Testing and Analysis of Iron

and Plastic T-joints in

Sprinkler Systems NEESR – GC: “Simulation of the Seismic Performance of Nonstructural Systems”

Joseph Dow

Home Institution: Lehigh University

REU Site: State University of New York, University at Buffalo

Advisors: Dr. Andre Filiatrault, UB- PI, and Dr. Gilberto Mosqueda, UB- Co-PI

PhD Student: Yuan Tian M.S. Student: Jessica Fuchs

2

Abstract

This paper details the research performed at the State University of New York;

University at Buffalo during the summer of 2009 as part of the NEES Grand Challenge Project

“Simulation of the Seismic Performance of Nonstructural Systems.” The research aims to

provide industry engineers with tools to improve the seismic resilience of ceiling-piping-partition

system. The research covered in this report focused specifically on t-joints in branch lines of

sprinkler piping systems. Cyclic loading of the various pipe materials led to moment and rotation

fragility curve generation. A preliminary analysis of the demands on piping systems was

performed using the data from this research to generate an interstory drift capacity for the joints.

The results of this analysis were then compared the interstory drift expected for different damage

states according to FEMA 356 documentation. Ultimately, this preliminary analysis showed that

the t-joints can reliably be installed at any location along a vertical pipe between two stories of a

building. Further verification of the expected joint rotation demands in piping systems based on

building interstory drifts is necessary and ongoing research will serve to provide that.

3

Table of Contents

Abstract ………...…………………………………………………………………….2

1. Introduction …………………………………………………………………........4

2. Methods ……………………………………………………………………………5

2.1. Methods of Experimentation on T-Joints ………………………..........5

2.1.1. Testing Setup and Instrumentation ………………………..5

2.1.2. Materials Tested ………………………………………………6

2.1.3. Loading Methods …………………………………………….6

2.2. Analysis of Experimental Data ……………………………………….7

2.2.1. Definition of a Fragility Curve ……………………………..7

2.2.2. Constructing a Fragility Curve …………………………….7

2.3. Analysis of Demand on Piping Systems ………………………………7

2.3.1. Real Life Scenario ……………………………………………..7

2.3.2. Assumed Configuration ……………………………………….8

2.3.3. Static Analysis …………………………………………………8

3. Results ………..………………………………………………………………….9

3.1. Fragility Curves ………………………………………………………....9

3.2. Interstory Drift Capacities…………………………………………..…11

3.3. Capacity Comparison with FEMA Document 356…………………...12

3.4. Assessment of Analysis Methods………………………………………13

4. Conclusion…………………………………………………………………….…..13

Acknowledgments……………………………………………………………….…..13

Works Cited …………………………………………………………….……….…14

Appendix ………………………………………………………………………….....15

4

1. Introduction

“Of the approximate $6.3 billion of direct economic loss to non-residential buildings that

occurred due to the 1994 Northridge Earthquake, only about $1.1 billion is due to structural

damage. (Kircher, 2003).” The NEES Grand Challenge Project “Simulation of the Seismic

Performance of Nonstructural Systems” commits significant resources and research efforts to the

study of the ceiling-piping-partition nonstructural system. With focus on suspended ceilings,

piping subsystems and components, and partition walls this research aims to study the

performance of these nonstructural components with a system approach, studying the interaction

of all three nonstructural aspects. The ultimate vision of the project is to provide “practicing

engineers and architects with verified tools and guidelines for the understanding, prediction and

improvement of the seismic response of the ceiling-piping-partition nonstructural system”

(Maragakis et al., 2007).

While a study of the ceiling-piping-partition system will occur in the future, this paper

discusses the sprinkler piping component testing performed at the State University of New York,

University at Buffalo during the summer of 2009. This component research led to fragility curve

generation for T-joints in schedule 40 black iron piping of 2”, 1” and 3/4" and CPVC piping of

2” diameter, with 1” and 3/4" CPVC piping research ongoing. Analysis of the moment and

rotation data obtained at leakage of the T-joint was used to mark the capacity of the T-joints

under seismic loading.

Throughout past earthquakes it has often been true that a structure was designed

adequately to withstand seismic activity but was still rendered unusable after the earthquake.

This incapacitation was frequently a result of water damage due to failed sprinkler and plumbing

systems. The Northridge Earthquake Hospital Water Damage Study reports that at the Los

Angeles County Olive View Hospital “drops to [sprinkler] heads twisted and failed at screwed

fittings. (Ayers & Ezer, 1996).” The report also states that at Holy Cross Medical Center 1220

sprinkler heads were replaced where “short drops to heads failed at screwed tee pipe or heads

struck the hard ceiling. (Ayer & Ezer, 1996).” Statements like those found in the Ayer & Ezer

Associates study are common following most earthquakes. Subsequently, it is these issues that

this nonstructural components research is working to investigate and remedy.

Ultimately, the importance of improving the performance of nonstructural systems is

undeniable, and sprinkler systems are a significant area to consider. Many reports similar to that

of Ayers & Ezer Associates have studied the resulting damage on sprinkler systems after an

earthquake. However, few research initiatives have inspected the fragility of the components in

sprinkler systems as well as the behavior of entire systems as definitively as this NEES Grand

Challenge project is working to do. Sprinkler components testing is only a portion of the overall

nonstructural components research being performed. Nevertheless, as will be described in this

paper, a simplified analysis of the demands on piping systems was possible and valuable insight

into the capabilities of sprinkler joints was achieved.

5

2. Methods

2. 1. Methods of Experimentation on T-Joints

2.1.1. Testing Setup and Instrumentation

In order to test the fragility of the t-joints in black iron and CPVC piping a test setup was

erected to displace the joint in both directions along „the bottom of the T‟, an axis perpendicular

to the center of the t-joint. The test setup can be seen below in Figure 1.

Figure 1 – Test Setup for T-Joint Testing

As can be seen in Figure 1, the test setup consisted of two 5 kip load cells at the ends of

the top of the T, a 22 kip actuator with a 6 inch stroke, a water intake and venting valve, 10 linear

potentiometers, and numerous LED/infrared lights to work in conjunction with the KRYPTON

coordinate tracking camera.

The water intake was connected to a faucet to fill the pipe arrangement with water to be

able to monitor when leakage occurred. A second valve was used to vent the air out of the piping

arrangement, leaving the setup with city water pressure in the pipe.

The actuator enacted a predetermined loading pattern to displace the joint to a certain

limit, be it 3 inches in either direction or 6 inches in one direction. A load cell on the actuator

reported the force exerted by the actuator along the pipe, while two 5 kip load cells measured the

shear force at each end of the T. This shear force measurement was used for verification of the

force reported by the actuator, as well as for tracking the force distribution when one side of the

t-joint yielded resulting in unequal forces on each side of the t-joint.

The KRYPTON coordinate tracking system uses a unique camera to track the movement

of an arrangement of blinking LED/infrared lights using the initial position of the lights as a

reference point. The displacement readings, taken at certain time intervals were then reported in

a spreadsheet format with a timestamp. Having the displacement data provided the ability to

calculate a rotation between the light on the edge of the joint and the light on the end of the pipe

next to the joint.

Eight of the ten linear potentiometers were arranged in pairs at the pipe connections to

gather data to be used in calculating rotation as well. At each of the pipe connections with the t-

6

joint along the top of the T, a potentiometer was mounted in the horizontal plane on the front and

back face. The potentiometers displaced as the pipe rotated locally in relation to the t-joint and

rotation was calculated by taking the difference in potentiometer measurements divided by the

diameter of the pipe, across which the sensors were placed. The remaining two potentiometers

were mounted on the outer ends of the top of the T to monitor slip of the cap within the collar on

the load cell.

2.1.2. Materials Tested

In testing the seismic performance of sprinkler piping this phase assessed the behavior of

branch line piping rather than the main piping which will be studied in the next phase. Branch

line piping tested was of 2 inch, 1 inch and 3/4 inch diameter. The testing completed entailed

pipe materials of both black iron schedule 40, and chlorinated polyvinyl chloride (CPVC)

schedule 40 pipe. Various connection types exist among piping in practice yet branch line piping

normally only uses glued or threaded connections. Therefore this testing studied threaded

connections of the black iron pipe and glued connections with the CPVC piping.

2.1.3. Loading Methods

Four tests were performed on each pipe size of 2 inch, 1 inch and 3/4 inch for each

material. The testing included one monotonic test and three cyclic tests using the loading

protocol shown below.

Figure 2– Monotonic and Cyclic Loading Protocols

The loading for the monotonic test depicts a maximum displacement of 6 inches, with a

constant loading rate of .01 in/sec. The monotonic test was performed as a baseline test because

regularly the joint would yield at a smaller displacement during cyclic loading than monotonic.

Three cyclic tests were performed in order to gather sufficient data to create the fragility curves

discussed later. The cyclic protocol above shows a gradually increasing displacement with each

cycle, at a maximum loading rate of .2 in/sec.

As the pipe was deformed during the tests an electric switch would mark the occurrence

of leakage on each end of the T-joint. Four potentiometers placed around the T-joint

continuously recorded data that was then aligned with the switch mark to determine the rotation

7

of the joint that caused the pipe to leak. For the monotonic test simply selecting the data at the

point of the switch was acceptable. However, for the cyclic tests the data was taken from the

previously experienced peak. For example, if the pipe leaked mid cycle the data was taken at the

previous loading extreme, because the pipe had been able to withstand rotation at that maximum.

2.2. Analysis of Experimental Data

2.2.1. Definition of a Fragility Curve

In “Developing Fragility Functions for Building Components for ATC-58” (Porter et al.),

a fragility function is defined as “the probability that a component of a given type will reach or

exceed a particular damage state, denoted by dm, as a function of EDP [engineering demand

parameter].” Essentially, the fragility curves developed portray the chance that a T-joint of a

certain size and material will leak at the corresponding moment or rotation. The median, xm, is

the moment or rotation that was extracted from the experimental data to then analyze the demand

on piping systems. The dispersion, β, is calculated as the logarithmic standard deviation of the

function and assesses the precision among the data points collected experimentally. Similarly, a

Lilliefors goodness-of-fit test judges whether the fragility function fits the data closely enough.

2.2.2. Constructing a Fragility Curve

Two fragility curves were constructed for each pipe diameter of each material. In order to

create a fragility curve the experimental data from the three cyclic tests was used. Specifically,

this data was the moment or rotation at the joint at the occurrence of first leakage. The equations

below show the steps necessary to calculate the median value and the dispersion.

Figure 3 – Fragility Curve Equations

2.3. Analysis of Demand on Piping Systems

2.3.1. Real Life Scenario

Throughout a building there are numerous piping configurations that exist. Commonly

thought of sprinkler piping exists within the ceiling between floors. Often times, the failures that

occur in the fire sprinkler system occur when this piping arrangement in the ceiling hits against

other objects, such as HVAC units or floor beams. The failures can also occur at the point of

interaction between the sprinkler head and the ceiling tiles of a drop ceiling or gypsum board

ceiling. Certain aspects of these occurrences will be tested later on in this research project. At

this point the data collected allows for an analysis of the moment that T-joints experience when

placed in a system.

8

2.3.2. Assumed Configuration

Figure 4 – Assumed Pipe Configuration (Fixed-Fixed Connection)

For this portion of the data analysis the intent is to connect, in a simplified manner, the

real world demands on a T-joint. The above pipe configuration shows the assumed arrangement

for the T-joint. The pipe is oriented in a vertical manner as would exist in a wall between two

floors. The connections at either end of the pipe were assumed to be fixed symbolizing the

support that exists at the two floor slabs.

2.3.3. Static Analysis

Figure 5– Moment Diagram and Demand Analysis Equations

The static analysis addresses a moment generate at the ends due to an offset between the

two fixed ends. From these assumptions and a linear analysis of moment acting at both ends of

the pipe, a moment function was derived. The moment diagram and equations shown above in

Figure 5 present the process followed to perform this analysis of demands on piping systems.

The moment equation was found and then solved for delta, ∆, the movement of one floor.

Concrete Slabs of Two Stories T-Joint

12’ Story Height

6EI∆/L2

6EI∆/L2

y

9

Varying the T-joint location, and using the moment known to cause leakage as determined from

the laboratory testing, a floor drift capacity was determined for the T-joint. This interstory drift,

which equaled the shift of a floor divided by the height between the slabs, was then graphed for

the various pipe sizes for both materials.

Essentially, this demand analysis determined where a T-joint could be placed along a 12

foot pipe in order to prevent leakage of that joint within certain drift expectations. The graphs

presented in the Results section depict the maximum interstory drift that a certain T-joint could

handle based on it‟s location along the 12 foot pipe.

3. Results

3.1. Fragility Curves

Median Moment (kip-in) Dispersion β Num. of Samples Lilliefors Test

BIT 3/4 '' 3.411 0.141 3 Passes

BIT 1 '' 5.791 0.062 3 Passes

BIT 2 '' 20.417 0.207 3 Passes

Figure 6 – Moment Fragility Curve and Data for Black Iron Threaded Pipe

Median Moment (kip-in) Dispersion β Num. of Samples Lilliefors Test

CPVC 2 '' 2.526 0.110 3 Passes

Figure 7 – Moment Fragility Curve and Data for CPVC 2” Pipe

10

Median Rotation (rad) Dispersion β Num. of Samples Lilliefors Test

BIT 3/4 '' 0.054 0.257 3 Passes

BIT 1 '' 0.033 0.507 3 Passes

BIT 2 '' 0.013 0.580 3 Passes

Figure 8 – Rotation Fragility Curve and Data for Black Iron Threaded Pipe

Median Rotation (rad) Dispersion β Num. of Samples Lilliefors Test

CPVC 3/4 ''

CPVC 1 ''

CPVC 2 '' 0.100 0.112 3 Passes

Figure 9 – Rotation Fragility Curve and Data for CPVC Pipe

The fragility curves in Figures 6 and 7 above show the moment results for the 2”, 1” and

3/4" schedule 40 black iron threaded pipe and the 2” CPVC pipe. The testing for the 3/4” and 1”

CPVC pipes is still ongoing. Overall, the data shown in the CPVC fragility curve and the black

iron threaded pipe fragility curves resulted in strong dispersion numbers and passed the Lilliefors

goodness-of-fit test, verifying that the data was strong and the curves accurately represent it. The

rotation fragility curves in Figures 8 and 9 follow suit in terms of fitting the data accurately. In

this phase of the project the analysis used only the moment data from these fragility curves.

11

3.2. Interstory Drift Capacities

Figure 10 – CPVC 2” Interstory Drift Capacity

Figure 11 – Black Iron Threaded Pipe Interstory Drift Capacity

-35

-25

-15

-5

5

15

25

35

0 50 100 150

Inte

r-st

ory

Dri

ft (

%)

y (in)

CPVC Pipe Drift vs. Joint Position

2" pipe

-15

-10

-5

0

5

10

15

0 50 100 150

Inte

r-st

ory

Dri

ft (

%)

y (in)

Black Iron Threaded Pipe Drift vs. Joint Position

2" pipe

3/4" pipe

1" pipe

12

The graphs in Figures 10 and 11 show the results from the simplified model of a real

world scenario. Shown on the vertical axes are the inter-story drifts, they are plotted against the

vertical position of the T-joint along the pipe. Each curve defines the capacity for drift for the

specific pipe material and diameter.

3.3. Capacity Comparison with FEMA Document 356

For Concrete Frames, Steel Moment Frames and Braced Steel Frames, FEMA document

356 lists transient interstory drift limits as shown below.

FEMA 356 Limits pg. 42 Collapse Prevention Life Safety Immediate Occupancy

Concrete Frames 4% transient 2% transient 1% transient

Steel Moment Frames 5% transient 2.5% transient 0.7% transient

Braced Steel Frames 2% transient 1.5% transient 0.5% transient

Figure 12 – FEMA 356 Interstory Drift Limits

The levels reported in FEMA 356 are Collapse Prevention, Life Safety, and Immediate

Occupancy. Collapse Prevention indicates a level of drift at which the structure experiences

serious damage and is pushed to the brink of collapse. Life Safety describes a situation where

there is visible damage to the structure, however, the occupants are able to evacuate the building

safely. Lastly, Immediate Occupancy defines a scenario where immediately after the seismic

activity has stopped the building is still able to be re-occupied and functioning.

BLACK IRON Pipe Size Concrete Frames Steel Moment Frames Braced Steel Frames

Collapse Prevention

BIT 2" 27" to 117" 36" to 108" 0" to 144"

BIT 1" 0" to 144" 0" to 144" 0" to 144"

BIT 3/4" 0" to 144" 0" to 144" 0" to 144"

Life Safety

BIT 2" 0" to 144" 0" to 144" 0" to 144"

BIT 1" 0" to 144" 0" to 144" 0" to 144"

BIT 3/4" 0" to 144" 0" to 144" 0" to 144"

Immediate Occupancy

BIT 2" 0" to 144" 0" to 144" 0" to 144"

BIT 1" 0" to 144" 0" to 144" 0" to 144"

BIT 3/4" 0" to 144" 0" to 144" 0" to 144"

Figure 13 – Acceptable Range for Black Iron Threaded Pipe: Based on FEMA 356

CPVC Pipe Size Concrete Frames Steel Moment Frames Braced Steel Frames

Collapse Prevention CPVC 2" 0" to 144" 0" to 144" 0" to 144"

Life Safety CPVC 2" 0" to 144" 0" to 144" 0" to 144"

Immediate Occupancy CPVC 2" 0" to 144" 0" to 144" 0" to 144"

Figure 14 – Acceptable Range for CPVC Pipe: Based on FEMA 356

13

The figures above report an acceptable range to locate the T-Joint to prevent leakage

according to the drifts found in FEMA document 356. The table of values found in the appendix

of this report is an example of the data that was studied to determine where the interstory drift

capacity of the specific pipe fell below the interstory drift defined in FEMA 356. As can be seen

in these tables the T-joint can be placed almost anywhere along the 12‟ pipe without leaking. It

must be kept in mind that this is only for the specific configuration studied and described

previously. Ultimately, there are certain limitations to this analysis procedure.

3.4. Assessment of Analysis Method

The analysis of demands on piping systems examined only a vertical pipe configuration

in the wall, which is assumed to behave linearly. Furthermore, there are numerous variations of

arrangements that T-joints may be placed in a structure and those scenarios must be looked into

to fully assess the vulnerability of piping systems. Additionally, the T-joints are subject to

collision with other nonstructural and structural components within a ceiling or wall that cause

damage other than the moment or rotation that was tested in this experimentation. The analysis

performed provides a valuable step in examining the demand and capacity of piping systems and

has identified further research that may be pursued in the future to fully asses these systems.

4. Conclusion

Thus far, the nonstructural component research performed in this portion of the Grand

Challenge project has provided valuable fragility data for both Black Iron and CPVC schedule 40

branch line pipe diameters. In the preliminary data analysis performed the results showed the T-

joints of these branch line pipe sizes were sufficient to handle nearly all drifts detailed in FEMA

356 document. However, the analysis methods do create certain limitations that prevent complete

translation to real life scenarios.

Further research into CPVC branch line pipe sizes must be completed and fragility of

larger pipe diameters of both CPVC and Black Iron must be assessed. Once this fragility data is

compiled it will be used in creating simulations of larger sprinkler piping systems of numerous

arrangements. The ultimate goal of creating valuable tools for industry professionals will be

satisfied through the compilation of the extensive experimental data achieved through this

testing.

Acknowledgments

The author would like to thank all who helped make this a valuable learning experience

and provided guidance along the way. He extends his gratitude to Dr. Andre Filiatrault, Dr.

Gilberto Mosqueda, PhD student Yuan Tian, and M.S. student Jessica Fuchs for advice,

guidance, and inclusion into the NEES Nonstructural project. In addition the National Science

Foundation and especially the George E. Brown, Jr. Network for Earthquake Engineering

Simulation deserve thanks for making this research experience possible and meaningful. The

author is also grateful for Tom Albrechcinski, Sofia Tangalos and Alicia Lyman-Holt‟s efforts in

organizing the entire REU program. The author also thanks the entire SEESL staff at the

University at Buffalo for their aid in experimentation and instrumentation of the test specimens.

14

Works Cited

Ayers, J. Marx (1996). “Northridge Earthquake Hospital Water Damage Study.” Ayers & Ezers

Associates, Inc. Los Angeles, California.

Bachman, K., Kennedy, R. and Porter, K. (2006). “Developing Fragility Functions for Building

Components for ATC-58.” Applied Technology Council.

Federal Emergency Management Agency (FEMA), (2000). “Prestandard and Commentary for

the Seismic Rehabilitation of Buildings.” (FEMA publication No. 356) FEMA. Washington,

D.C.

Kircher, C. A. (2003) “It Makes Dollars and Sense to Improve Nonstructural System

Performance,” Proceedings of Seminar on Seismic Design, Performance, and Retrofit of

Nonstructural Components in Critical Facilities, Newport Beach, California, pp. 109-119

Maragakis et al. (2007). “NEES Grand Challenge Project Proposal” “Simulation of the Seismic

Performance of Nonstructural Systems”.

National Fire Protection Association (NFPA), (2007). “Standard for the Installation of Sprinkler

Systems.” NFPA, Quincy, Massachusetts.

Todd, D., Carino, N. Chung, R., Lew, H., Taylor, A., and Walton, W. (1994). “1994 Northridge

Earthquake: Performance of Structures, Lifelines, and Fire Protection Systems.” National

Institute of Standards and Technology. Gaithersburg, MD.

15

Appendix

2” Black Iron Demand Analysis Data (As an example)

E= 29,000 ksi Moment of Inertia Calculations I=(π/64)(Do

4 - Di4)

Pipe Outside Diameter (in) Pipe Inside Diameter (in) Moment of Inertia

2.38

2.07

0.673727

1.32

1.05

0.089361

1.05

0.82

0.037473

2"

Fixed End Moment

6EI∆/L2 6EI/L

2= 5.65338281 Moment for 2" = 20.417 kip-in

L=12 feet 144

delta=(M/((2y/L)-1))*(L2/6EI)

y

delta drift (%)

Y

delta Drift(%)

0

-3.611466 -2.507962525

73

260.025555 180.5733

1

-3.6623318 -2.543285941

74

130.012777 90.28665

2

-3.7146508 -2.579618597

75

86.6751849 60.1911

3

-3.7684863 -2.617004374

76

65.0063886 45.14333

4

-3.8239052 -2.655489732

77

52.0051109 36.11466

5

-3.8809784 -2.695123907

78

43.3375924 30.09555

6

-3.9397811 -2.735959118

79

37.1465078 25.79619

7

-4.0003931 -2.778050797

80

32.5031943 22.57166

8

-4.0628993 -2.82145784

81

28.8917283 20.0637

9

-4.1273898 -2.866242886

82

26.0025555 18.05733

10

-4.1939606 -2.91247261

83

23.6386868 16.41575

11

-4.262714 -2.960218062

84

21.6687962 15.04778

12

-4.3337592 -3.00955503

85

20.0019657 13.89025

13

-4.4072128 -3.060564437

86

18.5732539 12.89809

14

-4.4831992 -3.113332789

87

17.335037 12.03822

15

-4.5618518 -3.167952663

88

16.2515972 11.28583

16

-4.6433135 -3.224523246

89

15.2956209 10.62196

17

-4.7277374 -3.283150942

90

14.4458641 10.03185

18

-4.815288 -3.343950033

91

13.6855555 9.503858

19

-4.9061425 -3.40704343

92

13.0012777 9.028665

20

-5.0004914 -3.472563496

93

12.3821693 8.598729

21

-5.0985403 -3.540652976

94

11.8193434 8.207877

22

-5.2005111 -3.611466036

95

11.3054589 7.851013

23

-5.306644 -3.685169424

96

10.8343981 7.523888

24

-5.4171991 -3.761943787

97

10.4010222 7.222932

25

-5.5324586 -3.841985144

98

10.0009829 6.945127

26

-5.6527294 -3.925506561

99

9.6305761 6.6879

27

-5.7783457 -4.01274004

100

9.28662695 6.449046

28

-5.9096717 -4.103938677

101

8.96639843 6.226666

29

-6.0471059 -4.199379111

102

8.66751849 6.01911

16

30

-6.1910846 -4.299364328

103

8.38792112 5.824945

31

-6.3420867 -4.404226873

104

8.12579858 5.642916

32

-6.5006389 -4.514332545

105

7.87956226 5.471918

33

-6.6673219 -4.630084661

106

7.64781043 5.310979

34

-6.8427778 -4.751928994

107

7.42930156 5.159237

35

-7.0277177 -4.880359508

108

7.22293207 5.015925

36

-7.2229321 -5.01592505

109

7.02771769 4.88036

37

-7.4293016 -5.159237194

110

6.84277775 4.751929

38

-7.6478104 -5.310979464

111

6.66732191 4.630085

39

-7.8795623 -5.471918236

112

6.50063886 4.514333

40

-8.1257986 -5.642915681

113

6.3420867 4.404227

41

-8.3879211 -5.824945219

114

6.19108463 4.299364

42

-8.6675185 -6.01911006

115

6.04710592 4.199379

43

-8.9663984 -6.226665579

116

5.90967169 4.103939

44

-9.2866269 -6.449046493

117

5.77834566 4.01274

45

-9.6305761 -6.687900066

118

5.65272945 3.925507

46

-10.000983 -6.945126992

119

5.53245861 3.841985

47

-10.401022 -7.222932072

120

5.41719905 3.761944

48

-10.834398 -7.523887575

121

5.30664397 3.685169

49

-11.305459 -7.851013121

122

5.20051109 3.611466

50

-11.819343 -8.207877354

123

5.09854029 3.540653

51

-12.382169 -8.598728657

124

5.00049143 3.472563

52

-13.001278 -9.02866509

125

4.90614254 3.407043

53

-13.685556 -9.503857989

126

4.81528805 3.34395

54

-14.445864 -10.0318501

127

4.72773736 3.283151

55

-15.295621 -10.62195893

128

4.64331347 3.224523

56

-16.251597 -11.28583136

129

4.56185183 3.167953

57

-17.335037 -12.03822012

130

4.48319922 3.113333

58

-18.573254 -12.89809299

131

4.40721279 3.060564

59

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