Study on seismic performance of new precast post-Tensioned beam-column connection (Part 2)

KẾT CẤU – CÔNG NGHỆ XÂY DỰNG 
Tạp chí KHCN Xây dựng – số 3/2017 3 
STUDY ON SEISMIC PERFORMANCE OF NEW PRECAST 
POST-TENSIONED BEAM-COLUMN CONNECTION (PART 2) 
TS. ĐỖ TIẾN THỊNH 
Viện KHCN Xây dựng 
Assoc.Prof.Dr. KUSUNOKI KOICHI 
Đại học Tokyo 
Prof. TASAI AKIRA 
Yokohama National University, Japan
Tóm tắt: Bài báo này trình bày kết quả nghiên 
cứu của 3 mẫu thí nghiệm liên kết dầm – cột biên bê 
tông cốt thép lắp ghép ứng lực trước được thí 
nghiệm tại Phòng Thí nghiệm Kết cấu của Đại học 
Quốc gia Yokohama, Nhật Bản. Mục đích của thí 
nghiệm nhằm kiểm chứng khả năng chịu động đất 
của loại liên kết này. Kết quả thí nghiệm cho thấy 
liên kết dầm - cột không có khóa chống cắt có độ 
trượt tương đối giữa dầm và cột và biến dạng dư lớn. 
Các mô hình thí nghiệm có khóa chống cắt có ứng 
xử rất tốt với biến dạng dư nhỏ, dầm gần như không 
bị trượt so với cột, hư hỏng của các cấu kiện dầm và 
cột rất ít, khả năng chịu lực tốt. 
Từ khóa: Khóa chống cắt, ứng lực trước không 
bám dính, bê tông lắp ghép, liên kết dầm – cột. 
Abstract: This paper presents experimental 
results of three precast prestressed concrete 
beam-column connection specimens which were 
tested at Structural Laboratory of Yokohama 
National University, Japan. The aim of the 
experiment is to prove seismic behavior of this type 
of connection. The experimental results show that 
the beam-column connection without shear key has 
large slip and residual deformation. The 
beam-column connections with shear key have good 
seismic behavior with small residual deformation, 
minor damage of beam and column, and nearly no 
slip between beam and column. 
Keywords: shear key, unbonded presstressed, 
precast concrete, beam-column connection. 
1. Introduction 
From the experimental results of the specimens 
in the Phase 1(1, 2), it can be seen that the unbonded 
post-tensioned precast concrete connection with 
shear bracket has high possibility to apply for 
long-span office buildings. However, there were still 
some undesirable behaviour of the specimens such 
as crush of concrete at the upper part of the beam, 
damage of the top of the shear bracket and the 
beam socket. The aim of this study, named Phase 2, 
is to improve the design of the connection in the 
Phase 1 to obtain enhanced performance and avoid 
unexpected failure modes. Moreover, shear friction 
at the beam to column interface was also 
investigated. This type of structure has advantages 
such as over large span, good seismic performance 
with minimum damage for beam and column 
elements, reusable like steel structure. This type of 
structure has high ability to apply in high seismicity 
like Japan as well as in low to moderate seismicity 
area like Viet Nam. . 
2. Test program 
2.1 Test specimens 
 There are three specimens named SB-A, SF-A, 
and SB-LA. These specimens corresponded to the 
specimens SB, SF, and SB-L in the Phase 1(1). The 
specimen with slab and spandrel beam was not 
included in this study. Brief outline and specification 
of the specimens is shown in Table 1, and 
reinforcement detail is shown in Figure 1. Shear 
strength of the bracket and the volume of PC bars 
were determined in the same way as in the Phase 
1(1). Consequently, the shear resistant area of the 
bracket and volume of the PC bars of the specimens 
in the Phase 2 were identical with those of 
specimens in the Phase 1.
KẾT CẤU – CÔNG NGHỆ XÂY DỰNG 
4 Tạp chí KHCN Xây dựng – số 3/2017 
Table 1. Specimens outline 
As seen from the test result of the specimens in 
the Phase 1, the top of the bracket was deformed 
after the test, caused by large concentrated stress. 
Therefore, in the Phase 2, the shear bracket was 
designed so that the stress at its top face does not 
exceed the yield strength of the steel: 
y
u
u A
Q
  (1) 
 where: 
Qu: ultimate shear force at the beam end (N); 
 y: yield strength of the steel (N/mm2); 
A: effective area of the top face of the bracket 
(mm2), A = b.le, where b was the width of the 
bracket (mm), and le was the effective length of the 
bracket which contacted to the beam socket (mm). 
The width and effective length of the bracket are 
shown in Figure 2. Total length of the bracket was 50 
Specimens SB-A SF-A SB-LA 
Beam 
Section (mm2) 300 x 500 
Fc (N/mm2) 69.9 60.4 68.6 
fy (N/mm2) 339.1 339.1 339.1 
fwy (N/mm2) 313.1 313.1 313.1 
PC bars 2-15 Grade C 2- 26 Grade A 2- 15 Grade C 
 0 ( N/mm2) 1.83 4.02 1.83 
P0/Py 0.72 0.72 0.72 
PC length (mm) 1500 1500 1500 
Column 
Section (mm2) 400 x 400 
Fc (N/mm2) 69.9 60.4 68.6 
fy (N/mm2) 534.4 534.4 534.4 
fwy (N/mm2) 313.1 313.1 313.1 
Bracket 
aw (mm2) 3036 - 4950 
Length L (mm) 50 - 50 
Where: Fc : concrete compressive strength, fy : yield strength of 
main reinforcement, fwy : yield strength of lateral reinforcement, 
 0 : initial beam compressive stress, P0 : initinal prestressed 
load, Py : PC bar yield load, aw : shear resistant area. 
Figure 1. Reinforcement details of the specimens 
KẾT CẤU – CÔNG NGHỆ XÂY DỰNG 
Tạp chí KHCN Xây dựng – số 3/2017 5 
mm from the column face. The gap between the 
beam and the column filled with mortar was 20mm. 
Hence the effective length le is 30mm. 
 In order to satisfy Eq. (1), the shape of shear 
bracket was redesigned as T-shaped with wide top 
horizontal plate to enlarge the effective area. The 
widths of top plates were 80mm and 110mm for 
specimens SB-A and SB-LA, respectively. 
For the U-shaped steel box, beside the design 
formulas used in Phase 1(1), the top horizontal plate 
of the steel box should be designed for bending 
moment, caused by the reaction force from the shear 
bracket. In order to limit flexural deformation, 
maximum tensile stress at the top face of the 
horizontal plate should not exceed the yield strength 
of the steel: 
 yu
  (2) 
Where: 
u: maximum tensile stress at the midpoint of 
upper face of the top plate (N/mm2); 
 y : yield strength of the material (N/mm2). 
In order to satisfy Eq. (2), thicker plate (t=25mm) 
and strengthen plates was used at the top of the 
steel box. Photos of the shear bracket and U-shaped 
steel box are shown in Figure 3.
Test results of the specimens in the Phase 1 
showed that the upper part of the beam near the 
column face was severely crushed. In order to 
prevent this damage, two 6-D150 interlock steel 
spirals were used at the top corner of the beam to 
confine the concrete. 
2.2 Test setup and loading history 
The experimental setup is shown in Figure 4. The 
lower end of the column was connected to the 
reacting floor by the pin while the upper end was 
connected to the reaction wall by horizontal two-end 
pin brace that is equivalent to a vertical roller. The 
cyclic load was applied to the beam end by the 1000 
kN hydraulic jack that attached to the beam end with 
the pin. The gravity load was applied to the beam as 
a concentrated vertical load at the distance of 215 
mm from the column face.
SB-A SB-LA 
Figure 2. Effective area of the top face of the bracket 
Column b 
A 
le 
Beam 
50 
20 
Plan view 
Figure 3. Shear bracket and U-shaped steel box 
KẾT CẤU – CÔNG NGHỆ XÂY DỰNG 
6 Tạp chí KHCN Xây dựng – số 3/2017 
The specimens were tested under simultaneous 
action of cyclic and gravity load. First, the gravity 
load was applied gradually to designated value, and 
then the cyclic load was applied. As mentioned 
before, the beams of the specimens were shortened 
from 4.3m to 2.215m, hence, in order to generate the 
same combination of moment and shear force at the 
beam column interface as in original condition; the 
gravity load was controlled according to the original 
gravity load QL1 and the cyclic load QCY as: 
CYLL QLL
LLQQ 
'1
12
1 (3) 
 Where: QL1 was the original gravity load, L1 was 
the original beam length, L1 = 4.3m, L2 was the new 
beam length, L2 = 2.215m, the beam length was 
considered up to column face, L’ was the distance 
from the gravity load to the column face, L’ = 0.215 m, 
QCY was the cyclic load. QCY has the same sign with 
QL if they act on the same direction, and vice versa. 
These terms are shown in Figure 5. 
3. Test results and discussions 
3.1 Visual Observation 
 Figure 6 shows the crack patterns of the 
specimens of Phase 1 (1) and Phase 2 at 4% drift 
angle. Much fewer cracks were observed in all 
specimens, compared to those of specimens in the 
Phase 1. Crush of concrete at the top of the beam 
near the column face was significantly diminished 
compared to specimens in the Phase 1, proving the 
effectiveness of the spiral steels. 
The bracket and beam socket after the test were 
shown in Figure 7. As seen in this figure, the shear 
bracket and beam socket were not suffered from any 
damage, although they experienced very large 
vertical load and high drift level. Especially in 
specimen SB-LA where the gravity load was 1.5 
times larger than that in other specimens. 
Furthermore, in case of specimens with shear 
bracket, it was effortless to separate the beam out of 
the column after the test, confirmed the disassemble 
capability of this type of structure. Eq. 1 satisfied to 
prevent the bracket from deformation. 
Figure 6. Crack patterns of specimens at 4% drift angle 
SF-A 
QL 
SB-LA 
QL 
QL
SB 
QL
SF 
QL
SB-L 
SB-A 
QL 
a) Phase 1 specimens(1) b) Phase 2 specimens 
Figure 4. Test setup 
Figure 5. Illustration of the terms in the Equation (3) 
a) Prototype model b) Actual specimen 
KẾT CẤU – CÔNG NGHỆ XÂY DỰNG 
Tạp chí KHCN Xây dựng – số 3/2017 7 
3.2 Hysteresis behavior 
The hysteresis characteristics of the specimens 
are shown in Figure 8 as the relationship between 
moment and drift angle. The superimposed dashed 
lines on this figure illustrate the hysteresis behavior 
and modeled as tri-linear skeleton curve. The 
moment and rotation angle at the limit states were 
determined as follow(6): 
 Decompression occur state: 
21 1
2 0.85
e
s eM BD

  
B (4) 
EIL
MR ss 3
 (5) 
Yield limit state: 
B
 2
85.0
1
2
1 BDM y
y
y 
 (6) 
pepyPC
y
PC
PC
y EIL
M
L
D
R  ,
35.0 
(7) 
Ultimate limit state, Mu = My. 
pepuPC
y
PC
PC
u EIL
M
L
D
R  ,
35.0
 (8) 
where: 
 e: = Pe/BD B; 
Pe: initial prestress force (N); 
B, D: width and height of the beam (mm); 
 B: concrete compressive strength (N/mm2); 
 y: = Py/BD B; 
Py: PC bars yield force (N); 
LPC: PC length (mm); 
E: Young modulus of the concrete (N/mm2); 
I: second moment of the beam section (mm4); 
L: beam length (mm); 
 pe: initial PC strain (); 
 py: PC strain at yielding (); 
 pu: PC strain at ultimate state (). 
Figure 8. Moment – drift angle relationship 
Figure 7. Shear bracket and beam socket after tested 
SB-A SB-LA 
KẾT CẤU – CÔNG NGHỆ XÂY DỰNG 
8 Tạp chí KHCN Xây dựng – số 3/2017 
All the specimens were successfully passed the 
drift of 4% in negative directions and 6% in positive 
direction. No fracture of PC bars was recorded. As 
seen in Figure 8, while the self-centering 
characteristics of the specimens SB-A and SB-LA 
were very good, that of specimen SF-A was poor. In 
the specimens with shear bracket, yield moment 
strength well exceeded the modeled values. 
Average experimental yield moments were 20% and 
35% larger than the calculated ones for specimens 
SB-A and SB-LA, respectively. In the specimen 
without shear bracket (SF-A), while the strength in 
the positive direction was almost the same with the 
modeled one, it was 80% of the modeled value in the 
negative direction. As illustrated in the Figure 9, 
when the beam slip occurs, the moment lever arm in 
negative direction was shorter than that in positive 
direction, made the flexural strength in negative 
direction smaller than that in the positive direction. It 
can be said that in the connection without bracket, 
under the effect of beam slip, it was difficult to predict 
the flexural strength of the connection. This was one 
of the disadvantage of the connection without shear 
bracket. 
3.3 Beam Slip and Friction Coefficient 
Figure 10 shows the relationship between the 
gravity load and quantity of beam slip at the 
beginning of the test (before applying of the cyclic 
load). The gravity load was applied monolithically up 
to 255 kN (SB-A and SF-A) and 382 kN (SB-LA). Up 
to gravity load of 255 kN, the amount of slip was 
mostly the same for all specimens, whether with or 
without shear bracket. It can be said that shear 
bracket did not contribute to the shear strength of the 
connection at this stage. For specimen SB-LA, when 
the gravity load exceeded 255 kN, the amount of 
beam slip significantly increased, expressed that the 
slip started to occur. 
The beam slip – drift angle relationships of three 
specimens are shown in Figure 11. It can be seen 
that the beam slip of specimen without shear bracket 
(SF-A) was almost the same with that of specimen 
SF in the Phase 1, excessive larger than that of the 
specimens with shear bracket (SB-A and SB-LA). 
From the test result, it concluded that the shear 
bracket successfully prevented the slip of the beam. 
Figure 12 shows the beam slip and the QB/PPC ratio 
relationship of the specimen SF-A. The dashed line 
expresses the upper bound of the ratio of each 
loading cycle and illustrates the friction coefficient . 
It can be seen that, beam slip occurred when the 
value of  was around 0.45.
Table 2. Summarized test results 
Specimens Loading Direction 
Md 
(kNm) 
Rd 
(%) My (kNm) 
Ry 
(%) Mmax (kNm) Rmax (%) My/Mycal 
SB-A 
  52.7 0.09 109.4 3.82 118.7 4.97 1.3 
  -50.3 -0.12 -94.2 -2.65 -95.4 -2.82 1.1 
SF-A 
  97.1 0.09 185.6 1.99 234.9 5.21 0.99 
  -84.7 -0.2 -152.5 -1.74 -178.7 -4 0.81 
SB-LA 
  53.8 0.07 101.9 3.85 110.9 5.62 1.2 
  -43.1 -0.15 -132 -2.61 -144.3 -1.82 1.5 
Where: Md, Rd : moment and story drift when opening occurred; My, Ry : moment and story drift at yielding; 
Mmax , Rmax : maximum moment and corresponded story drift; Mycal: calculated yielded moment strength; 
Figure 9. Illustration of moment strength 
Figure 10. Beam slip – gravity load relationship 
0
100
200
300
400
0.0 0.1 0.2 0.3 0.4
Slip (mm)
 Q
L 
(k
N
) SB-A
SF-A
SB-LA
KẾT CẤU – CÔNG NGHỆ XÂY DỰNG 
Tạp chí KHCN Xây dựng – số 3/2017 9 
3.4 Contribution of shear bracket and shear 
friction to the shear strength of the connection 
Figure 13 shows the locations of strain gages 
pasted on the U-shaped steel box and the observed 
strains of the specimens SB-A and SB-LA. Strain 
gages were attached at the top horizontal plate and 
vertical plates of the steel box. For the specimen 
SB-A, strain gages were attached at middle and 
upper part of the vertical plates to confirm whether 
the strain varied along the plate or not. It can be 
seen from the Figure 13 that the strains did not vary 
along the height of the vertical plates. From 2% drift 
angle, strains in these plates became stable. 
Maximum strains of the top horizontal plate in both 
specimens were 0.12%, about 50% of the yield 
strain. This improved that Eq. 2 was safe to design 
the steel box. 
The tensile force in vertical plates of the steel box 
was calculated as follow: aET ・・  (10) 
where: 
E: Young modulus of the steel (N/mm2); 
 : strain (); 
a: total sectional area of vertical plates (mm2). 
In Figure 14, Qb was the shear force resisted by 
the shear bracket. It can be seen that the reaction 
force from the bracket was resisted by vertical plates 
and transferred to bottom part of the beam. 
Therefore, it can be considered that the tensile force 
T in vertical plates of the steel box corresponded to 
the actual shear force transfer by the bracket. 
0.0
0.1
0.2
0.3
-6 -4 -2 0 2 4 6
S
tr
ai
n 
(%
)
Drift angle (%)
SB-LA
(T1+T3)/2
T5
y
S B -A
0.0
0.1
0.2
0.3
-6 -4 -2 0 2 4 6
Drift angle (%)
S
tr
ai
n
 (
%)
(T1+T3)/2
(T2+T4)/2
T5
y
Figure 11. Beam slip – drift angle relationship of all specimens 
0
5
10
15
20
25
0 1 2 3 4 5
Drift Angle (%)
B
e
am
 s
lip
 (
m
m
)
SB-A
SF-A
SB-LA
Phase 1 specimens 
Phase 2 specimens 
0 
5 
10 
15 
20 
25 
0 1 2 3 4 5 6 
B
ea
m
 s
lip
 (
m
m
)
Drift Angle (%)
SB
SF
SB-L
SB-S
Figure 12. Beam slip – friction coefficient relationship, SF-A 
QB : Beam shear force; N : PC force 
0.0
0.2
0.4
0.6
0.8
1.0
0 5 10 15 20 25 30 
=
Q
B
/
N
Beam Slip (mm)
SF-A
0.5
18
Figure 13. Strain of the U-shaped steel box 
KẾT CẤU – CÔNG NGHỆ XÂY DỰNG 
10 Tạp chí KHCN Xây dựng – số 3/2017 
As proposed in reference (3), shear strength of 
the bracket was designed by the equation: 
0.9
1.5 3
y
s w L
F
Q a Q (9) 
 where: Qs is the shear strength of the bracket, Fy 
is the yield strength of the steel plate, aw is the 
vertical shear resistance area, and QL is the shear 
force at the beam end induced by the gravity load. 
In this study, SN490C steel was used, Fy = 325 
N/mm2. Shear resistance area aw were 3036 and 
4950 mm2, for specimens SB-A and SB-LA, 
respectively. The value of shear strength Qs were 
342 kN and 557.3 kN for specimens for specimens 
SB-A and SB-LA, respectively. 
Table 2 shows the ratio of tensile force T and 
gravity load QL. It can be seen that at small drift 
angle, most of the shear force was resisted by shear 
friction (77% and 78% at 0.5% drift angle, for 
specimen SB-A and SB-LA, respectively). When drift 
angle increased, contribution of shear bracket 
increased (62% and 65% at 4% drift angle and 
neutral position). Moreover, at peak drift position, 
this contribution was less than that at neutral 
position. 
Table 3. Shear resistance of the bracket 
Specimen 
Drift 
angle 
(%) 
Tensile 
force T 
(kN) 
Shear strength 
of bracket Qs 
(kN) 
T/Qs 
SB-A 
0.5% 74.5 342.0 0.22 
1% 121.5 342.0 0.36 
2% 158.6 342.0 0.46 
3% 201.3 342.0 0.59 
4% 231.4 342.0 0.68 
-0.5% 117.9 342.0 0.34 
-1% 148.3 342.0 0.43 
-2% 163.9 342.0 0.48 
-3% 171.0 342.0 0.50 
Specimen 
Drift 
angle 
(%) 
Tensile 
force T 
(kN) 
Shear strength 
of bracket Qs 
(kN) 
T/Qs 
-4% 173.3 342.0 0.51 
SB-LA 
0.5% 70.5 557.3 0.13 
1% 131.5 557.3 0.24 
2% 190.8 557.3 0.34 
3% 226.7 557.3 0.41 
4% 236.8 557.3 0.42 
-0.5% 109.0 557.3 0.20 
-1% 146.9 557.3 0.26 
-2% 181.2 557.3 0.33 
-3% 179.2 557.3 0.32 
-4% 192.2 557.3 0.34 
It can be seen from Figure 14 that, the beam 
contacted the column through entire beam section at 
neutral position. At peak drift angle position, 
contacted area limited only on small areas at the top 
or bottom of the beam. After several cycles, the 
concrete and grout at these areas was crush and 
softened, causing the deterioration of friction 
coefficient. Similar results were found in the study by 
Okamoto(8). It can be concluded that the contribution 
of shear friction mechanism to the shear strength of 
the connection decreased when the drift angle 
increased, especially at peak drift angle position. 
4. Conclusions 
 From results of this study, following conclusions 
can be drawn. 
1) Modified shear bracket and beam socket worked 
well to transfer the shear force from the beam to the 
column, as well as satisfy the deformability of the 
beam at high level of drift. 
2) The specimens with shear bracket expressed very 
good seismic performance, with small residual 
deformation, fully developed and column element, 
even in very long span frame. It is high possibility to 
apply this type of connection in real precast building 
structures. 
3) The specimens without shear bracket 
experienced large beam slip and residual 
deformation. The slip occurred at the friction 
coefficient of 0.45. Performance of the system 
without bracket was inferior compares to the system 
with shear bracket. 
4) The slip of the beam was the cause of the 
Figure 14. Transfer of shear force from bracket to beam 
end 
KẾT CẤU – CÔNG NGHỆ XÂY DỰNG 
Tạp chí KHCN Xây dựng – số 3/2017 11 
difference of flexural strength between positive and 
negative direction. 
5) At small drift angle, most of shear strength of the 
connection was contributed by shear friction 
mechanism. When the drift angle increased, 
contribution of shear friction decreased and that of 
the shear bracket increased. 
REFERENCES 
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Quốc gia Yohohama. 
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Study on A New Precast Post-Tensioned 
Beam-Column Joint System”, Tạp chí Khoa học Công 
nghệ Xây dựng, số 4, trang 25-31. 
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Structural Design and Construction of Precast 
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[8] H. Okamoto, and T. Hirade (1997), “Shear transfer on 
the beam-column prestressed joint under earthquake 
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Ngày nhận bài:23/8/2017. 
Ngày nhận bài sửa lần cuối: 06/9/2017.