7 3 5 . 2 9 3 3 . 6 6 3 1 . 5 9 2 1 . 4 3 1 5 . 0 2 1 1 . 7 3 1 0 . 7 6

. 9 . 7 4 3 . 9 6 8 . 3 0 8 . 1 5 7 . 9 6 7 . 3 2 7 . 4 3 6 . 9 1 2 . 9 5 1 . 3 9 1 . 8 7 1 . 6 1 1 . 5 9 1 . 5 7 1 . 5 0 1 . 3 1 1 . 3 0 1 . 3 0 1 . 2 9 0 . 0 2 0 . 3 7 0 . 3 7 0 . 8 4 3 . 5 0 0 . 3 6 0 . 1 4 0 . 0 3 0 . 0 2 3 . 0 1

- 0 . 9 3 1 - 0 . 9 7 ; - 1 . 0 4 I - 3 . 3 9

- 1 6 . 3 6 1 - 2 1 . 8 4 1 - 2 4 . 2 1 1 - 3 0 . 5 6 ] - 3 0 . 9 9 2 - 4 4 . 5 9 1 - 6 3 . 9 8 1 - 7 1 . 5 1 2 - 9 9 . 7 2 :

- 1 0 0 . 3 5 I - 1 0 9 . 9 7 I - 1 3 9 . 5 8 I - 2 0 6 . 3 6 2

1 ^5 2 ^7 I 57 1 61 1 01 2 - 5 1 59 2 4 4

Z ' 4 23

i 32 2 26

30 I 41 L 13 I 39 : 10 I ? i

L 5 L 50 I I I 3 L 49

1 5

I 54 L 48 L 47 3 2 9 I 22 1 51 » 56 ) 46 3 43 J 25 1 12 J 23 i 17 » 2?

1 a

,> >

I 16 > 33 ! 9 ) 37 I 35

5 3

6

1 8

i 3 1

2 4

4 0

1 4

4 2

19

6 0

6 2

55

1 1

0 ^

53 66 36

' S I " i L A N T " _ :

• A X . » » ; - j . 4 » T ,

3 7 1 3 . C O 2 3 1 3 9 . iO 2 1 9 8 9 . » : 1 1 7 2 . 4 0 2

- 7 4 . 1 7 I 3 5 7 . 6 6 1 22 3 . l o I 1 7 9 . 4 0 1 1 ' 5 . ; 5 2 1 * 3 . « 3 z . 4 ' . . 5 : r l - o . 19 2 1 . ; . ! s, i I •". '5. C i 12 4 . 3 ) I 1 1 ' ' . 14 I l l j . 6 6 7 l ' ' 7 . 3 1 I

7 8 . 4 8 1 7 3 . 0 4 1 7 0 . 7 7 I » 3 . 3 2 2 4 9 . 0 0 I 4 6 . 8 5 4 6 . 2 4 I 4 6 . 1 1 I 4 0 . 3 3 1 3 9 . 2 1 I 3 6 . 1 0 I 3 4 . 5 4 3 3 . 5 6 1 3 2 , 7 0 1 3 0 . 1 2 2 2 2 . 8 1 1 2 2 . 5 6 2 2 . 3 6 1 1 9 . 5 5 2 1 8 . 1 2 1 1 7 . 6 2 I 1 4 . 3 3 1 l l - ' " = 1 1 . , - " ^ 3

' . 77 ? - ' . 7 4 •> T. 15 3 6 . 4 7 1 5 . 7 6 5 . 6 1 J 5 . 2 4 2 4 . 6 7 1 4 . 1 4 ; 3 . 9 4 3 2 . 3 0 : 1 . 6 7 •> 1 . 0 9 1 0 . 9 4 3 3 . 4 o I 1.*Z 3 " ' .3 ' i 3 0 . 2 0 3 - ' . 1 0 2

- O . - O 3 - 0 . 6 3 I - 2 . 3 9 I - 2 . 1 9

- 1 7 . 3 1 2

iJtJS

L C C .

36 44 2 7

••4 ^ t s 1

6 2 I

5 « ••z •«7 34

4 * 9 ^ 8 5 7

11 5

45 J

1 3

1 8

1 6 3 0

6 1

2 1

4 1

4 2 2 4

6 0

6 b 3 1

4 5 4 9

3 9

4 0

1 9

1 -

2 3

2 2

4 9

2 5

2 0 • a 5 1 •»3 7 9 5 6

5 4

1 5

4 7

I T

5 3

2 8 K

3 8

3

1 3

s2 3 5

9

- •7

5 0

7 2

1 9

- ' ! ^<. " ' IN Sf > • - : : :

< ;58 .7 - ' 6 3 5 . 2 3

i r ' . : 6 1 1 . 9 1

= . -3

2 . »3 2 . 3 5 ' . C 2 I . 1 0 1 . 2 3 ' • • »

1 . 7 7 2 . J 3

1 . 0 1 - T . 1 9 - ' . 4 : 5 - - I . 2 9 - 0 . 3 1 - 3 . 32 - " . . 7 -? . 6 4 - ^ . ?9 - I . 19 - I . 7 9 - 2 . 31 - 4 . 8 4 - 6 . 2 5 - 7 . C 4 - 0 . 4 0

- 1 1 . 4 9 - 1 2 . 1 0 - 1 4 . 55 - i 4 . < ; 7 - 1 5 . 2 4 - 2 ^ . 3 0 - 2 1 - 3 5 - 2 3 . 0 9 - ' 1 . 71 -:•' .z^ -2-.it - 31 . J4 - 3 7 . , 3 - 3 - 5 . : 5 -44 , . fc6 - 52 . 79 - 5 2 . 3 0 - 6 3 . 0 8 - 4 * . 3 4 - e « - ? 3 - 7 5 - 2 2 - 7 9 . „

- 1 0 2 . 7 7 - 1 0 4 . 12 - 1 3 2 . 1 5 - 1 4 6 . 3 4 - 1 6 0 . 8 9 - 1 3 I . < 0 - 2 5 0 . i\ - 2 5 3 . 3 4 - i 7-1.15 - ' 5 6 . 3 7 - 7 3 5 . X - 7 5 6 . 15

-3

5 53 1

* 4

35

3^ 52 . 7 12

^ 4s 13 i. * 71 .3 a2 5,

39 40

» ' 30 41

66 5 J 40 22 15 S3 23 14

5i 3

57 2

61 32 - X

19 :; .5 34


Material No.

1 2 3

Material Type

Glass Aluminum Sealant

i

http://-2-.it

144

I - - . ( . . - : : -.f'-.-.i.-) .^Si ScALA.'^r ••OOUUIS

T-.«C3i<« lAl . S T P ( C S 3 ~ M .

3 6 6 J - 9 C X 2 1 9 1 - 7 C Z 2 0 i i 3 . J C w 1755."Ô

2 ^ 1 . 6 1 Z 2 9 1 . 6 0 2

5 4 . 1 6 3 4< l .a5 Z 3 9 . 3 2 1 3 2 . 5 1 1 2 9 . 6 2 I 2 8 . 7 2 3 1 6 - 4 0 I 1 4 . 6 5 1 4 . J 7 3 1 3 . s 3 1 1 2 . 5 1 1 1 1 . 4 7 1 0 - 8 5 I 1 0 . 3 5 1 1 3 - 0 7 1

7 . 7 5 I 8 . 4 1 3 7 . 2 9 3 6 . 4 7 I S . 1 3 I 4 . 6 7 1 3 . 6 4 1 3 . 4 6 1 i . 0 3 1 3 . 0 3 i 2 . 8 4 I 2 - 5 9 3 2 - 5 £ 1 3 - 9 6 J 0 - 3 7 1 3 . 2 7 J

- 0 . 3 7 3 - 2 . 2 5 3 - 2 - 5 1 3 - 2 . 5 7 3 - 2 . 6 5 : - 4 . 2 9 3 - 4 - 3 4 I - 5 . 3 3 I - 9 . 4 5 I - 6 . 7 7 1 - 7 . o 0 1 - 8 . 2 5 1

- 1 0 . » 3 3 - 2 1 . 3 8 I - 2 6 . J 7 i - . 1 . 6 3 I - 4 4 . ^ 6 1 - 4 6 . 1 6 1 - 6 8 . 4 0 1 - 7 8 . 3 5 I

- 3 3 9 . 9 4 2 - 3 4 2 . 3 9 2 - 5 6 1 . 5 2 2 - 3 9 0 . 0 5 2

- 2 1 4 1 . 9 0 2 - 2 2 7 8 . 3 0 Z - 2 4 9 9 . 1 0 X - 7 1 6 6 . 5 0 2 - 7 - 9 O d . 2 0 Z

35

• 3

.. 1 J •J i

•i

1 ^ 1 9

1 3 2 1 I Q

1 7 15

i f

2,4 1

2 .' 5 0 4 t

3 1 - l ; 4 j

2 5

3 J

I 4 0

o S b l

4

'>2 £» 5

3 7

6 6 4 i

3 J 5

3 3

4 0 2 0

;a ^ 3 5 1

1

4 3 4 7

7 b 3

s 4 56 58 57 4-> 5 3 2 4 30 31 32 34 10 27 cb I o 5 2 4 4 i :

: - N w - -4 7 . ^ 4 ^ . .

4 / 7 , . i . :

i : » i i - ' ' - "• lOd 1.4-0 2 l - > r . l , ;

:>il.l'> I -.7-^.3 1 1 2 7 2 . * o 1 1 5 5 . 3 5 :. I 3 a . 7 3 1 1 3 1 . C J 1 1.' 1 . a J 1

7 2 . : - I 5 i . i 7 : 5 5 . ; . 2 3 : . - ' I 4 7 . 0 7 I 3 : . 2 7 I 5 ; . J'/ 1 2 6 . 2 2 I ^r .2< . J 2 0 . 3 5 1 I t . - 4 1 1 2 . 2 9 1 1 3 . J 3 3 1 2 . 4 3 1 i : . j 9 I

7 . 0 J J 5 . 4 1 3 4 . 3 4 J 2 . 7 1 : 3 . 4 i 1 C.I-) j 2 . 1 3 3

- 0 . 3 J i - 1 . 3 0 ; - 1 . 3 7 ; - l . o O 3 - 2 . 3 6 3 - 5 . 0 5 : - 9 . i 4 - T . 6 0

- l i . 5 l - 2 2 - 3 d - 2 4 . 6 4 - 2 6 . 2 7 - 3 1 . 7 3 - 3 4 . 9 2 - 4 1 . J c - 5 ' ; . 3 9 - o 3 . 0 4 - 9 5 . 1 3 - 9 9 . 1 7

- 1 0 6 . 1 2 - 1 2 1 . 5 1 - i d 2 . 1 7 - 2 5 3 . 3 7 - 2 9 1 . 4 1 - 2 9 7 . 3 6 - 4 * 6 . 5 7 - • J O S . 9 5

- 1 3 0 1 - 2 0 - 1 3 8 0 . 3 0 - 2 1 7 9 . e o - i 3 5 7 - 7 0 - 5 0 4 4 . i J - 8 3 1 3 . 1 0

i l .

3 4

J *

3 3 •t 1

4

^ r -J s. 1 -1 a

2 1 7

J .

- 5 1

5 ^ 4 ' ,

3 » • • J

12 3i.

<45 4 1 17

a 2 2 3

3 J .10 j 7

2 5 4v(

33 4 i

3 5 2 3

4 6 - 9

5i .

1 56 3 3

L 39 L JJ

17

i>4

6 0 4 2

I 14 1 5

1 -.7 1 i l l I 50 1 60 I 57 1 5 2 32 2 19 2 13 I t 1 I 2 ^6 2 27 2 - 4 2 IX 2 53 2 IJ Z 3o

SncAP •--*

5 c 4 . 3 , 2 , i i . G 6 i 2 3 7 . 1 3 2 1 5 1 . 5 3 1 1 1 7 . 3 7 1 i O t . 4 2 I I . 2 . 7J 2

7 2 . 3 3 I 'S7.?'. 2 3 2 . ">" 1 5 2 . 7 7 1 r 1 .25 1 ' " . 1 0 1 2 1 . 4 3 I - l . J T I . 7 . 3 5 I i : . i 7 1

5 .0- . I t . J 4 I 5 . I d 1 : . 3 7 1

- 0 . 1 3 3 - C . 3 0 3 - 1 . 3 3 3 - 1 . 4 1 1 - 2 . 0 7 2 - 3 . 1 0 I - 3 . 1 5 3 - 3 . 5 4 J - 3 . 7 6 3 - 4 . 4 5 3 - 4 - 7 6 ]

- 1 1 . 3 4 j - : 6 - i a - 1 7 . 1 9 : - 1 7 . 2 4 3 - 1 7 . 3 4 - 1 7 . 3 3 3 - 1 3 . 7 2 - 1 8 . 7 6 - 1 9 . 9 6 - 2 3 . 5 9 - 2 4 . 0 5 - 2 7 . 0 8 - 3 0 . 9 1 - 3 2 . 3 1 - 3 2 . 3 6 - 3 2 . 6 0 - 3 4 . 6 0 - 4 3 . 3 4 - 6 1 . 4 4 - 9 C - a 3

- 1 0 2 . 9 1 - 1 1 4 . 5 0 - 1 1 8 . 4 4 - 1 4 2 . 8 7 - 1 5 C . 5 7 - 1 9 4 . 0 9 - 1 5 9 . 3 9 - 2 1 1 . 2 7 - 2 1 9 . 3 1 - 3 0 C . 6 4 - 3 0 C . 6 6 - 3 4 9 . 5 8 - 3 5 1 . 5 1 - 3 6 9 . 7 6

T .

•*. . - c .

3o 34.

3.< 57

63 55

0 1 ••4

J"* 2 3 i l I J 21 : 9

22 4 ^ 15 l a

1.9

5 3 35 33 23 4 7

3 7 2 4

12 2 9

1 7 2 u 2 5 3 6 4 3 5o

1 43 \ 51

•«> L 7 L 5

1

L )ti 1 3 1 4 1 . 2 1 2 1 3 L a I 31 I 14 I 60 1 62 2 18 1 a4 1 58 2 10 2 32 2 34 1 60 2 26 2 19 2 53 2 0 2 27 2 52 2 -.5

••AX. P R I h . •* SrsESS Nl

3 7 7 9 . 0 0 c 3 6 6 2 . 5 0 2 2 2 5 3 . 9 0 2 2 C J 1 . 4 0 2 17 .^1 .13 2 1 7 o l . l O 2 0 9 4 . 7 6 1 4 d 0 . 7 1 1 1 2 5 . 3 0 2 2 7 6 . 3 7 1 2 0 1 . 3 9 2 1 6 4 . 0 7 2 . 6 2 . 4 5 149.6'» 1 1 4 3 . d 2 1 1 3 5 . 9 5 1 1 3 2 . 3 9 1 1 0 7 . 7 9 1

-53 .35 1 9 8 . 3 0 1 3 8 . 7 0 1 7 8 . 6 8 1 7 6 . 4 5 I 6 6 . 8 4 1 5 8 . 3 8 1 5 8 . 2 6 1 5 6 . 8 7 1 5 4 . 4 9 3 5 2 . 9 6 1 5 0 . 1 5 1 4 1 . 9 3 1 3 8 . 7 1 1 3 7 . 3 9 I 3 1 . 7 3 1 2 9 . 6 0 I 2 9 . 5 7 3 2 7 . 1 0 1 2 3 . 9 3 1 2 0 . 5 8 1 1 9 . 9 5 1 1 3 . 5 2 3 1 7 . 9 7 1 7 . 3 1 3 1 6 . 1 2 1 5 . 5 8 1 4 . 0 5 : 1 1 . 3 7

9 . 6 5 7 . 7 6 6 . 0 7 5 . 9 6 5 . 6 1 1 . 4 0 0 . 7 6 3 . 3 0

- 0 . 4 2 - 6 . 4 2 - 9 . 1 3

- 4 4 . 2 6 - 9 1 . 8 1

- 5 9 6 . 9 7 - 6 9 0 . 0 8 - 7 7 7 . 2 5

- 1 3 7 9 . 7 0 - 2 1 2 0 . 8 0 - 2 2 5 1 . 9 0

» I . j n . LOC-

54 5 5

4 5 3 4

1 8 9

2 3

5 3 6

5 2 1 9

6 5 6 6 1 3 5 8 1 6

2 1 6 4

6 3 6 2 5 9

7

a 5 7 2 4

2 3 1 2 4 1

6 1 1 4 4 9

6 0 3 1 4 8 1 7 4 2 3 9

4 0 2 2 3 8

1 5

1 4 3 1 2 0 \ 4 a 1 51 3 25 3 5 6 I 1 3 3 7 I 4 1 5 3 29 3 33 3 39 3 2 8 1 4 7 1 30 1 90 2 3 2 2 10 2 27 2 26 2 4 4 2 11 2 3 6

MIN. PRIN. STRESS

2 0 7 4 . 6 0 I S 7 9 . 8 0

2 3 0 . 0 9 3 2 . 9 3 2 8 . 8 3 2 6 . 4 0 2 4 . 0 1 U . 1 8 1 2 . 1 3 4 . 3 7 1 . 3 6 J . 75

- 0 . 8 6 - 0 . 9 0 - 3 . 9 4 - 3 . - ^ - 1 - 5 9 - 5 . 9 3 - 9 . 7 1 - 6 . 2 9 - 8 . 7 1

- 1 0 . 9 8 - U . 8 4 - 1 3 - 0 0 - 1 6 . 6 8 - 1 9 . 2 0 - 2 0 . 6 « - 0 . 2 T - 2 9 . 1 4 - 2 9 . 8 1 - 3 0 . 3 2 - 3 0 . 3 2 - 4 2 . 0 8 - 4 2 . 6 6 - 4 4 . 2 9 - 4 7 . 9 7 - 4 9 . 4 3 - 9 9 . 4 3 - 4 1 . 8 0 - 7 3 . 2 3 - 7 7 . 7 8

-as.u - 9 9 . 2 3 - 1 0 9 . 5 5 - 110 . 76 - 1 1 4 . 3 4 - 1 2 4 . 2 8 - 1 2 6 . 8 3 - 1 3 1 . 2 6 - 1 4 1 . 7 3 - 1 7 2 . 3 8 - 1 9 0 . 9 7 - 2 8 6 . 9 9 - 2 8 9 . 8 6 - 3 5 3 . 0 2 - 3 6 8 . 3 9 - 4 3 1 . 3 0 - 4 4 7 . 3 6

- 1 3 0 1 . 2 0 - 2 1 7 4 . 6 0 - 2 3 9 1 . 4 0 - 2 3 0 9 . 6 0 - 5 0 4 8 . 6 0 - 7 1 6 7 . 3 0 - 7 9 6 7 . 2 0 - 8 8 9 9 . 9 0

KAT.

2 2

2 1 1

1 3 3 1 3

3 3 1

3 3

3 3

; 3

2 I 1 1 1 3 3 3 I 3 1

1 1 1 I

1 1 1 1

I I 1

1 1 I I

1 I 1

1 1 1 1 2 I 2 2 2 1 2 2 2 2 2 2 2 2

toe 5 4

5 9 9

1 3

1 6

2 1 1 2 1 7

2

2 0 3 7

2 5 6

3 9 3 3 2 9 3 8

3 2 9

4 5 4 8

7 4 0

3 4 ) 4 6 9 1 3 9

5 6 4 1

2 2 5 9 4 9 1 9

2 4 4 2

2 3 4 7

1 4 6 2 3 0 5 0 3 1 6 1 5 8

6 3 5

6 0

6 4 6 9 6 6 97 18

34 19 32

1 2 7 26 53 52 10 4 4 11 36


Material No. 1 2 3

Material Type


145

OROEREO STRESSES SCENARIO-I I (SCLIO SPACERI M I T H 150 " S I SEALA.IT <«0ULUS

T-NORM l A T . STRESS mjN.

1 4 7 8 . 4 0 2 1 4 1 3 . 9 0 2

7 8 6 . 4 0 2 6 3 0 . 4 2 2 4 6 3 . 1 8 2 3 9 * . 2 7 2 a a . 9 3 2 U 0 . 7 1 2 2 1 0 . 9 6 2 2 1 0 . 9 3 2 1 7 8 . 7 0 2 1 0 3 . 8 3 2

7 3 . 9 1 I 3 2 . 1 0 3 3 1 . 1 6 I 2 1 . 7 6 1 2 1 . 3 9 3 2 0 . 2 4 3 2 0 . 2 0 I 1 7 . 9 2 1 1 6 . 9 3 1 1 4 . 4 4 1 1 4 . 2 1 1 1 4 . 0 6 3 1 3 . 5 3 3 1 1 . 4 * 1 1 0 . 9 1 1 1 0 . 4 9 1

9 . 1 9 1 8 . 9 3 1 8 . 1 8 1 8 . 0 1 1 7 . 7 2 3 7 . 3 9 3 7 . 1 6 1 3 . 9 9 1 3 . 6 4 1 1 . 7 4 3 1 . 6 2 1 1 . 0 9 1 0 . 5 8 1

- 0 . 0 8 1 - 0 . 1 9 1 - 0 . 2 9 3 - 9 . 3 7 3 - 0 . 3 8 3 - 0 . 5 1 I - 0 . 9 1 1 - 0 . 9 6 3 - 0 . 5 7 3 - 0 . 7 6 3 - 1 . 3 0 I - 1 . 4 7 I - 1 . 7 3 1 - 1 . 8 3 I - 1 . 9 4 1 - 2 . 0 3 I - 4 . 6 7 1 - 4 . 9 6 I - 7 . 7 2 1

- 1 0 . 8 2 I - 1 7 . 7 0 1 - 7 7 . 4 1 2

- 3 2 7 . 6 2 2 - 4 3 0 . 3 0 2

- 1 9 3 6 . 1 0 2

L K .

V4 11 3 6 10 5 2 2 7 32 3 6 5 3

9 5 4 19 3 1 5 6 3 0 5 0 91 12 1 6 66 13 1 4 4 2 17 4 6 2 2 4 9 4 1 6 0 19 2 1 2 6 2 0 4 3 9 7 6 4

8 2 5

6 4 0 3 9

2 9 9 2 8 3 9 3 3

3 4 7 2 9 3 8 3 7 6 2

I 6 9

4 6 3

9 7

61 4 8 9 8 2 3 26 18 4 5 55

l-HOtm 9 AT. STRESS NUM.

2 4 7 3 - 8 0 2 1 9 6 7 . 4 0 2 1 0 8 9 . 9 0 1

7 9 0 . 8 1 I 9 0 2 . 9 7 1 4 8 2 . 3 3 2 2 8 9 . 3 7 2 2 3 2 . 9 9 2 2 2 2 . 3 0 I 2 1 2 . 8 8 2 1 4 9 . 3 6 1 1 3 8 . 3 9 1 3 2 . 3 4 I 1 3 0 . 1 6 I 1 2 2 . 4 1 1 1 0 8 . 2 9 1

8 3 . 3 6 I 6 2 . 5 8 1 5 3 . 1 8 1 4 4 . 0 2 2 4 3 . 4 1 2 2 7 . 3 7 1 2 6 . 0 9 I 2 1 . 8 9 2 1 9 . 1 3 2 1 4 . 1 9 3

9 . 2 6 3 9 . 0 2 3 7 . 2 8 1 7 . 2 8 1 6 . 3 2 3 6 . 2 9 1 9 . 7 3 3 3 . 4 7 3 3 . 0 1 3 2 . 1 9 1 0 . 7 0 3 0 . 2 1 3 0 . 1 3 1

- 0 . 0 1 3 - 0 . 0 9 3 - 0 . 2 3 3 - 0 . 7 6 1 - 1 . 1 5 3 - 1 . 2 9 1 - 1 . 9 2 3 - 7 . 9 2 2

- 2 9 . 4 3 1 - 2 6 . 9 0 1 - 3 0 . 6 7 2 - 6 8 . 1 1 - 9 7 . 8 8 1

- 1 2 2 . 3 0 I - 1 3 9 . 9 9 1 - 1 3 6 . 9 9 1 - 1 3 8 . 1 1 I - 1 3 8 . 7 6 1 - 1 3 9 . 4 0 1 - 1 6 9 . 9 6 1 - 4 2 6 . 9 8 1 - 4 7 2 . 8 6 2 - 4 9 1 . 9 8 2 - 4 9 9 . 9 1 2 - 5 9 0 . 5 2 2 - 6 7 9 . 9 7 1 - 9 2 8 . 9 8 I

LOC.

3 6 10 66 63 62 2 7 11 53 59 4 4

I 4 5 3

13 16 21 58 2 4 18 19 30 4 9 2 6 32 56 91 12 4 8 4 7 17 42 4 6 20 4 3 3 9 2 9 35 41 28 33 29 40 3 7 50 38 4 9 57 31 52 23 22 19 14

2 3 6 7

6 0 61 59

? 94 34 64 69

SHEAR i T ' E S S

2 2 9 . 6 7 1 3 1 . 3 2 1 0 0 . 9 0

8 9 . 9 0 6 4 . 2 3 5 9 . 0 1 5 2 . 7 3 5 2 . 5 7 5 2 . 5 6 5 0 . 8 1 4 9 . 3 0 4 4 . 2 1 4 2 . 7 6 4 2 . 1 9 4 2 . 1 2 4 1 . 4 2 3 9 . 5 6 3 7 . 4 7 3 3 . 4 4 3 3 - 0 9 3 1 . 3 1 2 7 - 4 4 2 9 . 8 9 2 3 . 1 8 2 1 . 3 1 1 9 . 2 4 1 9 . 2 4 1 7 . 2 9 1 2 . 8 3 1 1 . 3 2 1 0 . 5 8 1 0 . 2 1

9 . 2 1 5 . 8 2 4 . 5 0 4 . 1 3 3 . 7 7 3 . 6 7 3 . 4 4 3 . 2 9 2 . 6 7 2 . 4 5 1 .68 1 .47 0 . 4 8 0 . 4 6 0 . 4 4 0 .4O 0 . 3 7 0 . 0 7

- 0 . 0 2 - 0 . 0 9 - 0 . 0 6 - 3 . 3 9 - 3 . 5 9 - 9 . 2 9 - 7 - 3 1 - 8 - 9 1

- 1 1 . 2 8 - 1 4 . 1 3 - 2 2 . 4 6 - 2 9 . 8 4 - 3 0 . 7 4 - 9 1 . 6 3

- 1 7 6 . 5 2 - 3 2 8 . 4 0

HAT. NUn.

2 2 2 1 1 1 2 2 2 1 2 2 I I 2 2 1 I 2 1 1 I I 1 1 I 1 I I I 1 1. 1 1 I I 3 i

3 3 1 3 1 I 3 3 3 3 3 3 3 3 3 1 I I I 2 1 2

1 t

2 2 2

4 4

45 54 66 64 62 13 53

a 30 27 26 60 23 34 32 13 57 52 41 59 49 21 31 39 61 58 19 22 47 16 63

7 9 1 3

43 46 51 56 50 38 24 48 17 12 20 25 37 33 28 35 29

4

6 3

19 65 11 40 14 42 13 36 55

<UX. PRIN. >TC»SSS

2 4 9 2 . 0 0 1 0 7 2 . 4 0 1 5 1 8 . 8 0 1 4 1 4 . 1 3 1 0 9 2 . 7 0

• " ' 0 . 9 4 5 0 8 . 9 1 . 9 9 . 3 2 4 6 5 . 4 3 2 7 5 . 4 9 2 2 6 . 3 2 2 1 9 . 4 9 2 1 4 . 4 4 2 1 3 . 3 3 1 9 3 . 3 0 1 4 5 . 4 9 1 3 8 . ' . 3 1 3 5 . 5 6 1 3 2 . 7 9 1 3 0 . 5 8 1 0 9 . 5 0 1 0 5 . 1 1

91 .3-5 8 0 . 2 0 7 9 . 9 9 6 7 . 3 1 5 3 . 2 5 5 1 . 3 6 4 6 . 9 " 4 1 . 2 3 3 8 . 7 8 3 8 . 7 2 3 2 . 6 8 3 1 . 7 3 2 9 . 5 3 2 2 . 6 8 2 2 . 6 3 2 2 - 2 6 2 2 . 0 7 2 0 . 2 6 1 9 . 7 9 1 9 . 8 7 1 5 . 3 6 1 4 . 9 9 1 4 . 0 9 1 2 . ' ' 4 1 1 . 1 '

•5 , -3 3 . 5 4 7 . 7 7 7 . 4 3 6 . 2 4 I . a a 1 . 8 2 1 . 4 5 0 . 2 2 0 . 0 1

- 0 . 0 0 - 0 . 0 3 - 0 . 2 2 - 0 . 3 9 - 0 . 5 4 - 1 . 5 9 - 4 . 0 9 - 4 . 1 7

- 3 7 9 . 6 0

8 AT a

«UM. LOC.

2 36 2 10 2 4 4 2 11 I 66 I 6 3 I 62 2 ?7 2 52 2 53 I 59 2 32 ? 9 2 34 2 54 1 1 I , I 13 I 5 I 9 1 16 2 19 1 21 1 30 I 31 1 58 1 ? 4 2 18 I 4 9 I 42 I 41 2 26 3 56

5 7 2 4 5 I 39 I 4C 3 51 t ^0 3 12 1 14 1 60 I »7 3 - 6 3 17 I 22 I 15 1 a , 3 43 3 20 1 4 8 1 23 3 25 I 6 •» 38 3 19 ^ 2 3 28 3 33 3 29 1 3 3 37 1 65 I 61 1 7 2 »5

" I - . . >3 ; • „ 4 » T .

STRESS *»LH.

7 4 C . 1 3 2 6 2 5 . 4 5 2 3 3 9 . 2 7 2 2 99 . 19 2 172 . 49 2 1 6 7 . 9 9

4 2 . 1 2 2 18 . 9 4 I 1 3 . 5 6 3 11 .C6 1 1 0 . 5 7 2

3.JO 3 8 . "'4 3 7 . 9 5 1 6 . 2 9 3 ' • . 2 7 •< 3 . 42 > 3 . 3 8 I 3 . 2 2 I 0 . d4 3 0 . 5 6 3 C . 1 5 I

- 0 . 2 9 3 - 0 . 3 7 3 - 0 . 3 9 3 - 0 . 5 7 3 - 1 . 3 7 3 - 1 . 5 5 I - 1 . 6 1 I - 1 . 9 1 1 - 2 . 0 7 1 - 2 . 2 9 I - 3 . 5 3 3 - 4 . 4 7 1 - 7 . 2 3 1 - 7 . 3 6 I - f . 5 9 i - 0 . 9 9 I

- 1 9 . 5 5 1 - 1 9 . 9 6 I - 2 0 . 7 7 I - 2 1 . 4 7 I - 2 2 . 3 4 1 - 29 . 1 4 1 - 3 1 . y * - 3 2 . 9 2 2 - 5 0 . 0 3 1 - 9 2 . :5 I - 9 4 . 2 4 2 - 9 6 . 3 6 1

- 1 2 4 . 5 4 I - 1 3 7 . 0 5 I - 1 3 8 . 2 3 I - 1 3 8 - 9 6 I - 1 J 9 . 9 C I - 1 4 0 . 0 0 I - I Tr . ft* - 3 3 4 . 9 6 2 - 4 2 7 . 8 6 - 4 6 7 . , 0 2 - 4 9 5 . 3 0 2 - 5 1 4 . - 9 2 - 5 5 2 . 3 4 : - 6 8 5 . 5« 1 - • 5 2 8 , 7 1 1

- 1 6 2 O . - 0 2

sOC.

3a 10 27 1 '

«»,« 53 1-5 l o 56 6 6

32 12 51 2 -17 4 6

20 13

3

4 i 25 21 23 !5 33 29 37 50

1 4

4 3 5

38 59 62 48 . 7 4 4

5^ 3"! 42 30 , 3 ••I 3 1 52 57 ' 3 26 22 15

2 3 6 7

14 60 IS a l . 5

3

5'. 34 64 a5 55


Material No.

1 2 3

Material Type


146

Y-««ORN MA STRESS NJ

2 2 4 9 . 6 0 2 2 2 0 0 . 6 0 2

7 9 1 . 3 3 2 7 0 7 - 3 4 2 4 9 4 . 4 6 2 1 6 4 . 9 6 2

4 0 . 3 9 1 3 6 . 4 6 1 3 3 . 0 3 1 2 9 . 2 1 1 2 9 . 6 8 1 2 2 . 3 8 1 2 0 . 8 7 2 1 9 . 4 9 2 1 9 . 5 9 1 1 1 . 3 3 I 1 1 . 3 4 1

7 . o 9 1 7 . 5 4 i 7 . 4 3 1 5 . 9 9 1 5 . 5 7 I 3 . 9 5 1 1 . 6 3 3 1 . 4 7 0 . 6 8 1 3 . 6 3 9 . 9 0 0 . 3 9

- 0 . 3 8 - 0 . 5 9 - 2 . 0 9 - 2 . 7 1 - 2 . 7 9 - 3 . 5 7 - 3 . 9 6 - 4 . 4 8 - 9 . 1 0 - 6 . 0 6 - 6 . 2 5 - 8 . 1 1 - 8 . 7 9 - 8 . 8 8 - 9 . 3 8

- 1 1 . 6 1 - 1 3 . 3 9 - 1 7 . 3 4 - 1 8 . 1 4 - 2 2 . 0 9 - 2 4 . 9 8 - 2 7 . 6 7 - 3 0 . 7 9 - i O . 8 4 - 3 2 . 7 2 - 3 9 . 3 9 - 3 7 . 8 0 - 4 0 . 9 6 - 4 8 . 5 2 - 9 9 . 9 3 - 9 5 . 7 7

- 2 1 7 . 5 0 - 2 1 7 . 5 1 - 4 9 7 . 3 0 - 6 6 7 . 7 2 - 9 0 0 . 3 8

- 2 4 9 0 . 7 0

JRDERED

f.

N . L O C .

1 1

4 4

2 6

9 2

3 6

2 7

2 3

9 8

2 4

9 7

4 8

4 7

3 4

3 2

4 9

7

9 0

2

1

4

9

6 1

6 2

2 9

1 2 8 6 9

1 3 3 I 6 3 ) 3 9 » 3 7 I 3 L 6 4 ) 3 8 L 3 0 I 6 > 2 9 L 4 0 3 4 3 ) 4 6 1 3 9 1 6 6 3 5 1 I 9 3 2 0 3 5 6 1 5 9 1 6 0 3 1 7 1 15 1 4 1 I 4 2 1 2 2 3 12 1 2 1 I 13 I 1 6 1 14 2 1 9 1 3 1 2 1 0 2 53 2 9 2 18 2 4 9 2 5 4 2 5 9

STRESSES SCEN

Z - N C R N 9 STRESS «1U

2 3 1 3 . 0 0 2 8 8 9 . 8 8 2 7 7 6 . 7 7 2 7 1 1 . 9 8 1 6 9 2 . 2 3 2 5 8 8 . 9 6 1 5 8 7 . 4 9 I 4 9 1 . 0 1 2 4 6 9 . 0 0 I 4 3 9 . 4 5 I 3 4 6 . 1 9 1 2 9 6 . 4 4 I 2 7 0 . 4 9 2 2 6 7 . 7 8 I 2 2 0 . 5 4 1 1 9 4 . 8 8 2 1 5 9 . 9 6 I 1 5 8 . 8 8 1

9 0 . 6 6 1 9 7 . 4 3 2 3 9 . 5 3 J 7 8 . 3 3 t 7 4 . 9 2 2 4 8 . 2 0 1 2 6 . 2 1 2 4 . 0 9 1 0 . 9 6 1

2 . 3 2 1 . 0 6 : 0 . 6 0 0 . 1 6

- 0 . 0 9 - 0 . 7 9 - 1 . 1 0 - 1 . 4 6 - 1 . 5 5 - 1 . 6 8 - 1 - 7 6 - 2 . 8 7 - 2 . 9 1 - 4 . 2 3 - 4 . 3 6 - 7 . 6 8 - ? . 1 8

- 1 3 . 5 5 - 1 3 - 6 5 - 1 5 - 0 4 - 2 6 - 4 7 - 2 9 . 3 7 - 4 1 . 9 7 , - 9 4 . 8 1

- 1 0 9 . 8 9 - 1 7 4 . 6 0 - 2 0 3 . 7 0 - 2 3 3 . 5 7 - 2 7 6 . S 9 - 3 0 5 . 6 9 - 3 9 3 . 3 8 - 3 8 9 . 4 8 - 4 0 0 - 5 3 - 4 5 6 . 5 4 - 4 8 5 . 6 3 - 5 3 3 . 2 1 - 5 6 2 . 5 8 - 6 6 3 . 7 1

- 3 0 8 3 . 3 0

A R I O - i l l

A T .

M . L K .

3 6

1 0

5 3

2

1 1

6 9

3

4 4

6

6 4

7

6 1

2 6 1 4

1 9

2 7

6 0

2 2

2 3

3 2

1 8

5 7

1 9

5 0

4 7

L 3 1 4 2

L 3 9 1 2 9 ) 2 8 i 3 5 ) 33 L 4 0 J 37 } 4 3 3 25 ] 4 6 3 3 8 5 5 1 I 4 1 3 2 0 3 5 6 I 4 8 3 17 2 45 3 12 I 4 9 1 3 0 I 58 2 52 1 59 I 2 4 1 2 1 1 6 2 1 16 1 13 I 63 1 9 2 9 1 6 6

5 2 55 2 34 1 4

I 2 5 4

( S O L I D SPACER) •

SHEAR « * T . STRESS NUM.

3 0 4 . 0 4 2 1 6 8 . 9 8 2 1 2 1 . 7 1 2

8 8 . 9 5 2 3 8 . 9 4 2 8 8 . 7 0 2 3 8 . 2 7 1 3 3 . 9 5 I 9 0 . 0 9 2 7 2 . 4 8 I 6 7 . 2 6 2 5 8 . 0 9 1 4 0 . 3 5 2 3 9 . 5 4 2 3 1 . 7 3 I 1 6 . 9 1 1 1 2 . 6 3 2

9 . 1 0 1 6 . 7 5 I 6 . 3 9 I 5 . 5 1 1 5 . 2 8 3 5 . 2 7 3 5 . 0 2 3 4 . 6 4 3 3 . 5 0 I 2 . 6 9 3 2 . 1 3 1 1 . 7 2 3 1 . 6 1 3 1 . 5 1 3 1 . 2 3 3 1 . 0 1 3 0 . 6 7 3 0 . 5 9 3 0 . 2 7 3 0 . 1 3 3 0 . 0 9 I

- 1 . 3 1 1 - 3 - 9 6 - 4 . 6 9 I

- 1 6 . 7 3 1 - 1 7 . 7 2 1 - 2 6 . 9 0 1 - 2 7 . 6 6 I - 2 8 . 7 0 1 - 3 1 . 1 3 1 - 3 2 - 1 0 1 - 3 3 . 4 1 1 - 3 5 - 0 9 I - 3 7 . 2 7 1 - 3 8 . 8 1 - 4 0 . 0 4 1 - 4 0 . 2 5 1 - 4 8 . 3 9 2 - 5 0 . 8 1 I - 5 4 . 6 9 1 - 9 9 . 3 3 - 9 3 - 4 6 I - 9 9 - 7 4 1 - 9 0 . 0 7 2

- 1 1 7 . 0 2 1 - 1 2 0 - 5 5 1 - 1 2 4 . 7 4 1 - 1 7 2 . 1 8 2 - 3 2 4 . 0 3 2

I ' M 15C

LOC.

5 5 •»r

5 2 «3

1

1 9

5 8

4 2

4 5

14

10

4 0

2 4

3 2 2 4

3 1

1 9

5 0

3

6 0

4 8

5 1

5 6

4 6

4 3

6 2

3 9

6

2 9 2 9

2 0

1 7

1 2 3 7

2 3

3 3

3 5 k

6 6

2 6 4

4 7

1 6

1 « 4

6 3

3

35

5

2 2

3 l U

7

50 36

15 30 20 41 26 57 13 22 54 44

' S : S E i L i ^

- A X . R R t S . S T P E s :

2 3 1 6 . 3 0 2 2 5 0 . 9 0 2 2 5 9 . 5 0

1 9 4 . 4 5 7 9 4 . 6 6 76 7 . 6 5 72 6 . 6 1 7 1 2 . 0 ' ' 5 9 0 . 7 0 5 6 9 . 1 , 4 e 5 . 3 1 4 ' O . J l 3 5 0 . 9 2 3 4 0 . 5 6 •> 0 1 . 1 4

2 5 3 . o « 2 3 2 . 2 - 5 l<?2-75 1 7 3 . 3 4 1 6 9 . 17 1 6 0 . 1 ' ! 1 2 1 . 2 6 1 0 5 . 5 3

9 7 . 7 9 a 5 . 8 i 7 7 . 7 9 7 6 . 4 7 6 9 . 6 7 5 7 . 5 2 5 5 . 4 9 5 0 - 3 3 4 1 . 1 4 3 9 . 9 3 3 1 . 0 7 2 ' . 1 8 2 6 . 5 ' 2 3 . 8 0 1 4 . 5 6

1..5 2 9 . 3 5 7 . 4 - ' 4 . 0 ! 3 . I d 3 . 1 7 2 . 9 3 1 . 7 7 1 . 7 1 t . i l 0 . 7 -0 . 5 0 0 . 4 2 0 . 2 3 3 . 0 2

- 0 . 6 5 - 1 . 5 9 - 3 . 8 1 - ' . 3 0 - 9 . 0 3 - 3 . 1 -- 3 . 7 5

- 1 3 . 5 0 - I 0 . 4 O - 3 6 . 2 0

- 1 " ^ . 7-5 - 4 , 0 . 5 4 - • 3 8 6 . 8 9

T rC-O'JLJS

- A T . • .uw. L O C .

2 3 6 2 44 2 l l 2 10 2 53 2 7 6 2 5 2 1 2 I 6 5 1 3 1 6 1 6 4 1 7 2 27 I 6 1 1 1 4 I 15 1 73 I 5 7 I 2 2 1 6 0 2 19

3 2

1 5 8 2 18 I 42 I 4 1 I 30 I 39 1 4 0 1 5 0 I 4 7 I 24 1 -.I 1 3 1 I 48 2 3 4 I 13 1 I 1 5 I ••

4 2

1 5 9 6 3

: 2 0 3 29 3 4 3 3 4 6 1 33 3 39 3 35 3 - 1 3 3 7 -< ' 5 3 5 6 3 20 2 4 5 3 17 1 6 6 1 3 3 12 I 2 1 1 16 2 9 2 55 ? r 4

• < I S . P f l N . : r 9 £ : s

6 5 1 , 2 9 4 9 3 . 1 8 431 . 3 ; 2 5 4 . i 3

1 0 . 2 » ^ . 2 2 7 . 6 7 T . 4 6 ' . t o '. . M 1 . 3 7 0 . 3 0 3 . 1 0

-" - . '-- 0 . 2 9 -1 .06 , - ! . 5 0 - 2 . 1 4 - 7 . 2 4 -3 ,5<> - . , ^ 6 — , 5 7 - 9 . 2 6 - ^ . 5 6 - 9 . 3 9 - 9 . 7 9

- 1 1 . " 5 - 1 4 . 39 - 1 7 . 5 6 - 1 9 . 2 9 - 3 C . 7 0 - 3 2 , 0 1 - 3 3 , 3 5 - 3 - . 03 - 5 7 . 1 3 - 5 0 . 0 1 - • > 1 . 75 - 6 1 . 2 4 - 6 1 . 4 5 - 6 1 . T4 - 6 5 . 7 0 - * 3 . "-a -•44 . «0 - 0 4 . it. - 9 J . 9 3

- I X . 3 4 - 1 34 . 36 - U l . 3 4 - 1 1 ; . 79 - 1 9 C . ^ - 2 0 - < . 76 - 7 2« . 3 9 - Z ' ^ . 16 - 3 OP . 36 - 3 2 6 . 30 - 3 5 3 . 5 1 - 4 0 0 . 5 3 - 4 2 ' . 2 ! - 4 5 8 . ,4 - 4 9 7 . 5 7 - 5 3 ' . . 14 - 5 6 2 .3(1 - a 6 » . 73 - 4 77 . •»-;

- ' 5 - , ' . r. - ' 0 9 t . •'0

" A T . t o * .

~ L

Z

2

2

I 1

1

I

2

1 1

7

1

3

I

3

1

I

1

3

3

3

I

3 1

7

3

I T

'' I

1

I

I

I

1

2

1

• '• I

I

2

1

2

' • I

• 1

; I I I 2

1 2 ? 2

L d C .

1 1

3 6

* 2 i 2 7

5 C 2

4 7 7

3 2

e l

2 3 3 5

3 3

2 ' '

1 5

2 7 a 4

3

e

2 5

3 3

, 3

4 8

• 4 2 0

5 1

in

6 U

1 7

1 2 k 9

1 5 ^ 7

; 4 3 1

- 0

€ ,

3 9

2 3

5 ' 5 *

- ?

10 3 0

;o - I

5 0

c*-^ 1

62 5 3 1'» t o 13

3 6 6

9 5

n 34

4 1

3".


Material No.

1 2 3

Material Type


147

3R0ERED STRESSES SCENARIO-IV (SOLID SPACER! « ITH 150 RSI SEALANT -OOULUS

Y-NORM MA STRESS NU

1 1 6 9 1 . 0 0 2 1 0 8 4 9 . 0 0 2

3 6 S 9 . 6 0 2 3 4 8 0 . 8 0 2 2 9 » 9 . 6 0 2 1 3 6 8 . 3 0 7

9 4 6 . 6 9 2 5 3 9 . 4 8 2 5 3 9 . 0 8 2 U 2 . 4 9 I 1 0 8 . 0 7 1

3 9 . 3 2 1 4 8 . 5 7 I 3 8 . 6 4 I 3 1 . 5 1 1 2 3 . 3 9 1 2 3 . 2 4 1 2 2 . 0 8 1 2 1 . 9 1 3 1 7 . 1 4 1 1 6 . 7 4 1 1 9 . 8 5 3

3 . 3 7 1 7 . 2 9 1 6 . 1 1 3 5 . 5 2 3 . 9 6 3 . 8 9 3 . 8 2 3 . 6 6 3 . 6 9 3 . 3 1

- 9 . 2 9 - 0 . 3 6 - 1 - 5 7 - 3 . 6 8 - 3 . 9 2 - 4 . 4 9 - 6 . 6 7 - 7 . 4 0 - 9 . 4 3

- 1 3 . 6 8 - 1 0 . 8 8 - 1 1 . 3 6 - 1 1 . 7 7 - 1 5 . 2 9 - 1 6 . 7 8 - 1 9 . 8 8 - 2 0 . 3 3 - 2 4 . 3 1 - 2 4 . 9 5 - 3 3 . 9 9 - 3 1 . 1 0 - 3 3 . 2 5 - 3 8 . 7 4 - 4 0 . 5 1 - 4 9 . 5 8 - 6 0 . 5 1 - 7 2 . 3 4 - 7 4 . 4 6

- 3 9 0 . 0 8 - 3 8 0 . C 9

- 2 6 0 2 . 5 0 - 2 9 9 1 . 9 0 - 3 2 9 9 . 8 0

- 1 2 8 1 9 . 0 0

T . N . L X .

1 1 4 4 5 2 3 6 26 2 T 1 0 3 4 32 3 1 3 0 2 4 5 7 5 8 4 7 4 8 5 0 4 9 5 6 2 3

7 1 5 1

6 6 3

) 4 6 L 6 2 ) 2 8 L 6 1 1 2 9 1 8 i 33 L 6 5 J 3 5 i 4 3 I 6 4 J 3 7 I 6 3 I 4 s 6 I 5 I 4 0 3 38 1 6 0 1 1 3 25 I 5 9 1 3 9 3 2 0 I 2 1 4 1 1 4 2 I 2 2 2 19 I 15 3 17 1 1 4 I 1 6 I 2 1 I 13 1 1 2 2 5 3 2 9 2 1 8 2 5 4 2 4 9 2 55

2 -NCRM « STRESS Û

1 3 4 3 0 . 0 0 2 7 6 6 7 . 2 0 2 3 4 5 5 . 7 0 2 3 1 8 7 . 2 0 2 2 1 0 0 . 0 0 2 1 9 3 2 . 3 0 2 1 1 9 4 . 3 0 2

9 1 6 . 8 4 1 6 0 7 . 9 1 1 4 1 6 . 5 7 2 3 7 5 . 7 0 2 3 5 5 . 8 1 1 3 0 7 . 6 6 1 2 9 2 . 0 7 2 2 3 7 . 2 4 1 1 6 2 . 6 6 1 1 3 1 . 5 0 1 1 2 8 . 7 0 1 1 2 3 . 2 0 I

9 1 . 4 0 1 4 8 . 1 3 1 4 7 . 8 0 1 4 6 . 9 3 I 3 3 . 7 7 1 3 2 . 3 8 ] 1 8 . 6 7 1 1 4 . 1 7 1 1 3 . 7 0 1 1 3 . 4 2 1 1 0 . 3 0 3

6 . 0 3 3 3 . 7 8 3 2 . 7 6 1 . 9 7 1 . 2 7 0 . 6 2

- 0 . 2 8 - 4 . 9 6 - 9 . 0 7 - 7 . 1 1 - 9 . 5 9

- 1 1 - 0 6 - 1 7 . 5 8 - 1 7 . 6 3 - 2 7 . 2 5 - 3 2 . 3 7 - 3 3 . 3 1 - 3 6 . 8 9 - 4 1 . 9 6 - 4 2 . 1 2 - 9 8 . 6 3 - 6 7 . 3 0 - 7 9 . 3 4 - 9 9 . 1 6

- 1 1 6 . 8 9 - 1 3 6 . 6 1 - 1 4 3 . 8 1 - 1 4 8 . 4 1 - 2 2 9 . 8 0 - 3 6 9 . 5 8 - 6 3 5 . 7 2 - 8 9 7 . 7 1

- 2 5 5 1 . 4 0 - 7 « 3 8 . 1 0 - 3 0 3 7 . 6 0

- 1 2 7 9 7 . 0 9

A T . M . L C C .

3 6 10 53 11 4 4 .

2 7 2 6

1 4

18 1 9 6 6

5 3 2 63 5 7 50 6 0 6 2 4 7 4 2 15 14 6 1 3 0 2 2 3 9 5 9

a t 5 6 ) 91 1 4 6 1 2 9 ) 28 ) 35 i 43 3 33 I 4 0 3 25 5 3 7 ; 2 0 3 38 3 17 1 4 1 1 2 3 1 4 a 1 12 1 3 1 I 58 I 4 9 1 6 4 1 24 2 4 5 1 7 1 2 1 1 13 1 16 1 65 2 32 1 6 1 3 1 2 7 9 2 55 2 34 2 54

SHEAR STRESS

5 6 6 . 0 8 5 6 5 . 1 7 5 1 9 . 1 0 4 4 6 . 4 8 4 4 6 . 4 7 3 1 6 . 0 4 2 3 4 . 1 6 2 2 8 . 9 7 1 9 4 . 7 9 1 6 7 . 1 6 1 5 9 . 3 4 1 1 3 . 3 3 1 0 1 . 2 3

9 5 . 0 0 9 5 . 0 0 6 2 . 3 6 6 0 . 5 2 5 6 . 4 2 5 6 . 2 3 5 1 . 3 3 5 0 - 0 9 3 8 . 9 1 3 4 . 3 9 2 9 . 1 4 2 8 . 1 3 2 8 . 0 9 2 6 . 2 0 2 6 . 2 0 2 5 . 8 0 2 5 . 6 9 2 2 . 0 4 2 1 . 7 1 2 1 . 5 9 1 6 . 2 1 1 3 . 5 9

9 . 2 3 7 . 0 8 6 . 5 7 6 . 2 0 5 . 5 6 5 . 3 1 4 . e 9 3 . 0 8 2 - 0 5 1 . 1 8 0 . 3 8 0 . 2 8

- 3 . 4 8 - C . 0 3 - 6 . 1 0

- 1 0 . 4 1 - 1 0 . 4 4 - 2 2 . 0 3 - 2 4 . 5 9 - 2 5 . 1 2 - 2 9 . 1 2 - 5 8 . 8 9 - 7 3 . 0 6 - 7 6 . 4 2 - 9 0 . 4 8 - 9 9 . 6 7

- 1 2 1 . 4 7 - 1 9 7 . 0 9 - 3 4 7 . 6 8 - 6 2 5 . 5 5 - 7 0 5 . 9 2

- * 7 . .•4JM.

7

2 7

2 7

2 2 7

2 2 2 I I 1 1 1 1 1 1 I I 1 1 1 I 1 3 3 3 3 I 1 I 3 1 1 1 3 I

, 3 3 1 3 3 3 1 3 I I I 1 I I 1 1 1 I

I i

2

L 3 C .

45 27 52 93

9 19 34 32 26 10 18 14 58 31 42

3 24

6 4

-.0 2

60 62 66

I 64 51 46 5a 43 50

3 5

38 7

16 25 20 30 17 29 12 37 28 33 63 35 65 48 61 59 47 22 21 ' . 0

15 39 59 i : 57 41

-44 54 36 11

« » X . R R I N . « A T . STRESS NOM.

1 3 4 6 9 . 0 0 , 1 1 7 4 9 . 0 0 ; 1 0 8 9 4 . 0 0 1

7 6 7 1 . 4 0 3 7 2 3 . 7 0 3 5 0 6 . 9 0 3 0 1 9 . 0 0 2 2 8 1 . 9 0

9 1 7 . 6 9 6 7 2 . 7 9 6 1 3 . 0 3 5 9 4 . 7 4 5 4 9 . 1 4 4 2 5 . 0 1 3 5 8 . 2 4 3 9 9 . 12 2 3 7 . 2 4 2 1 2 . 5 8 1 7 5 . 0 4 1 3 8 . 6 3 1 3 6 . 0 1 1 3 2 . 5 1 1 2 4 . 6 8 1 1 8 . 4 1 1 0 9 . 1 6 1 0 8 . 5 7 1 0 6 . 4 1 1 9 4 . 1 1

9 3 . 1 7 7 8 . 7 9 ' 1 . 1 0 5 9 . 5 9 5 4 . 6 9 4 4 . 1 3 4 2 . 7 4 3 4 . 0 7 1 4 . 7 5 3 1 . 1 7 3 0 . 7 4 2 9 . 4 1 2 7 . , 0 6 2 5 . 3 2 l - J . O l 1 7 . 2 6 1 7 . 0 4

9 . 9 3 9 . 6 3 3 . 0 2 9 . 3 4 5 . 2 4 1 . 5 0 1 . 4 9 1 . 3 2 3 . 5 1

- 0 . 5 9 - 1 . 3 6 - 5 . 3 9

- 1 6 . 2 3 - 1 7 . 9 0

- 2 1 . 5 8 - 3 2 . 3 3 - 4 9 . 6 8 - 5 1 . 2 0

- 2 1 1 . 8 7 - 2 0 3 7 . 5 0 - 2 9 7 9 . 6 0

6

1 7

I 2 I 1 7

1 3 1

1 3 7

I 3 3

3 3 I

1

I 1 7 •»

LOC.

36 1 1 • • 4

10 5 2 5 3 2 6 2 7

1 12

4 3 4 1 9 18 6 6

5 6 3 5 7 3 1 6 0 9 0 6 2 14 2 3 5 8 1 0 2 4 4 2 4 7 4 1

8 1 9 15 4 0 5 6 6 1 5 1 4 6 4 9 4 8 22 4 3

7 4 5 5 9 6 4 2 9

3 1 9 2 9

6 33 35 6 5 29 37 >0 17

2 I 3 12 16 21

9 45 - 4

• I N . » R I M . " A T . STRESS NUM. LOC.

1 4 4 1 . 4 0 2 3 1 2 " . 0 0 2 7 0 9 5 . 6 0 2 1 1 3 4 . 0 0 2 1 0 1 8 . 7 0 2

9 4 2 . 5 4 2 1 5 4 . 3 6 2

3 2 . 0 7 1 2 9 . 7 4 1 2 3 . 7 1

5 . 6 5 1 2 . 6 9 1 3 . 6 9 3

- 0 . 3 0 3 - 1 . 0 7 3 - 1 . 3 9 I - 2 - 0 5 3 - 3 . 7 9 I - 3 - 9 2 1 - 8 . 87 I - 8 . 9 2 3 - 9 . 4 1 I

- 1 0 . 0 3 3 - 1 1 . 9 1 - 1 6 . 2 5 3 - 1 7 . 8 7 3 - 18 . 72 1 - 2 0 . 8 0 1 - 2 1 . 2 8 3 - 2 2 . 0 7 3 - 2 9 . 5 7 3 - 2 7 . 0 9 3 - 3 2 . 3 9 1 - 3 9 . 3 8 1 - 4 0 . 1 1 3 - 4 1 . 1 4 1 - 5 0 . 7 7 1 - 5 4 . 0 1 - 5 8 . 5 8 - 4 2 . 1 9 - 7 0 . 14 - 7 4 . 98 - 7 9 . . 4 - 9 0 . 9 4 - 8 8 . 3 9

- 1 0 0 . 7 3 - 112 . 48 - 1 1 8 . 2 6 - 1 2 0 . 6 9 - 1 2 6 . 1 1 - 1 2 8 . 54 - 1 4 4 . 71 - 1 4 8 . 4 1 - 1 8 7 . 3 8 - 2 0 3 . 53 - 2 9 7 . 0 8 - 3 7 8 . 15 - • • 3 1 . 37 - 6 3 6 . 4 9 - 9 0 0 - ! 6

- 7 6 1 0 . 9 0 - 7 6 3 9 . 4 0 - ' 0 5 2 . 3 0 - 3 3 9 6 . 4 0

- 1 2 9 ' » . 0 0 - 1 2 8 1 6 . 0 0

36 11 4 4

2 6 27 1 0 32 3 0 , 7 5 0 6 6 6 1 29 35 33 5 7 2 9 6 2 a3

5 3 7

4 5 6

I 25 5 1 5 9 6 0 4 6 2 0 4 3 3 8 4 8 22

1 17 15 4 9

8 , 0

l-s L 6-. 1 12 L 3 1 L 4 2 1 2 4

' 1 58 1 14 1 4 1 . • « • I 2 1 s 23 I 16 I a5 I 13 2 l o 2 52 I 6 2 53 1 3 1 2 2 U 2 3 2 34 2 45 2 54 2 55


Material No.

1 2 3

Material Type


148

QROEREO STRESSES S C E N A R I O - 1 ( S P L I T SPACER!

y-NORM STRESS

9 4 1 7 . 6 0 1 8 2 0 . 4 0 1 9 3 S . 1 0

7 3 2 . 4 9 3 9 1 . 1 4

4 9 . 2 3 3 9 . 4 9 2 9 . 1 4 2 4 . 4 0 2 4 . 3 9 2 3 . 0 6 1 8 . 8 9 1 7 . 3 2 1 7 . 4 7 1 6 . 7 8 1 9 . 9 8 1 3 . 8 8 1 2 . 0 8 1 1 . 3 1 1 1 . 2 7 1 1 . 0 0 1 0 . 3 9 1 0 . 1 3

8 . 1 9 7 . 4 6 9 . 7 i 9 . 0 0 4 . 2 9 3 . 8 6 3 . 6 7 3 . 6 1 2 . 6 3 0 . 3 1 0 . 2 9 0 . 1 9 0 . 0 8 0 . 0 1

- 0 . 1 7 - 0 . 2 1 ' - 0 . 2 1 - 2 . 0 9 - 3 - 7 7 - 3 . 8 1 - 4 . 3 8 - 4 , 7 2 - 9 . 7 8 - 6 . 1 3 - 7 . 3 0 - 8 . 0 7

- 1 3 . 2 1 - 1 9 , 1 9 - 1 9 . 8 1 - 2 2 . 1 0 - 2 2 . 5 1 - 2 3 . 3 7 - 2 3 . 7 7 - 2 9 . 9 0 - 2 9 . 9 8 - 4 2 . 9 1 - 4 3 . 1 4 - 9 1 . 0 8

- 2 6 9 . 4 7 - 9 6 7 . 4 6 - 9 4 8 . 4 3

- 2 1 7 4 . 3 0 - 6 6 6 2 . 8 0

MA NUI L O C .

2 6 2 7 49 11 18 32 3 4 4 2 13 1 2 4 3 17 16 39 ? 9 21 41 22 3 4 14

2 9 9 6 0 1 9 4 0 6 6 2 0 3 7 6 9 6 2 6 1

6 3 9

5 1 9

9 3 4 6

4 8

3 3 3

4 7 4 8 2 3 7

28 64 63 91 29 96 24 29 10 98 30 97 31 49 50 52 59 36 19 44

Z-NCRM STRESS

8 7 8 9 . 4 0 2 2 4 3 . 4 0 1 7 7 6 . 9 0

6 4 6 . 6 6 4 6 5 . 8 1 2 9 4 . 0 7 2 8 6 . 5 3 2 4 0 . 7 2 2 0 2 . 1 9 1 6 7 . 6 1 1 6 9 . 1 3 1 3 6 . 5 3 1 2 7 . 9 3 1 1 2 . 4 9

0 4 . 7 7 9 7 . 0 7 5 3 . 2 8 4 2 . 3 1 3 6 . 7 0 3 9 . 4 7 3 9 . 3 1 2 1 . 5 9 1 9 . 2 8 1 9 . 1 7 1 7 . 9 1 1 7 . 6 1 1 1 . 7 4 1 0 . 8 3

9 . 9 3 9 . 7 3 8 . 3 9 8 . 4 2 3 . 9 0 3 . 4 9 2 . 0 8 1 . 1 6 0 . 9 4

- 0 . 3 9 - 0 . 6 1 - 0 . 9 3 - 1 . 9 3 - 3 . 5 8 - 6 . 5 9 - 9 . 4 4

- 1 9 . 1 4 - 1 0 . 3 9 - 1 0 . 7 9 - 2 8 . 9 9 - 3 7 . 4 9 - 6 9 . 1 9 - 7 6 . 6 7 - 9 7 . 1 1

- U 7 . 7 4 - 1 4 9 . 9 1 - 1 6 7 . 1 0 - 1 6 7 . 6 3 - 1 7 9 . 1 9 - 1 9 4 . 3 8 - 2 1 1 . 8 0 - 2 2 7 . 3 1 - 2 2 8 . 6 3 - 2 9 8 . 3 6 - 4 2 4 . 5 4

- 1 7 0 1 . 7 0 - 2 3 * 2 . 5 0 - 5 3 6 4 . 2 0

T . L X .

2 7 2 6 3 4

2 3 6

1 1 6 6 6 3 6 2 19 59 7 58 13 49 48 13 10 16 14 41 13 23 21 22 53 12 49 38 31 IT 40 37 20 24 33 39 46

9 30 23 ?l 56 39 25 29

8 42 54 47 52 SO 57 49

9 60 61 64 69 55 4 I

44 32 36

SHEAR STRESS NWI.

434.13 409.67 156.77 156.65 127.62 115.84 81.07 60.42 52.35 49.87 42.51 35.31 25.17 21.49 19.85 17.27 16.37 11.48 7.72 7.31 0.64 0.43 O.OI

-1.61 -1.62 -1.74 -3.06 -3.20 -7.34

-10-32 -10.79 -10.84 -11.08 -11.38 -11.39 -11.76 -11.79 -11.84 -12.02 -14.09 -14.51 -14.72 -15.57 -18.21 -19.75 -22-27 -26.88 -27.33 -28.11 -35.33 -37.21 -40.14 -53.90 -57.62 -73.97

-108.56 -109.07 -144.98 -149.19 -186.78 -186.85 -187.12 -214.27 -259.65 -312.39 -312.37

ITH 250 'S: OEALAS' «n?'JLj5

LOC.

26 44 27 65 57 63 61 59 10 VI 54 23 48 39 49 47 50 13 21 30 15

9 53 39 33 22 37 28 16 38 29 29 43 2C 46 51 17 12 56

< 1

40 7

42 3

6 31 24 14 60 36 62 64 58 52 66 45 18 55 U 19 34 32

9 4 4 7 . 8 0 9 7 0 3 . 0 " 1 3 3 1 . 3 0 1 5 5 3 . 3 0

3 1 8 . 7 5 6 4 7 . 8 3 4 8 1 . 4 3 4 6 6 . 6 4 3 1 3 . 1 3 2 9 6 . 7 6 2 5 3 . 4 6 1 9 6 . 0 5 1 9 3 . 6 0 1 7 2 . 9 3 1 6 0 . 7 9 1 2 9 . 0 2

3 9 . 7 5 3 8 - 7 1 3 2 . 9 « 6 7 . 7 5 6 7 . 0 2 6 " . 1 9 6 2 . 7 2 5 1 . 0 6 4 7 . 9 ? 4 4 . 5 0 3 9 . 4 2 3 8 . 0 8 3 2 . 5 5 3 1 . 2 6 3 0 . 2 4 3 0 . 0 5 2 0 . 3 7 . 2 9 . 2 9 2 9 . 5 1 2 6 . 6 6 2 6 . 5 6 2 4 . 7 2 2 4 . 4 / 2 4 . 1 6 2 0 . 5 1 1 9 . 3 1 1 » . U 1 5 . 8 9 1 9 . C 2 1 1 - 7 4 1 1 - 0 0

6 . 9 7 2 . 3 4 1 . 5 5 1 - 4 6 1 . 4 5 1 . 3 1 0 . 6 5 0 . 2 9 0 . 0 9

- 0 . 1 1 - 1 . 4 1 - 1 . 5 3 - 3 . 4 4 - » . 0 3

- 1 3 . 6 * - 4 7 . 2 8

- 1 4 5 . 6 2 - 9 4 7 . 6 3

- 1 6 6 8 . 1 0

L C C .

?6 7 7 34 4 5 11

2 18

3 6«

6 6 3 6 2 19 5 8 5 9

•»

4 9 32 65 41 10 14 4 8 57 13 2 3 6 4 16 61 12 5 4 42 4 3 39 24 31 17 2 1 6 0 38 , 0 15 22

9 20 5 3 4 6 37 91 35

5 4

3 3 I 9

4 7 10 28 5 6 2 9 25 5 2 5 0 5 5 3 6

• i n . 3R : •« . - A T . S T R E S S MUM.

? 7 I 7 . 30 1 8 1 6 . 3 0

2 0 0 . 2 7 1 8 . 7 9 1 4 . 9 0 1 1 . 5 7 9 . 3 3 9 . 1 6 9 . 1 5 4 . . 1 1 . 57 2 . 6 1 2 . 3 5 0 . 3 1 0 . 7 5 0 . 0 1

- O . 0 6 - • . 0 0 - ! . 79 - ' . 9 3 - 4 . 6 0 - 7 . 5 7 - 7 . 9 3 - 9 . 3 0 - * . 1 6

- 1 1 . 7 8 - 1 3 . 32 - l ' . 9 l - 1 9 . 4 9 - 1 8 . 6 0 - 2 1 . 3 7 - 7 2 . 1 0 - 2 4 . 7 ' - 2 6 . 5 3 - 2 7 . 72 - 2 8 . 3 7 -3<3.05 - 3 1 . 7 0 - ? Z . 2 9 - 4 7 . 37 - < . 4 . 0 9 - 4 5 . 3 1 - - = . 4 9 - 5 3 . ao - 5 9 . 38 - o O . 57 - 6 4 > . 6 3 - 5 0 . 5 6 - 9 4 . 1 3 - 3 4 . 2 4

- 1 2 1 . 5 4 - 1 6 8 . 8 1 - 1 8 7 . 3 2 - 1 8 9 . 5 3 - 2 2 3 . 5 2 - 2 3 0 . 5 4 - 2 5 9 . 7 1 - 3 0 0 . 3 1 - 3 0 6 . . 1 - 3 4 8 . 9 3 - 4 2 5 . C3 - 6 5 0 . . 6

- 2 2 0 2 . 3 0 - 2 4 2 2 . 0 0

. - 5 3 6 5 . 0 0 - a 6 ' ) 6 . 4 0

L C C .

2 6 2 7 11 13 16 22

2 21 15 18 12 - 3 38 37 17 53

o 9

35 33

3 7

20 2 9 4 0 4 6 4 « 5 9 34 14 39 5 1 62 2 9 5 6 25 23 3 0 '\ >'i

i , 9 2 4

10 63 3 1 ao - 7 54 59 5 0

4 4 5 60 6 1 5 7 6 4

4 65 52

1 55 1 5 32 36


Material No.

1 2 3

Material Type


'•J.<0£R£J STRESSES i C £ M A « l C - l I I S P L K 5?lCcH» -1T»- 250 PSI S£A«.AAr "CCU.US

149

r - N O R M M A T . STRESS NU

3 3 2 8 . 9 0 2 1 0 7 4 . 1 0 2 1 0 3 2 . 9 0 2

« 9 6 . 7 0 2 1 7 9 . 1 4 2 1 7 6 . 9 9 2 1 7 3 . 8 0 2 10 7 . 7 6 2

6 4 . 8 4 2 3 9 . 2 6 1 1 3 . 0 1 1 1 6 . 0 9 1 1 5 . 8 9 I 1 5 . 1 5 i 1 4 . 6 9 I 1 3 . 2 6 1 1 2 . 1 2 1 1 1 . 7 4 1 1 0 . 1 0 1

9 . 9 2 3 9 . 7 8 1 9 . 4 1 3 3 . 7 3 3 3 . 6 1 1 7 . 7 4 5 . 9 5 3 5 . 8 0 4 . 2 8 J 3 . 9 7 3 . 8 9 3 . 6 1 3 - 2 9 2 . 9 k ] 2 . 7 9 2 . 4 4 1 . 7 0 1 . 5 6 1 . 3 4 l - l 1 0 . 9 7 0 . 7 0 3 . 3 6 0 . 2 0 0 - 1 4 3 . 0 4 3 . 0 1

- 0 . i 2 - 0 . 4 9 — 0 . o 4 - 0 . 6 4 - 2 . 1 2 - 2 . 4 7 - 2 . 8 C - 3 . 7 7 - 4 . 9 1 - 5 . 5 1 - 7 . 2 4 - 9 . 9 4

- 1 4 . 1 8 - 1 6 . 1 4 - 1 7 . 4 9 - 2 1 . 0 7 - 3 4 . 4 2 - 3 7 . 6 7

- 2 3 7 . 6 5 - 7 7 0 . 3 9

M . u C C .

44 3 6 2 6 2 7 3 4 32 52 5 9 18 3 1 2 1 42 3 0 25 22 6 0 3 6 4 1 14 4 6 5 9

1 2 0 ) 4 3

13 I 5 1 1 2 9 L 16 L 62 1 5 6 L oS L 15 i 17 I 4 7 L 6 1 2 54 1 3 9 1 5 1 4 0 . 6 3 2 3 3 3 8 L 2 4 L 1 L 3 2 9 2 53 3 33 3 35 3 3 7 L ** I 2 1 4 8 3 12 1 7 I 3

2 10 1 6 4 I 6 3 1 2 3 1 5 7 2 1 1 1 58 1 5 0 1 4 9 2 19 I 45

Z-KCUP " 4 1 . STRESS : u j M .

3 9 8 8 . 6 0 2 1 9 6 2 . C O 2

6 6 9 . 7 5 2 3 2 1 . 8 1 I 3 8 1 . 6 3 1 2 5 0 . 4 9 1 1 7 7 . 1 8 I 1 4 C . 7 0 1 1 3 1 . : i 2 1 2 9 . 5 0 1 1 0 6 - 5 2 1

7 4 . C 6 1 5 6 . i 7 1 5 2 . 6 2 I 5 2 . 3 4 1 4 6 . 3 2 I 3 7 . 3 4 2 3 3 . 4 7 1 2 3 . 3 6 : 2 2 . 5 7 2 1 3 . 3 7 2 1 1 . 9 0 1 1 1 . C 9 1

9 . 2 0 2 6 . 6 6 3 4 . 2 2 3 3 . 7 9 2 3 . 7 8 3 2 - 3 7 3 2 . 3 3 3 z.ez 3 2 . 5 9 2 2 . 0 6 1 z.az I 1 . 4 6 3 1 . 2 6 3 1 . 3 9 1 : - 4 5 3 0 . 2 9 3 C I O 3

- C . 1 7 2 - 0 . 2 9 1 - C . 5 1 1 -O.t-^ 3 - 0 . 6 6 3 - 1 4 4 1 3 - 3 . 6 9 1

- 1 3 . 2 3 1 - 1 4 . 3 8 2 - 1 4 . 5 1 2 - 2 1 . 1 2 - 2 5 . 3 6 2 - 3 6 . 6 7 I - 4 < i . 8 8 1 - 5 6 . 1 2 1 - 5 9 . 7 3 I - 7 5 . 3 8 1 - 8 1 . 2 4 I

- 1 3 4 . c a 1 - 1 3 2 . 0 4 1 - 1 6 C . 2 6 I - 1 3 2 . 7 8 I - 2 2 7 . 9 9 2 - 2 7 9 . C d 1 - 3 7 2 . 1 1 I - a 2 3 . 2 7 2

L - C .

2 7 •.4 6 6 6 3 a2

1 4

2 6 5 9

5 3

13 16 53 2 1 55 24 4 9 45 5 2 3 3 4 8 10 25 2 9 1 1 4 6 4 3 5 1 2 9 53 42 4 1 17 5 6 39 2 8 35 3 3

5 4 0 4 7 37 J 3

12 50 3 1 54 13 57 n 2 3 ZZ 15 14

7 3 0

6 T

2 6 1 3 2 6 4 65 3 4

SHEAR ' A T . STRESS NUM.

1 7 2 . 2 9 2 1 6 7 . 4 6 1 1 2 ! . 9 6 1 1 2 9 . 0 3 1

9 3 . 1 3 2 9 2 - 4 2 1 E l . 6 9 2 7 2 . 9 5 I 4« . 9 4 2 . 4 . 7 8 2 • • 1 . 8 5 2 3 9 . 9 5 1 2 7 . 7 7 1 2 * . 3 9 1 3 1 . 1 4 2 1 . 3 3 1 1 2 . 5 4 2 1 2 . 3 3 1 1 1 . 5 3 2 1 1 . 2 3 i 1 1 . 0 3 1 1 C . 6 2 I

^ . 6 0 1 5 . 2 6 2 5 . 0 5 I a . 1 7 1 8 . 0 1 1 7 . a 6 2 t . 9 2 1 5 . 2 6 1 2 . 3 5 3 1 . 3 2 3 1 . 8 0 3 1 . 3 J 3 1 . 7 2 3 1 . 5 8 3 1 . 5 7 3 1 . 5 5 3 1 . 5 5 3 1 . 3 3 I 1 . 2 1 3 C . 9 3 3 C . 7 4 1 0 . 7 1 1 0 . 4 5 3 C . 1 2 2 C . 0 7 3 0 . 3 2 3 C . O l 2

- C - 3 0 1 - C . 4 5 1 - 1 . 0 6 I - 2 . 0 6 1

- 1 4 . 8 8 I - 2 1 . 9 3 I - 2 4 . 9 2 I - 2 8 . 3 1 2 - 2 9 . 7 0 - 4 1 . 6 1 L - t c . a 9 1 - 7 8 . 3 7 2 - 6 1 . 1 7 2 - 9 7 . 3 5 I

- 1 0 6 . 6 7 1 - 1 3 5 . 5 7 1 - 2 2 2 . 9 9 Z

L u C .

27 a5 57 63 45 a l . . 4 .

59 34 32 ' 52 23 33 41 13 39 10 50 2o 21 4 9

7 5

54 44

1 3

18 15 4 7 29 51 56 46 43 IZ 17 20 t c

22 38 23

• >

•* 33

9 35 37 53 31 16

6 3

24 40 14 19 42 60 62 59 11 6 4 58 66 36

MAX. P R I M . <îi1. STRESS Nl

4 0 0 9 . 5 0 2 3 3 3 1 . iO 2 1 9 8 4 . 6 0 2 1 0 3 3 . 0 0 2

5 5 5 . 6 3 1 4 2 0 . 3 3 1 2 6 4 . 7 2 1 1 3 4 . 0 6 2 1 8 1 . 3 8 2 1 8 1 . 3 3 2 1 7 7 . 3 6 I 1 6 0 . 7 5 1 1 5 3 . 3 - . 2 1 4 0 . 7 1 1 2 8 . 4 4 I 1 1 7 . 3 9 I 1 0 7 . 3 9 I

7 9 . 0 3 : 7 4 . 1 2 1 7 2 . 0 6 1 6 7 . 6 2 1 6 9 . 3 8 2 5 2 . 6 3 1 5 1 . 6 9 1 5 0 . 2 3 1 4 1 . 6 2 1 4 0 . 9 3 1 3 9 . 5 9 1 3 9 . 1 8 I 3 8 . 2 6 I 3 3 . 7 9 2 3 0 . 1 9 1 2 8 . 9 6 1 2 4 . 0 2 i 2 2 . 7 2 1 2 2 - 4 2 i 1 8 . 0 9 1 1 6 . 3 8 ; 1 6 • 3 8 1 9 . 6 2 1 3 - 4 3 1 4 . 9 3 1 0 . 4 0

9 - 3 4 9 . 2 4 8 . 3 5 6 - 9 2 6 . 7 3 6 . 5 4 4 . 8 7 4 . 4 0 4 . 1 9 2 . 3 9 1 . 6 8 1 . 4 1 1 . 1 2 0 . 6 2 0 . 4 3 0 . 2 9 0 . 0 9

- 0 . 3 8 - 0 . 6 2 - 2 . 1 2 - 2 . 2 3 - 3 . 7 3

- 2 1 . 4 5

i iM . s 3 C .

3 6 4 4 2 7 2 6 6 6 6 3 6 2 5 2 32 3 4

1 59 5 9

, 5 8 5 7

9 1 1

a 13 6 9 18 16 30 2 1 4 1 6 1 4 2 2 4 3 1 4 9 4 9 4 0 • 4 3 9 4 0 14 10 2 3

L 4 8 ! 2 3 I 7 2 S 4 6 S 2 0 i 4 3 » 5 1 i 2 9 1 4 7 2 5 4 i 5 6 I 15 3 17 2 5 3 3 2 8 3 3 8 1 6 1 3 3 3 3 3 3 9 2 9 3 1 2 3 3 7 1 2 1 7 1 5 0 2 19

M I N . P R I N . M A T . STRESS HUM. LOC.

I C 3 7 - 2 C 2 6 6 7 - 2 4 2 6 3 6 . C 9 2 1 3 1 . 4 8 2

1 4 . 3 9 1 6 . 3 8 3 5 . S O 1 3 . 7 9 3 3 . 2 9 3 3 - 1 1 2 2 . 8 7 3 2 . 2 2 3 1 . A 3 3 0 . 4 3 I 3 . 3 6 3 0 . 3 6 3 O . C l 2

• 0 . 1 8 1 - 0 . 2 2 2 - 0 . 2 5 3 - 0 . 4 7 3 - O . ' O 3 - 0 . 6 4 I H I . A 5 3 - 1 . 3 7 3 - 3 . 8 3 3 - 4 . 3 3 I - 4 . 9 6 1 - 9 . 3 9 1 - 6 . 6 8 1 - 6 . 9 9 1 - 9 . 9 6 1

- U . 7 0 2 - U . 7 4 i - U . 2 3 1 - 1 9 . 2 9 2 - 1 8 . 4 7 4 - 1 9 . 9 9 - 2 1 . 4 4 - 2 1 . 4 8

- : i .7o - a . 8 4 - J 9 . 4 7 - n . 8 9 - 3 9 . 3 8 - 3 9 . 4 6 - . 8 . 6 9 - 4 9 . 9 2 - 5 6 . 9 1 - 6 6 . 1 3 - . 7 . 7 1 - 7 7 . 4 1 - 8 8 . 7 0 - 9 6 . 9 9 - 9 7 . 1 8

- 1 0 4 . C 9 - 1 3 2 . 3 2 - 1 9 4 . * 2 - 1 6 0 . 2 6 - 2 2 0 . 9 6 - 2 3 2 . 8 8 - 2 4 1 . 3 6 - 3 1 0 . 3 9 - 4 3 5 . 8 8 - 7 8 1 . 1 8 - « 2 5 . 4 7

3 6 4 4 2 7 26 2 1 25 16 2 0 4 4 52 4 3 9 1 2 9

5 I T 5 6 53

1 9

23 33 35

. 3 7 38 12 * 7

8 2 4 13 4 8 62 10

! 5 9 3 1 18

t 34 I 39 L 4 2 1 4 0 L 6 6

3 0 I 5 9

4 1 50 4 9 63

I 2 2 19 2 3

1 14 1 7 2 11 1 6 0

1 3 8 1 6 1 3 1 9 7 1 2 1 6 1 2 32 2 19 1 6 4 1 65 2 4 9 2 34


Material No.

1 2 3

Material Type


150

T-NORM MA

STRESS NU

9 5 3 0 . 1 0 2 2 4 0 9 . 4 0 2 2 3 9 8 . 8 0 2 1 9 6 3 . 2 0 2

3 9 0 . 2 7 2 3 8 0 . 2 6 2

7 1 . 5 2 3 4 3 . 7 2 1 4 3 . 1 8 2 3 3 . 9 5 I 3 3 . 5 4 I 3 2 . 0 4 3 1 7 . 9 3 1 1 5 . 8 8 I 1 5 . 0 4 1

1 3 . 3 2 3 1 2 . 9 9 1 1 1 . 3 7 3 1 1 . 1 0 1 1 0 . 4 7 1 1 0 . 4 7 1

9 . 4 5 1 8 . 8 8 1

7 . 2 1 I 6 . 9 3 3

5 . 9 3 1 4 . 8 1 ] 4 . 6 6 4 . 2 7 \ 3 . 7 9 3 . 4 9 3 . 2 7 3 . 3 6 2 . 6 1 1 . 6 6 9 . 6 0 9 . 2 9

- 0 . 6 4 - 1 . 7 4 - 1 . 8 9 - 1 . 9 9

- 3 . 3 3 - 4 . 1 6 - 4 . 6 9 - 4 . 7 0 - 9 . 1 9 - 6 . 0 9 - 6 . 3 4 - 8 . 1 9 - 8 . 2 1

- 2 1 . 4 8 - 2 2 . 3 4

- 4 0 . 4 4 - 4 0 . 3 3 - 9 1 . 0 9 - 7 3 . 0 2 - 7 7 . 3 9

- 3 7 8 . 7 6 - 3 8 3 . 0 8 - 9 4 9 . 5 3 - 9 9 2 . 8 9

- 2 3 4 6 . 3 0 - 2 4 7 6 . 3 0 - 2 7 1 0 . 1 0 - 7 8 2 0 . 1 0 - 9 8 2 2 . 5 0

2RCEPE0

Y »

M . L I X .

59 5 4

4 5 18 5 3

9 12 13 19 1 6 2 1 17 15 14

2 2 0 2 2 2 9 5 9 3 9 6 0 4 1 4 2

1 1 3 8

4 0 6 6

L 6 9 L 8 L 4 L 6 1 L 6 2 L 6 3 3 7 L 9 > 9 1 1 3 5 i 3 3 ) 4 3 } 4 6 3 2 9 3 2 8 3 3 6 1 2 3 1 3 1 4 8 I 4 7 I 7 L 6 4 1 6 3 1 5 8 I 9 7 1 4 9 1 5 0 1 2 4 1 3 0 1 31 2 32 2 34 2 10 2 27 2 26 2 36 2 52 2 4 * 2 11

'-TOESSES SCEN

2-MCPM -t STRESS :.U

" 9 9 9 . 3 0 2 2 1 7 9 . 3 0 2 2 1 5 6 . 4 0 2 1 3 8 4 . 0 0 2

7 2 0 . 2 9 t 4 8 6 . 7 8 1 2 6 0 . 0 8 I 186 .17 1 176 .44 2 1 7 2 . 7 2 1 131 .83 1

9 1 . 7 9 I 8 4 . 8 5 I 76 .17 1 7 1 . 4 4 I 6 9 . 6 2 2 6 1 . 3 9 1 5 5 . 1 7 1 4 7 . 7 9 1 4 0 . 2 3 I 3 6 . 5 9 I 3 2 . 1 4 3 2 9 . 3 3 I 19 .53 1 1 4 . 6 3 3 1 3 . 7 2 I

9 , 3 4 3 6 . 1 3 ' 6 . 1 1 3 4 . 9 9 3 3 .88 1 0 . 4 4

- 0 . 2 9 - 0 . 4 7 - 1 . 2 1 - 1 . 4 3 - 1 . 4 9 - 1 . 9 3 - 1 . 7 3 - 2 . 9 0

- 1 1 . 4 6 - 1 7 . 0 6 - 3 9 . 1 4 - 4 4 . 9 1 - 6 3 . 1 8 - 7 4 . 0 8 - 7 4 . 8 4 - 8 9 . 8 8

- 1 0 0 . 4 8 - 1 0 3 . 6 2 - 1 1 3 . 2 7 - 1 1 4 . 9 1 - 1 2 0 . 7 1 - 1 2 6 . 0 2 - 1 9 7 . 5 4 - 2 9 6 . 0 1 - 2 9 6 . 1 0 - 3 1 6 . 8 3 - 4 6 5 . 0 0 - 8 9 8 . 8 0

- 1 4 1 4 . 1 0 - 1 4 9 9 . 8 0 - 2 4 4 6 . 6 0 - 2 6 5 1 . 7 0 - 5 9 4 8 . 2 0 - 9 5 4 6 . 6 0

ARIO-t ( S .

A T . H. L^C.

54 59 3 4

7

2 3 6

13 52 16 2 1

i 66 2 4 63 45 6 2 5 9 58

7 4 9 1 2 4 8 3 1 17

4 1 3 8

1 20 I 37 I 29

4 0 1 33 L 23 1 91 i 43 1 46 ) 35 3 28 1 29 3 56 I 39 I 30 I 42 I ZZ I 47 1 15 1 14 1 50 1 5 I 69 1 64 I 57 1 61 I 60 2 32 1 4 2 19 2 18 I 1 2 26 2 27 2 *«4 2 11 2 53 2 10 2 36

s l 9 SPACF!>)

:HEAR -4A STOCSS S'J

679 .77 2 4 4 0 . 1 4 2 290 .94 2 156.21 I 120.75 1 110 .66 I

93 .96 7 76 .82 I 74 .04 2 59 .89 1 57 .29 1 4C.96 1 27 .38 I 26 .26 1 24.72 1 21.10 I 17 .14 1 15.30 I 9 . 0 1 I 6 .49 1 9.36 1

- 0 . 3 2 3 - 0 . 4 2 t - 1 . 1 2 3 - 1 . 4 5 3 - 1 . 7 3 3 - 3 . 2 9 3 - 3 . 4 6 1 - 3 . 9 * 3 - 3 . 9 6 1 - 4 . 7 3 3 - 5 . 0 7 3

- 1 3 . 4 2 - 1 5 . 6 5 - 1 8 . 7 3 - 1 8 . 7 7 - 1 8 . 9 0 - 1 8 . 9 3 - 2 1 . 4 3 - 2 1 . 4 4 - 2 1 . 6 4 - 2 3 . 9 3 - 2 6 . 7 5 - 2 9 . 8 0 - 3 0 . 7 0 - 3 2 . 2 3 - 3 4 . 7 9 - 3 5 . 0 9 - 3 5 . 3 0 - 4 2 . 3 6 - 5 7 . 2 3 - 7 6 . 5 8

- 1 1 0 . 2 3 - 1 1 5 . 6 7 - 1 2 5 . 7 2 - 1 5 9 . 6 0 - 1 6 1 . 7 8 - 1 6 6 . 3 9 - 1 7 0 . 9 4 - 2 3 9 . 0 1 - 2 4 5 , 3 3 - 3 3 6 . 2 4 - 3 3 6 . 2 5 - 3 8 3 . 3 7 - 3 8 8 . 4 4 - 3 9 0 . 8 2

.,'7-4 252

M. u o : .

1 »

36 « i

aS 57 63 55 ••1 44

' 2 3 5= 41 21 22

12 O* 16 15 48 4 9 24 39 50 33 26 37 12 47 17 29 20

1 25 1 38 L 40 1 56 > 43 > 51 3 46 I 5 I 7 L 1 I 30 1 3 I 4 I 31 1 42 I 2 1 a I 6 1 14 1 60 1 62 I 64 I 58 2 18 I 66 2 32 2 34 2 10 2 26 2 19 2 53 2 0 2 . 27 2 52 2 45

•"OI : -^L^ ' . r ^ C T J L ^ O

• i » . ' R ( . N , - » 7 . iTPr-.s

9 9 0 5 . 8 0 2 •J5RI . I 0 2 2 4 A 2 . 6 - > ' 2167 .30 2 197" .19 2 1«55 .»0 2

' 2 1 . 9 0 1 4 H 8 . ; 3 I i l 7 . l l 2 2 6 4 . 8 4 1 7 7 7 . " 2 205.-.'5 I 190.3? ! i ' 4 . e o 174.0 0 2 149.22 I 13 9 .19 1 133 .87 I 115 .84 I 114.35 I 114 .09 1 " '4.51 1 7 6 . 3 9 I 71 .70 3 6 1 . 3 8 I 6 0 . 5 ' 1 5 7 . 4 * 1 52 .61 1 4 8 . 5 7 I 4 0 . 1 4 1 17 .09 I 3 2 . 9 0 2 3 2 . 5 8 1 3 1 . 2 9 2 8 . 4 4 1 2 8 . 2 7 1 25 .50 1 23 .36 1 23 .13 I 2 1 . 6 1 3 2 0 . 3 6 I 2 0 . 7 7 1 1 8 . 9 7 3 1 7. 30 3 17 .29 3 15 .67 7 15 .42 3 1 4 . 1 7 3

3 .20 1 6 .32 3 6 .79 I 5 .98 I 2 .10 1 1.19 3 0 .31 3

- 1 . 7 7 3 - 9 . 8 8 1 - 9 . 2 2 1

- 4 0 . 5 3 1 - 1 0 2 . 7 3 2 - 5 4 3 . 6 9 ; - 7 5 8 . 2 2 - 9 6 0 . 3 6

- 1 4 9 8 . 9 0 - 2 3 7 4 . 9 0 - 2 4 4 7 . 9 0

H. L^.C.

5 4

55 4 9 3 4

18 9

2 3

5 3 6

9 2 '16

13 16 19 a3 2 1 9 9 69 6 2

i 9 9 2 4

1 2 6 4 9 7 2 3 4 1

7 6 1 4 9 17 14

4 0 3 1 4 8 4 2 39 2 2 38 15 4 0 5 1 4 3 4 6 2 0 5 6 2 5

1 3 7

4

9 2 9 3 3 3 9 2 8

47 10 50 3 2

! 10 ! 27 ! 26 J 4 * 2 11 2 36

• I -;. ?f : s . o T o c r s

2398 .90 2174 .30

309.50 30.55 31 .37 31 .86 26 .18 13. 77 13.34 5 .79 -".79 2 . 1 9 1.90

- 1 . 0 4 - 1 . 5 4 - 1 . 7 0 - 4 . 2 9 - 5 . 14 - 9 . 3 2 - i . l 5 - 8 . C 7 - 3 . 1 2

- 1 0 . 9 6 - 14 . 8» - 1 8 . 3 4 - 2 0 . 2 5 - 2 0 . 5 7 - 2 2 . C8 - 2 4 . 3 5 - 2 8 . 2 5 - 2 9 . 4 3 - 4 0 . 9 8 - » o . 5 3 - 5 1 . 2 7 - 5 2 . 1 6 - 5 9 . 0 5 - 6 2 . 4 1 -63 . 39 - 7 4 . ' 2 - 9 1 . 8 6 - 8 5 . 9 9 - 8 6 . 2 6 - 9 9 . 8 8 - 9 1 . *4

- 1 0 4 . 7 9 - 1 0 7 . 6 0 - 1 1 5 . 8 4 - 1 4 6 . 3 4 - 1 5 7 . - . 0 - 1 9 2 . 8 4 - 1 9 8 . 0 0 - 2 1 4 . 3 1 - 2 8 9 . 3 9 - 3 2 3 . 7 4 - 3 9 3 . 9 3 - 4 16 .91 - 4 6 9 . 9 9 - 4 7 3 . 5 7

- 1 6 3 8 . 7 0 - 2 3 8 4 . 7 0 - 2 6 8 8 . 5 0 - 2 7 6 1 . 5 0 - 5 5 5 4 . 0 0 - 7 8 2 1 . 0 0 - 9 3 9 4 . 1 0 - 9 5 7 9 . 1 0

< i r . • JM.

2 ?

2

I 3 i

^ 1 I 2 3 3 3 3 3 1 1 3 3 I I 1 I I 3 3 3 3 I 1 I I I 1 1 I 1 1 1 1 I I 1 1

I 1 I 1 1 I I I I 2 2 2

I 2

2

2 2 2 2 2 2

LuC.

54

55 9

13 12 16 2 1 17

2 1.5 29 2 5 37 3 1 35

a 2 8 38 2 9

3 8

4 6 4 0

7 5 1 4 3 4 6 5 6 3 9 5 9 4 1 4 9 6 2 2 4 4 2 22 23 4 7 19 3 0 6 3 3 1 50 14

5 5 8 6 6 6 0 6 1 6 4 5 7 45

4 13 34 19

1 32 27 2 6

93 52 10 44 l l 36


Material No.

1 2 3

Material Type


151

r-NOIIM STKESS

1 9 7 9 . 1 0 14S4 .10

838.76 U0.9T 497,64 3S7.07 392.11 314.24 314.23 202.59 201.67 144.69 84,01 47.97 32.66 32.08 2a.oo 27.77 26.66 22.19 21.36 21.17 19.61 14.48 16.01 12.94 12.42 11.66 11.11 10.93 10.70 10.61 9.77 6.36 4.79 4,04 3.49 2.21 1,69 1,24 0.27

- 0 . 1 9 - 0 . 6 1 - 0 . 6 9 - 0 . 8 4 -0 ,89 -0.9C - 0 . 9 9 - 1 . 0 3 - 1 . 2 4 - 1 . 9 9 - 1 . 6 9 - 1 . 7 4 - 1 . 7 6 - 3 . 0 1 - 3 . 0 9 - 9 . 1 3 - 4 . 6 1 -9 .46 -7 .30 - 9 . 8 4

-20.99 -243-97 -341.47 -499.60

-1634.20

OROEREO

NAT. NUM. LOC.

2 4 4 2 11 2 10 2 3 6 2 3 2 2 2 7 2 94 2 9 3 2 9 2 3 4 2 32 2 19 1 31 3 36 3 12 1 30 3- 51 1 50 1 16 1 6 6 1 13 3 17 1 14 1 57 3 4 6 1 4 9 1 2 2 1 4 2 1 6 0 1 19 3 2 0 1 2 1 1 41 1 8 1 2 4 1 6 4 3 4 3 3 29 1 6 I 2 1 40 1 4 7 3 28 1 59 3 3 3 ; 3 1 62 3 2 9 3 39 1 1 I 6 I 3 9 3 37 1 6 3 1 5 1 6 3 3 38 I 7 1 61 1 48 1 58 1 23 2 26 2 13 2 4 5 2 33

STRESSES SCE

2-NCRM M STRESS Nm

2 6 8 7 . 2 0 2 2 3 8 3 . 1 0 2 128 5 . 0 0 1

9 3 1 . 0 7 1 5 8 4 . 4 8 1 5 7 2 . 8 6 2 2 5 9 . 6 1 2 2 4 3 . 4 6 1 2 2 1 . 6 9 2 1 9 9 . 6 8 2 1 6 3 . 5 1 1 1 6 3 . 3 5 t 1 4 7 . 4 7 1 1 4 4 . 8 4 1 1 3 4 . 9 2 1 1 2 2 . 4 9 1 1 0 9 . 8 9 1

6 7 . 0 0 1 3 3 . 7 0 1 4 9 . 7 2 2 4 5 . 1 1 2 3 1 . 6 0 1 2 C . 9 0 3 1 3 . 4 3 1 1 3 . 3 2 1 1 4 . 3 5 3 1 2 . 0 2 3 1 0 . 1 9 1 0 . 1 3

9 . 3 3 7 . 2 0 4 3 . 6 9 4 . 8 6 3 . 2 4 1 . 0 3 o.as 0 . 2 7 C . 2 ;

- C . O l - 0 . 0 9 - C . 3 9 - 1 . 2 4 - 1 . 4 0 — 2 . 6 2 - 2 . 8 3

- 1 1 . 1 7 - 1 6 . 2 9 - 1 5 . 7 0 - 3 0 . 9 6 - 3 6 . 2 5 - 8 2 . 9 5

- 1 1 6 . 1 5 - 1 2 5 . 3 9 - 1 3 9 . 7 4 - 1 5 4 . 7 5 - 1 6 0 . 3 3 - 1 7 3 - 6 8 - 1 7 8 - 2 6 - 1 9 1 . 8 1 - 2 5 4 - 3 0 - 5 0 7 . 3 7 - 5 3 4 . 7 0 - 5 7 5 . 2 2 - 5 9 4 . 7 C - 3 1 9 . 1 2

- 1 1 2 6 . 6 0

NARIO-II

AT-N . LOC.

3o 10 6 6 63 62 2 7 11 5 9 4 4 53 a

13 5

16 4 I

21 2 4 38 19 18 30 56 4 9 4 7

\ 12 1 51

42 L 50 » 17 ! 32 > 4 6 3 20 I 39 i 4 3 3 25 I 4 8 3 35 3 28 3 3 3 3 2 9 1 40 3 37 I 41 3 38 2 45 1 57 2 26 I 31 2 52 1 23 1 2 1 ZZ 1 3 1 6 I IS 1 7 1 14 1 60 2 54 1 a l 2 55 2 9 2 34 I 04 I 65

(SCLIC SPACERI <ITH 250

SHEAR MA STRESS NU

2 4 5 . 4 5 2 1 5 6 - 4 4 2 1 2 9 - 1 3 2

9 4 . 3 8 1 7 2 . 3 9 1 6 3 . 7 2 2 6 3 . 1 4 1 5 8 . 0 3 2 5 6 . 4 1 2 3 6 . 4 0 2 3 4 . 9 9 1 5 2 . 3 3 2 SC.37 1 4 9 . 1 3 I 4 3 . 6 6 2 4 3 . 3 5 2 4 1 . 9 1 1 3 9 . 6 5 1 3 9 . 4 3 2 3 9 . 3 6 1 3 3 . 5 9 1 3 C . 6 4 I 3 C . 2 3 1 2T..26 1 2 ( . 5 1 1 2 2 . 3 3 I 2 2 . 3 9 1 2 1 . 3 2 1 2 1 . 1 7 1 1 8 . 2 0 1 1 6 . 7 4 1 U . S 3 2 1 2 . 6 7 1

i . 0 2 1 5 . 6 3 1 3 . 8 6 3 3 . 7 5 3 2 . 3 0 : 3 . 3 4 3 . 3 1 3 . 3 0 1 . 9 7 1 . 6 0 C.60 0 . 5 3 C . 3 2 3 . 4 4 C .43 0 . 3 6 0 . 1 7 C .12 C . 0 3

- 0 . 0 5 - 1 . 7 7 - 3 . 3 1 - 5 . 9 1 - 6 . 1 1 - 7 . 7 5 - 9 . 8 1

- 2 2 . 2 9 - 2 6 . 0 6 - 2 7 . 4 1 - 3 3 . 1 1

- 1 2 4 . i 9 - L 9 4 . 1 4 - 3 9 7 . 0 5

9 . LOC.

44 45 54 66 64 18 62 11 53 .9 30 27 60 23 34 32 57 13 52 59 21 41 31 61 49 58 19 22 39 63 16 26 24

L 47 7

1 43 1 46 1 51 i 38 i 56 I 5

1 I 3 3 37 3 12 3 17 1 50 3 20 3 25 3 33 3 39 3 28 3 29 I 48 1 49

^ "• I 2 1 6 1 3 1 40 2 19 1 14 1 42 2 10 2 36 2 55

PSI SEA«.A«T XOOULUS

MAA. P R I N . STRESS

2 7 0 7 . 3 0 2 3 9 3 . 1 0 1 6 1 8 . 2 0 1 4 5 6 . 9 0 U 9 2 . 0 0

9 3 1 . 4 2 5 9 1 . 2 2 5 8 4 . 8 8 5 0 0 . 5 3 3 8 2 . 4 8 3 3 7 . 3 9 3 1 7 . 7 9 2 5 1 . 6 0 2 1 0 . 9 0 2 0 4 . 9 3 1 7 3 . 6 8 1 6 4 . 1 2 1 5 2 . 9 8 1 4 7 . 5 5 1 4 7 . 1 6 1 3 5 . 1 8 1 2 3 . 9 2 1 2 0 . 1 8

9 1 . 4 7 8 6 . 8 3 6 9 . 4 8 6 0 . 8 7 5 9 . 3 9 4 7 . 9 8 4 4 . 0 9 4 3 . 7 4 4 0 . 7 3 3 8 . 0 1 3 4 . 8 3 3 2 . 6 7 2 8 . 7 3 2 7 . 7 8 2 3 . 1 4 2 2 . 8 0 2 2 . 1 1 2 1 . 1 9 1 9 . 4 1 1 8 . 7 2 1 9 . 6 3 1 5 - 4 5 1 3 . 8 0 1 0 . 8 2 1 0 . 4 1

6 . 3 1 6 . 1 1 2 . 3 0 2 . 0 7 1 . 5 9 0 . 6 6 0 . 3 6 0 . 2 6

- 0 . 0 1 - 0 . 0 6 - 0 . 3 9 - 0 . 8 4 - 0 . 9 9 - 1 . 7 6 - 3 . 4 8 - 4 . 4 2

- 1 8 . 4 8 - 4 0 6 . 3 2

MAT. NUM.

2 2 2 2 I 1 1 2 2 2 2 2 1 2 2 1 1 2 1 1 1 1 1 1 1 1 1 2 3 1 1 1 2 1 3 3 I 1 1 1 3 1 I I 3 1 3 1 3 1 3 1 1 1 3 3 3 3 3 1 3 1 1 1 2 2

L O C

3 * 10 4 4 11 6 6 6 ) 6 2 2 7 9 2 94 9 3

9 9 9 32 3 4 13

8 1 9

9 16

4 1

2 1 31 3 0 2 4 98 18 5 6 42 57 4 9 4 5 4 1 12 9 1 90 6 0 * 0 39 17 14 47 22 46 19 20 64 4 3 23 2 9

6 2

4 8 3 8 39 2t 33 2 9

3 37 69 61

7 2 6 59

MEN. PRIM. STRESS

8 2 0 . 7 1 ( 1 0 . 4 8 3 4 9 . 0 9 2 9 4 . 7 9 1 7 8 . 9 9 1 7 4 . 9 7

3 9 . 3 9 2 4 . 3 4 2 0 , 3 0 1 9 . 1 0 1 4 . 5 4 1 1 . 2 9 1 1 . 0 4 1 0 . 1 3 9 . 3 0 5 . 7 9 4 . 1 3 4 . 2 9 2 . 2 7 0 . 7 4 0 . 3 2

- 0 . 6 1 - 0 . 8 8 - 0 . 9 4 - 1 . 0 4 - 1 . 2 7 - 1 . 7 9 - 1 . 8 4 - 2 . 0 3 - 2 . 1 9 - 3 . 0 8 - 9 . 4 9 - 3 . 6 0 - 4 . 3 2 - 4 . 7 9 - 7 . 6 4 - 7 . 8 8

- U . 3 9 - 1 7 . 0 2 - 2 0 . 5 1 - 2 2 . 2 0 - 2 3 . 1 9 - 2 3 . n - 2 7 . 6 8 - 3 6 . 4 2 - 3 9 . 1 9 - 4 8 . 3 9

- 1 1 0 . C 9 - 1 1 4 . 4 } - 1 2 8 . U - 1 3 9 . 7 6 - 1 9 4 . 1 4 - 1 8 3 . 2 0 - 1 7 3 . 8 7 - I U . 0 4 - 2 0 3 . 1 4 - 2 4 9 . 1 8 - 2 8 9 . 1 7 - 3 9 1 . 7 0 - 9 0 8 . 7 8 - 5 C 8 . I 9 - 5 7 8 . 8 9 - 5 9 7 . C8 - 8 2 9 . 4 3

- 1 1 2 6 . 6 0 - 1 7 6 2 . 4 0

MAT. 9 UN.

2 2 2 2 2 2 2 1 1 I 3 3 1 6

3 1 3 3 1 3 1 3 3 3 3 1 3 1 2 3 1 1 1 3 1 1 1 1 1 1

* 1 I 1 I 2 1 I 1 1 1 1 1 1 1 1 2 2 2 2 1 2 2 1 1 2

LOC.

10 36 2 7 11 4 4 93 19 16 56 66 12 31 13 50 17

8 20 44 24 29 21 28 3 3 2 9 3 9

1 43

4 3 2 37

9 6 1 4 7 3 8 99 62 4 8 49 58 39 42 30 40 4 1 31 32 57 2 3

2 2 2

3 6

19 7

14 60 26 94 18 49 41

9 3 4 44 69 99


Material No.

1 2 3

Material Type


152

V-MORM STRESS

2 9 9 6 . 9 0 2 4 2 2 . 9 0

9 1 3 . 2 9 7 9 3 . 0 1 5 9 1 . 5 4 1 9 8 . 9 1 4 2 . 6 6 3 7 . 9 2 3 4 . 2 8 3 6 . 0 6 3 9 . 8 8 2 9 . 9 1 2 4 . 3 0 2 2 . 0 7 1 4 . 2 2 1 1 . 7 2

7 . 3 4 7 . 2 9 7 . 2 1 6 . 9 0 6 . 9 2 5 . 8 8 3 . 6 7 2.ia i.ac 1 . 2 9 1 . 1 4 0 . 8 6 0 . 7 0 0 . 2 3

- 0 . 2 9 - 1 . 4 2 - 1 . 4 8 - 2 . 1 7 - 2 . 7 3 - 3 . 6 1 - 4 . 1 9 - 5 . 1 9 - 5 . 2 8 - 6 . < . 3

- 1 0 . 6 3 - 1 1 . O O - 1 1 . 4 3 - 1 2 . 9 4 - 1 3 . 5 1 - 1 8 . 3 2 - 2 1 . 1 9 - 2 2 . 9 0 - 2 3 . 6 3 - 2 4 . 5 0 - 2 6 . 0 8 - 3 1 . 4 1 - 3 4 . 2 1 - 8 9 . 7 8 - 4 1 . 9 8 - 4 2 . 5 6 - 4 3 . 1 7 - 4 1 . 2 2 - 6 6 . 8 4

- 1 9 6 . 1 2 - 2 9 9 . 7 8 - 2 9 9 . 7 9 - 5 7 3 . 6 6 - 7 3 8 . 5 0

- 1 1 0 9 . 3 0 - 2 8 1 6 . 2 C

ui<

M A T . N U M .

2 2 2 2 2 2 1 2 1 2 I I L 1 I I 1 1 1 1 1 1 I 3 3 1 3 3 1 i 1 3 1 1 3 1 I 3 I J

3

1 1 3 1 3 3 1 1 1 I 1 1 1 1 3 1

2

2

2 2 2

SEREC

L L I C .

1 1 4 4 2 6 5 2 3 6 2 7 2 3 3 4 2 4 3 2 5 8 4 8 57 4 7 4 9

7 1

9 0 4 5 2

6 1 6 2 2 8 2 9 6 3 3 3 3 3 6 9 3 7

3 3 8 3 0 6 4 4 3

6 4 0 2 9 3 9 4 6 2 0

3 5 9 5 1 6 3 5 6 17 19 4 1 4 2

2 1 13 14 16 12 31 19

:o 53

9 13 4 3 5 4 55

iTRESSES S C E N ;

2-KCRM !^ STRESS NUI

2 5 1 7 . 7 0 2 9 0 9 . 0 6 2 8 9 7 . 8 6 2 7 7 2 . 5 7 2 7 3 1 . 6 8 I 6 9 1 . 6 8 I 5 8 3 . 3 0 I 5 4 1 . 8 8 I 5 3 6 . 4 9 Z 4 7 7 . 2 5 1 3 7 4 . 6 2 I 3 5 8 . 6 8 I 3 2 5 . 7 3 2 3 0 3 . 2 9 1 2 5 1 . 2 7 1 2 0 0 . 9 8 2 1 3 2 . 1 5 1 1 8 0 . « C 1 1 0 1 . 3 6 1

9 9 . C 9 2 9 8 . 3 9 2 3 6 . 3 1 2 7 8 . 5 0 I 4 5 . 4 2 1 2 6 . 6 1 1 2 4 . 1 8 1 1 0 . 3 3 I

2 . 3 4 I 1 . 2 2 3 0 . 7 0 3 C . 3 7 3 0 - 1 7 3

- 0 . 1 2 - C . 6 9 - 1 . 1 6 3 - 1 . 4 2 - 1 . 5 6 - i . a i - 1 . 9 4 - 4 . J 1 - 4 , 4 2 - 4 . 3 1 - 9 . C 3

- 1 0 . 3 3 - 1 1 . 0 3 - 1 7 . 1 6 - 1 9 . 0 5 - 2 6 . 4 9 - 2 9 . C 7 - 4 7 . 0 2

- 1 1 4 . 1 0 - 1 1 9 . 6 2 - 1 9 a . 9 9 - 2 6 2 . C 4 - 2 6 6 . 9 7 - 3 1 4 - 3 2 - 3 8 4 . 3 8 - 4 0 5 . 2 2 - 4 2 4 . 2 1 - 4 7 1 . 7 5 - 5 3 5 . 9 3 - 5 4 C . 3 5 - 5 6 1 . 5 4 - 5 8 C . 5 4 - 6 4 6 . 2 5

- 3 6 4 3 . 9 0

I B I C - U I

it • *. L O C .

3 6 53 10 1 1 6 3

2 3

64 4 4

6 7

6 1 2 6 14 15 2 7 6 3 ZZ Zi 13 22 19 5 7 50 3 1 4 7 4 2 39 2 9 2 8 3 3

) 43 1 33 L 4 0 1 4 6 i 3 7 i 3 3 I 4 1 ! 2 3 i 3 1 I 4 8 j 20 3 5 6 3 17 1 4 9 2 45 3 12 1 5 8 1 39 2 32 I 5 9 I 24 1 2 1 1 6 2 I 16 1 13 I 3 1 63 2 9 1 5 2 55 I 6 6 1 4 2 34 1 1 2 5 4

( S C L i C SPACEi l l •

SHEAR STRESS

3 4 2 . 3 4 1 8 1 . 1 1 1 3 3 . 6 9 1 0 7 . 3 2 1 0 1 . 3 1 1 C 1 . 3 0

9 i . 6 6 8 5 . 5 1 3 3 . 3 0 7 7 . 9 1 7 C . 7 3 5 8 . 3 0 4 4 . o 3 4 2 . 2 2 2 3 . 3 6 1 6 . 1 2 1 1 . 0 6 1 C . 2 5

8 . 9 8 7 , 1 1 5 . 9 3 ! . 9 1 5 . 6 5 5 . 2 4 4 . 3 4 3 . 0 8 2 . 3 1 1 . 8 8 1 - 8 1 1 . 6 4 1 . 2 9 1 . 0 4 C . 7 3 C . 5 9 3 . 4 5 C . 3 4 C . I O

- 1 . 7 2 - 2 . 0 4 - 6 . 8 9

- I C . 4 4 - 1 4 . 6 7 - 2 3 . 6 5 - 2 4 . 0 3 - n . 6 6 - 2 6 . 9 4 - 3 1 . 1 8 - 3 4 . 1 8 - 3 7 . 5 6 - 2 7 . 7 7 - 4 2 . 2 9 - 4 2 . 7 7 - 4 3 . 7 7 - 5 2 . 6 1 - 5 6 . 9 4 - 5 9 . 1 3 - 5 9 . 4 3 - 4 5 - 7 0 - 3 5 . 4 3 - 3 8 - 6 3

- l i e . 5 4 - 1 2 C . 2 9 - 1 2 1 . 1 1 - 1 3 C - 7 8 - 2 C t . 9 3 - J 3 4 . 3 9

l A T . MUM.

2 2 2 2 2 2 2 1 1 2 1 I 2 2 1 2 1 1 1 1 3 3 3 3 I 3 L 3 3 3 3 3 I 3 3 3 3 1 1 1 I 1 I I 1 1 1

1 I I 1 1 2 I 1 I 2

I 1

2

1 1 2

2

I T H 2 50

uOC.

55 27 52 19 53

9 10 58 42 45 14 40 34 32 24 13 31 50

a 48 51 56 46 43

6 38

4 29 2 9 20 17 12 60 28 37 33 35

2 e2 ae 44 47 I t l

I 49

3 5

o3 33

7 22 6 1 59 36 21 39 15 26 30 4 1 11 57 13 23 54 1 4

P S I SEALANT MODULUS

M A I . P R I N -ITRESS

2 6 0 3 - 6 0 2 3 1 9 . 1 0 2 4 8 0 . 0 0

9 2 0 . 3 5 9 1 7 . 4 9 9 0 6 . 6 9 9 1 3 . 7 6 7 3 3 . 6 1 6 9 1 . 6 8 5 8 4 . 9 3 5 4 2 . 0 8 4 7 7 . 2 9 3 8 0 . 8 7 3 7 8 . 9 1 3 6 3 . 7 9 3 1 7 . 2 2 2 6 3 . 9 6 2 0 6 . 3 4 1 8 8 . 7 3 1 8 2 . 1 6 1 7 4 . 7 9 1 4 1 . 9 7 1 2 0 . 5 1

9 9 . 4 8 9 5 . 7 1 7 9 . 4 0 7 6 . 1 9 7 1 . 2 6 5 7 . 7 8 5 5 . 8 9 4 8 . 0 0 4 0 . 7 3 3 9 . 7 1 3 7 . 8 4 3 2 . 0 0 2 7 . 9 8 2 7 . 1 1

3 . 9 3 3 . 2 7 7 . 2 2 6 . 3 1 4 . 6 8 4 . 1 5 4 . 1 5 3 . 6 8 3 . 3 5 2 . 4 4 2 - 3 8 1 . 5 9 1 . 2 2 0 . 8 7 0 . 3 7

- 1 . 0 9 - 1 . . 0 - 4 . 3 8 - 5 . 8 1 - 8 . 8 4

- 1 0 . 2 2 - 1 0 . 9 1 - 1 1 . 2 3 - 1 6 . 5 1 - 1 9 . 0 1 - 4 0 . 0 9

- 2 4 3 . 1 3 - 4 8 5 . 6 4

- 1 0 9 2 . 5 0

N A T . NUM.

2 2 2 2 2 2 2 1 1 1

1 1 2 1 1 1 I 1 1 1 1 2 2 2 1 1 1 1 1 I 1 2 I 1 1 1 I 1 I 1 1 1 3 I I 3 3 3 3 3 3 3 3 3 3 3 2 3 1 1 1 3 1 2 2

• »

L O C

1 1 3 6 4 4 2 6 33 10 5 2 6 9

2 3

6 4 6

2 7 7

6 1 14 19 2 3 2 2 6 0 9 7 19 3 2 l l 9 8 4 2 4 1 3 0 3 9 4 0 5 0 3 4 2 4 4 7 4 9 3 1 4 8

5 1 4

13 5 9 4 3 6 1 62 2 9 4 6 28 3 8 33 3 9 3 7 23 5 1 2 0 5 6 4 9 17 6 6

8 2 1 12 16

9 5 5 5 4

M I R . P R I M . STRESS

7 4 9 . 8 9 9 5 0 . 1 3 4 7 8 . 9 9 3 1 8 . 4 8

1 8 . 6 3 1 3 . 9 4

8 . 4 2 7 . 8 4 6 . 3 2 4 . 6 7 0 . 7 7 9 . « 9 0 . 3 9

- 0 - 2 1 - 0 . 3 2 - 1 . 2 2 - 1 . J 4 - 1 . 7 2 - 2 . 3 8 - 3 . 6 9 - 4 . 5 7 - 4 . C 2 - 4 . C 3 - 6 . 7 2

- I 0 . C 3 - 1 1 . 0 6 - U , 4 2 - ( 8 . 3 2 - 2 3 . 0 3 - 2 3 . 4 ? - 2 8 . 8 1 - 3 9 . 9 1 - 3 9 . 3 3 - 4 3 . 2 2 - 5 9 . 9 1 - 6 0 . 7 2 - 4 0 . 7 6 - 6 1 . 8 2 - 4 2 . 3 9 - 6 8 . 57 - 7 1 . 7 8 - 3 6 . 3 2 - 9 9 . 1 9

- 1 0 1 . 8 1 - i c 2 . : i - 1 2 2 . 0 0 - 1 2 3 . 0 9 - 1 3 1 . 7 4 - 2 0 4 . 9 4 - 2 1 4 . 7 4 - 2 6 3 . C 6 - 2 6 9 . 3 4 - 3 0 8 . 2 1 - 3 6 0 . 1 1 - 3 8 9 . 1 0 - 4 C 8 . C 7 - 4 7 3 . 7 7 - 4 8 0 . 8 8 - 5 4 0 . 4 4 - 3 6 1 . 3 9 - 5 7 4 . 0 9 - 9 8 3 . 7 9 - 4 4 7 . 2 8 - 7 4 6 . 8 2

- 2 9 6 6 . 3 0 - 3 6 6 0 . 7 0

<Ar.

2 2 2 2 2 2 1 1 1 1 1 3 3 3 3 1 3 1 1 I 3 1 3 3 3 3 3 1 3 3 1 1 1 3 1 1 1 1 I 2 1 1 1 I I 2 1 1 2 1 1 I 2 I 1 1 1 2 1 1 2 2 1 2 2

2

U X .

1 1 3 6 4 4

• 2 6 2 7 3 2 4 7

7 2

50 6 1 28 39 33 2 9 6 9 37

3 6 4

6 38 4 8 23 4 3 44 2 0 3 1 6 0 17 9 6 4 9 I S 2 2 12 1 4 3 9 4 0 23 3 1 52 57 58 42 13 4 1 19 24 59 10 2 1 6 2 16 53 13

a 63

5 9

6 6 4

18 34

I 4 9 55 54


Material No.

1 2 3

Material Type


153

T - 9 0 I B 88 s n s s s 911

1 3 0 0 7 . 0 0 2 1 1 8 0 6 . 0 0 2 a 3 2 1 . 8 0 2 3 7 7 2 - 1 0 2 3 2 6 3 , 7 0 2 1 9 0 0 . 1 0 2

9 4 7 . 1 8 2 ! 9 « , 2 6 2 5 8 7 . 7 3 2 1 3 2 . 8 7 1 1 1 8 . 9 0 1 9 1 . 6 7 1 » « . a 8 1 3 8 . 2 6 1 3 1 . 0 5 1 2 S , 2 2 1 2 4 , 0 7 1 2 0 . 7 4 1 1 9 . 4 8 1 1 6 . « 3 1 1 5 . 7 8 3

7 . 7 8 1 5 . 6 6 2 9 , 6 6 1 5 , » 2 3 5 , 2 6 5 . 1 8 : 4 . 3 7 3 . 1 7 2 - 5 9 1 .15 0 . 5 2

- 0 . 1 8 - n . 6 3 - 1 . 6 3 - 3 . 2 5 - 3 . 7 » - i » -a7 - 5 . 9 0 - 6 . 7 0 - 9 . 8 «

- 1 0 . 6 0 - 1 1 . 3 6 - n . S 5 - 1 4 . 9 4 - 1 5 . 3 4 - 1 5 - 9 0 - 1 7 . 3 3 - 1 7 - 3 9 - 2 2 . 6 0 - 2 2 . 7 6 - 2 3 . 6 1 - 3 1 . 5 2 - 3 4 . 3 8 - 4 2 . 0 5 -4 2 . 3 7 - 5 4 . 6 5 - 6 1 - 5 1 - 7 9 , 5 9 - 9 8 . 7 9

- 4 8 7 . 6 7 - 9 9 7 . 6 8

- 2 9 0 1 . 6 0 - 3 U 2 S . 90 - 1 6 0 2 . 6 0

J W ^ * %M \^

- 1 * 1 5 1 . 3 0

o i o n n

r*

8 . I O C .

1 1 « 4 5 2 3 « 2 6 2 7 10 3 « 3 2 3 1 3 0 2 « 5 7 5 8 9 7 4 8 SO 4 9 2 3

7 5 6

3 S6 6 6 2 8 6 2

1 51 1 61 1 29 i 43 I 33 1 65 i 35 1 a 1 64 1 «3 3 37 1 « 1 5 1 6 1 40 3 38 1 1 1 60 1 59 a 25 2 19 1 39 3 20 1 2 1 42 1 41 1 22 1 15 1 18 3 17 1 16 1 21 3 13 3 12 2 53 2 9 2 18 2 ; » 2 45 2 55

S n z S S B SC78ARX

: - 9 0 8 a a AT. STB u s 8on .

1 8 5 2 5 . 9 0 2 8 * 4 1 . 6 0 2 3 8 7 0 . 0 0 2 3 5 6 3 . 7 0 2 2 2 7 3 . 7 0 2 2 1 1 1 . 1 0 2 1 2 7 8 . 9 0 2

9 3 9 . 1 7 1 6 0 5 . 3 5 1 4 6 7 . 3 9 2 4 2 2 . 8 4 2 3 1 0 . 6 8 2 2 8 0 . 3 2 1 2 3 3 . 0 4 1 177 .03 1 1 6 3 . 2 9 1 148 .12 1 140 .82 1 101 .79 1

9 8 . 1 9 1 9 6 . 2 0 1 8 8 . 1 2 1 6 7 . 6 4 1 5 3 . 5 3 1 4 5 . 2 3 1 4 2 . 9 8 1 3 1 . 1 7 1 1 6 . 7 7 1

8 .68 3 4 . 2 6 3 4 , 2 9 3 2 , 7 0 3 2 .45 3 2 . 3 1 3 2 . 1 3 3

- 0 . 6 5 3 - 5 . £ 6 1 - 6 . 7 6 3 - 7 . 9 8 3 - 8 - 4 3 1 - 8 - 9 1 3

- 1 3 . 2 0 1 - 1 3 . 4 4 3 - 1 5 - 0 4 1 - 1 8 . 6 9 1 - 1 9 . 3 * 3 - 3 2 - 4 0 1 - 3 5 . 6 7 1 - 3 8 . 7 7 1 - 4 1 - 7 2 1 - 4 3 . 2 9 3 - 4 4 . 7 3 1 - 9 9 . 6 9 1 - 9 0 . 6 3 1 - 9 9 . 1 8 2

- 1 5 5 . 2 3 1 - 1 9 6 . 0 1 1 - 1 9 7 . 0 0 1 - 2 6 0 . 9 6 2 - 3 5 * . 7 8 1 - 6 4 5 . 6 9 1 - 9 3 2 . 5 6 1

- 2 9 2 9 . 3 0 2 - 3 2 2 7 . 4 0 2 - 3 2 8 3 - 7 0 2

- 1 4 3 5 2 - 0 0 2

9-17

LOC.

38 10 S3 11

*« 2 7 26

1

« i a 19 32

5 6 6 5 7 6 0 6 3 5 0 6 1 4 7 1« 15 6 2 42 2 2 6 « 3 0 39 5 6 4 6 5 1 2 9 4 3 2 8 35 33 4 0 25 20 59 3 7 6 5 38 2 3 41 17 48 3 1

a 4 9 12 5 8

7 2 * 4 5 2 1 16 13 52

6 3 2 9

55 34 5 4

<S0L2D sfACzi ) w i r a 250

s a i u 3 T H S 3

6 1 8 . 7 9 6 0 1 , 3 1 572 -59 4 9 6 . 0 3 4 9 8 . 0 2 350 .45 2 5 3 . 1 7 2 * 9 . 5 2 229 .96 1 9 9 . 7 * 19« ,02 109.39

99 ,86 90 .66 86 .38 6 5 . 8 1 59 .83 59 .66 53 ,53 5 0 . 47 50 .«2 33 .96 31 .50 29 .81 2 8 . * 7 28 .46 28 .03 27 .92 25 .10 2 « . 9 1 24 .50 2 3 . 4 7 22-73 19.67 17 .01

7 .52 7 .41 6 .97 5 .95 5 .86 4 .39 2-67 2-15 1,65 3.49

- 0 - 2 3 - 1 - 1 5 - 4 - 2 3 - 5 - 0 7 - 8 . 1 9

- 1 0 . 7 * - 1 5 . 3 8 - 2 6 . 3 6 - 3 2 - 3 9 - 3 2 - 5 6 - 3 5 - 9 6 - 5 7 . 9 0 - 5 8 - 6 1 - 7 9 . 5 1 - 9 3 - 7 6 - 9 9 - 7 1

- 1 3 0 - 4 3 - 2 0 4 . 5 7 - 4 0 3 . 2 6 - 6 7 1 . 2 9 - 9 2 9 . 6 7

a i T . 108.

2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 3 3 1 1 1 1 1 3 1 3 1 3 3

" 3 3 3 3 3 3 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1

2 2 1

bOC.

2 7 45 52 53

9 19 3« 32 26 10 18 1 * 5 8 31 42

8 6 4 2

40 2 * 60

1 62 51 46 54 43

3 5

64 64 SO 38

7 23 30 20 29 17 12 37 28 33 33 48 14 63 65 47 6 1 59 49 21 22 15 55 39 13 57 41 23 44 54 36 11

r s z aiLxn eoooios

aAZ. P 8 I J . STt lSS

1 *547 .00 13079 .00 11811.00

8 * 4 7 . 3 0 4097 .00 392&.20 3 2 8 9 . 9 0 2 * 9 2 . 10

940 .22 7 3 1 . 11 616 .93 6 1 1 . 1 3 6 1 0 . 5 9 «7a.S2 2 8 2 . 4 7 2 3 9 . 6 7 225 .66 172 .38 169 .64 154 .47 1 * 8 . 2 * 1 « * , 7 0 133 ,76 115 .59 109 ,81 104 ,90 104 .69 102 .96

9 9 . 1 7 9 7 . 9 1 7 9 . 5 9 7 8 . 5 9 6 0 . 7 7 5 7 . 18 3 3 . 0 2 49 -78 • 2 . 7 6 4 0 . 4 8 3 3 . 4 3 33- 19 3 0 . 4 * 3 0 . 2 1 28 -22 20-06

8 .89 8 .70 7-70 6.S2 3 . 7 * 3 .30 2 .23 2-19 2 .13 1.15

- 2 . 3 1 - 2 . 6 0 - 4 . 2 7

- 1 7 - 9 * - 1 9 . 4 7 - 4 0 . 2 6 - 4 2 - 8 3 - 5 1 . 5 0 - 5 4 . 6 *

- 3 8 6 . 18 - 3 2 2 7 . 1 0 - 3 4 1 2 - 0 0

I I I . 108-

2 2 2 2 2 2 2 3 1 2 2 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 3 3 1 1 1 3 1 3 3 1 1 3 1 3 2 3 3 3 3 1 1 3 1 1 2 2 2

U K .

3 6 11

«* 10 5 3 S3 2 6 2 7

1 33 19

* 3 6 18

5 6 6 5 7 3 1 6 0 1 * 6 3 5 0 2 3 3 0 • 2 5 8 2 * 6 1 * T 13 6 2 4 1 3 9 2 2 6 *

8 • 0 5 6 4 6 5 1 • 3 * 9 * 8

7 2 9

3 3 8 2 8 5 9

6 3 5 6 5 33 • 5 2 5 3 7 2 0 1 7

2 13 12 2 1 16

9 55 5 *

t Z I . 7 8 1 1 -S T 8 B 8

3 7 3 0 . 3 0 3 * 9 1 . 3 0 3 2 M . 3 0 1 2 * 8 . 2 0 1119-10

961 .84 167. JO

30-52 30 .07 19.79 3 .04 3 . 9 0 1-21

- 0 . 2 8 - 1 . 4 3 - 3 . 0 2 - 3 - 3 7 - 3 . 7 5 - 6 - 6 9 - 8 . J S

- R ) . 0 4 - 1 0 . 6 4 - 1 1 . 7 1 - 1 2 . * 0 - l * . 8 7 - 1 6 . 0 2 - n - 9 2 - 3 0 . 3 4 - 2 1 . 0 4 - 2 3 . 9 1 - 2 1 . 7 4 - 2 5 . * 0 - 2 7 . 1 2 - 3 1 . 7 * - 3 3 . 4 0 - « 3 . 4 7 - 4 3 - 7 8 • 4 3 . 8 7 - 9 1 . n - 5 8 - 2 6 - 4 1 . 3 2 - 6 3 . 3 2 - 7 5 . 1 7 - 7 9 . 3 * - 3 4 . 2 3 - 9 7 . 2 3

- 1 0 3 . J 2 - 1 0 3 . 6 * - 1 1 1 . 3 7 - 1 2 0 . 9 0 - 1 2 9 - 3 6 - 1 6 5 - 3 9 - 1 9 4 . C 2 - 2 3 9 . 9 8 - 2 3 6 - 0 3 - 3 3 4 - 19 - 3 6 4 . 7 8 - 5 * 3 . 8 6 - 6 * 6 - 6 5 - 9 3 5 . 7 0

- 2 9 1 2 . 7 0 - 2 9 3 1 . 3 0 - 3 3 0 0 . 3 0 - 1 7 0 2 . 9 0

- 1 * 1 5 1 . 9 0 - 1 * 3 6 7 . 3 0

BAZ-m .

2 2 2 2 2 2 3 1 1 1 1 1 3 3 3 3 1 1 1 1 3 1 1 1 1 3 1 3 3 3 3 3 1 3 1 1 3 1 1 1 1 1 1 1 1 J 1 1 1 1 1 1

. 2 1 3 1 3 1 1 3 3 3 2 3 3

U K .

3 6 11 • 4 2 4 2 7 10 3 3 3 0 * 7 9 4 6 6 6 1 3 8 3 5 3 3 3 9 6 3 5 7 6 2

S 1 7

* 6 *

1 6 9 5 6 6 0 2S 3 0 4 6 3 1 • 3 5 9 3 8 • 8 3 3 17 I S 4 9 • 0 3 9

7 3 1 4 3

8 12 14 2 * 5 8 * 1 3 3 3 1 16 19 13 5 2

6 S3

3 2

18 9

] * 45 55 S *

Matprial Information

Material No.

1 2 3

Material Type

Documents

THE STRUCTURAL MECHANICS BEHAVIOR OF SEALED …