strength and ductility testing of experimental structural ... · pdf filea project report...

Strength and Ductility Testing of

Experimental Structural Fuses

Rudy Che Lin Wright

A project report submitted to the faculty of

Brigham Young University

in partial fulfillment of the requirements for the degree of

Master of Science

Paul W. Richards

Richard J. Balling

Fernando S. Fonseca

Department of Civil and Environmental Engineering

Brigham Young University

April 2016

Copyright © 2016 Rudy Che Lin Wright

All Rights Reserved

ABSTRACT

Strength and Ductility Testing of

Experimental Structural Fuses

Rudy Wright

Department of Civil and Environmental Engineering, BYU

Master of Science

Small steel specimens were tested for their shear properties to establish a basis for the

development of a structural fuse intended for use in steel moment frames. The purpose of the

experiment was to find optimum geometries that would produce high strength and ductility in the

structural fuse. Varying geometries of rectangular specimens were tested specifically for their

strength, ductility, and energy dissipation characteristics. The specimens with a small width /

height aspect ratio when loaded in the direction of the height exhibited higher strength and

energy dissipation. The geometry of the specimens showed a slight correlation to the ductility of

the fuse. Recommendations have been made for future testing of fuses to improve the fuse

geometries and testing procedures.

ACKNOWLEDGEMENTS

This research was made possible through Brigham Young University and the support

from Dr. Paul Richards. His vision and oversight were an enormous help by providing direction

and encouragement for the study.

I would also like to thank Jacob Linford for the initial research he performed. The testing

and analysis he performed was instrumental and paved the way to further this study.

Special thanks go to all others who helped me in performing this research including my

dear wife, Katie, and my supportive family.

iv

TABLE OF CONTENTS

ABSTRACT .................................................................................................................................... 3

TABLE OF CONTENTS ............................................................................................................... iv

LIST OF TABLES ......................................................................................................................... vi

LIST OF FIGURES ..................................................................................................................... viii

1 Introduction ............................................................................................................................. 1

2 Background .............................................................................................................................. 3

3 Test Specimens ........................................................................................................................ 5

General Specimen Geometry ........................................................................................... 5

Material Properties ........................................................................................................... 7

4 Procedure ................................................................................................................................. 9

Specimen Loading Rig ..................................................................................................... 9

MTS Universal Testing Machine ................................................................................... 10

Documentation and Data Retrieval ................................................................................ 12

Loading Protocol ............................................................................................................ 12

4.4.1 Loading Protocol A ................................................................................................. 12

4.4.2 Loading Protocol B ................................................................................................. 13

5 Results ................................................................................................................................... 15

Visual Observations ....................................................................................................... 15

Strength and Stiffness..................................................................................................... 16

Energy Dissipation ......................................................................................................... 20

6 Analysis ................................................................................................................................. 22

Strength Characteristics.................................................................................................. 22

Ductility Characteristics ................................................................................................. 23

Energy Dissipation Characteristics ................................................................................ 24

7 Conclusion ............................................................................................................................. 27

8 Recommendations for Future Testing ................................................................................... 29

APPENDIX A. .............................................................................................................................. 31

APPENDIX B. .............................................................................................................................. 47

vi

LIST OF TABLES

Table 3-1: Fuse Geometries & Aspect Ratios................................................................................. 6

Table 5-1: Initial Stiffness & Force Results ................................................................................. 17

Table 5-2: Cumulative Energy Dissipation, Load Protocol A ...................................................... 20

viii

LIST OF FIGURES

Figure 3-1: Test Specimen .............................................................................................................. 5

Figure 3-2: General Specimen Geometry ...................................................................................... 6

Figure 3-3: Tension Yield Strength ................................................................................................ 7

Figure 4-1: Assembled Specimen Loading Rig Diagram ............................................................... 9

Figure 4-2: Exploded Loading Rig Diagram ................................................................................ 10

Figure 4-3: Loading Rig in UTS Testing Machine ....................................................................... 11

Figure 4-4: Loading Protocol A .................................................................................................... 13

Figure 4-5: Loading Protocol B .................................................................................................... 14

Figure 5-1: Displaced Fuse Stages ................................................................................................ 16

Figure 5-2: Plastic Displacement Angle vs. Load (Test 3: Specimens 11-17 & 14B) ................. 18

Figure 5-3: Plastic Displacement Angle vs. Load (Test 4: Specimens 21-27) ............................. 19

Figure 5-4: Cumulative Energy Dissipation, Load Protocol A..................................................... 21

Figure 6-1: Aspect Ratio (W / H) vs. Maximum Shear Force ..................................................... 22

Figure 6-2: Aspect Ratio (W / H) vs. Maximum Shear Stress...................................................... 23

Figure 6-3: Aspect Ratio (W / H) vs. Displacement Angle at Max Force .................................... 24

Figure 6-4: Aspect Ratio (W / H) vs. Cumulative Energy Dissipated .......................................... 24

Figure 6-5: Aspect Ratio (W / H) vs. Cumulative Energy Dissipated / Shear Area ..................... 25

Figure 6-6: Aspect Ratio (W / H) vs. Cumulative Energy Dissipated / Shear Volume ................ 26

1

1 INTRODUCTION

The following report will show test procedures and results for small-scale structural fuses tested

for strength and ductility. The intent of the structural fuse is for use with steel moment frames

designed to resist ground-motions due to earthquakes. It is anticipated that the strength and

ductility of a fuse can be predicted based upon the fuse geometry. The results of the tests will be

presented and analyzed to determine optimum fuse configurations and geometries that will result

in both high strength and ductility. These results will provide a basis for a new design of

specialized steel moment frame connections.

3

2 BACKGROUND

The design of steel moment frames has evolved in recent history due to increased research and

development of the effectiveness of various connections during earthquakes

The main method for energy dissipation and ductility in steel moment frames is currently

achieved through inelastic rotations and bending in the beams near the connections. These

connections are effective at achieving high levels of ductility and strength, however they require

an extensive amount of preparation and field welding, which in turn increases the construction

time and cost of steel moment frame structures. These systems are effective at maintaining life-

safety, but repairing the moment frame after a significant ground-motion can also be costly.

Other energy dissipation mechanisms include shear deformations (rather than axial or bending

deformations) which are implemented in a select number of lateral force resisting systems. These

shear deformations are of interest because the structural fuse presented in this report relies

mainly on shear deformation. The application presented is a unique application of the energy

dissipation mechanism.

The aim of this research is to develop a structural fuse that has predictable strength and ductility

and can be used in steel moment frame connections. It is anticipated that the implementation of

the structural fuse will improve the constructability and performance of steel moment frames as

well as reduce the costs associated with repairing frames after a major earthquake.

5

3 TEST SPECIMENS

Fifteen different specimens were manufactured and tested in two separate runs: Test 3 and

Test 4. An example test specimen is shown in Figure 3-1. Test 3 includes specimens 11-17 and

14B and Test 4 includes specimens 21-27. Specimen 14B was loaded according to a different

loading protocol as noted in section 4.4.2. Test 1 and Test 2 were performed previously,

however, the results are not presented here.

Figure 3-1: Test Specimen

General Specimen Geometry

Figure 3-2 shows the general geometry for all specimens tested. Each specimen consists of two

identical fuses with a specific height and width. See Table 3-1 for a detailed list of all specimens.

The results and analysis in this report have been reduced to consider each fuse, not the dual fuse

specimens.

6

Figure 3-2: General Specimen Geometry

Table 3-1: Fuse Geometries & Aspect Ratios

Specimen Thickness Height Width Shear Area Volume

# (in.) (in.) (in.) (in.2) (in.

3) H / T W / T W / H

11 0.125 1.00 1.00 0.1250 0.1250 8 8 1

12 0.125 1.00 0.75 0.1250 0.0938 8 6 0.75

13 0.125 1.00 0.50 0.1250 0.0625 8 4 0.5

14 0.125 0.75 0.75 0.0938 0.0703 6 6 1

15 0.125 0.75 0.50 0.0938 0.0469 6 4 0.667

16 0.125 0.50 0.50 0.0625 0.0313 4 4 1

17 0.125 0.50 0.25 0.0625 0.0156 4 2 0.5

14B 0.125 0.75 0.75 0.0938 0.0703 6 6 1

21 0.125 0.75 1.00 0.0938 0.0938 6 8 1.333

22 0.125 0.50 1.00 0.0625 0.0625 4 8 2

23 0.125 0.25 1.00 0.0313 0.0313 2 8 4

24 0.125 0.56 0.75 0.0704 0.0528 4.504 6 1.332

25 0.125 0.38 0.75 0.0475 0.0356 3.04 6 1.974

26 0.125 0.38 0.50 0.0475 0.0238 3.04 4 1.316

27 0.125 0.25 0.50 0.0313 0.0156 2 4 2

Aspect Ratio

7

Material Properties

Two tension tests were performed on tension coupons provided by the manufacturer to verify the

material strength of the fuses. The material was found to have an average axial yield strength fy =

52.6 ksi. The yield strength of the material was used to calculate the theoretical yielding force for

each fuse.

Figure 3-3: Tension Yield Strength

fy = 51.8 ksi

0

10

20

30

40

50

60

70

0.0 0.5 1.0 1.5 2.0 2.5

Axia

l S

tres

s (k

si)

Displacement (in.)

Tension Specimen 3A

fy = 53.5 ksi

0

10

20

30

40

50

60

70

0.0 0.5 1.0 1.5 2.0 2.5

Axia

l S

tres

s (k

si)

Displacement (in.)

Tension Specimen 3B

9

4 PROCEDURE

Specimen Loading Rig

Each specimen was inserted into the custom loading rig prior to testing. The rig was specially

designed to test each specimen for its shear properties and also prevent out-of-plane

deformations. The rig includes (2) outer brackets that attached to the specimen with (4) ¾-in.

high strength bolts through the outer holes of the test specimen. (2) center brackets attached to

the middle of the specimen using (2) ¾-in. high strength bolts through the middle holes of the

test specimen. Each bolt was attached using a slip-resistant washer and a corresponding nut and

tightened using a pneumatic wrench. C-clamps were placed at the ends of the brackets during

bolt tightening to ensure that the brackets remained aligned. See Figure 4-1 and Figure 4-2 for

diagrams of the loading rig.

Figure 4-1: Assembled Specimen Loading Rig Diagram

Outer Brackets

Center Brackets

Test Specimen

10

Figure 4-2: Exploded Loading Rig Diagram with Specimen

MTS Universal Testing Machine

A 110 KIP Capacity MTS test machine (Model # 312.41) with a flat wedge grip was used to load

the specimens. See Figure 4-3. Special precautions were taken to ensure that the loading rig was

centered between the two terminals of the MTS machine to maintain that the specimen was

symmetrically loaded during testing.

Test Specimen

Bolt Location,

Typical

Center Bracket

Center Bracket

Outer Bracket

Outer Bracket

11

Figure 4-3: Loading Rig in UTS machine

12

Documentation and Data Retrieval

Data was recorded by the MTS testing machine and by video. The MTS machine recorded both

loads and displacements every 0.5 seconds. Video documentation was performed for every

specimen.

Loading Protocol

The specimens were loaded cyclically in shear at increasing displacement levels according to the

two loading protocols described in this section. All specimens except specimen 11-17 and 21-27

were tested using Loading Protocol A. Specimen 14B was tested using Loading Protocol B.

4.4.1 Loading Protocol A

The initial set of loads includes six cyclical displacements of ± 0.025 in. at a rate of 0.1 cycles /

second. The second set of loads includes six cyclical displacements of ± 0.0375 in. at a rate of

0.1 cycles / second. The third set of loads includes four cyclical displacements of ± 0.05 in. at a

rate of 0.07 cycles / second. The fourth set of loads includes two cyclical displacements of ± 0.1

in. at a rate of 0.04 cycles per second. The fifth through thirteenth load sets have incrementally

increasing displacements of ± 0.05 in. each with a displacement rate of 0.04 cycles per second.

See Figure 4-4. Numbered labels have been provided in Figure 4-4 at each half-cycle for use in

the analysis of the specimens.

13

Figure 4-4: Loading Protocol A

4.4.2 Loading Protocol B

Loading Protocol B was identical to Loading Protocol A except that the initial load cycles

(cycles 1-32) were omitted. The initial set of loads includes two cyclical displacements of ± 0.1

in. at a rate of 0.04 cycles / second. The second through tenth load sets have incrementally

increasing displacements of ± 0.05 in. each with a displacement rate of 0.04 cycles per second.

See Figure 4-5. Numbered labels have been provided in Figure 4-5 at each half-cycle for use in

the analysis of the specimens.

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0 50 100 150 200 250 300 350

Dis

pla

cem

ent

(in

.)

Time (s)

14

Figure 4-5: Loading Protocol B

33

34

35

36

37

38

39

40

41

42

43

44

45

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0 50 100 150

Dis

pla

cem

ent

(in

.)

Time (s)

15

5 RESULTS

The visual observations of the specimens during testing as well as the strength, stiffness and

energy dissipation characteristics of the specimens have been summarized here. Detailed

summaries of all tested specimens have been included in Appendix A.

Visual Observations

During the initial cycles of loading the fuses deformed plastically without visible signs of failure.

As the displacements of the fuses increased, the fuses showed discoloration of the steel at the

corners of the fuse and some fuses showed discoloration in the center of the shear area. At larger

displacements small cracks appeared at the corners of the fuses and the fuses achieved their

ultimate loads. The small cracks propagated vertically into large tears. The stages of the loading

are shown for specimen 16 in Figure 5-1.

16

Figure 5-1: Initial Fuse (Top-Left) Discolored Fuse (Top-Right)

Cracked Fuse (Bottom-Left) & Torn Fuse (Bottom-Right)

Strength and Stiffness

The stiffness and force results of the test have been summarized in Error! Reference source not

found.. The hysteresis plots for each specimen have been compiled in Appendix B.

17

Table 5-1: Initial Stiffness & Force Results

Due to a low resolution of data recording, especially during the initial loading phase of each

loading protocol, some estimation was used to determine the initial stiffness of each specimen.

Due to the response of some specimens, there may not have been a distinct yield point. For

analysis purposes, the force found at t = 0.5 seconds was applied as the yield force for each

specimen.

The plastic displacement of each specimen at each load step was found by subtracting the elastic

displacement at that load step. The plastic displacement was then converted into a plastic

displacement angle by dividing the displacement by the shear fuse width. See Figure 5-2 and

Figure 5-3 for the compiled plastic displacement angle plots for all specimens.

Initial Yield Maximum Cycle at Displacement Disp. Angle

Specimen Stiffness Force Force Max Force at Max Force at Max Force

# (lb / in.) (lb) (lb) (in.) (rad)

11 228,330 1,592 3,123 35 0.0974 0.097

12 269,135 2,097 3,507 35 0.0940 0.125

13 306,909 2,470 4,000 35 0.0977 0.195

14 200,421 1,399 2,419 34 0.0939 0.125

15 244,891 1,845 2,834 34 0.0889 0.178

16 175,676 1,125 1,589 34 0.0746 0.149

17 230,641 1,069 2,055 34 0.0888 0.355

14B 179,454 1,748 2,653 36* 0.1427 0.190

21 152,316 1,147 1,740 35 0.0975 0.097

22 78,244 493 878 34 0.0889 0.089

23 19,399 108 301 41 0.1949 0.195

24 128,058 644 1,323 34 0.0940 0.125

25 67,869 337 643 26 0.0476 0.063

26 96,246 706 870 26 0.0476 0.095

27 47,672 230 443 16 0.0357 0.071

* Specimen 14B was loaded according to Loading Protocol B.

18

Figure 5-2: Plastic Displacement Angle vs. Load (Test 3: Specimens 11-17 & 14B)

-4000

-2000

0

2000

4000

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

Sh

ear

Forc

e, V

(l

bs.

)

Displacement Angle, γ (radians)

Plastic Displacement Angle vs. Load, Specimen 11

-4000

-2000

0

2000

4000

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

Sh

ear

Forc

e, V

(l

bs.

)



-4000

-2000

0

2000

4000

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

Sh

ear

Forc

e, V

(l

bs.

)



-4000

-2000

0

2000

4000

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

Sh

ear

Forc

e, V

(l

bs.

)



-4000

-2000

0

2000

4000

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

Sh

ear

Forc

e, V

(l

bs.

)



-4000

-2000

0

2000

4000

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

Sh

ear

Forc

e, V

(l

bs.

)



-4000

-2000

0

2000

4000

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

Sh

ear

Forc

e, V

(l

bs.

)



-4000

-2000

0

2000

4000

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

Sh

ear

Forc

e, V

(l

bs.

)


Plastic Displacement Angle vs. Load, Specimen 14B

19

Figure 5-3: Plastic Displacement Angle vs. Load (Test 4: Specimens 21-27)

-4000

-2000

0

2000

4000

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

Sh

ear

Forc

e, V

(l

bs.

)



-4000

-2000

0

2000

4000

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

Sh

ear

Forc

e, V

(l

bs.

)



-4000

-2000

0

2000

4000

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

Sh

ear

Forc

e, V

(l

bs.

)



-4000

-2000

0

2000

4000

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

Sh

ear

Forc

e, V

(l

bs.

)



-4000

-2000

0

2000

4000

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

Sh

ear

Forc

e, V

(l

bs.

)



-4000

-2000

0

2000

4000

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

Sh

ear

Forc

e, V

(l

bs.

)



-4000

-2000

0

2000

4000

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

Sh

ear

Forc

e, V

(l

bs.

)



20

Energy Dissipation

The cumulative energy dissipated by the shear fuses was calculated by summing over time the

product of the force and displacement at each time step. Cycle 32 was used as an arbitrary

measuring point for the cumulative energy dissipated.

The energy dissipation results have been summarized for Loading Protocol A in Error!

Reference source not found. and are shown graphically in Figure 5-4.

Table 5-2: Cumulative Energy Dissipation, Load Protocol A

Energy Energy Diss. / Energy Diss. / Energy Diss. / Energy Diss. /

Specimen Dissipated Height Width Shear Area Volume

# (kip-in.) (kip-in. / in.) (kip-in. / in.) (kip-in. / in.2) (kip-in. / in.

3)

11 3,685 3,685 3,685 29,479 29,479

12 4,286 4,286 5,715 34,289 45,719

13 4,988 4,988 9,975 39,900 79,801

14 3,117 4,155 4,155 33,244 44,325

15 3,818 5,091 7,636 40,724 81,449

16 2,370 4,739 4,739 37,914 75,828

17 3,170 6,341 12,681 50,724 202,898

21 2,281 3,041 3,041 24,330 24,330

22 1,179 1,571 1,179 18,858 18,858

23 296 592 296 9,477 9,477

24 1,866 7,465 1,866 26,520 35,360

25 980 1,740 1,306 20,626 27,501

26 1,381 3,634 1,841 29,076 58,152

27 705 1,855 1,410 22,553 45,106

*Energy dissipated is the cumulative energy lost to plastic deformation at load cycle 32

21

Figure 5-4: Cumulative Energy Dissipation, Load Protocol A

11

12

13

14

15

16

17

21

22

23

24

25

26

27

0

1000

2000

3000

4000

5000

6000

0 50 100 150 200 250 300 350 400

Cu

mu

lati

ve

En

ergy D

issi

pat

ed (

kip

-in

.)

Time (s)

22

6 ANALYSIS

The (W / H) aspect ratios of the specimens were used as a comparison tool between test

specimens in all categories. This parameter was correlative in the analysis of the testing of the

shear fuses and is useful in making conclusive statements about the fuse geometries.

Strength Characteristics

The fuses in general exhibited strength proportional to the shear area of the fuse. The specimens

with smaller (W / H) aspect ratios generally achieved higher maximum force values than those

specimens with (W / H) aspect ratios ≥ 1. See Figure 6-1. Specimens with (W / H) aspect ratios

≤ 1 also achieved higher maximum shear stresses, see Figure 6-2.

Figure 6-1: Aspect Ratio (W / H) vs. Maximum Shear Force

11

12

13

14

15

16

17

14B

21

22

23

24

2526

27

-

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

4,500

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

Max

Sh

ear

Forc

e, V

(lb

)

Aspect Ratio (W / H)

23

Figure 6-2: Aspect Ratio (W / H) vs. Maximum Shear Stress

Ductility Characteristics

Each of the fuses generally achieved the same range of load cycles and displacements before

weakening occurred, with the exception of the fuses with very high (W / H) aspect ratios. The

displacement angles at the maximum load however was different for each specimen. A majority

of the fuses achieved a displacement angle between 0.06 and 0.2 radians. Specimen 17 had an

outlier displacement angle of 0.355 radians. See Figure 6-3. The relatively large size of the fillets

at the corners of specimen 17 may have decreased the stress concentrations at the corners of the

fuse, allowing the fuse to achieve a much higher displacement angle before cracking.

11

12

13

14

15

16

17

14B

21

22

23

24

25

26

27

0

5

10

15

20

25

30

35

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

Max

Sh

ear

Str

ess,

τ(k

si)


24

Figure 6-3: Aspect Ratio (W / H) vs. Displacement Angle at Max Force

Energy Dissipation Characteristics

The fuses with smaller (W / H) aspect ratios generally dissipated more energy than those with

high (W / H) aspect ratios, see Figure 6-4.

Figure 6-4: Aspect Ratio (W / H) vs. Cumulative Energy Dissipated

11

12

13

14

15

16

17

14B

21 22

23

24

25

26 27

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

Dis

pla

cem

ent

An

gle

, γ

(rad

)


11

12

13

14

15

16

17

21

22

23

24

25

26

27

-

1,000

2,000

3,000

4,000

5,000

6,000

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

En

ergy D

issi

pat

ed (

kip

-in

.)


25

The value of cumulative energy dissipation up to load cycle 32 for each fuse was divided by the

shear area of the fuse to obtain an efficiency of the shear area to dissipate energy, and has been

plotted against the (W / H) aspect ratio of each fuse, see Figure 6-5. The fuses with small (W / H)

aspect ratios were more efficient at dissipating energy in terms of shear area than those with high

(W / H) aspect ratios.

Figure 6-5: Aspect Ratio (W / H) vs. Cumulative Energy Dissipated / Shear Area

The value of cumulative energy dissipation up to load cycle 32 for each fuse was divided by the

volume of the fuse to obtain an efficiency of the shear volume to dissipate energy, and has been

plotted against the (W / H) aspect ratio of each fuse, see Figure 6-6. The fuses with small (W / H)

aspect ratios were more efficient at dissipating energy in terms of shear volume than those with

high (W / H) aspect ratios. Specimen 17 was extremely efficient at dissipating energy, possibly

due to its low (W / T) and (H / T) ratio. This suggests that specimens that are very thick

compared to their width and height are more efficient at dissipating energy.

11

12

13

14

1516

17

21

22

23

24

25

26

27

-

10,000

20,000

30,000

40,000

50,000

60,000

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

En

ergy D

issi

pat

ed / S

hea

r A

rea

(kip

-in

. /

in.2

)


26

Figure 6-6: Aspect Ratio (W / H) vs. Cumulative Energy Dissipated / Shear Volume

1112

13

14

1516

17

21 22 23

2425

2627

-

50,000

100,000

150,000

200,000

250,000

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

En

ergy D

issi

pat

ed / S

hea

r V

olu

me

(kip

-in

. /

in.3

)


27

7 CONCLUSION

The results and analysis of the testing show that the specimens with a small (W / H) aspect ratio

performed much better in terms of strength and energy dissipation. Those specimens in Test 3

(11-17 & 14B) all had (W / H) aspect ratios ≤ 1 and outperformed the specimens tested in Test 4.

It is also noted that specimens with low (W / T) ratios and low (H / T) ratios may be more

efficient at dissipating energy. There was not a strong correlation between the fuse geometry and

the ductility of the specimen, however Section 8 contains recommendations on improvements

that can be made to the fuse geometries that could potentially improve ductility.

29

8 RECOMMENDATIONS FOR FUTURE TESTING

The following are recommendations for future testing to improve upon the geometries of the

fuses and to improve the testing procedure.

1) Most specimens achieved approximately the same levels of displacements regardless of

geometry. This may be due to the stress concentrations and cracking at the corners of the

fuses that developed because of the small fillets at the corners. Modifying the geometry

of the fuses by increasing the size of the fillets or by using a non-rectangular geometry

may improve the strength and ductility of the fuse.

2) The relative thickness of the fuses may significantly affect the strength and ductility of

the fuse. Further testing should be performed on specimens with small (W / H) aspect

ratios with varying relative thicknesses.

3) Due to a low resolution of data recording by the MTS machine (data was recorded every

0.5 seconds) some estimation was made to find the initial stiffness and the yield force of

each specimen. It is recommended that, if possible, a higher resolution be used so that a

distinct yield force and stiffness can be found from the recorded data.

31

APPENDIX A.

32

Height H = 1 in.

Width W = 1 in.

Thickness t = 0.125 in.

Height : Width H : W = 1

Height : Thickness H : t = 8

Width : Thickness W : t = 8

Shear Area A = 0.1250 in.2

Initial Stiffness k = 228,330 kip / in.

Maximum Force F = 3,123 lbs.

Max. Shear Stress τmax = 24,985 lbs. / in.2

Disp. at Max Force Δmax force = 0.0974 in.

Angle at Max Force γmax force = 0.0974 rad.

Cycle at Max Force Cycle = 35 Specimen 11 Dimensions

Energy Dissipated34 E34 = 5,003 kip-in.


Specimen 11 at time 3:36 (Cycle 35, Load Protocol A) of cyclic shear testing

Specimen 11

Aspect Ratios

Max Force, C35 3,123 lbs

-4000

-3000

-2000

-1000

0

1000

2000

3000

4000

-0.4 -0.2 0.0 0.2 0.4

Sh

ear

Fo

rce,

V (

lbs.

)

Plastic Displacement Angle, γ (radians)

Shear Force, V vs. Plastic Displacement Angle, γ

33

Height H = 1 in.

Width W = 0.75 in.


Height : Width H : W = 1.3













Specimen 12

Aspect Ratios


-4000

-3000

-2000

-1000

0

1000

2000

3000

4000

-0.4 -0.2 0.0 0.2 0.4

Sh

ear

Fo

rce,

V (

lbs.

)



34

Height H = 1 in.

Width W = 0.5 in.















Specimen 13

Aspect Ratios


-5000

-4000

-3000

-2000

-1000

0

1000

2000

3000

4000

5000

-0.4 -0.2 0.0 0.2 0.4

Sh

ear

Fo

rce,

V (

lbs.

)



35

Height H = 0.75 in.

Width W = 0.75 in.







Maximum Force F = -2,419 lbs.


Disp. at Max Force Δmax force = -0.0939 in.

Angle at Max Force γmax force = -0.1252 rad.





Specimen 14

Aspect Ratios

Max Force, C34 -2,419 lbs

-3000

-2000

-1000

0

1000

2000

3000

-0.4 -0.2 0.0 0.2 0.4

Sh

ear

Fo

rce,

V (

lbs.

)



36

Height H = 0.75 in.

Width W = 0.5 in.















Specimen 15

Aspect Ratios

Max Force, C34 -2,834 lbs -3000

-2000

-1000

0

1000

2000

3000

-0.4 -0.2 0.0 0.2 0.4

Sh

ear

Fo

rce,

V (

lbs.

)



37

Height H = 0.5 in.

Width W = 0.5 in.















Specimen 16

Aspect Ratios


-2000

-1500

-1000

-500

0

500

1000

1500

2000

-0.4 -0.2 0.0 0.2 0.4

Sh

ear

Fo

rce,

V (

lbs.

)



38

Height H = 0.5 in.

Width W = 0.25 in.















Specimen 17

Aspect Ratios


-2500

-2000

-1500

-1000

-500

0

500

1000

1500

2000

2500

-1.0 -0.5 0.0 0.5 1.0

Sh

ear

Fo

rce,

V (

lbs.

)



39

Height H = 0.75 in.

Width W = 0.75 in.











Cycle at Max Force Cycle = 36* Specimen 14B Dimensions



Specimen 14B at time 1:12 (Cycle 36*, Load Protocol B) of cyclic shear testing

Specimen 14B

Aspect Ratios


-3000

-2000

-1000

0

1000

2000

3000

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

Sh

ear

Fo

rce,

V (

lbs.

)



40

Height H = 0.75 in.

Width W = 1 in.















Specimen 21

Aspect Ratios


-2000

-1500

-1000

-500

0

500

1000

1500

2000

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

Sh

ear

Fo

rce,

V (

lbs.

)



41

Height H = 0.5 in.

Width W = 1 in.







Maximum Force F = -878 lbs.








Specimen 22

Aspect Ratios

Max Force, C34 -878 lbs

-1000

-800

-600

-400

-200

0

200

400

600

800

1000

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

Sh

ear

Fo

rce,

V (

lbs.

)



42

Height H = 0.25 in.

Width W = 1 in.







Maximum Force F = 301 lbs.





Energy Dissipated34 E34 = 765 kip-in.



Specimen 23

Aspect Ratios

Max Force, C41 301 lbs

-400

-300

-200

-100

0

100

200

300

400

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

Sh

ear

Fo

rce,

V (

lbs.

)



43

Height H = 0.563 in.

Width W = 0.75 in.



Height : Thickness H : t = 4.5












Specimen 24

Aspect Ratios


-1500

-1000

-500

0

500

1000

1500

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

Sh

ear

Fo

rce,

V (

lbs.

)



44

Height H = 0.38 in.

Width W = 0.75 in.















Specimen 25

Aspect Ratios


-800

-600

-400

-200

0

200

400

600

800

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

Sh

ear

Fo

rce,

V (

lbs.

)



45

Height H = 0.38 in.

Width W = 0.5 in.















Specimen 26

Aspect Ratios


-1000

-800

-600

-400

-200

0

200

400

600

800

1000

-0.4 -0.2 0.0 0.2 0.4

Sh

ear

Fo

rce,

V (

lbs.

)



46

Height H = 0.25 in.

Width W = 0.5 in.















Specimen 27

Aspect Ratios

Max Force, C16 -443 lbs -500

-400

-300

-200

-100

0

100

200

300

400

500

-0.4 -0.2 0.0 0.2 0.4

Sh

ear

Fo

rce,

V (

lbs.

)



47

APPENDIX B.

Load-Displacement Hysteresis:

1. Displacement vs. Load, Specimens 11-17, 14B, 21-27

2. Plastic Displacement vs. Load, Specimens 11-17, 14B, 21-27

3. Displacement Angle vs. Load, Specimens 11-17, 14B, 21-27

4. Plastic Displacement Angle vs. Load, Specimens 11-17, 14B, 21-27

48

Displacement vs. Load (Test 3: Specimens 11-17 & 14B)

-4000

-2000

0

2000

4000

-0.2 -0.1 0.0 0.1 0.2

Sh

ear

Forc

e, V

(l

bs.

)

Displacement (in.)

Displacement vs. Load, Specimen 11

-4000

-2000

0

2000

4000

-0.2 -0.1 0.0 0.1 0.2

Sh

ear

Forc

e, V

(l

bs.

)

Displacement (in.)


-4000

-2000

0

2000

4000

-0.2 -0.1 0.0 0.1 0.2

Sh

ear

Forc

e, V

(l

bs.

)

Displacement (in.)


-4000

-2000

0

2000

4000

-0.2 -0.1 0.0 0.1 0.2

Sh

ear

Forc

e, V

(l

bs.

)

Displacement (in.)


-4000

-2000

0

2000

4000

-0.2 -0.1 0.0 0.1 0.2

Sh

ear

Forc

e, V

(l

bs.

)

Displacement (in.)


-4000

-2000

0

2000

4000

-0.2 -0.1 0.0 0.1 0.2

Sh

ear

Forc

e, V

(l

bs.

)

Displacement (in.)


-4000

-2000

0

2000

4000

-0.2 -0.1 0.0 0.1 0.2

Sh

ear

Forc

e, V

(l

bs.

)

Displacement (in.)


-4000

-2000

0

2000

4000

-0.2 -0.1 0.0 0.1 0.2

Sh

ear

Forc

e, V

(l

bs.

)

Displacement (in.)

Displacement vs. Load, Specimen 14B

49

Displacement vs. Load (Test 4: Specimens 21-27)

-4000

-2000

0

2000

4000

-0.2 -0.1 0.0 0.1 0.2

Sh

ear

Forc

e, V

(l

bs.

)

Displacement (in.)


-4000

-2000

0

2000

4000

-0.2 -0.1 0.0 0.1 0.2

Sh

ear

Forc

e, V

(l

bs.

)

Displacement (in.)


-4000

-2000

0

2000

4000

-0.2 -0.1 0.0 0.1 0.2

Sh

ear

Forc

e, V

(l

bs.

)

Displacement (in.)


-4000

-2000

0

2000

4000

-0.2 -0.1 0.0 0.1 0.2

Sh

ear

Forc

e, V

(l

bs.

)

Displacement (in.)


-4000

-2000

0

2000

4000

-0.2 -0.1 0.0 0.1 0.2

Sh

ear

Forc

e, V

(l

bs.

)

Displacement (in.)


-4000

-2000

0

2000

4000

-0.2 -0.1 0.0 0.1 0.2

Sh

ear

Forc

e, V

(l

bs.

)

Displacement (in.)


-4000

-2000

0

2000

4000

-0.2 -0.1 0.0 0.1 0.2

Sh

ear

Forc

e, V

(l

bs.

)

Displacement (in.)


50

Platic Displacement vs. Load (Test 3: Specimens 11-17 & 14B)

-4000

-2000

0

2000

4000

-0.2 -0.1 0.0 0.1 0.2

Sh

ear

Forc

e, V

(l

bs.

)

Displacement (in.)

Plastic Displacement vs. Load, Specimen 11

-4000

-2000

0

2000

4000

-0.2 -0.1 0.0 0.1 0.2

Sh

ear

Forc

e, V

(l

bs.

)

Displacement (in.)


-4000

-2000

0

2000

4000

-0.2 -0.1 0.0 0.1 0.2

Sh

ear

Forc

e, V

(l

bs.

)

Displacement (in.)


-4000

-2000

0

2000

4000

-0.2 -0.1 0.0 0.1 0.2

Sh

ear

Forc

e, V

(l

bs.

)

Displacement (in.)


-4000

-2000

0

2000

4000

-0.2 -0.1 0.0 0.1 0.2

Sh

ear

Forc

e, V

(l

bs.

)

Displacement (in.)


-4000

-2000

0

2000

4000

-0.2 -0.1 0.0 0.1 0.2

Sh

ear

Forc

e, V

(l

bs.

)

Displacement (in.)


-4000

-2000

0

2000

4000

-0.2 -0.1 0.0 0.1 0.2

Sh

ear

Forc

e, V

(l

bs.

)

Displacement (in.)


-4000

-2000

0

2000

4000

-0.2 -0.1 0.0 0.1 0.2

Sh

ear

Forc

e, V

(l

bs.

)

Displacement (in.)

Plastic Displacement vs. Load, Specimen 14B

51

Plastic Displacement vs. Load (Test 4: Specimens 21-27)

-4000

-2000

0

2000

4000

-0.2 -0.1 0.0 0.1 0.2

Sh

ear

Forc

e, V

(l

bs.

)

Displacement (in.)


-4000

-2000

0

2000

4000

-0.2 -0.1 0.0 0.1 0.2

Sh

ear

Forc

e, V

(l

bs.

)

Displacement (in.)


-4000

-2000

0

2000

4000

-0.2 -0.1 0.0 0.1 0.2

Sh

ear

Forc

e, V

(l

bs.

)

Displacement (in.)


-4000

-2000

0

2000

4000

-0.2 -0.1 0.0 0.1 0.2

Sh

ear

Forc

e, V

(l

bs.

)

Displacement (in.)


-4000

-2000

0

2000

4000

-0.2 -0.1 0.0 0.1 0.2

Sh

ear

Forc

e, V

(l

bs.

)

Displacement (in.)


-4000

-2000

0

2000

4000

-0.2 -0.1 0.0 0.1 0.2

Sh

ear

Forc

e, V

(l

bs.

)

Displacement (in.)


-4000

-2000

0

2000

4000

-0.2 -0.1 0.0 0.1 0.2

Sh

ear

Forc

e, V

(l

bs.

)

Displacement (in.)


52

Displacement Angle vs. Load (Test 3: Specimens 11-17 & 14B)

-4000

-2000

0

2000

4000

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

Sh

ear

Forc

e, V

(l

bs.

)


Displacement Angle vs. Load, Specimen 11

-4000

-2000

0

2000

4000

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

Sh

ear

Forc

e, V

(l

bs.

)



-4000

-2000

0

2000

4000

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

Sh

ear

Forc

e, V

(l

bs.

)



-4000

-2000

0

2000

4000

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

Sh

ear

Forc

e, V

(l

bs.

)



-4000

-2000

0

2000

4000

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

Sh

ear

Forc

e, V

(l

bs.

)



-4000

-2000

0

2000

4000

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

Sh

ear

Forc

e, V

(l

bs.

)



-4000

-2000

0

2000

4000

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

Sh

ear

Forc

e, V

(l

bs.

)



-4000

-2000

0

2000

4000

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

Sh

ear

Forc

e, V

(l

bs.

)


Displacement Angle vs. Load, Specimen 14B

53

Displacement Angle vs. Load (Test 4: Specimens 21-27)

-4000

-2000

0

2000

4000

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

Sh

ear

Forc

e, V

(l

bs.

)



-4000

-2000

0

2000

4000

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

Sh

ear

Forc

e, V

(l

bs.

)



-4000

-2000

0

2000

4000

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

Sh

ear

Forc

e, V

(l

bs.

)



-4000

-2000

0

2000

4000

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

Sh

ear

Forc

e, V

(l

bs.

)



-4000

-2000

0

2000

4000

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

Sh

ear

Forc

e, V

(l

bs.

)



-4000

-2000

0

2000

4000

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

Sh

ear

Forc

e, V

(l

bs.

)



-4000

-2000

0

2000

4000

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

Sh

ear

Forc

e, V

(l

bs.

)



54

Plastic Displacement Angle vs. Load (Test 3: Specimens 11-17 & 14B)

-4000

-2000

0

2000

4000

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

Sh

ear

Forc

e, V

(l

bs.

)



-4000

-2000

0

2000

4000

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

Sh

ear

Forc

e, V

(l

bs.

)



-4000

-2000

0

2000

4000

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

Sh

ear

Forc

e, V

(l

bs.

)



-4000

-2000

0

2000

4000

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

Sh

ear

Forc

e, V

(l

bs.

)



-4000

-2000

0

2000

4000

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

Sh

ear

Forc

e, V

(l

bs.

)



-4000

-2000

0

2000

4000

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

Sh

ear

Forc

e, V

(l

bs.

)



-4000

-2000

0

2000

4000

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

Sh

ear

Forc

e, V

(l

bs.

)



-4000

-2000

0

2000

4000

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

Sh

ear

Forc

e, V

(l

bs.

)


Plastic Displacement Angle vs. Load, Specimen 14B

55

Plastic Displacement Angle vs. Load (Test 4: Specimens 21-27)

-4000

-2000

0

2000

4000

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

Sh

ear

Forc

e, V

(l

bs.

)



-4000

-2000

0

2000

4000

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

Sh

ear

Forc

e, V

(l

bs.

)



-4000

-2000

0

2000

4000

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

Sh

ear

Forc

e, V

(l

bs.

)



-4000

-2000

0

2000

4000

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

Sh

ear

Forc

e, V

(l

bs.

)



-4000

-2000

0

2000

4000

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

Sh

ear

Forc

e, V

(l

bs.

)



-4000

-2000

0

2000

4000

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

Sh

ear

Forc

e, V

(l

bs.

)



-4000

-2000

0

2000

4000

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

Sh

ear

Forc

e, V

(l

bs.

)



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