Study on Buckling-Restrained Knee Brace Damper
with Round Steel Core Bar(‫߱؛‬਌ࡒΝ༽͏ͪ࠴۸߈଍๏似ξϱϏʖͶ‫ͤؖ‬Ζ‫)ڂݜ‬ָҒखಚ೧݆ 2022 ೧ 9 ݆
Togtokhbuyan Munkhunur

Acknowledgments

ACKNOWLEDGMENTSFirst and foremost, I am extremely grateful to my supervisor, Professor Hiroshi Tagawa, for his
invaluable guidance, kindness, and patience during my Ph.D. study. His work ethic, humility, andwisdom inspired and motivated me during critical times when I needed encouragement. From
weakness to strength, grass to grace, and nothing to something, the knowledge he has imparted to me
will be a great asset throughout my future career. He taught me the value of tolerance, patience, andtrust in my future academic life. Thanks once again for all his encouragement and unconditional
support. I would also like to thank the assistant professor, Dr. Xingchen Chen, for her technicalsupport in my study. Her humility, diligence, knowledge, and mentorship made it very encouraging
during my Ph.D. I would like to express my deepest gratitude to Dr. Tsoggerel Tsamba, thecoordinator of the MJEED project, for allowing me to study under her project. Very special thanks to
my dear friend Mr. Mateus Segura Jhon Alexander, who helped me greatly from the beginning to theend of my Ph.D. I could not have reached this stage without his support.
My deepest appreciation goes to the Japanese and Mongolian governments for giving me an
opportunity to study in such a beautiful, peaceful, and charming country and to get higher education
to be more confident with the career path I am taking.
I would like to express my gratitude to my colleagues in the Department of Civil Engineering andArchitecture of the Mongolian University of Science and Technology. They have proudly supported
me to the extent that it has exceeded all reasonable expectations.
I sincerely thank Professors, Naohiro Nakamura, Hiroyuki Miura, and Dr. Xingchen Chen who
reviewed and revised my dissertation to make it more readable and reasonable.
I would like to thank my lab mates for the cherished time spent together in the lab, and in social
settings, especially Mr. Feng Shuai, Mr. Zhang Sijin, and Mr. Koga Shotai for their treasured support,
which was really influential in shaping my experimental results during my Ph.D. I would like to say
to them, “The winds of fortune are blowing in your favor” I have no doubt you will succeed in yourachievement soon.
My deepest appreciation also goes to my family, who gave me the time to concentrate on my studies.
Special thanks to my wife for carrying the children and for her positivism, patience, and support
during my critical time to accomplish my dissertation. My beautiful self-carrying daughters,
Sunderiya and Binderiya, are truly amazing, and their independence gives me the strength to go
forward and achieve my study goal.

iAbstract

ABSTRACTThis thesis aims to investigate an innovative application of simple Buckling-Restrained Knee
Braces (BRKBs) to distribute plasticity at the beam ends of rigid moment connections and to reveal
the applicability of a novel slender cover tubed BRKB for welded and weld-free steel framing systems.
A slender knee brace configuration is proposed, consisting of a steel core bar and tubular buckling
restrainer. The advantages of tube buckling restrainers include relatively easy implementation forsimpler construction and lighter weight compared to mortar-filled buckling restrainers. Two phasesof the testing program were performed to achieve the goals of this study. The first phase of the testing
program was conducted between February 5th, 2020, and March 2nd, 2020, while the second phase
was conducted between January 27th, 2021, and February 2nd, 2021, at the Building Structure
Laboratory of Hiroshima University. In each chapter of this dissertation, the work done during the
research period is summarized as follows.
Chapter 1 starts with a background of the strengthening methods of the steel beam-to-column
connections used in steel construction and gives brief explanations of the yield mechanisms of thebeam-to-column connections when a knee brace is implemented on them. In addition, the problem
statement, the research objectives, and the scope of the dissertation are presented in this section.
In Chapter 2, a literature review of the historical development of the research process on the kneebrace systems is given.
In Chapter 3, the procedure of the displacement-controlled cyclic loading tests is presented on
examination of the spreading of the plasticity behaviors of rigid moment connections using the
proposed BRKBs. Structural performance metrics, such as hysteretic behavior, strength capacity
under a given loading, and strain distributions at beam flanges, were measured.
In Chapter 4, an extensive numerical study reveals the optimal parameters for the proposed BRKBs.
The results show that the optimal parameters of the proposed slender BRKBs significantly improveload-bearing capacity and reduce stress concentrations in the vicinity of the rigid beam-to-column
connections.
In Chapter 5, the results of the test programs such as displacement-controlled compression andcyclic loading tests in investigating the deformation capacities of the proposed novel slender BRKBs
with cover tubes are presented. Several contraction allowances were adopted in the proposed BRKBs.
Specifically, by increasing the number of contraction allowances, undesirable failure mechanisms thatare global instability and local buckling of the restrainer ends can be suppressed effectively because
the more uniform plastic deformation of the core bar can be achieved longitudinally.

iiAbstract

Chapter 6 summarizes the conclusions of this study and highlights its future extended studies. The
final section contains several appendices containing the comparative numerical studies in which aneffect of the typical knee brace on the spreading plasticity at the beam was contrasted with theproposed design plasticity mechanisms. In addition, in the last part of this dissertation, the drawing
schemes of the test setups with geometric explanations are attached more clearly.

iii

Table of Contents

TABLE OF CONTENTSACKNOWLEDGMENTS.................................................................................................................. I
ABSTRACT .......................................................................................................................................II
LIST OF TABLES ........................................................................................................................... VI
LIST OF FIGURES ........................................................................................................................ VII
NOMENCLATURE AND ABBREVIATIONS ............................................................................. IX
1. INTRODUCTION .......................................................................................................................... 1
1.1

Background .............................................................................................................................. 1

1.2

Problem Statement .................................................................................................................. 3

1.3

Research objectives ................................................................................................................. 4

1.4

Scope ......................................................................................................................................... 4

1.5

Dissertation outline.................................................................................................................. 6

2. LITERATURE REVIEW .............................................................................................................. 8
3. EXPERIMENTAL STUDY FOR THE ASSESSMENT OF SPREADING PLASTICITY IN
RMC .............................................................................................................................................. 11
3.1

General ................................................................................................................................... 11

3.2

Design and theory of the proposed BRKB .......................................................................... 11
3.2.1 Determination of the position and strength of the proposed BRKB .............................. 11
3.2.2 Details of the proposed BRKB ....................................................................................... 13
3.2.3 Design theory of the buckling restrainer ........................................................................ 14

3.3

Cyclic loading tests ................................................................................................................ 15
3.3.1 Test specimens ................................................................................................................ 15
3.3.2 Testing setup ................................................................................................................... 18
3.3.3 Testing data measurement .............................................................................................. 18
3.3.4 Loading conditions and global relative rotation (drift) angles ....................................... 19

3.4

Test results .............................................................................................................................. 20
3.4.1 Load and global relative rotation angle relationship ...................................................... 20
3.4.2 Full plasticity initiation .................................................................................................. 23
3.4.3 Variation in strain distributions ...................................................................................... 26
3.4.4 Residual deformation in the final stage of loading ........................................................ 27iii

Table of Contents

4. NUMERICAL STUDY FOR THE ASSESSMENT OF SPREADING PLASTICITY IN RMC........................................................................................................................................................ 39
4.1

Scope of the finite element analysis...................................................................................... 39

4.2

Element selection ................................................................................................................... 39

4.3

Key parameters of FEA models ........................................................................................... 40

4.4

Steel materials ........................................................................................................................ 43

4.5

Contact modeling ................................................................................................................... 43

4.6

Loading and boundary conditions ....................................................................................... 43

4.7

Analysis results ...................................................................................................................... 43
4.7.1 Effects of the M16 steel bar on overall strength ............................................................ 43
4.7.2 Effects of the M22 steel bar on overall strength ............................................................ 45
4.7.3 Stress distributions along the beams .............................................................................. 47
4.7.4 Results for the base beam models .................................................................................. 49
4.7.5 Results for the M16 steel core bar BRKB beam models ............................................... 49
4.7.6 Results for the M22 steel core bar BRKB beam models ............................................... 49
4.7.7 Detailed assessment of the spreading of plasticity in FEA ............................................ 49

5. EXPERIMENTAL STUDY FOR THE SLENDER BRKB ...................................................... 53
5.1

General ................................................................................................................................... 53

5.2

Outline of the proposed BRKB dampers ............................................................................ 53

5.3

Details of the proposed BRKBs ............................................................................................ 54

5.4

Design method for the proposed damper ............................................................................ 57

5.5

Compression tests .................................................................................................................. 59
5.5.1 Test specimens ................................................................................................................ 59
5.5.2 Core bar and contraction allowances ............................................................................. 61
5.5.3 Buckling restrainer and cover tube ................................................................................ 62
5.5.4 Testing setup and data measurement .............................................................................. 62

5.6

Compression loading test results .......................................................................................... 65
5.6.1 Load-displacement relationship ..................................................................................... 65
5.6.2 Variation in the strains for the cover tube and buckling restrainer................................. 67
5.6.3 Residual deformation after compression loading ........................................................... 70

5.7

Cyclic loading tests ................................................................................................................ 72
iv

Table of Contents

5.7.1 Test specimen ................................................................................................................. 72
5.7.2 Testing setup ................................................................................................................... 75
5.7.3 Data measurement of testing .......................................................................................... 76
5.7.4 Global rotation angles and loading conditions ............................................................... 79
5.8

Cyclic loading test results ..................................................................................................... 79
5.8.1 Load and global rotation angle relationship ................................................................... 79
5.8.2 Strains for the cover tube and buckling restrainer.......................................................... 82
5.8.3 Residual deformation after cyclic loading ..................................................................... 83

6. CONCLUSIONS AND FUTURE RESEARCH NEED ............................................................ 89
6.1

Experimental and numerical study for assessment of spreading plasticity in RMC ...... 89
6.1.1 Conclusions .................................................................................................................... 89
6.1.2 Future research need ...................................................................................................... 89

6.2

Experimental study for the novel slender BRKBs.............................................................. 90
6.2.1 Conclusions .................................................................................................................... 90
6.2.2 Future research need ...................................................................................................... 91

References ......................................................................................................................................... 92
Appendix A ........................................................................................................................................ 97
Appendix B...................................................................................................................................... 102
Related publications………………………………………………………………………………109v

Lists of Tables

LIST OF TABLES
Table 1 – Material properties of specimens ................................................................................... 17
Table 2 – BRKBs used for FEA..................................................................................................... 42
Table 3– Assessment of the spreading of plasticity for FEA ......................................................... 51
Table 4– Geometrical parameters of the test specimens used in the compression loading tests ... 59
Table 5 – Material properties of the compression loading test specimens .................................... 61
Table 6 – Section modulus of the tubes used in the compression tests ......................................... 62
Table 7 – Geometrical parameters of the proposed dampers used in the cyclic loading tests ....... 74
Table 8 – Material properties of the cyclic loading test specimens ............................................... 74
Table 9 – Section modulus of the tubes used in the cyclic loading tests ....................................... 75
Table A1 – Assessment of the spreading of plasticity for the TKB beams……………………….99

viList of Figures

LIST OF FIGURES
Fig. 1.1. The configuration of strengthened beam-to-column connections (AISC). ........................ 1
Fig. 1.2. KBs as an alternative to conventional rigid and pin connections. ..................................... 2
Fig. 1.3. Expected plasticity behaviors in various types of beam-to-column connections: ............. 3
Fig. 1.4. Flowchart of chapter dissertation structure ........................................................................ 6
Fig. 2.1. Application of the KBs in a single storey frame. ............................................................... 8
Fig. 3.1. Scheme of the theoretical design method. ..................................................................... 12
Fig. 3.2. Proposed BRKB. .............................................................................................................. 13
Fig. 3.3. Theoretical dimensions of the proposed BRKB damper.................................................. 15
Fig. 3.4. Schemes for three specimens and their geometric measurements (units: mm). .............. 16
Fig. 3.5. Detailed geometries of BRKB dampers........................................................................... 17
Fig. 3.6. General apparatus for testing specimens. ........................................................................ 18
Fig. 3.7. Test setup and measurement plans. .................................................................................. 21
Fig. 3.8. Global relative rotation of the test assembly. ................................................................... 22
Fig. 3.9. Cyclic loading protocol. ................................................................................................... 22
Fig. 3.10. Relationship between load and global relative rotation. ................................................ 24
Fig. 3.11. Strain distributions of the specimen T-N........................................................................ 28
Fig. 3.12. Strain distributions of the specimen T-S. ....................................................................... 30
Fig. 3.13. Strain distributions of the specimen T-L. ....................................................................... 32
Fig. 3.14. Comparisons of strain distributions along the beam between ....................................... 34
Fig. 3.15. Residual deformation of beams in the final stage of loading for three specimens. ....... 35
Fig. 3.16. Residual deformation of BRKBs in the final stage of loading for two specimens. ....... 38
Fig. 4.1. FE model of the proposed BRKB and beam.................................................................... 40
Fig. 4.2. Geometry of the BRKB dampers for the FE models: ...................................................... 41
Fig. 4.3. Relationship between load and global rotation of beams ................................................ 44
Fig. 4.4. Relationship between load and global rotation of beams ................................................ 46
Fig. 4.5. Equivalent Von Mises stress distributions in the final stage of loading .......................... 47
Fig. 4.6. Equivalent Von Mises stress distributions in the final stage of loading .......................... 48
Fig. 4.7. Equivalent Von Mises stress distributions in the final stage of loading .......................... 50
Fig. 5.1. Structural configuration of the proposed system: ............................................................ 54
Fig. 5.2. Configuration of the proposed buckling-restrained knee brace (BRKB) damper ........... 55
Fig. 5.3. Details and exploded view of the proposed damper. ....................................................... 55
Fig. 5.4. Process followed to build the proposed damper. ............................................................. 56
vii

List of Figures

Fig. 5.5. Geometrical parameters of the proposed BRKB dampers: .............................................. 57
Fig. 5.6. Basic dimensions of the specimens for the compression loading tests............................ 60
Fig. 5.7. Test setup and measuring system for the compression loading tests. .............................. 63
Fig. 5.8. Strain gauge locations. ..................................................................................................... 64
Fig. 5.9. Load–displacement relationship. ..................................................................................... 66
Fig. 5.10. Brace axial load and strain relations. (a) for L-BR and (b) and (c) for S-BR................ 67
Fig. 5.11. Brace axial load and strain relations for SCT48-D. ....................................................... 68
Fig. 5.12. Brace axial load and strain relations for LCT48-2D...................................................... 68
Fig. 5.13. Brace axial load and strain relations for SCT54-D. ....................................................... 68
Fig. 5.14. Brace axial load and strain relations for LCT54-2D...................................................... 69
Fig. 5.15. Brace axial load and strain relations for SCT57-D. ....................................................... 69
Fig. 5.16. Brace axial load and strain relations for LCT57-2D...................................................... 69
Fig. 5.17. Residual deformation in the final stage of loading for the reference specimens. .......... 70
Fig. 5.18. Residual deformation in the final stage of loading for the SCT specimens................... 71
Fig. 5.19. Residual deformation in the final stage of loading for the LCT specimens. ................. 72
Fig. 5.20. Basic dimensions of the dampers for the cyclic loading test specimens. ...................... 73
Fig. 5.21. General apparatus for the cyclic loading test. . .............................................................. 76
Fig. 5.22. Photographs of the cyclic loading test setup .................................................................. 77
Fig. 5.23. Cyclic loading tests program. ........................................................................................ 77
Fig. 5.24. Vertical load and story drift angle relations for three specimens ................................... 80
Fig. 5.25. Brace axial load and strain relations for specimen SCT60-D. ....................................... 84
Fig. 5.26. Brace axial load and strain relations for specimen LCT60-2D. .................................... 84
Fig. 5.27. Brace axial load and strain relations for specimen LCT60-3D. .................................... 85
Fig. 5.28. Residual deformation in the final stage of cyclic loading for the BRKBs. ................... 86
Fig. A1. Plastic strain energies for the BRKB and TKB………………………………………….97
Fig. A2. Equivalent Von-Mises stress distributions……………………………………………....98
Fig. A3. Relationship between an axial load and axial deformation of the TKBs……………….100
Fig. A4. Relationship between load and global relative rotation for the TKB beam models…….100

viii

Nomenclature and Abbreviations

NOMENCLATURE
Ab
cs
csh

: cross-sectional area of the steel core bar: clearance between the screw part of the core bar and buckling restrainer: clearance between the shank part of the steel core bar and buckling restrainer tube

D: inner diameter of the buckling restrainer tube

ds

: core bar screw diameterdsh: core bar shank diameterdt: averaged displacement values measured by d3 and d5

db: averaged displacement values measured by d4 and d6

dct: inner diameter of the cover tube

D: outer diameter of the buckling restrainer tube

Dct

: outer diameter of the cover tube

E

: Young’s modulus of steel

Eb: Young’s modulus of steel core bar

hf: vertical distance between dt and db

I: beam moment of inertiaIB: buckling restrainer moment of inertia

L: total length of the beamlb

: effective buckling length of the core barlc: total length of the core bar

M yB: restrainer tube flexural strengthMy: beam flexural strengthMB: bending moment of the beam at point BMC: bending moment of the beam at point CN: brace axial force

N EB: buckling strength of the restrainer tube

Ny

: core bar / brace yield strengthSF: restrainer tube safety factorT: restrainer tube thickness

Py: concentrated load at the beam tip regarding yield strength

Py1: predicted load relative to the beam-end plasticity for specimen T-N

Py2: predicted load relative to the beam-end plasticity for specimen T-S

Py3: predicted load relative to the beam-end plasticity for specimen T-L

R: global relative rotation angleixNomenclature and Abbreviations

Rtotal: total global rotation angle

Rj: beam end plate rotation angle

Rct: the ratio of the section modulus corresponding to the buckling restrainer and cover tube

wi

: distance between points B and C

Zct: elastic section modulus of the cover tube

Zbr

: elastic section modulus of the buckling restrainerα: BRKB inclination angle

δb: elongation of the core bar

σy: yield stress of the steel material' BPy: deflection of the beam at point B due to force Py' BN y: deflection of the beam at point B due to axial force Ny

ABBREVIATIONSAISC: American institute of steel construction

BRKB : Buckling-restrained knee brace: Finite element analysis
FEA
KB: Knee brace

RMC: Rigid moment connection

TKB: Typical knee bracexChapter 1 Introduction

1. INTRODUCTION
1.1 Background
The rigid moment beam-to-column connections (RMCs) play an essential role in the performanceof the steel framing structures for gravity and lateral loadings. Since they transfer a bending moment
to a column, the resulting concentrated forces of the beam flange at the column face can cause
unexpected damage or brittle fracture in the vicinity of the connection, particularly if the connection
design does not meet seismic design requirements. After unforeseen damage and modes of brittle
failure were observed on the RMCs of framed structures during the Northridge (1994) and Hyogokennanbu (1995) earthquakes, various studies concluded that the welded areas for the RMCs were very
vulnerable to seismic motion [1]–[6]. Expected plasticity tended to occur at beam ends without any
yielding in the rest of the structure. Thus, the American Institute of Steel Construction (AISC) has
adopted many improvements and strengthening strategies for welded RMCs based on making theconnection stronger than the beam [7], [8]. Cover plates, haunches, and upstanding ribs werecommonly welded to the beam flanges. Alternatively, beam flanges were widened to increase thestrength of connection capacity, and beam flanges were reduced away from welds to decrease demandat the connections, as shown in Fig. 1.1(a)-(e). In those design approaches, the plasticity occurrence
is imposed in the beam away from the welded region at the column face.

Top cover
plate

(a)

Bottomcover plate

Upstanding
rib

HaunchReducedbeam
sectionHaunch
(b)

(c)

(d)

(e)

Fig. 1.1. The configuration of strengthened beam-to-column connections (AISC).
Following the Kobe earthquake (January 17, 1995), RMCs have been improved in various aspects
to prevent brittle fractures around connection areas in Japan. To ensure adequate plastic deformation
capacity of RMCs, improved scallop-type welding joints have been proposed and widely used for
low-to-middle-rise steel building moment frames [9], [10]. Although these modified connections havedemonstrated satisfactory performance in the laboratory, the quality of welds is difficult to control inpractice. Therefore, researchers have proposed knee bracing (KB)1 approaches for strengthening the1

In most cases, sufficient stiffness KBs are used to intend relocating the plastic hinges away from the column face.

1Chapter 1 Introduction

connection to mitigate the stress concentration at the weld area. The advantages of the KB are
replacement and repair costs can be less since the damage is concentrated in those elements. "Thisconfiguration provides more flexibility in architectural design than laterally braced frames andreduces constructional difficulties of typical rigid connections such as implementing special welding
and inspection of the quality on the welding" [11]. As shown in Fig. 1.2(a), the KBs are generally
used for the RMCs to relocate stress concentrations away from the welds and for the weld-freeconnections (pin-connections) as the main energy dissipater to resist the lateral load. The meaning of
weld-free implies an idea in which bolts are utilized in beam-to-column connections to minimize thenumber of welds. When sufficient ductility KBs are adopted in the RMCs, the occurrence of plasticity
initiates the outer portion of the KBs at the beam end, as shown in Fig. 1.2(b). In this case, the force
induced by lateral load is transmitted by KB through column flange mainly, while the beam-to-column
connection absorbs a certain amount of energy simultaneously.
In contrast, when the KBs are adopted in pin-connections, as shown in Fig. 1.2(c), the plasticity
occurs at the KBs (KBs are buckled) without yielding the main elements such as beam and column,
as shown in Fig. 1.2(d). For instance, the KB absorbing whole energy may lead to early instability ofthe structural system due to brace buckling or connection damages. More and more sufficient ductility
typical KBs than those used in RMCs are probably needed for pin-connection systems to ensure thestability of structural systems. To avoid such ineffective design, applications of BRKBs for weld-freeconnection systems have been widely accepted in Japan.
Rigidconnection

Load

Pin
connection

Plasticity

KB

KB

Load

KB

KB
(a)

(b)

Plasticity
(c)

(d)

Fig. 1.2. KBs as an alternative to conventional rigid and pin connections.
(a) RMCs with the KB, (b) Plasticity occurrence at the outer portion of the KB at the beam end,(c) Weld-free connection with KB, and (d) Buckling of the KBs.
Since typical KBs exhibit buckling during the seismic motion, various configurations of nonbuckling KBs named buckling-restrained KBs (BRKBs) 2 have been widely proposed in steel

2

BRKBs consist of buckling restrainers and core elements.

2

Chapter 1 Introduction

structural systems. The amount of energy absorption in the BRKBs system is more than the typicalKBs system. In addition, the cyclic behavior of the BRKBs is probably more stable than the typical
KBs. Generally, to ensure the required ductility for the seismic design of a structural system, thepossible yield mechanism should be determined in advance. If the beams and columns are intended
to be in an elastic range, the yield mechanism should initiate by yielding of the knee element. In thisstructural system, mostly weld-free connections, in some cases known as simple shear or pin
connections, are utilized with the BRKBs. These braces absorb the seismic energy as a replaceable
ductile fuse.
In contrast, the influences of the slender BRKBs on the RMC systems have not been completely
elucidated by the researchers. Their structural yield mechanism that affects the plasticity of beams isstill little-known. Therefore, in order to fill this research gap, the study, which will be discussed in
the following sections, is carried out in this research.
1.2 Problem Statement
In the RMCs, expected plasticity tends to occur at beam ends without any yielding in the rest of
the structure, as shown in Fig. 1.3(a). Additional strengthening methods need to be implemented tomake a connection stronger unless the seismic performances of ordinary RMCs should meet theseismic design requirements. In this regard, the application of KBs is the most common strategy forrehabilitating existing structures and constructing new structures. When using typical KBs for RMCs,
plasticity occurs outside the KBs at the beam end depending on the brace strength, as shown in Fig.
1.3(b).

Plasticity
regionTypical KB

(a)

Weak
beam

Beam

Strongcolumn

Plasticity
regionStrongcolumnWeakbeam

Plastic
deformation
region(b)Column

Weak
beam

Rigid
connection

Pin connection

Plasticity
spreadingStrongcolumnRigidconnection

Rigid
connection

Proposed
BRKB

(c)

(d)

Fig. 1.3. Expected plasticity behaviors in various types of beam-to-column connections:(a) typical RMC, (b) RMC with a typical KB, (c) pinned connection with a BRKB,
and (d) RMC with the proposed BRKB.
For the weld-free connections, mainly the BRKBs are used to remain the beams and columns in
the elastic range. In this system, the energy induced by the seismic load is only dissipated by the3Chapter 1 Introduction

BRKBs, as shown in Fig. 1.3(c). Fig. 1.3(d) shows the spreading plasticity around the beam end dueto the proposed BKRBs with a proper configuration used for the RMCs. The study on this assumption
has not been fully investigated for the seismic design procedure of the RMCs structural system so far.
Therefore, this study proposes one of the possible BRKBs for design purposes, known as a steel corebar BRKB damper, and presented the study's progress in the first half of this dissertation. As a resultof the first half of this study, this study also proposes a novel slender cover-tubed BRKB damper withsteel core bars in the second half of this dissertation. In this novel slender BRKB damper, the cover
tube increased the number of contraction allowances. Specifically, by increasing the number ofcontraction allowances, undesirable failure mechanisms that are global instability and local bucklingof the restrainer ends can be suppressed effectively because the more uniform plastic deformation of
the core bar can be achieved longitudinally. In addition, to overcome the struggle in weld quality
assurance for the RMCs, the second proposal of this dissertation, which is the novel slender BRKB
damper with the cover tube, can be utilized for weld-free connections. In these regards, theconsistency of the proposed novel slender BRKB damper for both RMCs and weld-free connections
should be assessed by experimental investigations within this study.
1.3 Research objectives
In general, this research consists of two objectives. The first objective was to investigate aninnovative application of BRKBs for spreading plasticity at the beam ends of RMCs. The second
objective was to investigate a novel slender BRKB damper for the spreading plasticity around thebeam end in RMCs and the steel framing systems in weld-free connections.
1.4 Scope
The scope of this dissertation comprises two phases of the research program. Each phase has two
substages. In the first phase, the steel bar core BRKB damper was proposed for the RMCs to decrease
the stress concentration at the weld region during the seismic loads, as shown in Fig. 1.3(d). In thisregard, one experimental program with an extended numerical analysis was conducted to investigate
the behavior of the spreading plasticity in the RMCs based on the applicable design criteria of the
proposed BRKB dampers. The extended numerical analysis verified the results of the experimental
program and assessed the additional design criteria of the proposed dampers, which have not beentested in the experimental program.
In the second phase, a novel slender cover-tubed buckling-restrained BRKB damper was developedfor both RMC and weld-free beam-to-column connections. Two substages of experimental programs
have been carried out to assess the major cyclic behavior of the proposed BRKBs affecting theperformance of weld-free connections. A series of experimental studies on relatively long and slender4

Chapter 1 Introduction

BRKBs with round steel core bars were conducted using monotonic and cyclic loading tests for the
first substage and second substage, respectively, in this phase.

5Chapter 1 Introduction

1.5 Dissertation outline
As shown in Fig. 1.4, the study follows two main key phases: assessment of spreading plasticity inimproved-scallop RMC using the proposed damper; assessment of the cyclic performance of the
proposed slender damper with the cover tube. Based on the key phases, this dissertation has been
structured in the following chapters:
Chapter 1 starts with a background of the strengthening methods of the steel beam-to-column
connections used in steel construction and gives brief explanations of the yield mechanisms of thebeam-to-column connections when a knee brace is implemented on them. In addition, the problem
statement, the research objectives, and the scope of the dissertation are presented in this section.
Chapter 2 presents preliminary studies beginning with a literature review of the historicaldevelopment of the research process on the knee brace systems and summarizing further research on
the energy dissipation capacities of the different configurations of knee braces used for beam-tocolumn connections. This section also discusses the recent studies on applications of a steel bar used
as an energy dissipator for beam-to-column connections.
Chapter 3 examines the performance of the spreading plasticity around the beam end using the
proposed steel core bar BRKB dampers for the improved-scallop RMCs. In this regard, the beam-tocolumn connection subassembly specimens with two different lengths of the proposed dampers were
tested. Their results are compared with the result of the reference specimen (no-brace beam-to-column
connection subassembly). The discussion then considers the relationships between load and global
relative rotation, strain distributions of upper and lower flanges of beams, and visual inspection ofplasticity behavior of both beams and dampers for each specimen.
CHAPTER 1
Introduction
Assessment of spreading
plasticity in improved-scallop
RMC using the proposed damper

CHAPTER 2
Literature review

Assessment of the cyclic
performance of the proposed
slender damper with the cover tube

CHAPTER 4
Numerical study for theassessment of spreading
plasticity in RMC

CHAPTER 3
Experimental study for theassessment of spreading
plasticity in RMC

CHAPTER 5
Experimental study for theslender BRKBCHAPTER 6
Conclusions

Fig. 1.4. Flowchart of chapter dissertation structure
6Chapter 1 Introduction

This chapter reveals that the shorter damper has shown a high satisfaction for the spreading plasticity
around the beam end in stable conditions (no damage). As against, for the longer brace, a noticeable
bending behavior with minor thread failure was observed in the upper exposed section of the core bar
after the cyclic loading tests. Based on the discussion on the comparison of the behavior of spreading
plasticity for each specimen, the extensive numerical analysis was conducted in the following chapter
4.
Chapter 4 presents the extensive numerical studies using finite element analysis to examine theadditional design criteria for the proposed shorter dampers. Specifically, to this end, the onedirectional one-way loading analysis provided by ANSYS was employed in this section. The analysis
results exhibit good agreement with the laboratory testing results. In addition, the percentage of thedifference between the FE analysis and test results in each specimen for the relationship between loadand global relative rotation is less than 7% regarding each peak value of the cyclic loadings. Moreover,detailed descriptions of the FEA parameters and results are provided in this chapter.
Chapter 5 examines the energy dissipation capacities of the proposed novel slender cover tube
BRKB dampers using weld-free beam-to-column connections. Since chapter 3 revealed that
noticeable damage was inspected in the exposed portion of the steel core bar for the longer BRKB
damper, the number of contraction allowances were provided by the cover tube in this novel slender
BRKB damper. Specifically, by increasing the number of contraction allowances, undesirable failure
mechanisms that are global instability and local buckling of the restrainer ends can be suppressed
effectively because the more uniform plastic deformation of the core bar can be achieved
longitudinally. To examine the energy dissipation capacities of this new damper, two series of test
programs, such as compression and cyclic loading tests, were carried out, and their results are
discussed and summarized in this chapter. In addition, this new damper can be applied in weld-freebeam to column connection to overcome the struggle in weld quality assurance in the RMC.
Chapter 6 summarizes the conclusions of this entire study within two subsections and offers
suggestions for further inquiry investigations because future research is highly needed to extend thisstudy. The last section contains several appendices with the comparative numerical studies in whichan effect of the typical knee brace on the spreading plasticity at the beam was contrasted with theproposed design plasticity mechanisms. In addition, in the last part of this dissertation, the more
precise drawing schemes of the test setups with geometric explanations are attached.

7

Chapter 2 Literature review

2. LITERATURE REVIEWThe KBs were used as the main ductile fuse element for conventional diagonal bracing systems in
the early stages of their development [12]–[15][16]. For example, one of the earliest studies of knee
bracing systems was proposed by Aristizabal-Ochoa in 1986 [17]. In that research, the conventional
bracing technique was composed of two structural elements: knee and diagonal braces, as depicted inFig. 2.1. The bracing technique was known as the Disposable Knee Bracing system (DKB), and inwhich it was recommended that the size of knee elements should be 50% lighter than the beam orcolumn size. The knee element provides ductility, whereas the diagonal brace remains elastic when
the test specimen is subjected to a lateral load. The study concluded that a system comprising a kneebrace and diagonal braces was effective in rigid and semi-rigid beam-to-column connections.
B
h
KB

H

Fig. 2.1. Application of the KBs in a single storey frame.
Mofid et al. [18] and Huang et al. [19] conducted additional two studies based on the achievementof the above studies. They investigated a particular form of DKB and proposed a simple technique,using graphs and charts for the design of the DKB. In addition, they revealed that position andstiffness of the knee were the most important factor affecting the lateral resisting ability of the KB
frame, followed by a strong influence on its energy dissipating behavior.
Leelataviwat et al. [20] conducted an experimental study on the knee-braced moment frames. They
utilized relatively short knee braces without a diagonal brace to relocate plastic hinges away from thecolumn face. In that study, plastic activities of the beam, which form outside of the knee brace portion
at the beam end, were confined by the knee brace. They concluded that cyclic tests on relatively largescale specimens indicated that knee-braced RMCs behave in a ductile manner with stable hysteretic
characteristics. Energy was dissipated by KB buckling and beam yielding outside of the KB regions.
Hsu and Li [6] assessed the seismic performance of RMC frame systems with the H-section kneebraces. The KBs were placed for the frame systems in two plane directions: in-plane and out-of-plane.
The test results showed that the cyclic energy dissipated significantly regardless of whether bucklingof the KB occurred in two plane directions. However, they suggested that KBs with an in-plane
controlled buckling mechanism can practically be adapted for knee bracing frame systems.

8Chapter 2 Literature review

As it can be seen that most of the previous studies on typical knee braced systems intended todesign the KBs yielding followed by the occurrence of plastic hinges is formed out of the knee portion
at the beam end. Since typical KBs exhibit buckling when the load induced by the seismic activities
reaches a certain critical value, other approaches for the KB systems have been introduced to restrict
that failure mechanism. In this respect, various configurations with a different ductile manner ofbuckling-restrained knee braces (BRKBs) that meet the requirements of the high architectural
versatility of the structures have been investigated for weld-free connection frames. The approachreferred to as the BRKB weld-free system, also called the simple shear beam-to-column connection,is becoming popular in Japan and other countries.
Chusilp et al. [21] first proposed a new structural system known as the weld-free system with acompact BRKB comprising the core plate coated by a friction-reduced material and steel tee section
buckling restrainer. It can be mentioned here that the configuration of their proposed BRKB was morecompact than devices previously proposed in studies by Watanabe [22], and Iwata et al.[23]. The
study revealed that the hysteretic behavior of their proposed weld-free system was shown to be fourtimes greater than expected design consideration against the large ground motions. To construct a bidirectional frame, Kawai et al. [24] suggested a new weld-free system using square tube columns
instead of wide-flange columns. Their study tested the full-scale beam-to-column connection with the
BRKBs. The suggested connection with the proposed damper could possess stable hysteresis
characteristics under large seismic excitation. Thus, the application of a multistory or a single-story
structural frame system with BRKBs has been investigated marginally with the time-history andnonlinear static and dynamic analyses [25]–[27]. Meanwhile, researchers have also extensively
carried out studies of experimental verification on the performance of the BRKB in different design
aspects [28], [29].
Inoue and Suita [30] and Tagawa and Kaneko [31] proposed BRKBs that consist of two main parts,
namely buckling-restrainers and core elements, in which the core elements are placed between two
buckling-restraining plates. These studies adopted the pin beam-to-column joint to examine thedamper deformation. Consequently, research has revealed that BRKBs with the proper configuration
have shown good hysteretic behavior under cyclic loads up to controlled story drifts. In these systems,
the beams were fully elastic under the forces caused by the knee braces.
Although diverse forms of steel core elements have been used in various BRKBs, studies on steel
core bars for BRKBs are still in their infancy. Steel core bar BRKB dampers are essential advancedenergy dissipation technology for precast concrete, timber, and steel beam-to-column connections[32]–[36]. Previous studies on post-tensioned structures have proven that steel core bar BRKB
dampers are effective for external fuse-type dissipaters for beam-to-column connections. For example,
9Chapter 2 Literature review

a recent study by Tagawa et al. [37] investigated the application of buckling-restrained round steel
bar dampers to bolted steel beam-to-column connections. Dampers were attached between the bottom
flange of the beam and column flange to dissipate energy as same as that damper used in timber
structures. A curious consideration on that study was that the authors revealed that the screwing
process through the bar ends plays an essential role in the performance of the core bar dampers. The
study also concluded that the geometrical characteristics of the shank parts should be carefully takenin the application of the proposed dampers. The cases of using steel round bars for the bracing systems
are addressed in the next paragraphs in more detail.
Fujii and Tagawa [38] proposed a buckling-restrained brace (BRB) using steel core bars restrainedby double-round steel tubes separated by spacers. Their study revealed that the proposed BRBs withsteel core bars provided sufficient capacity under cyclic loading by controlling contraction allowances.
Takamatsu and Tamai [39] experimented with a non-compression knee brace in which steel bars wereused as the main braces for T-shaped RMCs. In their study, the steel bars exhibited excellent behavior
under cyclic loading. Such RMCs are applicable to the rehabilitation of moment-resisting framed
structures, although steel core bar compressive states were not considered in their study.
Mateus et al. [40] have proposed a buckling-restrained brace composed of round steel bar cores
restrained by inner round steel tubes and an outer square tube. Their experimental results revealed
three important design factors: the applicability, restraining capacity, and end-coupler performance ofthe proposed braces. One crucial statement on their conclusions related to our study was that "whenthe number of contraction allowance zones is increased, the efficacy and performance of the bracebecomes more satisfactory."
Reviewing the literature may lead back to the following summaries: The less stability or excessive
strength and stiffness of the typical knee braces (TKBs) cause stress concentration in the beam end
or induce plastic strain energy concentration outside of the knee brace portion at the beam,
respectively. Instead of expecting the occurrence of the failure mechanism in desired positions as
stated above, spreading the plasticity around the beam end can be one of the critical aspects of theresearch on strengthening steel beam-to-column connections. As seen from previous studies, a lackof studies on the spreading plasticity around the beam end has been investigated. Hence, the spreading
plasticity around the beam end for the RMCs will be assessed by experimental and numericalinvestigations applying a steel bar core BRKBs damper. Overall, two types of slender BRKBs will beconsidered in this research. One of them is proposed for RMCs to spread plasticity, while anothernovel slender BRKB is proposed for both RMCs and weld-free beam-to-column connections toretrofit existing or new structures. Finally, the proposed damper's performances will also be examinedin various design criteria using a series of experiments and numerical studies.
10Chapter 3 Test program for spreading plasticity around the beam end

3. EXPERIMENTAL STUDY FOR THE ASSESSMENT OF SPREADING PLASTICITY IN
RMC
3.1 General
This chapter first describes the design and theory of the proposed BRKB. Next, cyclic loading
experimental studies with steel core bar BRKBs are presented to demonstrate the ability to disperse
stress concentrations from beam-to-column connection areas. Additionally, an extended numericalanalysis of one-way loading (brace compression side) is presented. Based on the results of ouranalysis, several applicable BRKB design criteria for the spread of plasticity in connection areas are
established.
To mitigate the stress concentration at the weld area using the improved scallop-type moment
beam-to-column connections, this study proposes an innovative application of steel core bar BRKBs
to spread plasticity around beam ends. The typical knee braces (TKBs) cannot achieve a similar effectfor the spreading of plasticity compared to our proposed BRKB damper. TKBs` less stability orexcessive strength and stiffness cause stress concentration in the beam end or induce plastic strainenergy concentration outside of the knee brace portion at the beam, respectively (see Appendix A).
When slender BRKBs are used for RMCs, KB yielding followed by beam end plasticity is spread
both inside and outside the KB areas. In this study, an excessively stiff column was intentionally usedbecause the behavior of the column was discarded entirely.
3.2 Design and theory of the proposed BRKB
3.2.1 Determination of the position and strength of the proposed BRKBThis study proposed that a cross-section of the steel core bar in the BRKB and the distance wi at
which the BRKB is connected to the beam at point B, as depicted in Fig. 3.1(a), can be determinedusing a simplified theoretical design method in the elastic range, as illustrated in Fig. 3.1(b). The
cantilever beam is subjected to a concentrated load Py at its free end, as depicted in Fig. 3.1(a). First,
the downward deflection of the beam at point B due to the concentrated load Py is determined, as
shown in Fig. 3.1(c). Second, the upward deflection of the beam at point B due to the reaction force,Ny, produced in the steel core bar is determined, as shown in Fig. 3.1(d). The reaction force, N,
produced in the steel core bar is obtained using the compatibility equation of the total deflection of
the beam at point B and the elongation of the steel core bar. Finally, the appropriate distance wi,
corresponding to the selected steel core bar, is obtained when the bending moment between points B
and C is equalized ( M B

M C ), as shown in Fig. 3.1(e), after several iterations of the above-

mentioned procedure.

11

Chapter 3 Test program for spreading plasticity around the beam end

C
.

B

D

Ny . w

L. -wi

Mc

Vc

i

L.

(c)

Py
A

C

B
' BP y

'BN y

(e)

b)

Beam geometry andwi
its section properties
Step-2
Step-3
2
P w
Py , N y ,  Ab ?
' B P y = y i (3L  wi )6 EI
Step-5
Step-4
3
N cos α  lb
( N y cos α)wiGb ='BN y = Ab Eb
3EI
Step-6'BP y  'BN yCD
N cos α B
N y . wi
L. -wiA

Step-1

G b  N ?

.

(d)

Start

,
,

Py
(a)
A

y

C

B

A

L. -wiMB

Check the force
N Ny ?

MC

No

Step-8Yes
Determine the beam deflection
at point B due to N y
Step-9wi

Check the bending moment diagram.

End

Flowchart description:
Step-1. Selection of an arbitrary distance wi,.
Step-2. Calculation of the cross-sectional area of the steel core bar Ab ,Set M B M C M y , Py N y cos αPyMyL  wi

, Ny

Py
cos α

 Ab

Ny

My

Vy

L  wi V y cos α

Step-3. Determination of the downward deflection of the beam at point B due to theconcentrated load Py.
Step-4. Determination of the upward deflection of the beam at point B due to the reaction
force N y cos α in the steel core bar.
Step-5. Determination of the elongation of the steel core bar due to the reaction force N .
Step-6. Determination of the force N using the equilibrium compatibility equation at point B.
Step-7. Check whether force N N y ?
Step-8. Determination of the beam deflection at point B.
Step-9. Check the bending moment diagram.
Fig. 3.1. Scheme of the theoretical design method. (a) cantilever beam subjected to aconcentrated load at beam tip, (b) flowchart of selection of distance wi. (c) downward
deflection of the beam at point B due to Py, (d) upward deflection of the beam at point B due
to force Ny cosα in the steel core bar. (e) bending moment diagram.
12

Chapter 3 Test program for spreading plasticity around the beam end

3.2.2 Details of the proposed BRKB
Fig. 3.2 presents the components and assembled views of the proposed BRKB. The primaryloading-resistant member, namely the steel core bar, is placed inside a round steel tube (bucklingrestrainer), as shown in Fig. 3.2(a). The left and right screw connectors connect it to the column andbeam flanges, respectively, where the right screw connector is welded to the beam at a steel fabrication
plant in advance. For ease of construction, the left screw connector is prepared separately by the
fabricator and erected with the other members at the construction site. The two opposing screws
provide adjustment capabilities during assembly. To avoid collisions between the tube restrainer andsurrounding connectors caused by global relative rotation angles, beam deflection, etc., twocontraction allowances are provided in the proposed BRKB based on previous experimental
experience [38], [40]–[43]. A commercial spring is attached to the lower contraction allowance zone
to hold the tube restrainer during cyclic loading testing, as shown in Fig. 3.2. According to the FEMA350 standard, for RMC frames, a service median strength degradation global relative rotation angle
capacity of 0.02 rad and ultimate capacity of 0.03 rad are required [44]. The expected elongations of
the steel core bars were calculated for the BRKB specimens based on these criteria. The screw partsof the steel bar are inserted into the connectors and restrainer tube, as shown in Fig. 3.2(b). The
theoretical dimensions and design theory of the proposed BRKB are described in the following
section.

Right screw
connecter

Weak beam

Right screw
BR tubeSpringBR tubeUpper
contraction
allowance
Left screw
connecter

SpringStrongcolumnSteel core
bar

Lower
contraction
allowance

Left screw
connecter
Brace
End-plate

Left screw(a) Components of the BRKB(b) Detailed view of the BRKB setup

Fig. 3.2. Proposed BRKB.

13

Chapter 3 Test program for spreading plasticity around the beam end

3.2.3 Design theory of the buckling restrainer
Fig. 3.3 presents the theoretical dimensions of the proposed BRKB, where D, d, and t represent theouter diameter, inner diameter, and thickness of the buckling restrainer, respectively. To prevent
instability in the steel core bar, the screw parts are inserted into the restrainer and connector at a
distance of 2ds, where ds indicates the diameter of the screw part of the steel core bar. The proposed
BRKB member selection process uses theories introduced in previous studies [41]–[43], [45]. The
theory and design of the proposed BRKB consider the interactions between restrainers and coreelements in terms of their strength and stiffness. The restrainer flexural yield strength should satisfy
Eq. (3.1).

‫ܯ‬௬஻ ൒ܰ௖ ܿ௦௛ͳ െ ܰ௖ Τܰா஻

(3.1)

where M yB is the yielding moment capacity of the buckling restrainer, Nc (= [Ny) is the core bar
yield strength amplified by the compression-to-tension overstrength and strain hardening, and an
amplification factor of [  is assumed. The parameter csh is the clearance between the shank partof the steel core bar and buckling restrainer tube. N EB is the Euler buckling load of the buckling
restrainer, which is defined by Eq. (3Error! Reference source not found..2).

(3Error! R
eference
sourcenotfound..2)

ଶ

ܰா஻ ൌ

ߨ ‫ܫܧ‬஻݈௕ଶ

where EI B is the flexural rigidity of the restrainer, and lb is the effective buckling length of the steel
core bar (between the edges of the left and right screw connectors). For our design purposes, Eq. (3.1)
can be rearranged to incorporate the safety factor, as shown in Eq. (3.3).

 ൌ൫‫ܯ‬௬஻ ൯ߦܰ௬ ܿ௦௛ቆቇͳ െ ሺߦ ܰ௬ Τܰா஻ ሻ

14

൒ͳ

(3.3)

Chapter 3 Test program for spreading plasticity around the beam end

Insertion
length 2d s
A

B

A

B

Insertion
length 2d s

Lower contraction
allowancelbCore length lc

A-A

B-B

D
d

D
d

t

cs / 2

2d s

t

Upper
contraction
allowance

Insertion
length 2d s

d s csh / 2

d shFig. 3.3. Theoretical dimensions of the proposed BRKB damper.

3.3 Cyclic loading tests
3.3.1 Test specimens
In this section, three specimens were fabricated and tested to investigate the spreading of theplasticity behavior of beams. These specimens are representative of a no-brace beam (T-N), shortbrace beam (T-S), and long-brace beam (T-L). Fig. 3.4 presents the three specimens and theirgeometries. Table 1 lists the material properties of the specimens. A section of H-250ൈ 125 ൈ 6ൈ 9(H-depthൈ flange width ൈ web thickness ൈ flange thickness) beam with a length of 1.4 m wasutilized for each specimen and attached to a section of H-250ൈ 250 ൈ 19 ൈ 25 column (built-up
section), as shown in Fig. 3.4. The strong built-up column is completely fixed to the reaction frame.
Additionally, BRKBs are attached to either the beam or column at a 45° inclination. The experimental
study test parameters were selected based on the brace lengths lb and lc, as shown in Fig. 3.4 and Fig.
3.5, where lb represents the core bar effective buckling length (between the edges of the left and rightscrew connectors) and lc represents the actual length of the core bar.
A clearer description of the BRKBs is presented in Fig. 3.5. A round steel tube section withdimensions of 48.6 × 12 mm (diameter D × thickness t) is used for the buckling restrainer in all BRKB
specimens. Structural double-threaded anchor bolts with the ABR product specification are used forthe core bars. A preliminary simplified finite element analysis (FEA) study was conducted to analyze
the spreading of plasticity along RMC beams, where only a steel bar was used as a KB under bracetension state loading [46]. In this analysis, various geometric characteristics, such as longer and
15

Chapter 3 Test program for spreading plasticity around the beam end

shorter knee braces with M16, M22, and M30 steel bar sections, were considered in our models. This
preliminary study revealed that the M22 bar positively affected the spreading of plasticity aroundconnections. Therefore, the M22 steel core bar was selected to test in this section. The core bars have
M22 threads at both ends and have a non-threaded section (called the shank) with a diameter of 20.2mm based on the JIS B 1220 standard. According to the ABR specification, the shank section should
deform instead of the threaded sections before yielding.
Built-up column
H250x250x19x25

Beam
H250x125x6x9

Beam
H250x125x6x9

25
.

1400
.

.

770
.

.
300

250
.

45
.

300
.

250
.

25

.

1400
.
470

1850
.

.
390

1850
.

390
.

Built-up column
H250x250x19x25.

BRKB
M22W300(a) Specimen T-N(b) Specimen T-S
Built-up column
H250x250x19x25

Beam
H250x125x6x9

25

.

1400
.
270

.

.
500

250
.

1850
.

.
390

500
.

45
.
.

BRKB
M22W500(c) Specimen T-L
Fig. 3.4. Schemes for three specimens and their geometric measurements (units: mm).
Our experimental study adopted a steel core bar with a sufficiently stiff restrainer to prevent
unexpected buckling when the brace was subjected to compressive force. However, a relatively thinbuckling restrainer will be discussed later in Sections 1 and 4.7. As mentioned previously, the core16

Chapter 3 Test program for spreading plasticity around the beam end

bar threaded sections are inserted into the restrainer and screwed into the end connector by a distanceof 45 mm.
Table 1 – Material properties of specimens
Steel grade

Name

Yield stress(Τଶ )SN400B
SN400B
ABR400STKM 13A
SN400B

Beam
ColumnM22 barRound tube
End plate

313
303
307
287
351

M22W 300
45

163
45

105

110

45

45

45

15

105

45

45

20

45

536

15

lb = 288lb = 571

Tube 48.6x12

Tube 48.6x12
536

48.6

253

M22 L=378 R
163

105

16

110

446
571

253

L

27
30
32
58
28

M22W 500

288

20

Elongation
(%)

48.6

110

Ultimatestress(Τଶ )
458
452
461
464
483

L

M22 L=661

R

110

446

105

lc = 378

lc = 661(a) The geometry of M22W300 BRKB(b) The geometry of M22W500 BRKB

damper for T-S (units: mm)

damper for T-L (units: mm)

Fig. 3.5. Detailed geometries of BRKB dampers.
Therefore, the shank sections will not be exposed when the rotation angle reaches 0.02 rad, which
can occur in a large earthquake event. The contraction allowance was determined based on aconventional design check, which was mentioned in Section 3.2.2, and a length of 35 mm was selectedto satisfy the requirements.

17

Chapter 3 Test program for spreading plasticity around the beam end

3.3.2 Testing setup
Tests were performed at the building structure laboratory of Hiroshima University. Fig. 3.6 presents
the general apparatus used for testing specimens. A built-up BRKB is assembled on the beam andcolumn, as shown in Fig. 3.6 (detail A). In general, out-of-plane displacements are entirely
constrained by out-of-plane stoppers, as shown in Fig. 3.6 (B and C). In this experimental study, thecolumn of the specimen attached to the reaction frame is fully fixed. Thus, the beam-sway mechanism
can likely be different in our experimental study. However, because the goal of this study is to examine
the wider area of plasticity on the beam, a strong column/weak beam philosophy is valid to eliminate

B
A
BRKB
damperContraction
allowance
zone

Jack constrainer

Rigidconnection

B

Out-of-plane-stopper

A

Reaction frame

C

Beam
H250x125x6x9

Out-of-planestopper

Load cell

plasticity in the column in this entire study proposal.

Roller

Vertical jack

Strong column
RollerC

Fig. 3.6. General apparatus for testing specimens.

3.3.3 Testing data measurement
A vertical load P was applied using a hydraulic actuator (maximum force of 1000 kN and stroke of
500 mm) at the beam tip. The downward direction is assigned a positive sign, as shown in Fig. 3.7
and Fig. 3.8. The following testing data were measured: (1) vertical load and corresponding verticaldisplacement of the beam tip, (2) rotation of the beam-end plate, (3) strains of the beam upper andlower flanges, and (4) deformation of the BRKBs for specimens T-S and T-L.
Displacement sensor d1 is used to obtain the vertical displacement of the beam tip. Displacement
sensors d3 to d6 are utilized to measure the displacement of the beam end-plate rotation, as shown in
18

Chapter 3 Test program for spreading plasticity around the beam end

Fig. 3.7(b). Displacement sensors d7 and d8 are attached to the BRKBs to measure the elongation of
the steel core bars in the T-S and T-L specimens. Finally, the beam upper and lower flange strains aremeasured by a series of strain gauges corresponding to each specimen, as shown in Fig. 3.7(c) and
Fig. 3.7(d).
3.3.4 Loading conditions and global relative rotation (drift) angles
As mentioned in the previous section, the rigid columns prevent any influence from column
deformation on the test results. Additionally, to exclude influence of the beam end-plate rotation angle
Rj, global relative rotation angle R as defined in Fig. 3.8 is used for loading protocol. Note that R is
continuously obtained during the test using measured values of Rj and the total rotation angle Rtotal.
R, Rtotal, and Rj are calculated using Eqs. (3.4), (3Error! Reference source not found..5), and(3Error! Reference source not found..6).

ܴ ൌ ܴ௧௢௧௔௟ െ ܴ௝

(3.4)

݀ͳ
ܴ௧௢௧௔௟ ൌ‫ܮ‬(3Error!R
eference
source notfound..5)

݀௧ െ ݀௕ܴ௝ ൌ݄௙

(3Error!R
eference
source notfound..6)

where dt and db represent the averaged displacement values measured by d3 and d5 at the beam top
flange level, and d4 and d6 at the beam bottom flange level, respectively, and hf represents the verticaldistance between the dt and db displacements. The loading protocol is presented in Fig. 3.9. The left
vertical axis represents the global relative rotation angel, and the right vertical axis represents thebeam tip displacement. Displacement-controlled cyclic loading was applied in the test program, andit increased gradually until the beam exhibited strength deterioration. Two loading cycles were
performed for each amplitude level of δp, 2δp, 3δp…, and 8δp. Despite the effects of the brace on thetest specimen, the full plastic moment of the beam tip deflection δp was determined based on the T-N
specimen. This value was determined to be 9 mm in this study.

19

Chapter 3 Test program for spreading plasticity around the beam end

3.4 Test results
3.4.1 Load and global relative rotation angle relationshipFig. 3.10 presents the test results for the cyclic responses of the three specimens, which were
subjected to cyclic loading, reaching R(rad) = 5.14%. As shown in Fig. 3.10, the hysteretic loops ofeach loading cycle exhibit suitable shapes for each specimen. The horizontal dashed lines in eachgraph indicate that the vertical loading reaches the plastic moment limit in the corresponding crosssections of the beams. The notation Py1 indicates the predicted load relative to the beam-end plasticity
for specimen T-N. For Py2 and Py3, the predicted loads are relative to the beam plasticity at the brace
top-end connections associated with specimens T-S and T-L, respectively, as shown in Fig. 3.10(e).
Any load beyond these points results in fully plastic deformation. Fig. 3.10(d) presents comparisons
between the peak strength values of each specimen in each cycle. Up to R(rad)= r 3.21%, nosignificant changes in strength were observed between the positive and negative loading sides for thethree specimens. In addition, all three specimens met the AISC seismic requirements [47], i.e., themeasured flexural resistance at the moment connection should be at least 0.8Mp of the connectedbeam at a story angle of R(rad) = r 4%, where Mp denotes the nominal plastic moment of the beam.
For the T-N specimen, no changes were observed in the peak strength values for both the positive andnegative loadings. For the T-L and T-S specimens, the strengths continued to increase beyond R(rad)= +4%. For the T-L specimens, strength degradation was initiated before the story drift reached R(rad)=  4%. In addition, it can be seen from the T-S specimen that the appropriate parameters of the
proposed brace can increase the seismic resistance under cyclic loads. The residual deformation
behavior up to the final loading stage is discussed in Section 3.4.4.

20

Chapter 3 Test program for spreading plasticity around the beam end

d7d8

Out-of-plane stopper

d1
Strain gauges 25
1400
470/270390

300/500

250

d3,d5

-P

d4,d6
Strain gauges

d7
,d
8

d3

+P

d4
(a) Photograph of the test setup(b) Displacement sensor positions (T-S)

Gauges on the top flange

Gauges on the top flange

300

50

50 50 50

100

100

50
15

100

15

50 50 50f27* f25* f26 f27

f22 f23 f24 f24* f25 f25* f26 f27

f28 f29 f30 f30* f31

f32*

f33* f31* f32 f33

f28 f29 f30 f30* f31 f31* f32 f33

f34 f35 f36 f36* f37

f38*

f39* f37* f38 f39

f34 f35 f36 f36* f37 f37* f38 f39

15

f26*

15

f22 f23 f24 f24* f25

Gauges on the bottom flange

15

Gauges on the bottom flange
f1

f2

f3

f5

f6*

f7* f5*

f6

f7

f1

f2

f3

f8

f9

f10 f11 f12

f13*

f14*

f13 f14f8

f9

f10 f11 f12

f15 f16 f17 f18 f19

f20*

f21*f19* f20 f21

50 50 50 50 50

1

2

3

4

100

5

100

6

50 50 50

7

8

9 10

f4

f5 f5*

f6

f7

f13 f14f15 f16 f17 f18 f19 f19* f20 f21

Knee
brace

(c) Strain gauges (T-N) and (T-L)

50 50 50 50 50

1

2

3

4

100

5

6

15

f4

50

7

8

(d) Strain gauges (T-S)

Fig. 3.7. Test setup and measurement plans.

21

Knee
brace

Chapter 3 Test program for spreading plasticity around the beam endܴ௝Undeformed
centerline of beam

d1

݀௧

ܴ௝

݄௙

ܴ௧௢௧௔௟ ܴ

݀௕

-P
+P

L
Beam span

Fig. 3.8. Global relative rotation of the test assembly.

90

Global relative rotation R (rad)

0.04
0.03

W300
W500

+R
L=14000.02
0.01

0.0514

R

0.05

0.0064+P

0.032

0.01920.012872

0.045
0.038554

0.0257

36
18

0.00
-0.01
-0.02
-0.03
-0.04
-0.05
-0.06

0
-0.0064-0.0128-0.0192-0.0257-0.032-0.0385-0.045-0.0514

Relative displacement Gp (mm)

P

0.06

-18
-36
-54
-72
-90

0

2

4

6
8
10
Cycle Number

12

Fig. 3.9. Cyclic loading protocol.

22

14

16

18

Chapter 3 Test program for spreading plasticity around the beam end

3.4.2 Full plasticity initiation
In this section, the full plasticity initiation for each specimen is described using a skeleton curve.
Fig. 3.10(e) presents comparisons between the skeleton curves of the three specimens. There are six
points: A, B, and C (representing the full plasticity predicted loadings Py1, Py2, and Py3 on the negativeside), and A*, B*, C*, (representing the full plasticity predicted loadings Py1, Py2, and Py3 on thepositive side), which were compared to reveal the loads at the full plasticity initiation points for eachspecimen. The first full plasticity that occurred close to the beam end for specimen T-N was initiatedfrom R(rad) = +1.13% (Point ‫ ) כ‬and R(rad) =െͲǤͻ% (Point A). In the case of specimen T-S, full
plasticity was initiated at R(rad) = +1.45 % (Point ‫ ) כ‬and R(rad) = -1.23% (Point B). In the case of
specimen T-L, full plasticity was initiated at R(rad) = +2.37% (Point ‫ ) כ‬and R(rad) = 2.1% (Point ).
Overall, the full plasticity of each specimen initiates slightly earlier on the negative loading side thanon the positive loading side. It is noteworthy that the proposed BRKB can enhance a system's strength
capacity and delay the full plasticity initiation along the beam adequately. Furthermore, in thefollowing section, the strain distribution behaviors are presented for the test specimens to describe
additional details of the plasticity distributions along the beams.

23

Chapter 3 Test program for spreading plasticity around the beam end

150

FEA result
Test result

100

P (kN)

50

Py1=80kN

0

-50
-100

Py1=-80kN-150-7 -6 -5 -4 -3 -2 -1 0 1 2
R (% rad)

3

4

5

6

7

(a) T-N150

Py2=102kN

FEA result
Test result

100

P (kN)

50

Py1=80kN

0
Py1=-80kN

-50
-100

Py2=-102kN-150-7 -6 -5 -4 -3 -2 -1 0 1 2
R (% rad)

3

4

5

6

7

(b) T-S
Fig. 3.10. Relationship between load and global relative rotation.

24

Chapter 3 Test program for spreading plasticity around the beam end

150

Py3=125kN

FEA result
Test result

100

P (kN)

50

Py1=80kN

0-50

Py1=-80kN-100
Py3=-125kN-150-7 -6 -5 -4 -3 -2 -1 0 1 2
R (% rad)

3

4

5

6

7

(c) T-L

150

0

-50

W300
W500

L=1400

+P

+R
136kN
123kN
103kN

-110kN-127kN-139kN

Peak
strengths

R=0.04

P (kN)

50-R

R=-0.04

100

-P

T-N
T-S
T-L

-100
-150

Peak
strengths-7 -6 -5 -4 -3 -2 -1 0 1 2
R (% rad)

3

4

5

6

7

(d) Peak values of strength per cycle
Fig. 3.10. Relationship between load and global relative rotation (continued).

25

Chapter 3 Test program for spreading plasticity around the beam end

150
100

P (kN)

50

Py3=125kN
C*
B*

T-N
T-S
T-L

Py1=80kN
Py2=102kN

A*
Py1

0

-50

W300
W500

Py1=-80kN

Py3

L=1400

A

-100
-150

Py2

B
Py3=-125kN

Py2=-102kN

C-7 -6 -5 -4 -3 -2 -1 0 1 2
R (% rad)

3

4

5

6

7

(e) Skeleton curves of three specimens
Fig. 3.10. Relationship between load and global relative rotation (continued).

3.4.3 Variation in strain distributions
In our experimental study, the strain distributions of the beam upper and lower flanges weremonitored at 8 to 10 longitudinal positions, depending on the BRKB length. Fig. 3.11 to Fig. 3.13
present the strain distributions (gauge position versus microstrain) of the beam flanges for eachspecimen under a given external load. The strain in the range of the global relative rotation angle up
to R(rad) = േ3.85% was considered in this study.
For all specimens, position 1 experiences dominant strains with respect to the observed drift angle
in the tensile states of the beam flanges, as shown in Fig. 3.11(a) and Fig. 3.11(d). However, the peakvalues of the compressive strain state for both the upper and lower flanges of the beam for specimen
T-N are dominant at position 2, as shown in Fig. 3.11(b) and Fig. 3.11(c). These strain distribution
behaviors along the beam flanges are particularly evident for the pure cantilever RM connection frame.
Furthermore, in the short BRKB specimen T-S, the strain distributions slightly decrease frompositions 1 to 8 in terms of the tensile states of the upper and lower flanges, as shown in Fig. 3.12(a)and Fig. 3.12(d). However, for the compressive states of the upper and lower flanges, the dominantstrains occur at different positions. For example, as shown in Fig. 3.12(c), there is no significant
increase or decrease in the strain distribution along the beam when the global relative rotation angles
are R(rad) = −0.64% and R(rad) = −1.28%. Furthermore, when the global relative rotation angle
26

Chapter 3 Test program for spreading plasticity around the beam end

reaches R(rad) = −3.85%, the dominant strain is observed at position 2. This can be explained asfollows. When the
BRKB steel core bar yields, position 2 exhibits less resistance to the large amplitude of cyclicloading. In contrast, for the lower flange compressive state, the strain, which is correlated to all
corresponding global relative rotation angles, is distributed continuously along the beams, as shownin Fig. 3.12(b).
Furthermore, in the long BRKB specimen T-L, the strain distributions are dominant in the BRKB
inner portion of the beam in each tensile and compressive stress state, as shown in Fig. 14. For
example, when the values of the global relative rotation angles are between R(rad) = +0.64% andR(rad) = +3.21%, the strain values spread dominantly along the inner portion of the BRKB on thebeam, as shown in Fig. 3.13(a) and Fig. 3.13(b). However, slight spreading can be observed in theouter portion of the BRKB for large amplitudes of rotation angles. Therefore, the strain values are
dominant in the BRKB inner portion in both the lower and upper beam flange tensile and compressive
states, as shown in Fig. 3.13(c) and Fig. 3.13(d).
The strain distributions of the three specimens only exhibit differences of R(rad) = ±3.21%
compared to each other, as shown in Fig. 3.14. The strain distribution along the beam tends to stabilize
the corresponding beam flanges at the monitored positions of specimen T-S. It can be observed thatthe brace length significantly affects the strain distribution. The effects of the shorter brace are
significant in terms of the spread of plasticity of the BRKB RMC developed in this study. In addition,
for both the T-S and T-L specimens, the stress concentrations around gauge position-1 weresignificantly reduced compared to that in the T-N specimen. For instance, it can be seen from Fig.
3.14(a) and Fig. 3.14(b) that the strain value at gauge position-1 was higher than 25000 P m/m for the
T-N specimen and lower than 20000 P m/m for the T-S and T-L specimens in both the bracecompression and tension sides.
3.4.4 Residual deformation in the final stage of loading
Fig. 3.15 presents the residual deformation at the beam flanges after the loading tests. Overall, local
buckling was initiated beyond R(rad) = േ3.85% for all three specimens. The yellow circles in eachfigure represent the local buckling locations, which can be observed at the flanges around the beam
end close to the column face for specimen T-N, as shown in Fig. 3.15(a). The local buckling behaviorsof the upper and lower flanges are relatively symmetric and asymmetric relative to the beam’s neutral
plane and symmetry plane, respectively.

27

Chapter 3 Test program for spreading plasticity around the beam end

The local buckling in the lower flange is smaller than that in the upper flange of the T-S specimen,
as shown in Fig. 3.15(b). For this specimen, on the lower flange backside, new local bucklingdeveloped outside of the BRKB area after extensive cyclic loading, as shown in Fig. 3.15(b–2).

25000
20000

+R

W300
W500

15000

+P
L=1400Microstrain

10000
5000
0

Hy=1527

Hy=1527

Brace
top-end, T-S-5000-10000R(rad)=0.64%
R(rad)=1.93%
R(rad)=3.21%-15000Brace
top-end, T-L

R(rad)=1.28%
R(rad)=2.57%
R(rad)=3.85%-20000
0

1

2

3

4

5

6

7

8

9

10

11

Gauge positions(a) Upper flange for tensile

25000
R(rad)=0.64%
R(rad)=1.93%
R(rad)=3.21%

20000
15000

W300
W500

5000

+R
+P
L=1400Hy=15270Brace top-end
location, T-S-5000

Brace top-end
location, T-L

Microstrain

10000

R(rad)=1.28%
R(rad)=2.57%
R(rad)=3.85%-10000-15000-20000
0

1

2

3

4

5

6

7

Hy=1527

8

9

10

Gauge positions(b) Lower flange for compressive
Fig. 3.11. Strain distributions of the specimen T-N

28

11Chapter 3 Test program for spreading plasticity around the beam end

25000

15000

Brace top-end
location,T-S

10000

Microstrain

R(rad)=-1.28%
R(rad)=-2.57%
R(rad)=-3.85%

Bracetop-end, T-L

R(rad)=-0.64%
R(rad)=-1.93%
R(rad)=-3.21%

20000

5000

Hy=1527

Hy=1527

0

-5000

R

-10000W300
W500-15000P
L=1400-20000
0

1

2

3

4

5

6

7

8

9

10

11

Gauge positions(c) Upper flange for compressive

25000

R

Brace top-end
location, T-S

20000
15000

P

W300
W500

L=14005000
0Hy=1527-5000

Brace top-end
location, T-L

Microstrain

10000Hy=1527-10000R(rad)=-0.64%
R(rad)=-1.93%
R(rad)=-3.21%-15000R(rad)=-1.28%
R(rad)=-2.57%
R(rad)=-3.85%-20000
0

1

2

3

4

5

6

7

8

9

10

11

Gauge positions(d) Lower flange for tensile
Fig. 3.11. Strain distributions of the specimen T-N (continued).

29

Chapter 3 Test program for spreading plasticity around the beam end

25000
20000
W300

15000

L=1400+R+P

Microstrain

10000
5000
0

Hy=1527

Hy=1527

R(rad)=0.64%
R(rad)=1.93%
R(rad)=3.21%

R(rad)=1.28%
R(rad)=2.57%
R(rad)=3.85%-5000-10000-15000Brace top-end
location, T-S-20000
0

1

2

3

4

5

6

7

8

9

7

8

9

Gauge positions(a) Upper flange for tensile

20000

+R

15000

W300

L=1400 +P

Microstrain

10000
5000

Hy=1527

Brace top-end
location, T-S

25000

0

-5000
-10000Hy=1527-15000-200000R(rad)=0.64%
R(rad)=1.93%
R(rad)=3.21%

R(rad)=1.28%
R(rad)=2.57%
R(rad)=3.85%

1

4

2

3

5

6

Gauge positions(b) Lower flange for compressive
Fig. 3.12. Strain distributions of the specimen T-S.

30

Chapter 3 Test program for spreading plasticity around the beam end

25000
R(rad)=-0.64%
R(rad)=-1.93%
R(rad)=-3.21%

20000
15000

Microstrain

10000

R(rad)=-1.28%
R(rad)=-2.57%
R(rad)=-3.85%

Hy=1527

5000

W300

P
R

L=14000-5000-10000Brace top-end
location, T-S-15000 Hy=1527-20000
0

1

2

3

4

5

6

7

8

9

Gauge positions(c) Upper flange for compressive

25000

P
R

20000
15000

W300

Microstrain

10000

L=14005000 Hy=1527
0Hy=1527-5000-10000Brace top-end
location, T-S

R(rad)=-0.64%
R(rad)=-1.93%
R(rad)=-3.21%-15000-200000

1

2

3

R(rad)=-1.28%
R(rad)=-2.57%
R(rad)=-3.85%
4

5

6

7

8

9

Gauge positions(d) Lower flange for tensile
Fig. 3.12. Strain distributions of the specimen T-S (continued).

31

Chapter 3 Test program for spreading plasticity around the beam end

20000
W500

+R
+P
L=1400Hy=1527

Hy=1527

R(rad)=0.64%
R(rad)=1.93%
R(rad)=3.21%

R(rad)=1.28%
R(rad)=2.57%
R(rad)=3.85%

15000
10000

Microstrain

Brace top-end
location, T-L

25000

5000
0

-5000
-10000-15000-20000
0

1

2

3

4

5

6

7

8

9

10

11

9

10

11

Gauge positions(a) Upper flange for tensile

25000
R(rad)=0.64%
R(rad)=1.93%
R(rad)=3.21%

20000
15000

R(rad)=1.28%
R(rad)=2.57%
R(rad)=3.85%

Brace top-end
location, T-L

Microstrain

10000
5000

Hy=15270-5000-10000Hy=1527-15000+R
L=1400 +P

W500-20000
0

1

2

3

4

5

6

7

8

Gauge positions(b) Lower flange for compressive
Fig. 3.13. Strain distributions of the specimen T-L.

32

Chapter 3 Test program for spreading plasticity around the beam end

25000
R(rad)=-0.64%
R(rad)=-1.93%
R(rad)=-3.21%

20000
15000

Microstrain

10000

Brace top-end
location, T-L

Hy=1527

5000

R(rad)=-1.28%
R(rad)=-2.57%
R(rad)=-3.85%

Hy=1527

0

P
R

-5000
-10000-15000

W500

L=1400-20000
0

1

2

3

4

5

6

7

8

9

10

11

9

10

11

Gauge positions(c) Upper flange for compressive

25000

P

R

15000

W500

L=140010000

Microstrain

Brace top-end
location, T-L

20000

5000
0

Hy=1527-5000Hy=1527-10000R(rad)=-0.64%
R(rad)=-1.93%
R(rad)=-3.21%-15000R(rad)=-1.28%
R(rad)=-2.57%
R(rad)=-3.85%-20000
0

1

2

3

4

5

6

7

8

Gauge positions(d) Lower flange for tensile
Fig. 3.13. Strain distributions of the specimen T-L (continued).

33

Chapter 3 Test program for spreading plasticity around the beam end

25000

+R

20000

W300
W500

15000

T-N
T-S
T-L

+P
L=1400Microstrain

10000Hy=1527

5000
0

-5000

Hy=1527-10000Brace
top-end, T-S-15000Brace
top-end, T-L-20000
0

1

2

3

4

5

6

7

8

9

10

11

Gauge positions(a) Three specimens for R(rad) = ൅3.21%

25000
P

W300
W500

15000

L=140010000

Microstrain

T-N
T-S
T-L

R

20000

Hy=1527

5000
0

-5000

Hy=1527-10000Brace
top-end, T-S-15000Brace
top-end, T-L-20000
0

1

2

3

4

5

6

7

8

9

10

11

Gauge positions(b) Three specimens for R(rad) = െ3.21%
Fig. 3.14. Comparisons of strain distributions along the beam between
three specimens for R(rad) = േ3.2%.

34

Chapter 3 Test program for spreading plasticity around the beam end

For the long BRKB specimen T-L, residual deformation occurred in the beam BRKB inner area, as
shown in Fig. 3.15(c). The occurrence of local buckling differs from that on the column faces of theother specimens. It can be concluded that a properly sized slender BRKB relative to the beam length
can spread plasticity over long distances both inside and outside of the BRKB area under large global
relative rotation. Based on these findings, the proposed short BRKB specimen T-S is more effective
for the spreading of plasticity on the beam than the other two specimens.

1)

2)

Front view

Local buckling

Local buckling

Back view= +5.1%= +5.1%

3)

4)

Local buckling

Local buckling

Back view
Front view= 5.1%=

5.1%(a) Specimen T-N
Fig. 3.15. Residual deformation of beams in the final stage of loading for three specimens.

35

Chapter 3 Test program for spreading plasticity around the beam end

Fig. 3.16 presents the BRKB behaviors of the T-S and T-L specimens in the latter stages of loading.
It can be seen that the ductility of both the shorter and longer braces is satisfactory. No damage canbe observed on the exposed screw sections for the shorter brace core bar, indicating that these areas
maintained elasticities during our tests, as shown in Fig. 3.16(a). However, for the longer brace, a
noticeable bending behavior with minor thread failure is observed in the upper exposed section of thecore bar after the cyclic loading test, as depicted in Fig. 3.16(b). The shorter and longer braces adopted
the same commercial springs at the lower exposed portion of the core bar to hold the tube restrainer,
as depicted in Fig. 3.2. Therefore, the weight of the longer brace tube restrainer enlarges the upper
contraction allowance zone.

1)

2)

Back view
Local buckling

Local buckling

Front viewR

= +5.1%= +5.1%

3)

4)
Front view
Back view
Local buckling

Local buckling= 5.1%=

5.1%(b) Specimen T-S
Fig. 3.15. Residual deformation of beams in the final stage of loading for three specimens(continued).

36

Chapter 3 Test program for spreading plasticity around the beam end

1)

2)
Local
buckling

Local buckling

Back view
Front viewR

= +5.1%= +5.1%

3)

4)

Local buckling

Local buckling

Front view

Back view== 5.1%

5.1%(c) Specimen T-L
Fig. 3.15. Residual deformation of beams in the final stage of loading for three specimens(continued).

37

Chapter 3 Test program for spreading plasticity around the beam end

Noticeable bending(a) BRKB for specimen T-S(b) BRKB for specimen T-L

Fig. 3.16. Residual deformation of BRKBs in the final stage of loading for two specimens.

38

Chapter 4 Numerical study for spreading plasticity around the beam end

4. NUMERICAL STUDY FOR THE ASSESSMENT OF SPREADING PLASTICITY IN RMC

4.1 Scope of the finite element analysis
The main goal of the finite element analysis (FEA) in this study was to examine the spreading ofplasticity on beams using diverse parameters for the proposed BRKB that were not considered in theexperimental study. To this end, the one-directional one-way loading analysis provided by ANSYS
15.0 [48] was employed in our numerical simulations. RMC models with diverse geometriccharacteristics for the proposed BRKBs were developed using this software. The analysis results
exhibit good agreement with the laboratory testing results discussed in the previous section, as shownin Fig. 3.10(a) to Fig. 3.10(c). Slight differences were observed between the test and FEA results,
except for the Bauschinger effect due to the bilinear isotropic hardening rules. In addition, thepercentage of the difference between the FE analysis and test results in each specimen for the
relationship between load and global relative rotation is less than 7% regarding each peak value ofthe cyclic loadings. Moreover, detailed descriptions of the FEA parameters and results are provided
in the following sections.
4.2 Element selection
Because shell elements facilitate thin feature modeling, six-degree-of-freedom four-node
SHELL181 elements were used for beam modeling. These elements have capabilities for plasticity
and large deformation and are relatively easy to mesh. They can also reduce computational expenses
to a certain degree. However, depending on the variety of buckling restrainer thicknesses and theirinteractions with core damper surfaces, SOLID186 (high-order 3D 20-node solid elements thatexhibit quadratic displacement) elements were used in our simulations of the BRKB dampers,
allowing the bending responses of the dampers to be captured more accurately than those of the shellelements.
Additionally, 3D node-to-surface CONTA175 elements were used between the surface elements inthe beam, while 3D eight-node surface-to-surface CONTA174 elements were applied to the solid
components in the BRKB model. For the target elements, 3D TARGE170 elements, which areassociated with the aforementioned contact elements, were utilized in both the shell and solid
elements. Fig. 4.1 presents the geometric characteristics of the numerical model and its meshing. To
achieve the highest possible solution accuracy, hexahedron (hex) meshes were used for all numericalmodels. Additionally, stress concentration areas, such as scallop regions, were meshed more delicately
than the other parts. In Fig. 4.2, the core bar damper, restraining tube geometries, and meshing are
illustrated in detail. The mesh sizing process began with a course meshing until the mesh was fine39

Chapter 4 Numerical study for spreading plasticity around the beam end

L=1400

Backing bar

A-A

Constraint points

Beam
H250x125x6x9

W300

Web stiffenerConstraint points

End plate
A
+P

BRKB

Uniform Hex
meshing

Scallop
Fixed support

A

Backing barr
W300

470

630

Fig. 4.1. FE model of the proposed BRKB and beam.
enough to prevent any further changes in the observed results. As a result of several attempts of theabove-mentioned procedure, sufficient fine mesh sizing for the plasticity-relevant zone was adopted
in the FE analysis, as shown in Fig. 4.1. The core bar threads were not considered in our numericalanalysis because they were already evaluated in a previous study [37]. This type of screw bar FEA
using a simplified model without screws is applicable with high accuracy. The bonded contact
assumption described in the following section represents the high-strength screw sections in our
numerical analysis.
4.3 Key parameters of FEA models
All of the FE BRKB models listed in Table 2 were analyzed and an H-section H250 × 125 × 6 × 9
beam was used in all models. For convenience, each model is numbered and named in the first andsecond columns, respectively. A total of 30 BRKB models, excluding the base models, were analyzed
to investigate the behavior of the distributed plasticity on the beams. Base models such as non-braced
and non-restrained models are shown in rows one to three. Here, “c0t0” represents a non-restrained
steel bar KB beam model. The characteristics of cs and csh, and t represent the clearances between thecore bar and restraining tube, and the thickness of the tube, respectively, as shown previously in Fig.
3.3. Because the clearance between the restrainer and the core member strongly affects design
performance [43], [49]–[52], determining an appropriate clearance is one of the most important
processes for the BRKB damper design. This process was conducted by examining the various safety
factors of BRKB beams under compressive loads in our numerical analysis. The parameter D / t
represents the diameter-to-thickness ratios of the restraining tubes. Based on the theory discussed inection 3.2.3, each BRKB model's safety factor (denoted as SF) was determined, as shown in Table 2.
40

Chapter 4 Numerical study for spreading plasticity around the beam end(a)screw part

20.33 shank part

110
(b)

22
105

163
378

screw partshank part

14.7

100
A

173
368

16

95

B

shank part(c)

16, 22

A

253

B

B-B

A-A

Buckling restrainer

(d)

D
t

253
shank part
FEA model and meshing of dampers

C

End connector

C

End
connector

Buckling restrainer
C-C

(e)

Fig. 4.2. Geometry of the BRKB dampers for the FE models:(a and b) M22W300 and M16W300 shank bars, respectively, (c) complex configuration of the
BRKB damper, (d) buckling restrainer, and (e) numerical model of the damper and its meshing.

41

Chapter 4 Numerical study for spreading plasticity around the beam end

Table 2 – BRKBs used for FEA
BR tube
№

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

Name

D

t

D/t

Clearance
Shank part 
csh
csh/2
cs
cs/2

Base beam models
Non-braced beam (bare beam)
M16W300 - c0t0 (only bar with no BR tube)
M22W300 - c0t0 (only bar with no BR tube)
M16 steel core bar BRKB beam models
M16W300 c1t1–t5
M16W300 - c1t1
20
1
20
3.29
1.65
2
M16W300 - c1t2
22
2
11
3.29
1.65
2
M16W300 - c1t3
24
3
8
3.29
1.65
2
M16W300 - c1t4
26
4
6.5
3.29
1.65
2
M16W300 - c1t5
28
5
5.6
3.29
1.65
2
M16W300 c2t1–t5
M16W300 - c2t1
22
1
22
5.29
2.65
4
M16W300 - c2t2
24
2
12
5.29
2.65
4
M16W300 - c2t3
26
3
8.7
5.29
2.65
4
M16W300 - c2t4
28
4
7
5.29
2.65
4
M16W300 - c2t5
30
5
6
5.29
2.65
4
M16W300 c3t1–t5
M16W300 - c3t1
24
1
24
7.29
3.65
6
M16W300 - c3t2
26
2
13
7.29
3.65
6
M16W300 - c3t3
28
3
9.3
7.29
3.65
6
M16W300 - c3t4
30
4
7.5
7.29
3.65
6
M16W300 - c3t5
32
5
6.4
7.29
3.65
6
M22 steel core bar BRKB beam models
M22W300 c1t1–t5
M22W300 - c1t1
261
263.67 1.835
2
M22W300 - c1t2
282
143.67 1.835
2
M22W300 - c1t3
30
3
103.67 1.835
2
M22W300 - c1t4
32
4
83.67 1.835
2
M22W300 - c1t5
345
6.8
3.67 1.835
2
M22W300 c2t1–t5
M22W300 - c2t1
281
285.67 2.835
4
M22W300 - c2t2
302
155.67 2.835
4
M22W300 - c2t3
323
10.7 5.67 2.835
4
M22W300 - c2t4
344
8.5
5.67 2.835
4
M22W300 - c2t5
365
7.2
5.67 2.835
4
M22W300 c3t1–t5
M22W300 - c3t130
130
7.67 3.835
6
M22W300 - c3t2
322
167.67 3.835
6
M22W300 - c3t3
343
11.3 7.67 3.835
6
M22W300 - c3t4
364
97.67 3.835
6
M22W300 - c3t5
385
7.6
7.67 3.835
642

Brace safety
factor, SF

1
1
1
1
1

-0.05
0.34
0.78
1.29
1.85

2
2
2
2
2

0.03
0.32
0.64
1.01
1.41

3
3
3
3
3

0.07
0.32
0.59
0.89
1.23

1
1
1
1
1

0.002
0.31
0.64
1.01
1.42

2
2
2
2
2

0.04
0.27
0.52
0.79
1.09

3
3
3
3
3

0.06
0.25
0.46
0.68
0.93

Chapter 4 Numerical study for spreading plasticity around the beam end

4.4 Steel materials
The primary material properties used for FEA were the same as those listed in Table 1. The vonMises yield criterion was adopted to identify yielding. This criterion obeys the bilinear stress-strain
relationship with the isotropic hardening rule, where the hardening ratio is considered to be 0.005.
Additionally, material and geometric nonlinearities were adopted in our FE simulations.
4.5 Contact modeling
Modeling the contact interactions between bodies was the most critical component of our numericalanalysis. In this study, pairs of contacts were established as follows. Shell assembly meshes such as
the web, flanges, and beam end-plate model were connected at their edges using mesh connection
contact techniques. This connection method is faster than using contact elements at the edges of
surface bodies. Additionally, a bonded contact, which is a linear type of contact, was placed between
the brace right screw connector and beam bottom flange. The core bar and brace connectors interactedwith the bonded contact. Regarding the small frictional force of the BRKBs, no significant benefits
were observed in terms of the strength of the beam models used in this study. Therefore, to reduce thecomputational expense, the friction forces between the restraining tube and core bar were represented
by the greasy surfaces.
4.6 Loading and boundary conditions
As shown in Fig. 4.1, a fixed support with six degrees of freedom was established at the BRKB
lower connector and beam end. As mentioned previously, monotonic loading analysis using thedisplacement control method was adopted for our numerical analysis. The displacement at the beam
tip was as high as 63 mm (0.045 rad), which is greater than the global relative rotation angle of 0.02
to 0.03 rad. To avoid out-of-plane global buckling of the beam, the displacement in the Z direction
was constrained at both the loading position and constraint points on the beam top flange, as shownin Fig. 4.1. Fig. 4.2 presents the geometry of the BRKB damper and its meshing method for our FEA
models.
4.7 Analysis results
4.7.1 Effects of the M16 steel bar on overall strength
The load-displacement relationships for the different safety factors of our BRKB models are plottedin Fig. 4.3 and Fig. 4.4..
In Fig. 4.3, one can see that the M16 steel bar models provide a large safety factor that cansignificantly enhance the system strength. In these graphs, the red and black dashed lines represent
the base model results. To investigate the influence of restraining tubes on the overall strength43Chapter 4 Numerical study for spreading plasticity around the beam end

120

120

II III

IV

1.15

0
0

1.95

1 1.4

4

0

100

80

80

Bare beam

20

P (kN)

100

P (kN)

12040

c1t3, SF=0.78
c2t3, SF=0.64
c3t3, SF=0.59
Bare beam
M16c0t0
M16c1t3
M16c2t3
M16c3t323
R (% rad)4

2.86 3R (% rad)

c3t2
4

5

d)

c1t4, SF=1.29
c2t4, SF=1.01
c3t4, SF=0.89

60

Bare beam
M16c0t0
M16c1t4
M16c2t4
M16c3t420011.65 240001(b) M16W300-c (1,2,3) t2

120

M16c0t0

c2t2

c1t2

5

(a) M16W300-c (1,2,3) t1

60

Bare beam
M16c0t0
M16c1t2
M16c2t2
M16c3t220023
R (% rad)c3t2, SF=0.32

I

40

Bare beam
M16c0t0
M16c1t1
M16c2t1
M16c3t1

2060

c2t2, SF=0.3240

c1t2, SF=0.34

60

I

80

P (kN)

c1t1, SF=-0.05

P (kN)

80

c3t1, SF=0.07

100c2t1, SF=0.03

100

III

II

5

(c) M16W300-c (1,2,3) t3

0

1

2
3
R (% rad)(d) M16W300-c (1,2,3) t4

Fig. 4.3. Relationship between load and global rotation of beams
for M16W300-c (1,2,3), t (1,2…5) models.

44

4

5

Chapter 4 Numerical study for spreading plasticity around the beam end

120
100

P (kN)

80
c1t5, SF=1.85
c2t5, SF=1.41
c3t5, SF=1.23
Bare beam
M16c0t0
M16c1t5
M16c2t5
M16c3t5

60
40
20
0
0

1

2
3
R (% rad)45(e) M16W300-c (1,2,3) t5
Fig. 4.3. Relationship between load and global rotation of beams
for M16W300-c (1,2,3), t (1,2…5) models (continued).
performance of the models, the curved lines were divided into several ranges for the small-safetyfactor brace models, as shown in Fig. 4.3(a) and Fig. 4.3(b). As a result, the strength variations canbe observed more clearly. In each graph, one can see that even a slight increase in the brace safety
factor delays strength degradation significantly. The strength degradation of the systems was initiatedbeyond the ranges “I” corresponding to different global relative rotation angles as a result of bracebuckling. It is noteworthy that the small-safety-factor models with large clearances, such as c3t1 (SF= 0.07) and c3t2 (SF = 0.32) exhibit significant load-bearing capacity, as shown in Fig. 4.3(a) and
Fig. 4.3(b). This can be attributed to the fact that increasing the clearance leads to enhanced tube
restrainer stiffness (area moment of inertia). The models with large thicknesses and small clearances,such as c2t3 (SF = 0.64), c1t4 (SF = 1.29), c2t4 (SF = 1.01), c1t5 (SF = 1.85), and c2t5 (SF = 1.41)
exhibit adequate strength capacities under the applied loading, as shown in Fig. 4.3(c), Fig. 4.3(d),and Fig. 4.3(e). In such cases, the buckling of the core member is sufficiently restrained.
4.7.2 Effects of the M22 steel bar on overall strength
As shown in Fig. 4.4, as the steel core bar diameter increases to 22 mm, strength deterioration isnoticeably delayed in each load-displacement curve. It is evident that models with t = 1 mm result ingreater strength deterioration with respect to the global relative rotation angles. The BRKB buckling
behavior is plotted more clearly in Fig. 4.4(a). The design of a slender BRKB with a steel core bar

45

Chapter 4 Numerical study for spreading plasticity around the beam end

100

100

60
40

2.055
0

1

c1t2, SF=0.31
c2t2, SF=0.27
c3t2, SF=0.25
Bare beam
M22c0t0
M22c1t2
M22c2t2
M22c3t260
40Bare beam
M22c0t0
M22c1t1
M22c2t1
M22c3t1

20
0

80

P (kN)

c1t1, SF=0.002

P (kN)

80

c3t1, SF=0.06

120

c2t1, SF=0.04

120

20
0

2
3
R (% rad)450(a) M22W300-c (1,2,3) t1

100

100

80

80

40
Bare beam

20

c1t3, SF=0.64
c2t3, SF=0.52
c3t3, SF=0.46
Bare beam
M22c0t0
M22c1t3
M22c2t3
M22c3t3

P (kN)

P (kN)

120

M22c0t012
3
R (% rad)4

4

5

c1t4, SF=1.01
c2t4, SF=0.79
c3t4, SF=0.68
Bare beam
M22c0t0
M22c1t4
M22c2t4
M22c3t4

60
40
20
0

0

0

2
3
R (% rad)(b) M22W300-c (1,2,3) t2

120

60

1

5

0

(c) M22W300-c (1,2,3) t3

1

2
3
R (% rad)(d) M22W300-c (1,2,3) t4

Fig. 4.4. Relationship between load and global rotation of beams
for M22W300-c (1,2,3), t (1,2…5) models.

46

4

5

Chapter 4 Numerical study for spreading plasticity around the beam end

120
100

P (kN)

80
c1t5, SF=1.42
c2t5, SF=1.09
c3t5, SF=0.93
Bare beam
M22c0t0
M22c1t5
M22c2t5
M22c3t5

60
40
20
0
0

1

2
3
R (% rad)45(e) M22W300-c (1,2,3) t5
Fig. 4.4. Relationship between load and global rotation of beams
for M22W300-c (1,2,3), t (1,2…5) models (continued).
should be considered when determining the core bar cross-section. The influence of the proposed
BRKBs on each model's plasticity development is detailed in the following section.
4.7.3 Stress distributions along the beams
Fig. 4.5 to Fig. 4.7 present the equivalent von Mises stress distributions in the final loading stage
from our analysis.

Unit: MPa(a) Bare beam

Unit: MPa(b) M16W300-c0t0

Unit: MPa(c) M22W300-c0t0

Fig. 4.5. Equivalent Von Mises stress distributions in the final stage of loading
for the reference models.

47

Chapter 4 Numerical study for spreading plasticity around the beam end

Unit: MPa(a) M16W300-c1t1, SF = −0.05

Unit: MPa(b) M16W300-c2t1, SF = 0.03

Unit: MPa

Unit: MPa(c) M16W300-c3t1, SF = 0.07

Unit: MPa(d) M16W300-c1t3, SF = 0.78 (e) M16W300-c2t3, SF = 0.64

Unit: MPa

Unit: MPa(f) M16W300-c3t3, SF = 0.59

Unit: MPa

Unit: MPa(g) M16W300-c1t5, SF = 1.85 (h) M16W300-c2t5, SF = 1.41 (i) M16W300-c3t5, SF = 1.23
Fig. 4.6. Equivalent Von Mises stress distributions in the final stage of loading
for the M16 steel core bar BRKBs.

48

Chapter 4 Numerical study for spreading plasticity around the beam end

4.7.4 Results for the base beam models
The stress distributions of the base beam models are presented in Fig. 4.5(a) to Fig. 4.5(c). The
yellow areas in these graphs represent the yielding of each member under external loading. It isapparent that an unrestrained core bar cannot disperse plasticity along the beam under an applied
force.
4.7.5 Results for the M16 steel core bar BRKB beam models
Fig. 4.6(a) to Fig. 4.6(i) present the M16 steel core bar BRKB beam model results, where plastic
stresses are dominant in the beam-to-column connection areas of all models. As the safety factor
increases to or exceeds one, plasticity is spread along the beam flanges without restrainer yielding, asshown in Fig. 4.6(g) to Fig. 4.6(i). Yielding is initiated from the beam-to-column connection area andbrace damper simultaneously, followed by slight yielding of the beam flanges in the outer area of the
KB. Therefore, our numerical analysis indicates that the thinner steel core bars (M16) have a weakerinfluence on the spreading of plasticity in the beams.
4.7.6 Results for the M22 steel core bar BRKB beam models
Fig. 4.7(a) to Fig. 4.7(i) present the results of the equivalent von Mises stress distributions in the
final loading stage for the M22 steel core bar BRKB beam models. The majority of the M22 steel
core bar BRKB models with large or small safety factors exhibit satisfactory performance for ourdesign purposes by spreading plasticity along the beams. However, for the small-safety-factor models,
the restraining tubes exhibited significant instability during our analysis, similar to the M16 models,
as shown in Fig. 4.7(a) to Fig. 4.7(f). However, the proposed BRKBs with M22 steel core bars and asafety factor greater than or equal to one are able to disperse the plasticity along the beam sufficiently,
as shown in Fig. 4.7(g) to Fig. 4.7(i). In these cases, yielding is initiated in both the KB and beam
inner/outer sections at the brace location simultaneously without brace buckling.
4.7.7 Detailed assessment of the spreading of plasticity in FEA
For all FEA models, the behavior of plasticity spreading in the beams, which depends on the BRKB
dimensions, was assessed for the small and large plasticity spreading ranges, as shown in Table 3.
These ranges correspond to the inner and outer sections of the KBs. First, the three symbols ∆(plasticity same as the base model), ٗ ሺ      ሻǡ  ٖ ሺ ሻ refer to the range of plasticity spreading in the relevant sections. The

performances of the buckling restrainers, which are denoted by the “+” signs in Table 3, were assessed
based on the elasticity, plasticity, and buckling behavior of each model. Finally, all models wereclassified into one of three plasticity categories: A (very satisfactory), B (satisfactory), and C(unsatisfactory).
49

Chapter 4 Numerical study for spreading plasticity around the beam end

Unit: MPa

Unit: MPa(a) M22W300-c1t1, SF = 0.002 (b) M22W300-c2t1, SF = 0.04

Unit: MPa

Unit: MPa(c) M22W300-c3t1, SF = 0.06

Unit: MPa

Unit: MPa(d) M22W300-c1t3, SF = 0.64 (e) M22W300-c2t3, SF = 0.52(f) M22W300-c3t3, SF = 0.46

Unit: MPa(g) M22W300-c1t5, SF = 1.42

Unit: MPa(h) M22W300-c2t5, SF = 1.09

Unit: MPa(i) M22W300-c3t5, SF = 0.93

Fig. 4.7. Equivalent Von Mises stress distributions in the final stage of loading
for the M22 steel core bar BRKBs.

50

Chapter 4 Numerical study for spreading plasticity around the beam end

According to these classifications, the three base models are unsatisfactory because the nonrestrained steel bars could not spread plasticity under the applied loads. Instead, plasticity wasconcentrated in the connection areas, as mentioned in Section 4.7.4.

KB outerportionas baseSpreading ofplasticity
Satisfaction

KB inner portion

Underelasticity

Name

Under
plasticity№

Performance of thebuckling restrainer
BuckledPlasticity spreading ranges
in the beams

Safety factor

Table 3– Assessment of the spreading of plasticity for FEA

small large small large
Eq. (3) A B C
Base beam models
1
Non-braced beam (bare beam)ξ
2
M16W300 - c0t0 (only bar with no BR tube)
ξ3
M22W300 - c0t0 (only bar with no BR tube)
ξM16 steel core bar BRKB beam models
M16W300 c1t1–t5
4
M16W300 - c1t1
∆
+
−0.05
ξ
5
M16W300 - c1t2
∆
+
0.34
ξ
6
M16W300 - c1t3
ٗ
ٖ
+
0.78
ξ
7
M16W300 - c1t4
ٗ
ٖ
+
1.29
ξ
8
M16W300 - c1t5
ٗ
ٖ
+
1.85
ξ
M16W300 c2t1–t5
9
M16W300 - c2t1
∆
+
0.03
ξ
10 M16W300 - c2t2
∆
+
0.32
ξ
11 M16W300 - c2t3
ٗ
ٖ
+
0.64
ξ
12 M16W300 - c2t4
ٗ
ٖ
+
1.01
ξ
13 M16W300 - c2t5
ٗ
ٖ
+
1.41
ξ
M16W300 c3t1–t5
14 M16W300 - c3t1
∆
+
0.07
ξ
15 M16W300 - c3t2
ٗ
ٖ
+
0.32
ξ
16 M16W300 - c3t3
ٗ
ٖ
+
0.59
ξ
17 M16W300 - c3t4
ٗ
ٖ
+
0.89
ξ
18 M16W300 - c3t5
ٗ
ٖ
+
1.23
ξ
ǡ, and Cindicate very satisfactory, satisfactory, and unsatisfactory, respectively.ٗǡٖǡand ∆ the rates of the spreading of plasticity along the beams for “high,” “low,” and “same as the nonbraced base model,” respectively.

For the M16W300 models, excluding the t = 1 and t = 2 models with small tube restrainer
thicknesses, the plasticity was spread slightly along the outer portions of the KBs. However, theplasticity spreading ranges in the beams adjacent to the KB outer sections did not increase until the
final loading stage. This can be explained by the excessive buckling of the BRKBs, which occurredbecause the small diameters of the steel core bars could not resist the applied loads, as discussed in51

Chapter 4 Numerical study for spreading plasticity around the beam end

KB outerportionSpreading ofplasticity
Satisfaction

KB inner portion

Underelasticity

Name

Under
plasticity№

Performance of thebuckling restrainer
BuckledPlasticity spreading ranges
in the beams

Safety factor

Table 3– Continued

as base small large small large
Eq. (3) A B C
M22 steel core bar BRKB beam models
M22W300 c1t1–t5
19 M22W300 - c1t1
ٗ
ٖ
+
0.002
ξ
20 M22W300 - c1t2
ٗ
ٗ
+
0.31
ξ
21 M22W300 - c1t3
ٗ
ٗ
+
0.64
ξ
22 M22W300 - c1t4
ٗ
ٗ
+
1.01
ξ
23 M22W300 - c1t5
ٗ
ٗ
+
1.42
ξ
M22W300 c2t1–t5
24 M22W300 - c2t1
ٗ
ٖ
+
0.04
ξ
25 M22W300 - c2t2
ٗ
ٗ
+
0.27
ξ
26 M22W300 - c2t3
ٗ
ٗ
+
0.52
ξ
27 M22W300 - c2t4
ٗ
ٗ
+
0.79
ξ
28 M22W300 - c2t5
ٗ
ٗ
൅
1.09
ξ
M22W300 c3t1–t5
29 M22W300 - c3t1
ٗ
ٖ
+
0.06
ξ
30 M22W300 - c3t2
ٗ
ٗ
+
0.25
ξ
31 M22W300 - c3t3
ٗ
ٗ
+
0.46
ξ
32 M22W300 - c3t4
ٗ
ٗ
+
0.68
ξ
33 M22W300 - c3t5
ٗ
ٗ
+
0.93
ξ
ǡ, and Cindicate very satisfactory, satisfactory, and unsatisfactory, respectively.ٗǡٖǡand ∆ the rates of the spreading of plasticity along the beams for “high,” “low,” and “same as the nonbraced base model,” respectively.

Section 4.7.5. Therefore, all M16W300 models were included in category C for the classificationof plasticity.
Our FEA revealed that the M22W300-c1t5 and M22W300-c2t5 models provide very satisfactory
performance, as indicated by the green color in Fig. 4.7(g) and Fig. 4.7(h). In these models, theplasticity spreads over wide areas in both the inner and outer sections without BRKB buckling.
Therefore, it was concluded that the theoretical safety factor (value of at least one) of the proposed
BRKB could be achieved for our design purposes. The half clearance between the screw section of
the steel core bar and restraining tube cs/2 should be controlled in the range of 1 to 2 mm.

52

Chapter 5 Test program for novel slender BRKBs

5. EXPERIMENTAL STUDY FOR THE SLENDER BRKB

5.1 General
This chapter developed a novel slender cover-tubed BRKB damper with the steel bar core to spread
plasticity around the beam end in the RMC, and experimental verification of its deformation capacity
was performed using weld-free beam-to-column connection. The advantages of the proposed damper
are reduced weight compared to conventional knee braces or mortar-filled BRKBs and higharchitectural flexibility for the retrofitting of large-span welded steel moment-resisting systems. It
was revealed that the proposed damper could also effectively improve the lateral stiffness of weldfree connection systems. Specifically, by increasing the number of contraction allowances,
undesirable failure mechanisms that are global instability and local buckling of the restrainer ends
can be suppressed effectively because the more uniform plastic deformation of the core bar can beachieved longitudinally. In other words, the adoption of several contraction allowance zones with theproper design of the cover tubes for the proposed dampers significantly improves the performance ofthe proposed dampers. The study conducted compression loading tests on nine BRKBs and cyclicloading tests on three full-scale specimens with a weld-free beam-to-column connection. The test
results are discussed, emphasizing the deformation capacities of the proposed dampers.
5.2 Outline of the proposed BRKB dampers
Fig. 5.1 presents possible configurations of the structural system with the proposed novel slender
BRKB damper. In some cases, retrofitting is more complex and difficult to organize because of theextreme diversity and the aesthetic focus on the structural integrity in existing buildings and obstaclesof the non-structural or structural elements such as wall and bolted connection of the column-tree
connection. Fig. 5.1(a) presents an application of the BRKB for either retrofitting or strengthening
the column-tree connection. Likewise, the proposed damper can be applied to the pin-connection
interior or external steel frames, as shown in Fig. 5.1(b) and Fig. 5.1(c), to dissipate the seismic input
energy during ground motion. In this weld-free system (pin connection), the beams are connected tothe column flanges only at the top flanges by T-stub members with bolts. The beams rotate about theends of their top flanges. As a result of implementing the BRKB in a weld-free system, the damper
can freely deform without causing significant damage to the beams, floor slab, and other nonstructural members under excessively large story drifts. Therefore, in Section 5.7, a description of anexperimental study in which only a weld-free connection is used with BRKBs to reveal the cyclic
response of the proposed dampers is provided.

53

Chapter 5 Test program for novel slender BRKBs

T-Stub

B

A

Beam

Beam

Proposed
BRKB

(a)

B

ColumnColumnBeam

Pinconnection

A

Proposed
BRKB

Column

A

(b)

(c)

Fig. 5.1. Structural configuration of the proposed system:(a) bracing for the column-tree connection; (b) double-side bracing; and (c) single-side bracing.

5.3 Details of the proposed BRKBs
The configuration of the proposed BRKB is shown in Fig. 5.2. Fig. 5.3 shows the details andexploded view of the proposed damper, where each element of the BRKB is numbered from 1 to 11.
The roll-threaded ends of the steel bar cores 2 and 3 are connected by a central coupler 1 andplaced inside detached round steel tubes 5 and 6 (buckling restrainers). The coupler acts as aconnector and transmits the force from one core bar to another. Buckling restrainer tubes with
sufficient stiffness and strength are set outside the core bars to ensure the stability of the steel corebars. For ease of construction, one of the steel bar cores is threaded by right screws at its ends, andthe other is threaded by right and left screws at its ends. The two opposing screws make available
adjustment capabilities during the erection process. In addition, a sufficient-strength steel cover tube

8 is placed at the center of the damper and locked by Allen bolts 9 to ensure the damper remains
stable under axial loading, as shown in Fig. 5.2. The relative movement of the cover tube along thelongitudinal direction of the damper is prevented by four pieces of the Allen bolts screwed throughthe central coupler. In this study, four contraction allowances, as indicated by the roman numbers I,
II, III, and IV, are adopted in the proposed BRKB based on preceding experimental experience [29],[38], [40]. These contraction allowances provide high flexibility to the steel bar core during applied
loading conditions. Two pieces of commercial springs 4 and 7 are inserted into the core bars at thelower construction allowance zones to hold the tube restrainer during the loading tests, as shown in54

Chapter 5 Test program for novel slender BRKBs

Fig. 5.2, in regions I and III. Finally, the left and right screw connectors 10 and 11 are attached tothe assembled damper to achieve sufficient holding force during earthquakes. Fig. 5.4 presents
explanations of the step-by-step built-up processes of the proposed damper.

Left screw
connector

Cover tube
SpringI

CentralcouplerA

II

Cover tube
Opposite-screw
steel core bar
Centralcoupler
Lower side

Allen bolt
III

SpringA

Right screw
connector

B

IV

B
Tube
restrainer
Right-screw
steel core bar

Allen bolt
B-B

A-A

Upper side

Fig. 5.2. Configuration of the proposed buckling-restrained knee brace (BRKB) damper

Fig. 5.3. Details and exploded view of the proposed damper.

55

Chapter 5 Test program for novel slender BRKBs

L

R

R

Step-1: Screw the steel core bars
andto the coupler , and insert the spring

Step-2: BR tubes

and

R

.

are inserted.

Step-3: Place the cover tube

Step-4: Lock the cover tube.

by Allen bolts

Lower side

Upper side

Step-5: Insert the spring

Step-6: Place the right and left screw connectors

and.

Fig. 5.4. Process followed to build the proposed damper.

56

Chapter 5 Test program for novel slender BRKBs

5.4 Design method for the proposed damper
Fig. 5.5 presents the geometrical parameters of the proposed BRKBs. First, a superior stiff buckling
restrainer for the base damper (L-BR) (Fig. 5.5(a) and Fig. 5.5(b)) was selected based on the theory
discussed in previous Section 3.2.3 [41], [43]. For example, the flexural rigidity and yield strength of
the restrainer were designed with a safety factor, SF, utilizing the design method described in Section
3.2.3.

2d s

ds

lr
50

ds

2d s

Upper

ower
side

Spring

A

B

A

B

side

lbr
lb
l

C

30

2d s

30
lin

ds

30
lin

100

30
ds

2d s

Upper

ower
A
Spring

B

B-B

lr

C-C
t

C

side
Spring

Dbr
d

lct
l

t

Spring

C

Dbr
d

A-A

lr

cs / 2ds

csh / 2

d sh

lbr

tct

lr

lr

tct

side

Dct
dct

(b)

B

Dct

(a)

A

lr
50

lbr

(c)

SpringCore bar
Central coupler

Cover tube

Buckling-restrainer tube

Fig. 5.5. Geometrical parameters of the proposed BRKB dampers:(a) Base damper, (b) proposed damper, and (c) detailed view of the proposed damper.

57

Chapter 5 Test program for novel slender BRKBs

The steel bar core was considered to be relatively flexible in the proposed damper. A sufficiently
stiff restrainer is expected to restrain the buckling amplitude of the steel bar core under compression
loads without rippling. The threaded sections of the steel bar core were inserted through the connector
at a distance of 2ds for both the compression and cyclic loading tests, where ds expresses the diameterof the threaded section. In contrast, the insertion length of the threaded sections in the buckling
restrainer must satisfy the following condition: if the rotation angle of the connection reaches 0.03
radian, the shank part should not be exposed [37]. In this regard, the insertion lengths of the threadedparts into the buckling restrainer were designed with a dimension of 2ds in the cyclic loading test,
whereas only ds could be adopted in the compression tests. Two contraction allowance zones wereadopted for the base damper (L-BR specimen, which is discussed in Section 5.5.1), considering the
expected axial deformation of the steel bar core under given loads.
Fig. 5.5(b) and Fig. 5.5(c) show the proposed cover-tubed BRKB. As the number of contraction
allowance zones was increased, the efficacy and performance of the damper were expected to become
more satisfactory [40]. Thus, the central coupler split the base damper into two parts. Four contraction
allowance zones were employed. A detailed description of the proposed damper is presented in
Section 5.3. To ensure stability of the proposed damper, a cover tube with an outer diameter Dct andthickness tct was utilized, as shown in Fig. 5.5(b). To obtain the optimal parameters of the cover tubes,
the ratio of the section modulus corresponding to the buckling restrainer and cover tubes wasconsidered. A cover tube with a larger elastic section modulus than the buckling restrainer canprobably support a load that is capable of inducing flexural loads in the buckling restrainer that arethen transferred to the cover tubes. This ratio can be determined by Eq. (5.1).

ܴ௖௧ ൌ

ܼ௖௧
ܼ௕௥

(5.1)

where Zct and Zbr are the elastic section modulus of the cover and buckling restrainer tubes,
respectively, which are defined by Eqs. (5.2) and (5.3), respectively:
ସ
ସ ሻ
െ ݀௖௧
ߨሺ‫ܦ‬௖௧ܼ௖௧ ൌ͵ʹ‫ܦ‬௖௧

(5.2)

ସ
െ ݀ସሻ
ߨሺ‫ܦ‬௕௥
͵ʹ‫ܦ‬௕௥

(5.3)

ܼ௕௥ ൌ

58

Chapter 5 Test program for novel slender BRKBs

Dct and dct are the outer and inner diameters of the cover tube, respectively, and Dbr and d are theouter and inner diameters of the buckling restrainer, respectively, as shown in the section views in
Fig. 5.5(b).
5.5 Compression tests
5.5.1 Test specimens
Compression tests were conducted on nine specimens, including the base damper (L-BR), to reveal
the load-bearing capacities of the proposed BRKB. The proposed damper specimens differed in thegeometrical parameters of their cover tubes, such as the insertion length, lin, and cross sections. Fig.
5.6 shows the geometrical dimensions of all the specimens, while Table 4 summarizes the detailed
characteristics of the specimens.

Inner diameter, dct(mm)Length, lct (mm)Insertion length, lin(mm)Group1 (Reference specimens)
1
N-BR
M20 110 1080
2
L-BR
2
M20 110 1080
40
9
900
3
S-BR
4
M20
90
530
40
9
390
Group2 (Short cover tube specimens)
4 SCT48-D
4
M20
90
530
40
9
390 48.6
5 SCT54-D
4
M20
90
530
40
9
390
54
6 SCT57-D
4
M20
90
530
40
9
390
57
Group3 (Long cover tube specimens)
7 LCT48-2D 4
M20
90
530
40
9
390 48.6
8 LCT54-2D 4
M20
90
530
40
9
390
54
9 LCT57-2D 4
M20
90
530
40
9
390
57

Thickness, tct (mm)Outer diameter, Dct(mm)

STKM13A
Length, lbr (mm)STKM13A
Thickness, t (mm)ABR

Outer diameter, Dbr(mm)

Cover tube

Core length, l (mm)Buckling
Restrainer tube

Screw length, lr (mm)Core bar

Screw diameter, ds(mm)Quantity

NameCont. allow.

Table 4– Geometrical parameters of the test specimens used in the compression loading tests

3.5
6
8

41.6
42
41

240
240
240

40
40
40

3.5
6
8

41.6
42
41

320
320
320

80
80
80

Abbreviations. ABR: Specifications of structural double-threaded anchor bolts. STKMA: Steel grade for structuralsteel tubes.

In general, the specimens were categorized into three groups: reference, short cover tubes (SCT),
and long cover tube specimens (LCT). The reference specimens were assumed to consist of only the59Chapter 5 Test program for novel slender BRKBs

40

(a)

1000

Lower

Upper

side

side
110

860
1080

110

50

900

50

40

(b)

Lower

Spring

side

40

30

Spring

side

100

20
90

350

lin = 40

20
330

40

(e)

30

Lower
side

30

Springlin = 80
290

30
390
Upper

lin = 40
240
1080
100

390

20

90

30
Spring

Dct

side

100

390

20

side

330
30

30

Spring
Dct

(d)

30

Spring

side

530

30

Lower

Upper
20

530

40

390

20
90

110

30

Spring

350

side

30

390

20
90

20

860
1080

30

Lower

40
Upper

20

110

(c)

40

390
Upper

lin = 80
40
320
1080

20

side

290

Fig. 5.6. Basic dimensions of the specimens for the compression loading tests.
(a) N-BR, (b) L-BR, (c) S-BR, (d) representative SCT specimens, and(e) representative LCT specimens.

60

Chapter 5 Test program for novel slender BRKBs

core bar (N-BR), long buckling restrainer base damper (L-BR), and four contraction allowance zones
with no cover tube specimen (S-BR), as shown in Figs. 6(a),6(b), and 6(c), respectively. The reference
specimens were identified based on the length of the buckling restrainer (N for none, S for shortbuckling restrainer, and L for long buckling restrainer). In contrast, Fig. 6(d) represents the proposed
damper with the short cover tube specimens, while Fig. 6(e) represents the long cover tube specimens.
For example, for SCT48-D, 48 indicates the outer diameter of the cover tubes, Dct = 48. D indicatesthe insertion length, lin, of the cover tube to the buckling restrainer. This compression loading test
considered only two insertion lengths lin : lin = Dbr and lin = 2Dbr. Dbr is the diameter of the buckling
restrainer. In addition, the material properties of the main damper components are listed in Table 5.
The predicted core bar yield strength Ny and the Euler buckling load of the buckling restrainer that
correspond to the L-BR specimen were obtained based on these data; the predicted values were Ny =83 kN and N EB = 230 kN, respectively.
Table 5 – Material properties of the compression loading test specimens
Steel grade

name

ABR400STKM 13A
STKM 13A
STKM 13A
STKM 13A

M20 barRound tube 40 x 9
Round tube 54 x 6
Round tube 57 x 8Round tube 48.6 x 3.5

Yield
stress(Τଶ )
322
304
367
302
393

Yield strain(microstrain)
1570
1483
1790
1473
1917

Ultimatestress(Τଶ )
469
458
489
451
412

Elongation
(%)
28
59
59
58
54

5.5.2 Core bar and contraction allowances
In the compression test, double-threaded structural anchor bolts M20 were used for the steel bar
cores, in which the non-threaded section had a diameter of 18.2 mm (ABR product specifications and
JIS B1220 standard). As mentioned in Section 5.4, the core bar threaded sections were inserted
through the buckling restrainer at a distance of 20 mm and screwed through the end connector with adimension of 40 mm for each specimen.
For the common BRBs, a stopper is often attached to the middle part of the steel core to keep thebuckling restrainer's position by welding and widening the cross-sectional area. However, it isdifficult for the steel core bar to mount the stopper in its middle because any processing such as
welding and widening cannot be done. Thus, in this study, an ultra-high deflection coil spring with asize of SWY30-35 was selected as the stopper for the lower contraction allowance zones, where 30
and 35 indicate the outer diameter and the initial length of the spring, respectively. The allowabledeflection of the spring was 22.8 mm. As shown in Fig. 5.6, a dimension of 30 mm was adopted in
61

Chapter 5 Test program for novel slender BRKBs

each contraction allowance zone. As presented in Fig. 5.6(c), when a 35 mm length spring is attachedto the lower contraction allowances in each part of the steel bar core, the allowable deflection of thespring should ensure that the planned 30 mm gap is maintained owing to the gravity force of thebuckling restrainer.
5.5.3 Buckling restrainer and cover tube
A round steel tube of 40 × 9 mm having diameter Dbr = 40 mm and thickness t = 9 mm was selected
for the buckling restrainer in the base damper specimen L-BR. The same round steel tube section wasthen used for the other specimens except N-BR specimen. The clearances were estimated as cs = 2
mm and csh = 3.67 mm. The safety factor of the base damper was SF 1.65 . The yielding momentBcapacity of the buckling restrainer was M y1047 kN × mm . These values were calculated byequations used in the Section 3.2.3.
For the cover tube specimens, the section of the restrainers was the same as that of the base damper.
By contrast, the size of the cover tubes was varied for comparison. Dimensions of 48.6 × 3.5 mm, 54
× 6 mm, and 57 × 8 mm were utilized for the SCT and LCT specimens, as shown in Table 5, basedon the Rct assumptions in Section 5.4. In this compression test, three Rct corresponding section
modulus of the cover tubes were considered: Rct

0.9 , Rct

1.7 , and Rct

2.3 , as listed in Table 6.

Two cover tube insertion lengths, lin, were considered: 40 mm and 80 mm. Finally, the performances
under compression loading tests were classified into three satisfactory scales: highly satisfactory,
satisfactory (acceptable), and unsatisfactory, as shown in Table 6 and discussed in Section 5.6.1.

SCT54-D

LCT54-2D

SCT57-D

LCT57-2D

Rct
Performances

LCT48-2D

Z ct /mm /SCT48-D

3

S-BR

Zbr /mm3/

L-BR

Table 6 – Section modulus of the tubes used in the compression tests

5705
-

5705
-

5705
5217
0.9
∆

5705
5217
0.9
∆

5705
9796
1.7
∆

5705
9796
1.7
ٖ

5705
13307
2.3
ٖ

5705
13307
2.3
ٗ

ٗǡٖǡand ∆indicate highly satisfactory, satisfactory (acceptable), and unsatisfactory, respectively.

5.5.4 Testing setup and data measurement
To examine the behavior of the proposed BRKB damper, compression loading tests were performed
using a UH-F1000 hydraulic universal test machine equipped with easy-to-see display measurement
control, as shown in Fig. 5.7. The test specimens were placed vertically in the loading machine, and62

Chapter 5 Test program for novel slender BRKBs

Cylindric support
P

UH-F1000
A

A

1000
1200

2800

B

B
Gaugesd1

d2
CC
Spring
Floor

Load cellFig. 5.7. Test setup and measuring system for the compression loading tests.
vertical load P was applied to the upper cylindrical connector. Cylindrical end supporters were utilized
at each end of the damper in the compression loading test. In addition, a mobile loading cell wasplaced beneath the lower cylindrical end-supporter to measure the vertical load, P, as shown in Fig.
5.7 (right side).
For the reference specimens, strains of the buckling restrainer tubes at position 1 of specimen LBR, and positions 1 and 2 of specimen S-BR, are as shown in Fig. 5.8(a) and Fig. 5.8(b), respectively.
For the specimens with cover tubes, the strains of the cover tube edges were measured at gauge
positions 2 and 3, and the strains of the restrainers were measured at gauge positions 1 and 4, as shownin Fig. 5.8(c). Fig. 5.8(d) shows the strain gauge positions around the tube surface. In addition,
displacement sensors d1 and d2, as shown in Fig. 5.7, were utilized to measure the average verticaldisplacement of the specimens under loading conditions.

63

Chapter 5 Test program for novel slender BRKBs

50

(a)

450
1C

1B,D

ower

side

450

20

30

(b)

195

ower
side

20

(c)

2C

1C

2A

20

20

1A

side

90

350
530

4B,D 4C

20

4A
330

90

195
2B,D

3C

2C

lin 3A

2A lin

3B,D

Bl

ct

30

195

Upper
side

20
90

350
530

B

195

side
110

195
1B,D

195

ower

A

195
2B,D

90

30

Upper
20

1A
860
1080

110

50

A

195
1C

1B,D

1A
330

20

1080

A-A
(d)

B-B
3C

1C
1D

1B

3B

1A

3D
3A

Fig. 5.8. Strain gauge locations.
(a) L-BR, (b) S-BR, (c) representative SCT and LCT specimens, and(d) Cross-sections of A and B.

64

30

Upper
side

Chapter 5 Test program for novel slender BRKBs

5.6 Compression loading test results
5.6.1 Load-displacement relationshipFig. 5.9 presents the load–displacement relationships of all the test specimens subjected tocompression loads. The notation Py indicates the predicted yield load of the steel bar core. The primaryhorizontal axis indicates an applied compressive displacement, D, at each specimen. In contrast, thesecondary horizontal axis presents the applied compressive displacement normalized by the yielddisplacement, Dy. The value of Dy for specimens N-BR and L-BR is 1.47 mm and reflected in Fig.
5.9, while for the specimens with four contraction allowance zones, the value of Dy is 1.32 mm andreflected in Fig. 5.9(b) and Fig. 5.9(c).
In the case of the specimens in group 1, compared to the N-BR specimen (only bar), the highest
increase in the maximum load of up to 111.5 kN was attained in the base damper specimen (L-BR)
with a displacement of 38.6 mm, as shown in Fig. 5.9(a). The N-BR and S-BR specimens showed asimilar trend in the elastic stage. It can be seen that, if the proposed four contraction allowance zones
BRKB have no cover tube, the failure mode is the same as that of the bar specimen at a load of 38
kN.
For the specimens in group 2, (Fig. 5.9(b)), the axial load capacities tended to increase slightly in
SCT48-D with Rct = 0.9 and SCT54-D with Rct = 1.7, the first two cover tube specimens, withmaximum loads of 40 kN and 52 kN, respectively. However, these two specimens no longer resist
any additional load owing to the failure of the cover tubes, as the photographs in Section 5.6.3. It isnoted here that the SCT48-D and SCT54-D specimens, including N-BR and S-BR, buckled before
yielding of the steel bar core. In addition, as the section modulus of the cover tube increased to Rct =2.3 with a shorter insertion length lin, the axial load capacity tended to increase after core bar yielding,as the results for specimen SCT57-D reveal. The maximum load that was attained was 111 kN.
For the specimens in group 3, (Fig. 5.9(c)), the load resistance capacity tended to increase as theinsertion length of the cover tubes increased. In particular, specimen LCT57-2D possessed an axial
load capacity that was more significant than those of the other two LCT specimens. The behavior ofoverstrength, as shown in Fig. 5.9(c), will be assessed by cyclic loading tests and discussed regarding
the brace compression-to-tension ratio in Section 5.8.1.
Overall, the following discussion can be summarized. When the Rct was less than 1.0, the damper
could not achieve the design purpose regardless of the cover tube insertion length. When the Rct was
1.7, it was observed that the insertion length, lin, was more influenceable for the load-bearing capacityof the proposed damper. For example, the specimen SCT54-D was unsatisfactory, while the specimen
LCT54-2D was satisfactory. Moreover, when the Rct was 2.3, the specimen SCT57-D was also
65

Chapter 5 Test program for novel slender BRKBs

satisfactory. In contrast, the specimen LCT57-2D was highly satisfactory, in which a continuous
strength increment was observed, as shown in Fig. 5.9(c).

150

0

D/Dy
20

10
N-BR

125

30

S-BR

150

L-BR

Py = 84 kN

D/Dy
20

10
SCT48-D(b)

30

SCT54-D40
SCT57-DPy = 84 kN

P (kN)

100

75
50

75
50

25

25

0

10

20

30
40
D (mm)

50

0

60

0

10

(a) Reference specimens,

150

0

20

D/Dy
20

10

30

40

Py = 84 kN

100
75
50
25
0

LCT48-2D

030
40
D (mm)(b) SCT specimens,

(c)

125

P (kN)

0

0

125

(a)

100
P (kN)

40

10

20

LCT54-2D

3040
D (mm)

LCT57-2D5060(c) LCT specimens
Fig. 5.9. Load–displacement relationship.

66

50

60

Chapter 5 Test program for novel slender BRKBs

5.6.2 Variation in the strains for the cover tube and buckling restrainer
Fig. 5.10 to Fig. 5.16 show the relationship between the axial load and strain of the buckling
restrainer and cover tubes for each specimen. The vertical dashed lines illustrate the yield strain
corresponding to the buckling restrainer and cover tubes of the proposed damper. By employing large
contraction allowances for specimen L-BR, the strain values of the buckling restrainer increased
significantly, as shown in Fig. 5.10(a). In the case of specimen S-BR, the strain values at the buckling
restrainers and the maximum axial load were lower than those of the other all specimens, as shownin Fig. 5.10(b) and Fig. 5.10(c).
12050Microstrain

Microstrain

50

25

0

0

10

2A
2C

2B
2D
50

20

25

30

(c)

0

Axial load (kN)

(b)

-25

1B
1D

-50

1A
1C

-25

Hy 

1B
1D

40

-50

-2000

0

1A
1C

2000

20

1000

40

0

60

Hy 

80

-1000

Axial load (kN)

100

Axial load (kN)(a)

Microstrain

Fig. 5.10. Brace axial load and strain relations. (a) for L-BR and (b) and (c) for S-BR.
Overall, the test results reveal that the strain values at the buckling restrainers were lower than theyield strain for the specimens in all the groups under given loads, as shown in Fig. 5.11(a) and Fig.
5.12(a), Fig. 5.13(a) and Fig. 5.14(a), and Fig. 5.15(a) and Fig. 5.16(a). However, the strain values
in the cover tubes for the specimens in group 2 exceeded the yield strain regardless of the tube
thickness corresponding to the given loads, as shown in Fig. 5.11(b), Fig. 5.13(b), and Fig. 5.15(b).
In contrast, the strain values at the cover tubes for the specimens in group 3, Fig. 5.14(b) and Fig.
5.16(b) were remained below the yield strain, except for specimen LCT48-2D, as shown in Fig.
5.12(b). It is important to note that when the ratio of the section modulus, as defined with Eq. (5.1),
is less than 1, for example, Rct =0.9, the strain values of the cover tube were exceeded yield strain
regardless of the cover tube length, as shown in Fig. 5.11(b) and Fig. 5.12(b). In contrast, when theratio Rct increases to 1.7 for the specimen LCT54-2D, the strain values of the cover tube are attained
to remain below the yield strain, as shown in Fig. 5.13(b).
Furthermore, specimen LCT57-2D with a ratio of the section modulus of Rct = 2.3 achieved good
performance, as shown in Fig. 5.16(a) and Fig. 5.16(b), until the final loading stage. Finally, it was
revealed that these two parameters, lin and Rct, possibly play essential roles in the design of our
proposed BRKB.
67

Chapter 5 Test program for novel slender BRKBs

50(a) buckling restrainer

Hy 

Axial load (kN)

2C
2D

3A
3B

3C
3D

0

0

2A
2B

Microstrain

2500

Microstrain

10

4C
4D

-2500

4A
4B

-5000

-1000

-2000

0

1C
1D

Hy 

20-10000

1A
1B

30

2000

10

40

Hy 

20

1000

30

0

Axial load (kN)Hy 

40(b) Cover tube

-7500

50

Fig. 5.11. Brace axial load and strain relations for SCT48-D.
100(b) Cover tube

Microstrain

Hy 

Hy 

Axial load (kN)

0

2A
2B

2C
2D

3A
3C

3B
3D

0

20

4C
4D

-2500

4A
4B

-5000

-1000

-2000

0

1C
1D

40

-10000

1A
1B

60

2000

20

80

Hy 

40

1000

60

0

Axial load (kN)Hy 

80

Microstrain

2500(a) Buckling restrainer

-7500

100

Fig. 5.12. Brace axial load and strain relations for LCT48-2D.
60(a) Buckling restrainer

Hy 1790

2C
2D

3A
3B

3C
3D

Microstrain

Fig. 5.13. Brace axial load and strain relations for SCT54-D.

68

2500

2A
2B

0

0

-10000Microstrain

Hy 1790

20
10

4C
4D

2000

4A
4B

1000

1C
1D

0

0

1A
1B

-1000

10

30

-2500

Hy 1483

40

-5000

Axial load (kN)Hy 1483

20

-2000

Axial load (kN)4030(b) Cover tube

50

50

-7500

60

100
Axial load (kN)Hy 

3A
3B

3C
3D

Microstrain

2500

2C
2D

0

0

2A
2B

-2500

Microstrain

20

4C
4D

-5000

4A
4B

40

-7500

1C
1D

60

-10000

-2000

0

1A
1B

80

2000

20

1000

40

(a) Buckling
restrainer

0

60

-1000

80

(b) Cover tubeHy 

100

Hy 

120

Hy 

120

Axial load (kN)

Chapter 5 Test program for novel slender BRKBs

Fig. 5.14. Brace axial load and strain relations for LCT54-2D.
120

80
60

Hy 
2A
2B

2C
2D

3A
3B

-2500

-1000002000

Microstrain

20

4C
4D

1000

4A
4B

-5000

40

0

1C
1D

-1000

1A
1B

-2000

0

(a) bcukling
restrainer

3C
3D

0

60

20

Hy 

100

80

40

(b) Cover tube

Microstrain

2500

Hy 

-7500

Axial load (kN)100Hy 

Axial load (kN)

120

Fig. 5.15. Brace axial load and strain relations for SCT57-D.

0

2A
2B

2C
2D

3A
3B

3C
3D

Microstrain

Fig. 5.16. Brace axial load and strain relations for LCT57-2D.

69

2500

20

-2500

40

-5000

4C
4D

60

-7500

Microstrain

Axial load (kN)

4A
4B

80

Hy 

Hy 
1C
1D

100

-100000

1A
1B(b) Cover tube

120

2000

20

1000

40

0

60

Hy 

80

-2000

Axial load (kN)

100

-1000

120

140

0

(a) Buckling140
restrainer

Hy 

160

160

Chapter 5 Test program for novel slender BRKBs

5.6.3 Residual deformation after compression loading
Fig. 5.17 to Fig. 5.19 illustrate the residual deformation for all the specimens in the final loading
stages. Fig. 5.17(a) – Fig. 5.17(c), Fig. 5.18(a) – Fig. 5.18(c), and Fig. 5.19(a) – Fig. 5.19(c) represent
the deformations of the specimens in groups 1, 2, and 3, respectively.

(a)

(c)

(b)

Fig. 5.17. Residual deformation in the final stage of loading for the reference specimens.
(a) N-BR, (b) L-BR, and (c) S-BR
For specimen L-BR, slight bending was observed in the middle of the buckling restrainer owing to
the axial force acting on the steel bar core being transferred to the BR prior to the core bar yielding,as shown in Fig. 5.17(b). When the compressive load was increasingly applied to the steel bar core,
it induced a plastic hinge at the exposed portion of the steel bar core in the upper contraction allowance
after the core bar yielded. The maximum axial load was Nmax = 111 kN. Moreover, it can be seen from
specimen S-BR that, when the proposed damper had no cover tube, plastic hinges quickly occurredin the steel bar core, as shown in Fig. 5.17(c). The maximum load, which leads to core bar bucklingin the earlier stage of the applied loading, was only Nmax = 30 kN. The flexural buckling of the steel
bar core on its exposed portion caused an excessive lateral deflection in specimen S-BR.
Furthermore, to improve the stability of the proposed damper, a cover tube insertion length of lin =40 mm was employed for the specimens in Group 2. In the first two specimens, specimens SCT48-D
70

240

240

Chapter 5 Test program for novel slender BRKBs

(b)

(a)

(c)

Fig. 5.18. Residual deformation in the final stage of loading for the SCT specimens.
(a) SCT48-D, (b) SCT54-D, and (c) SCT57-D
and SCT54-D, with Rct = 0.9 and 1.7, respectively, an excessive distortion was formed at the edge ofthe cover tube because of its insufficient insertion length as shown in Fig. 5.18(a) and Fig. 5.18(b).
These local failure behaviors were caused by a maximum axial load equal to Nmax = 40 kN. In
specimen SCT57-D with an Rct = 2.3, the edge failure of the cover tube was visibly small. In contrast,
the buckling restrainer was slightly deformed near the upper edge of the cover tube under the given
loads, as shown in Fig. 5.18(c). The maximum axial load was measured at Nmax = 100 kN.
Although the insertion length of the cover tube increased to lin = 80 mm for specimen LCT48-2D,
global buckling occurred owing to the specimen’s small Rct of 0.9. Plasticity initiation was slightly
delayed with Nmax = 80 kN compared with specimen SCT48-D. It is noted here that the small thicknessof the cover tube could not sustain the normal force acting on it from the buckling restrainer, as shownin Fig. 5.19(a). Moreover, plasticity patterns, similar to those of specimen LCT48-2D, were observedin specimen LCT54-2D (Fig. 5.19(b)). The maximum axial load was Nmax = 117 kN.
Finally, as a result of the compression loading tests, a specimen with sufficient strength and a very
stable BRKB was obtained, which was specimen LCT57-2D. No significant failure was observed inthis specimen except for the shortening of the steel core without failure of the buckling restrainer and
71

320

320

320

Chapter 5 Test program for novel slender BRKBs

(a)

(c)

(b)

Fig. 5.19. Residual deformation in the final stage of loading for the LCT specimens.
(a) LCT48-2D, (b) LCT54-2D, and (c) LCT57-2D.
cover tube, as shown in Fig. 5.19(c). In addition, the compression loading tests revealed that the
number of contraction allowances strongly influenced the load-bearing capacities of the proposed
dampers under given axial loads. Nevertheless, extended cyclic loading tests were conducted on
different parameters of the cover tube BRKBs to examine the cyclic response of the proposed dampers.
5.7 Cyclic loading tests
5.7.1 Test specimen
The compression loading tests revealed that the dampers LCT54-2D and SCT57-D with cover
tubes with Rct of 1.7 and 2.3, respectively, exhibited satisfactory design performance. In contrast,
LCT57-2D with Rct of 2.3 exhibited highly satisfactory. Considering the compatibility of the crosssections between the buckling restrainer and cover tube, the effect of the cover-tube insertion lengths
was examined for a fixed Rct value, which was 1.4 in the cyclic loading test specimens, as listed laterin Table 9. Three dampers, SCT60-D, LCT60-2D, and LCT60-3D, were prepared and tested toinvestigate their cyclic responses. Fig. 5.20 presents the basic dimensions of the three dampers

72Chapter 5 Test program for novel slender BRKBs

40
Spring

60.5

145
425
918

25

P

95

306
40

Spring

135

45

10

Beam
H250x125x6x9
.
1400
.
390
770.

Upper side
45

10

25

lin=135

40

Spring

110

10

95

306

90

145
325
918

95

306
40
Spring

(c)

110
25

lin=90

60.5

45

10

10

25

110

45

45

Upper side

95

306

40

SpringUpper side

110

(b)
Lower side

145
225
918

25

45

Lower side25

lin=4560.5

Lower side

(a)

10

95

306

45

40
Spring

110

45

45

95

306

45

110

A
T-Stub

A

795
.

(d)

45

B

B

1850

P

BRKB

Centralcoupler
SpringCover
tube

Built-up column
H250x250x19x25

Fig. 5.20. Basic dimensions of the dampers for the cyclic loading test specimens.
(a) SCT60-D, (b) LCT60-2D, (c) LCT60-3D, and (d) sub-assemblage.

73

Chapter 5 Test program for novel slender BRKBs

and the sub-assemblage of the cyclic loading tests. As previously mentioned, cover tube insertion
lengths lin of 45, 90, and 135 mm were selected as the experimental study test parameters, as shownin Fig. 5.20(a) to Fig. 5.20(c). As noted here, these values imply that lin = Dbr, 2Dbr, and 3Dbr for eachdamper.
The geometric characteristics and material properties of the dampers are listed in Table 7 and Table
8, respectively. Their identifications were the same as those used in the compression loading tests. A
round steel tube of 45 × 10 mm was used for the buckling restrainers, while that of 60.5 × 7 mm wasused for the cover tubes. Table 9 presents the section modulus of tubes.

Length, lbr (mm)Outer diameter, Dct(mm)

Thickness, tct (mm)

Inner diameter, dct(mm)Length, lct (mm)Insertion length, lin(mm)

STKM13A

Thickness, t (mm)STKM13A
Outer diameter, Dbr
(mm)

ABR
Core length, l (mm)Cover tube

Screw length, lr (mm)

SCT60-D
LCT60-2D
LCT60-3D

Buckling
Restrainer tube

Screw diameter, ds
(mm)

1
2
3

Core bar

Quantity

NameCont. allow.

Table 7 – Geometrical parameters of the proposed dampers used in the cyclic loading tests

4
4
4

M22
M22
M22

95,11095,11095,110

511
511
511

45
45
45

10
10
10

386
386
386

60.5
60.5
60.5

7
7
7

46.5
46.5
46.5

235
325
415

45
90
135

Abbreviations. ABR: Specifications of structural double-threaded anchor bolts. STKMA: Steel grade for structural steel
tubes.

Table 8 – Material properties of the cyclic loading test specimens
Steel grade

name

ABR400STKM 13A
STKM 13A

M22 barRound tube 45 x 10
Round tube 60.5 x 7

Yield stress(Τଶ )
302
283
283

74

Yield strain(microstrain)
1473
1380
1380

Ultimate stress(Τଶ )
453
442
435

Elongation
(%)
29
61
68

Chapter 5 Test program for novel slender BRKBs

Table 9 – Section modulus of the tubes used in the cyclic loading tests
Z br /mm3/
Zct /mm3/
Rct

SCT60-D
8090
5705
1.4

LCT60-2D
8090
5705
1.4

LCT60-3D
8090
5705
1.4

Performances

∆

ٖ

ٗ

ٗǡٖǡand ∆indicate highly satisfactory, satisfactory (acceptable), and unsatisfactory, respectively.

The steel-core-bar configuration based on the fabrication standards JIS B 1220 is the same as that
described in Section 5.5.2. However, the diameters of the core bar were 22 mm and 20.2 mm at thethread and shank parts, respectively. The insertion length of the core bar threaded parts into therestrainer was 40 mm. The core bar was screwed through the end connector with 45 mm. Under these
conditions, the shank part should not be exposed if the rotation angle of the beam reaches 0.02 radian.
Four contraction allowance zones with a total distance of 70 mm were employed for all the dampers.
The lower contraction allowance zones with the coil spring are marked green for each damper. In
addition, the safety factor, SF, of the buckling restrainer was calculated, implying the theory
introduced in the previous Section 3.2.3. According to the calculation, the safety factor was SF = 2.
Fig. 5.20(d) illustrates the sub-assemblage used for the cyclic loading test. In order to observe thecyclic behavior of the proposed damper, a strong column and a sufficient strength beam were selectedin the sub-assemblage. A 1.4 m beam of the hot-rolled H-section with dimensions of H-250 × 125 ×
6 × 9 and a built-up section column with dimensions of H-250 × 250 × 19 × 25 were utilized. The
length of each member was taken based on the damper length in this study. In addition, theperformances of specimens under cyclic loading tests were also classified into three satisfactory
scales: highly satisfactory, satisfactory (acceptable), and unsatisfactory, as shown in Table 9 anddiscussed in Section 5.8.3.
5.7.2 Testing setup
Fig. 5.21 illustrates the design of the general apparatus used for the cyclic loading tests. The outof-plane displacements are entirely constrained, as shown in Fig. 5.21(a). Four rollers attached to thebeam ensure that the beam moves freely over the surface of the vertical constrainer without any directbeam-to-constrainer interaction. The sub-assemblage that includes a beam, column, and the proposed
BRKB is attached to the reaction frame fully fixed and loaded by a vertical jack at the beam tip. As
illustrated in Fig. 5.21(b) and Fig. 5.21(c), a beam-to-column weld-free connection (pin connection)
was adopted to reveal the energy dissipation capacity of the proposed damper. In this regard, the shapeof the T-stub element was used for the connection, as shown in Fig. 5.21(c). Thus, the beam andcolumn behaviors can be regarded as entirely elastic. An assembled BRKB was connected by the right75

Chapter 5 Test program for novel slender BRKBs

and left screw connector to the beam and column of the specimen at a 45° inclination, as shown in

Vertical jack(b)

Proposed
BRKB

Roller for theout-of-plane
constrainer

Column(c) T-stubconnection

Right screw
connectorPinconnection

ColumnLoad cell(a)Out-of-planestopper

Fig. 5.21(b). In addition, Fig. 5.22 shows photographs of the actual test setup.

Beam

Left
screw
connector

Fig. 5.21. General apparatus for the cyclic loading test. (a) Test setup configuration, (b) view of
the BRKB placement, and (c) detailed view of the weld-free connection.

5.7.3 Data measurement of testingFig. 5.23 presents the cyclic loading tests program. A hydraulic jack with a stroke of 500 mm anda maximum force of 1000 kN was applied at the beam tip. The downward direction of vertical load P
was assigned a positive sign, as shown in Fig. 5.23(a). The following data were measured: (1) verticaldisplacement of the beam tip, G , regarding vertical load, P, (2) rotation of the beam relative to thebeam-to-column pin connection, and (3) strains of the buckling restrainer and cover tube for eachspecimen. Sixteen strain gauges were mounted at each specimen to record its strain behavior, as
shown in Fig. 5.23(d).
Displacement sensors d1 and d2 to d5 were utilized to measure the vertical displacement of thebeam tip and the rotation of the beam, respectively. Finally, displacement sensors d6 and d7 wereplaced along the axis of the BRKBs to measure the elongation of the steel bar cores.

76

Chapter 5 Test program for novel slender BRKBs

B

C
T-Stub

F

Right
Screw
connectorE

Pinconnection

BRKB

left
Screw
connector

BRKB

T-StubRollerSpringH
G

Fig. 5.22. Photographs of the cyclic loading test setup

d1

P

Beam
H250x125x6x9
.
1400
.
390
770.

d 2, d 4

P

45

BRKB

1850

d 3, d 5795.

DOut-of-plane stopper

Out-of-plane stopperAd 6, d 7
Built-up column
H250x250x19x25(a) displacement measurements plan
Fig. 5.23. Cyclic loading tests program.
77

P

R

0.03

+P

+R

795

0.04

56
(iii)

L=1400(i) (ii)

0.02

42
28
14

0.01
(iv)

0.00

0

Displacement G (mm)Global rotation R (rad)Chapter 5 Test program for novel slender BRKBs

-0.01

-14

-0.02

-28

-0.03

-42

-0.04

-56
0

2

4

6
8 10 12
Cycle Number

14

16

18

(b) loading protocol,-P

G

Fully elastic
columnUndeformed centerlineof beamܴ+P

Beam length L(c) global rotation of the reference beam,

193

193

4B,D 4C 3B,D 3C

25

4A

3A

193

193

2B,D 2C 1B,D 1C

918

2A

1A

(d) gauge positions on the dampers.
Fig. 5.23 Cyclic loading tests program (continued).

78

10

Chapter 5 Test program for novel slender BRKBs

5.7.4 Global rotation angles and loading conditions
Displacement-controlled cyclic loading was used in the test. Fig. 5.23(c) shows the global rotationof the reference beam. As shown in Fig. 5.23(c), the global rotation angle of the test specimen wasdetermined based on a pure cantilever beam ( RG L ).

The loading protocol is shown in Fig. 5.23(b). The right vertical axis represents the beam tip
displacement imposed on the controlled global rotation angle, and the left vertical axis illustrates theglobal rotation angle. In the cyclic loading test, the initial displacement was calculated as G
corresponding to R(rad)R(rad)

0.5% . The loading was increased up to R (rad)7 mm

4% in increments of

0.5% . Each increment consisted of two cyclic loading steps. The beam and column wereconsidered fully elastic to observe the cyclic response of the proposed damper, as shown in the test
setup design. After each loading cycle, the loading was stopped, and a visual inspection of thespecimen, including dampers, was performed.
5.8 Cyclic loading test results
5.8.1 Load and global rotation angle relationshipThis section discusses the effect of the test parameters on the cyclic responses of the three dampers,
and the results are illustrated in Fig. 5.24. The horizontal dashed lines marked as Py in each graphindicate the predicted yielding load of the steel bar core.
The specimen with damper SCT60-D achieved a global rotation of R(rad)of the R(rad)r 4% expected for the test specimens. Following the R (rad)r 3% , which is 75%

r 0.5% increment,

which consisted of two loading steps, the BRKB remained in the elastic range. At this stage, noyielding was apparent for each member of the dampers, such as the buckling restrainers and cover
tubes. Significant strength deterioration was initiated in the specimen with the SCT60-D damper at a
global rotation of R(rad)R (rad) 1% (point (i)) after the cover tube edge failed in the second cycle of 1% (point (ii)). The failure continuously occurred upon the further increase in the global

rotation, as shown in Fig. 5.24(a). The maximum load at points (i) and (ii) was 50 kN on the bracecompression side and slightly over 50 kN on the brace tension side.
The specimen with the LCT60-2D damper achieved a global rotation R(rad)the second cycle R(rad)r 4% . However, in 4% , a sudden strength degradation occurred because of the buckling of

the bottom restrainer tube, as shown in Fig. 5.24(b) (point (iii)). At this stage, the maximum bracecompressive load reached 124 kN. In contrast, the maximum tensile load reached 80 kN.

79

Chapter 5 Test program for novel slender BRKBs

150
100

795

(a)

P (kN)

50

P
+P

R
+R

L = 1400(ii)(i)

Py = 39 kN

0slippage-50 Py = 39 kN

60

-100
-150
-0.06

-0.04

45

145
235

45

-0.02

0.00
R (rad)

0.02

0.04

0.06

(a) SCT60-D

100

(b)
795

150

P

R

+P
L = 1400

+R

(iii)

P (kN)

50
Py = 39 kN

0slippage-50

Py = 39 kN

60

-100
-150
-0.06

-0.04

90

-0.02

145
325

0.00
R (rad)

90

0.02

0.04

0.06

(b) LCT60-2D
Fig. 5.24. Vertical load and story drift angle relations for three specimens
during the cyclic loading tests.

80Chapter 5 Test program for novel slender BRKBs

100

(c)
795

150

P

R

+P

+R

L = 1400

P (kN)

50
Py = 39 kN

slippage

0
Py =

-50

39 kN
(iv)

(iv)

-100
60

135

-150
-0.06

-0.04

-0.02

145
415

135

0.00
R (rad)

0.02

0.04

0.06

(c) LCT60-3D

1.3
1.2
1.1
1.0

(d)

E = 1.2

E = 1
L1CT60-2D
L2CT60-3D

E

0.9
0.8
0.7
0.6
0.5
0.4

0.
00
0. 5-1
00
5
0. -2
01
0. -1
0
0. 1-201
0. 5-1
01
5
0. -2
02
0. -1
0
0. 2-202
0. 5-1
02
5
0. -2
03
0. -1
0
0. 3-203
0. 5-1
03
5
0. -2
04
0. -1
04
-2

0.3
R (rad)-cycle(d) compression-to-tension ratio
Fig. 5.24. Vertical load and story drift angle relations for three specimens
during the cyclic loading tests (continued).
81

Chapter 5 Test program for novel slender BRKBs

Finally, the specimen with the LCT60-3D damper exhibited sufficient ductile behavior until thesteel bar core reached the rupture point corresponding to the second cycle R(rad) 4% , as shownin Fig. 5.24(c) (point (iv)). At this stage, the maximum load P reached 106 kN. In contrast, themaximum load, P, corresponding to the tensile side of the brace, reached 78 kN. In addition, theobserved maximum load that led to bracing in the compression state of the specimen with the LCT602D damper was slightly larger than that of the specimen with the LCT60-3D damper.
For the proposed BRKBs, it was observed that the insertion length of the cover tube plays anessential role in its cyclic loading responses. For example, when lin = Dbr = 45 mm (SCT60-D), thedamper could not dissipate energy well, whereas the other two dampers could. In addition, slightslippage was observed during the cyclic loading tests for each result. It is likely that jack-to-beam orbrace-to-beam connection bolts were affected for the above reason because of their rigidity.
Fig. 5.24(d) presents the variation in the brace compression-to-tension ratio [40], [43], defined as
the ratio of the maximal compressive force to the maximal tensile force for each cycle. In Japan, theBCJ specification [38] permits E d 1.2 , while the US standard AISC 341 [40] permits E d 1.3  1.5 .
The results of this study are based on the BCJ specifications. It can be observed that the specimen
with the SCT60-D damper could not meet these criteria. Therefore, its results were neglected in thisstudy. Specimen with the LCT60-2D damper met these criteria between global rotations
R (rad)0.01  2 and R (rad)criteria between R (rad)0.03  2 , while specimen with the LCT60-3D damper met these

0.01  1 and R (rad)0.035  1 . Finally, it is concluded that the specimen

with the LCT60-3D damper exhibited the most efficient energy dissipation capacity among the
proposed dampers.
The performances of the cyclic loading tests are shown in Table 9. The dampers with the varying
lengths of the cover tube and constant Rct were used to examine their structural performances in cyclicloading tests. Considering design performances, the specimens with the SCT60-D, LCT60-2D
dampers, and LCT60-3D damper were unsatisfactory, satisfactory, and high satisfactory
performances, respectively.
5.8.2 Strains for the cover tube and buckling restrainer
Fig. 5.25 to Fig. 5.27 show the relationship between the axial load of the braces and the measured
strains for BRKBs for each specimen. Considering beam-tip load, P, the axial load of the brace wasobtained from moment equilibrium in the tested model. The vertical dashed lines indicate the yieldstrain, and the horizontal dashed lines represent the Euler buckling load of the buckling restrainer
tube for base BRKB (L-BR). Fig. 5.25(a) and Fig. 5.25(b) illustrate the measured strains for the82

Chapter 5 Test program for novel slender BRKBs

buckling restrainer tubes, while Fig. 5.25(c) and Fig. 5.25(d) present the results of the strains of thecover tubes for each specimen.
For the specimen with the SCT60-D damper, the strain values induced in the buckling restrainer
were noticeably smaller than the values induced in the cover tube, as shown in Fig. 5.25(a) and Fig.
5.25(b). The strains on the buckling restrainer were symmetric among gauge positions 1 and 4. In
contrast, an excessive asymmetric spreading of the strains was observed in gauge position 3, as shownin Fig. 5.25(d). This behavior illustrates that the cyclic response of the damper with a lin = Dbr insertion
length of the cover tube was not satisfactory.
For the specimen with the LCT60-2D damper, the buckling restrainer experienced dominant strains
for the induced axial force, as shown in Fig. 5.26(a) and Fig. 5.26(b). The cover tube strains remainedin the elastic range except those at gauge positions 2 B and 3 B, as shown in Fig. 5.26(c) and Fig.
5.26(d). As the load increased, the strain values at gauge positions 1 B, 4 B, and 4 D for the buckling
restrainer, and the cover tube strains at gauge positions 2 B and 3 B exceeded the yield strain
simultaneously, as shown in Fig. 5.26(a) to Fig. 5.26(d).
For the specimen with the LCT60-3D damper, all the strain values for the buckling restrainer andcover tubes did not exceed the yield strain and met the Euler buckling criteria. The strain values forthe cover tube and buckling restrainers were visibly lower than those of the other two specimens, as
illustrated in Fig. 5.27. This behavior indicates that no plastic deformation or buckling failure
occurred during the cyclic loading test for the damper in the specimen with the LCT60-3D damper.
5.8.3 Residual deformation after cyclic loading
Fig. 5.28 shows the tested specimens and the residual deformation of the proposed BRKBs after
the cyclic loading tests. Fig. 5.28(a) shows that the cover tube end of SCT60-D loses its stability
owing to the insufficient insertion length for the given loads. Likewise, global buckling occurs in
LCT60-2D when the cover tube insertion length increases by two times the insertion length in thedamper in the specimen with the SCT60-D damper, as shown in Fig. 5.28(b). Finally, the specimen
with the LCT60-3D damper achieved superior performance when the system was carefully designed
and detailed, as shown in Fig. 5.28(c). These behaviors indicate that the damper stability capacity isstrongly governed by the insertion length of the cover tube as long as the damper is designed to meet
all the strength and stiffness requirements. Moreover, a detailed visual inspection of the disassembled
BRKBs was conducted, and three failure patterns were observed for the buckling restrainers, cover
tubes, and steel bar cores.
For the specimen with the SCT60-D damper, an undesirable plastic hinge at the upper edge of thecover tube began to occur at a low amplitude of cyclic loading and continuously developed up to the83Chapter 5 Test program for novel slender BRKBs

-100

-1000

0
Microstrain(c) Cover tubeHy 

0
-50

-100
-150
-2000

-1000

2000

150

2A
2B

0
Microstrain

1000

2C
2D

Hy 

Hy 
-1000

0
1000
Microstrain(d) Cover tube

50

2000

0
-50

-100
-150
-2000

2000

4C
4D

1( N1100

Hy 

50

4A
4B

-150
-2000

Deformation
at the gaupe
position-2

100
Axial load (kN)

1000

-50

-100

1( N1

-150
-2000

150

1C
1D

0

Hy 

1A
1B

50

Hy 

-50

Axial load (kN)0

Axial load (kN)50b) Buckling restrainer100Hy 

Axial load (kN)

100

150

(a) Buckling restrainerHy 

150

-1000

3A
3B

0
Microstrain

1000

3C
3D

2000

Fig. 5.25. Brace axial load and strain relations for specimen SCT60-D.
400

1( N1

0

1A
1B

-100

1C
1D

200
100

Hy 

Axial load (kN)

100

1( N1300

Hy 

200

Hy 

Axial load (kN)

300

0

-100

-200

Hy 

400

4A
4B

4C
4D

-200
(a) Buckling restrainer

-300
-2000

-1000

0
Microstrain

1000(b) Buckling restrainer
-300
-2000
-1000
0
Microstrain

2000

1000

Fig. 5.26. Brace axial load and strain relations for specimen LCT60-2D.

84

2000

300

100

Hy 

200

0
2A
2B

-100

2C
2D

200
100

Hy 

300

Hy 

400

Axial load (kN)400

Hy 

Axial load (kN)

Chapter 5 Test program for novel slender BRKBs

0
3A
3B

-100

-200

3C
3D

-200
(d) Cover tube
-300
-2000
-1000

(c) Cover tube

-300
-2000

-1000

0
Microstrain

1000

2000

0
Microstrain

1000

2000

Fig. 5.26. Brace axial load and strain relations for specimen LCT60-2D (continued).

400

0
1A
1B

-100

1C
1D

0
4C
4D

0
Microstrain

1000

2000

300

300

Hy 

0
2A
2B

-100

2C
2D

Axial load (kN)400
Hy 

400

200
100

1000

2000

Hy 

-1000(b) Buckling restrainer
-300
-2000
-1000
0
MicrostrainHy 

-300
-2000

100

4A
4B

-200

(a) Buckling restrainer200Hy 

100

-100

-200

Axial load (kN)200

Hy 

Axial load (kN)

100

1( N1300

Hy 

200

1( N1
Hy 

Axial load (kN)

300

400

0
3A
3B

-100

3C
3D

-200

-200

(d) Cover tube
-300
-2000
-1000

(c) Cover tube

-300
-2000

-1000

0
Microstrain

1000

2000

0
Microstrain

1000

Fig. 5.27. Brace axial load and strain relations for specimen LCT60-3D.

85

2000

Out-of-plane stopper

Chapter 5 Test program for novel slender BRKBs

Detail A

A
Cover tube
distorted(a) SCT60-D

Detail B

B

BR tubebuckled(b) LCT60-2D
Fig. 5.28. Residual deformation in the final stage of cyclic loading for the BRKBs.
86

Chapter 5 Test program for novel slender BRKBs

Detail CCCore barruptured(c) LCT60-3D
Fig. 5.28. Residual deformation in the final stage of cyclic loading for the BRKBs (continued).
final loading stage. This failure mechanism leads to excessive plastic deformation at the edge of thecover tube and slight bending of the buckling restrainer and steel bar core, as shown in the right photoof Fig. 5.28(a).
The specimen with the LCT60-2D damper was intended to be adequately involved in the plastic
work for the given loads. However, it was revealed that the 2Dbr insertion length of the cover tube
was insufficient to resist the relatively higher amplitude of the cyclic loading responses. Spiralbuckling behavior was observed at the upper steel bar core, while the lower buckling restrainer,
including the steel bar core, was slightly bent, as shown in the right photo of Fig. 5.28(b).
After completion of all the cyclic loading stages, no severe failures were observed in the buckling
restrainer and cover tubes for the specimen with the LCT60-3D damper. Higher mode buckling andspiral buckling simultaneously occurred in the lower and upper steel bar cores until the global rotation
angle R (rad)4% was reached. This behavior indicates that the 3Dbr insertion length of the cover

tube in the BRKB is sufficient for plastic work. However, when the elongation of the steel bar core
introduced in BRKBs exceeds the plastic limits at R(rad)87

0.04  2 , (see point (iv) in Fig. 5.24(c)),

Chapter 5 Test program for novel slender BRKBs

fractures occur at the screw part placed in the lower contraction allowance zone, as shown on the rightphoto of Fig. 5.28(c).
The assessment of the Rct for the cyclic loading tests against the compression loading tests is shownin Table 9. The specimen with the LCT60-3D damper showed high satisfaction for design purposes
without a global buckling. In contrast, the specimen with the LCT60-2D damper was considered
acceptable because the brace compression-to-tension ratio was achieved for design purposes, as
shown in Fig. 5.24(d).

88Chapter 6 Conclusions and Future Research

6. CONCLUSIONS AND FUTURE RESEARCH NEED
6.1 Experimental and numerical study for assessment of spreading plasticity in RMC
6.1.1 Conclusions
In sections 3 and 4, the cyclic behavior of RMCs with slender BRKB dampers was examined. First,
T-shaped partial frame prototype models were tested with the proposed BRKBs to evaluate the load
resistance ability of the braces and the plasticity behavior of the beams. An extensive numerical study
was then performed to investigate the plasticity behavior of the beams and braces under one-way
loading based on the test results. A steel core bar was used for the configuration of the proposed
BRKBs, to downsize the connection between the KB and the beam flanges compared to conventional
KBs. By adopting a slender BRKB in an RMC, a specific yielding sequence was formed near the
beam and brace that was not observed in typical KB systems. The following conclusions can be drawn
from this study.
x

Relative to the beam length, shorter BRKBs provided better results in terms of dispersing
plasticity along the beam during the numerical and experimental studies.

xBased on the extended numerical analysis, it was determined that a small-diameter steel
core bar (M16) for BRKBs was less effective for the design purposes.

x

Despite the thickness of the tube restrainer t = 1 models, all M22 steel core bar BRKB
models with SF < 1 exhibited excellent ability to spread plasticity along the beams.
However, a small safety factor cannot satisfy the stability requirements of the BRKBs.

x

In contrast, in the M22 steel core bar BRKB models with SF > 1, yielding was initiated in
the beam and brace simultaneously without failure of the brace, and plastic hinges werewidened significantly along the beam, producing satisfactory behavior.

x

Accordingly, it was concluded that the theoretical safety factor (value of at least one) of the
proposed BRKBs could be achieved for the design purposes. The half clearance between
the screw section of the steel core bar and restraining tube cs/2 should be controlled in therange of 1 to 2 mm for the models used in the case study.

6.1.2 Future research need
These sections have evaluated the behavior of only certain welded beam-to-column connections
using the proposed BRKB. However, more research is needed to evaluate the benefits of the proposed
BRKB for whole RMC frames.

89Chapter 6 Conclusions and Future Research

6.2 Experimental study for the novel slender BRKBs
6.2.1 Conclusions
The first half of this dissertation investigated the behavior of plasticity amplification on a rigid
beam-to-column connection using a steel-core-bar round tube buckling-restrained knee brace damper
BRKB under cyclic loading tests. This study showed that the proposed damper significantly reduced
the stress concentration at the rigid beam-to-column connection. The second half of this study
proposed and tested a novel long BRKB with a steel bar core damper using a round central coupler,
tube restrainer, and a cover tube with weld-free beam-to-column connections. Overall, theexperimental study was conducted in two stages.
In the first stage, compression loading tests were conducted on nine specimens, including the basedamper, using a UH-F1000 pressure machine to evaluate the energy dissipation capacities upon theapplication of compression loads. In this stage, the insertion length, lin, and the ratio of the section
modulus of the cover tube against the buckling restrainer were examined.
In the second stage, based on the investigations in the first stage, extensive cyclic loading tests
were carried out on three additional specimens with the BRKBs to investigate the effect of theirinsertion lengths on the cover tubes. In these tests, lin was selected as the test parameter, and it was
equal to Dbr, 2Dbr, and 3Dbr for each damper, where Dbr denotes the outer diameter of the buckling
restrainer.
As a result of both experimental studies, the following conclusions can be drawn.
x

The advantages of the proposed damper are easy to assemble compared to conventional
buckling-restrained braces and a high architectural flexibility for the retrofitting of largespan weld-free or welded steel moment-resisting systems.

x

By increasing the number of contraction allowances, undesirable failure mechanisms thatare global instability and local buckling of the restrainer ends can be suppressed effectively
because the more uniform plastic deformation of the core bar can be achieved longitudinally.
In other words, the adoption of several contraction allowance zones with proper design ofthe cover tubes for the proposed dampers significantly improves the performance of the
proposed dampers.

x

The study revealed that the damper stability capacity is governed by the insertion length ofthe cover tube, lin, and ratio of the section modulus of the cover tube against the buckling
restrainer, Rct. For the compression responses of the proposed dampers, when the Rct wasless than 1.0, the damper could not achieve the design purpose regardless of the cover tube
insertion length. When the Rct was 1.7, it was observed that the specimen SCT54-D was
90

Chapter 6 Conclusions and Future Research

unsatisfactory. In contrast, the specimen LCT54-2D was satisfactory for the design
performance. Finally, when the Rct was 2.3, the specimens SCT57-D and LCT57-2D
exhibited satisfactory and highly satisfactory, respectively.
x

For the cyclic responses of the proposed dampers, the damper with the insertion length oflin = 3Dbr exhibited high satisfaction with the load-bearing capacity. An Rct of 1.4 can berecommended when designing the proposed dampers if a sufficient insertion length isadopted for the proposed damper.

6.2.2 Future research need
Overall, these experimental studies were performed on a specific number of test specimens to study
the compression and cyclic behavior of the proposed dampers. Therefore, future research should
investigate the behavior of a large number of damper models using finite element analysis.

91

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96

Appendix A

APPENDIX A
In this appendix, to assess the spreading of plasticity around typical knee braced beams in a moment
connection, three different section areas of equal-sided double angles TKB beam models wereanalyzed. Their results are discussed in Table A1. Furthermore, the results of stress distributions foreach TKB beam model are plotted in Figs. A1 and A2 and are compared with the proposed BRKB
damper for the global relative rotation 0.02 and 0.05 radians. The numerical analysis method used inthis section is the same as the method used in section 4. The relationships between an axial load andaxial deformation of the TKBs are shown in Fig. A3. In which their results are compared with theresults of the proposed BRKB damper. Fig. A4 illustrates relationships between load and global
relative rotation for each TKB beam, in which the red color indicates the results of the proposed
BRKB damper.
As shown in Fig. A3(c) and Fig. A4(c), although it seems that TKB ( A 40x5) is very efficient forour design purpose, the large strength and stiffness of TKB do not cause the spreading of plasticity atthe beam as our proposed damper. The strength increases gradually in the KB tension side for each
TKB beam within -0.04 radian, while the strength in the KB compression side degrades compared to
the KB tension side. Because flexural buckling of the TKBs causes excessive lateral deflection and it
continuously occurs for given further loads (see Fig. A4 (a), (b), and (c)).

Unit: mJ(a) BRKB beam (0.02 radian)(b) BRKB beam (0.05 radian)(c) TKB beam ( A 40x5) 0.02 radian(d) TKB beam ( A 40x5) (0.05 radian)Unit: mJ

Fig. A1. Plastic strain energies for the BRKB and TKB ( A 40x5) beams
regarding 0.02 and 0.05 radians of loading.
97

Unit: MPa

Unit: MPa

Unit: MPa(g) Only bar KB beam (0.05 radian)(d) The proposed BRKB beam (0.05 radian)(b) Bare beam (0.05 radian)(h) Brace buckling (0.05 radian)98

BRKB (0.05 radian)(e) Final configuration of theFig. A2. Equivalent Von-Mises stress distributions regarding 0.02 and 0.05 radians of loading.

(f) Only bar KB beam (0.02 radian)(c) The proposed BRKB beam (0.02 radian)(a) Bare beam (0.02 radian)

Appendix A

Unit: MPa

Unit: MPa

Unit: MPa(p) TKB beam ( A 40x5) (0.05 radian)(m) TKB beam ( A 40x3) (0.05 radian)(j) TKB beam ( A 30x3) (0.05 radian)(q) Brace buckling (0.05 radian)(n) Brace buckling (0.05 radian)(k) Brace buckling (0.05 radian)

99

Fig. A2 Equivalent Von-Mises stress distributions regarding 0.02 and 0.05 radians of loading (Continued).

(o) TKB beam ( A 40x5) (0.02 radian)(l) TKB beam ( A 40x3) (0.02 radian)(i) TKB beam ( A 30x3) (0.02 radian)

Appendix A

-50

0

50

100

150

200

150

-3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
KB axial deformation (mm)

-200

-150

BRKB
TKB (40x5)

Py1=-80kN-3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
KB axial deformation (mm)Compression-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
R (% rad)

-150

100

Tension
Py1=80kN

Py1=-80kN

TKB (40x5) beam

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
R (% rad)Py1=80kN

BRKB beam(a) TKB ( A 30x3)(b) TKB ( A 40x3)(c) TKB ( A 40x5)
Fig. A4. Relationship between load and global relative rotation for the TKB beam models.

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
R (% rad)

-150

-100
Py1=-80kN

-100

0

50

100

150

-100

Py1=-80kN

TKB (40x3) beam

-50

0

Py1=80kN

BRKB beam-50

P (kN)-50

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50

TKB (30x3) beam

50

BRKB beam

1000Compression

-150

BRKB
TKB (40x3)

-150
-200

-100

-50

0

50

100

150

200

Py1=-80kN

Py1=80kN

Tension

-100

-50

0

50

100

150

200

Appendix A(a) TKB ( A 30x3)(b) TKB ( A 40x3)(c) TKB ( A 40x5)
Fig. A3. Relationship between an axial load and axial deformation of the TKBs.

-3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
KB axial deformation (mm)Compression

BRKB
TKB (30x3)

Py1=-80kN

Py1=80kN

TensionKB axial force (kN)

100

150

-200

-150

-100

KB axial force (kN)

P (kN)

KB axial force (kN)

P (kN)

Appendix A

Table A1 – Assessment of the spreading of plasticity for the TKB beams
Model nameKnee braces
SectionConfigurations
area (mm2)Description of the plasticity spreading
behavior
Stress is concentrated in the beam end (see Fig.

Bare beam

The proposed
BRKB beam

Buckling
restrainer-

A1 (a) and (b)).
Stress and plastic strain energy in the beam-end

320(Core bar)are spreading due to the proposed damper, as
shown in Fig. A1 (c), (d), and (e), and Fig. A2 (a),(b), respectively.

Only bar KB
beamStress is concentrated in the beam end (see Fig.
320

A1 (f), (g), and (h)).
The cross-section area of the TKB is close to the

TKB beam( A 30x3)

steel core bar, where stress is concentrated in the345

beam end due to the lack of stability of the TKB(see Fig. A1 (i), (j), and (k) and Fig. A3 (a)).
The cross-section area of the TKB, which was
obtained based on the design theory of section 2,

TKB beam( A 40x3)

is larger than the steel core bar, where the stress467

is concentrated in the beam end due to the lack ofstability of the TKB (see Fig. A1 (l) (m), and (n)and A3 (b)).
The cross-section area of the TKB is larger than
the area that is obtained by the design theory ofsection 2, where the stress spreading behavior is

TKB beam( A 40x5)

similar to the proposed system (see Fig.A1 (o),751(p), and (q)). However, excessive strength andstiffness of the TKB induce the large plastic strainenergy outside of the KB portion at the beam (seeFig. A2 (c) and (d), and Fig. A3 (c)).

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67(3RELATED PUBLICATIONS:

1.

“Steel rigid beam-to-column connections strengthened by buckling-restrained knee braces using

round steel core bar dampers,” Munkhunur T, Tagawa H, Chen X, Engineering Structures, Vol. 250, p.
113431, 2022.
2.

“Experimental study on slender buckling-restrained knee braces with round steel core bar cores,”Munkhunur T, Tagawa H, Chen X, Frontiers of Structural and Civil Engineering, accepted for
publication.
3.

“Finite element analysis on steel beam-to-column joint strengthened by buckling-restrained kneebrace using round steel core bar,” Munkhunur T, Tagawa H, Chen X, 12th Pacific Structural Steel
Conference Tokyo, Japan, November 9th to 11th, 2019.
4.

“Experimental study on steel beam-to-column joint strengthened by buckling-restrained kneebrace using steel core bar,” Munkhunur T, Tagawa H, Chen X, 17th World Conference on Earthquake
Engineering, 17 WCEE Sendai, Japan, September 13th to 18th, 2020.

109