MINISTRY OF EDUCATION AND TRAINING
NATIONAL UNIVERSITY OF CIVIL ENGINEERING
Vo Manh Tung
RESEARCH THE IMPACT OF THE BEAM-COLUMN
JOINT DEFORMATION ON SEISMIC BEHAVIOR OF
REINFORCED CONCRETE FRAME
Major: Civil Engineering
Code: 9580201
SUMMARY OF DOCTORAL DISSERTATION
Ha Noi –2018
The work was completed at:
NATIONAL UNIVERSITY OF CIVIL ENGINEERING
Academic supervisor: Assoc. Prof. PhD. Nguyen Le Ninh
Reading Committee:
Prof. PhD. Nguyen Tien Chuong
Assoc. Prof. PhD. Nguyen Ngoc Phuong
PhD. Nguyen Dai Minh
The doctoral dissertation will be defended at the level of the State
Council of Dissertation Assessment's meeting at the National
University of Civil Engineering.
at ..... hour .....', day ..... month ..... year 2018
The dissertation is available for reference at the libraries as follows:
- National Library of Vietnam;
- Library of National University of Civil Engineering
1
INTRODUCTION
1. The necessity of the topic
The beam-column joint (BC joint) is the intersection of beams
and columns. Underneath the earthquake effects, reinforced
concrete BC joint have complex behavior and their destructive
behavior often leads to the collapse of the frame. Determination
of shear strength and simulated behavior of BC joint has been
proposed. However, these models are not general and have a
broad consensus. In design, the BC joint is still considered to be
the rigid zone.
At present, in the modern design of earthquake resistance, the
BC joint must have sufficient strength to ensure that the beams
and columns around it develop the desired plastic deformation.
In order to solve this problem, the design codes of
earthquakeresistance have very strict requirements for the
calculation and details, but avoid the problem of distortion, a
very important factor affecting behavior of the frame when
earthquake.
In Vietnam, there are currently no studies on the behavior of
reinforced concrete BC joint. The BC joint is considered an rigid
zone. Therefore, the "Research the impact of the BC joint
deformation on seismic behavior of reinforced concrete frame" is
very necessary.
2. Aims of the research
a. An overview of the models of durability and behavioral
simulations of earthquake resistant reinforced concrete BC joint;
b. Experimental study of the types of reinforced concrete BC
joint in Vietnam in order to clarify the problems: the possibility
of deformation and force bearing, criteria for shear strength,
suitable to the plastic responseof frame.
c. Study of nonlinear calculation frames taking into consideration
BC joint deformation designed in accordance with TCVN 9386:
2012.
3. Object and methodology of the research
Object: the reinforced concrete BC joint are available in actual
2
construction in Vietnam.
Methodology: theory combined with experiments.
4. Significant contributions of the dissertation
a. The experiments showed that the types of reinforced
concrete BC joint available in Vietnam are deformed when
earthquake; The joint is designed in accordance with TCVN
9386:2012, which is inelastic failure, and the TCVN 5574:2012
and SP 14.13330.2011 (Russian Federation) are brittle failure,
not suitable to create ductile mechanism for the frame structure.
Identification of the main factors affecting the behavior of the
BC joint and the conditions to ensure the shear strength of the
joint designed in Vietnam.
b. The proposed three models simulate the shear deformation
and bond slip of the BC joint. The use of these models in static
and dynamic analysis of reinforced concrete frames designed in
accordance with TCVN 9386: 2012 shows that the deformation
of the BC joint significantly changes the overall response of the
structural frame.
5. Dissertation structure
The dissertation includes Introduction, 5 main chapters,
Conclusion, list of published works by author, references and
appendices.
CHAPTER 1. BACKGROUND OF THE REINFORCED
CONCRETE BEAM-COLUMN JOINT
AND RESULTS ACHIEVED
1.1 THE FAILURE OF BC JOINT UNDER SEISMIC ACTIONS
There are two types of failure that are commonly observed after
earthquakes: (a) shear failure of the joint and (b) failure of the
reinforcing anchor. Cause due to lack of stirrups and anchor
reinforcement is not enough in the joint area.
1.2 CLASSIFICATION OF BC JOINTS
The joints are classified according to: (a) the geometry and
way of anchoring the reinforcement of beam (outer, inner), (b)
the behavior of the joint (elastic, inelastic), (c) the detail of the
joint(brittle, ductile).
1.3 THE FORCE IMPACT ON BC JOINT
3
Consider an interior joint, which is subjected to forces acting
from the beams and columns (Figure 1.9a), resulting in internal
forces as shown in Figure 1.9b. Balancing these internal forces
will be the shear force horizontally Vjh:
Vjh = Cb1 +C sb1 +Tsb 2 -Vc (1.1) or Vjh = Tsb1 +Tsb 2 -Vc (1.2)
So Vjh = (A s1 +A s 2 )0 f y -Vc (1.3) in which Cb1- compression
forced in concrete, Tsb1, Tsb2 or Csb1-tensile and compression in
beam reinforcements , Vc- shear force of columns above and
below the joint, As1 or As2– the areas of beam reinforcements,
λ0and fy – overstrength factor and tensile strength of
reinforcement.
Figure 1.9
The force
acting on
the interior
joint
Horizontal shear stress τjh and vertical shear stress τjv:
V
V
jh = jh = jv jv (1.5), in which bj, hc and hb
b j hc b j hb
correspondingly, the effective width of the joint, column and
beam height
For exterior joint: Vjh = A s10 f y - Vc (1.7)
1.4. METHODS FOR DETERMINING SHEAR STRENGTH OF JOINT
1.4.1.The model determines the shear resistance of joint
There are many computational models that have been
proposed and classified in four ways. The following are the two
most commonly used computing models.
1.4.2.Model of Paulay and Priestley
4
According to Paulay
and Priestley, the shear
strength of the joint is a
combination of strut
mechanism and truss
mechanism. The first
one
contributes
to
Figure 1.12 Transmission shear
horizontal shear force
mechanisms: a) strut; b) truss;
Vch and vertical
al shear
force Vcv from the diagonal compression force Dc (Fig. 1.12a),
while the second one contributes to the horizontal shear force Vsh
and Vsv with the diagonal compression force Ds out through the
bond of the reinforcement of the column and beams in the joint
region (Fig. 1.12b).
With this model, Paulay and Priestley set up equations for
calculating the horizontal strength Vjh and vertical shear strength
Vjv.
1.4.3 Model of A. G. Tsonos (1999, 2001)
Tsonos' shear strengthmodel is also comprised of two
mechanisms as proposed by Paulay and Priestley, but Tsonos
argues that these mechanisms produce an evenly distributed
stress field. Tsonos then establishes the relationship between the
vertical compression stress σ and the shear stress τ in the joint
and consequently horizontal shear of joint: Vjh = hc b j (1.45)
(1.45).
1.5 THE SHEAR STRENGTH OF THE JOINTS
S IN ACCORDANCE
WITH THE DESIGN STANDARDS
This section deals with the determination of shear strength in
the design standards ACI 318M-2011,
2011, NZS 3101 (2016), TCVN
9386: 2012, EN 1998-1-1: 2004 and AIJ 1999.
1.6 COMMENTS ON METHODS FOR DETERMINING THE SHEAR
STRENGTH OF THE JOINTS
The theoretical basis used to determine the shear strength Vjh
are very different in the design of the earthquake resistance. US
standards focus on the dimensions of joint and the concrete
strength fc. The Vietnamese and European standards focus on the
amount of stirrups in the joint and the axial force Nc of column.
5
1.7 BC JOINT MODELS FOR NONLINEAR ANALYSIS
There are many models for simulating the deformation of the
BC joint that have been proposed for more than 60 years. The
following are the most prominent models of computation.
• The model is based on the experimental studies of Townsed
and Hanson (1973), Anderson and Towsend (1977).
• Models based on theoretical research combined with
experiments:Plastic hinge models of Otani (1974), Banon et all
(1981), Fillipou et al. (1983, 1988), El-Metwally (1988), Alath
và Kunnath (1995), Pampanin (2002); Nonlinear springs models
of Biddah và Ghobarah (1999), Elmorsi et al. (2000), Lowes et
al. (2003), Altoontash (2004), Shin và LaFave (2004), Unal and
Burak (2010).
Model reviews: the models based on experiments are nontypical and objective, nonlinear springs models that reflect the
actual behavior of the joints rather than the plastic hinge models,
but need for specific software and large computing volume.
1.8 COMMENT FROM THE STUDY OF OVERVIEW
1. Under the impact of earthquakes, in the region of the BC joint
appears large vertical and horizontal forces.
2. There is not yet a rational model of the shear bearing
mechanism of BC joints that is unanimously accepted. The
criteria for evaluating shear strength in the standards differ
considerably. Paulay's and Priestley's models allow for the most
rational interpretation of the shear bearing of joint and are
included in many standards including Vietnam.
3. The recent nonlinear springs models are considered to be the
most practical simulation of BC joint, but its application is
limited due to the need for specific software and large computing
volumes. At present, there are no studies on the behavior of RC
reinforced concrete under earthquake in Viet Nam
CHAPTER 2. DEFORMATIONS OF BC JOINTS
2.1 DEFORMATIONS OF BC JOINTS
Under the impact of the earthquake, the BC joints is subject to
very large shear forces will be deformed.
2.2 THE COMPONENTS OF DEFORMATION
6
Figure 2.2.. Joint deformation a)
Shear deformation,
eformation, b) fixed
fixed-end
rotation
The deformation of the BC joint
consists of two components: the shear deformation of the joint
panel γj and the θsl rotation of fixed-end (Figure 2.2).
2.3.THE FIXED-END ROTATIONS
The longitudinal bars of the beam usually passes through or
anchors to the joints.. They tend to be pulled out of the anchor
anchorage
zone when subjected to the force induced by the rotating θsl at the
end of the beam (fixed-end rotation). Let s be the slip of the bars
(Fig. 2.4):
s
sl =
(2.1) in which:: ξ – is
(1 )
the neutral axis depth, normalised
to the effective depth, d
The fixed-end
end rotation at yielding
y db f y
Figure 2.4. Fixed end is: y , sl = 8 f (2.5) in which:
c
rotation θsl
ϕy, db, fy và fc corresponding to the
curvature of beam, the diameter of bar,, the tensile strength of the
reinforcement and the compressive strength of the concrete at
yielding.With the increase in the loads,, the deformation of the
bar extends into the joint zone. The length of yield deep
deeper ly,p
cause the additional slip ( s ly,p) as well as additional fixed end
rotation at ultimate: Δθu,sl= ϕuly,p
(2.6) with u - ultimate curvature
at end of beam. According to
Fardis Δθu,sl= 5,5dbϕu (2.88) with
cyclic load.
The bond of bars in the joint
region
is the decisive factor for
Figure 2.8 M - θsl
the magnitude of the rotation θsl.
7
The strength of bond in the joint depends on many factors:
confined concrete, diameter of bar db, compressive strength of
the concrete fc, surface of bar …bond slip models have been
proposed by many authors, that's remarkable is the model of
Biddah (Hình 2.8). Based on the results of the Morita and Kaku
experiments, Biddah determined the slips of the bars as well as
the slopes K1 and K2 of the model.
2.4 THE SHEAR DEFORMATION OF JOINT
The shear deformation γ of joint caused by shear stress τ
determined by (1.5) mainly due to the bond along the
longitudinal bars of the beams and the columns passing through
the joints. The shear stress is important factor affecting the
durability and stiffness of the joint. The standards ACI 318M-11,
NZS 3101 (2006), TCVN 9386:2012 and EN 1998-1-1:2004 has
evaluated shear resistance of joint as function of compression
strength fc of concrete, not to take into account the stirrup ratios.
2.5 COMMENTS ON DEFORMATIONS OF THE JOINTS
1. The joint deformation consists of: rotation of the θsl at the
end of the beams and shear deformation γj of the joint core.
2. The magnitude of θsl is the consequence of the loss of bond
and the yield of the longitudinal bar of beam. The bondstrength
depends on many factors, in which the confinement of concrete
core effect is the most important.
3. The magnitude of γj is determined indirectly through the
shear stress τjh from the experiment. In order to minimize the
deformation joint, the design standards introduce different limit
values τjh.
CHAPTER 3. EXPERIMENTAL RESEARCH BC JOINT
3.1 THE OBJECTIVE OF EXPERIMENTAL RESEARCH
1. Evaluation of the behaviors of the BC joint is designed in three
ways: (1) according to TCVN 9386: 2012, (2) impact load
according to TCVN 9386: 2012, calculated and detailed
according to TCVN 5574: 2012 and (3) according to SP
14.13330.2011.
8
2. Determine the deformation of the joint and the influencing
factors.
3. Evaluate and analyze the factors affecting the behavior of the
types of BC joint existing in Vietnam under earthquake;
Establishment of the models of joints designed in accordance
with TCVN 9386: 2012 for nonlinear analysis.
3.2.DESIGN THE SPECIMENS
Experimental specimens were interior BC joints in 1:1 scale,
extracted from a 3-storey spaceframe constructed in Thanh Xuan
district, Hanoi, designed in three scenarios. Detailed of the
specimens is given in Fig. 3.3 (NK1 according to TCVN 9386:
2012), Figure 3.4 (NK2 according to TCVN 9386: 2012 and
TCVN 5574: 2012) and Figure 3.5 (NK3 according to SP
14.13330.2011).
Figure 3.3. Model NK1
Figure 3.4. Model NK2
3.3.THE PROPERTIES OF
MATERIAL
The
mechanical
properties of concrete and
reinforcement are given
respectively in Tables 3.2
and 3.3. The specimens and
mechanical properties of the
Figure 3.5. Model NK3
materials were determined at
the Laboratory and Building Inspection of the University of Civil
Engineering.
9
Table 3.2. Properties of concrete
Specimen
NK1
NK2
NK3
Age at test (days)
83
90
80
fc at test (MPa)
31.5
32
31.7
εc
0.002
0.002
0.002
Ec (MPa)
30000
30000
30000
Table 3.3 Properties of reinforcing steel
Bar
Ф18 – AII
Ф16 - AII
Ф6 - AI
fy (MPa)
310
320
235
fu (MPa)
480
510
400
Es (MPa)
210000
210000
210000
3.4. SCHEMATIC OF TEST SETUP AND LOAD ROUTINE
The installation and
loading of the test
specimens is shown in
Figure 3.9 with a pin at
the bottom of the column
Figure 3.9. Schematic of test setup
and free to move at the
two ends of the beam
and the top of the free
column subjected to the
vertical action P = 300
kN
and
horizontal
reversal effect.
a) Ideal relationship b) Actual relationship
Figure 3.10 Definition of displacement
ductility factor
shown in Figure 3.10b.
The loading process
consisted
of
two
stages: force control
and
displacement
control (Figure 3.12).
At the displacement
control stage, the yield
deflection Δy of the
samples
was
approximated
as
10
3.5 MEASUREMENT DATA AND
DEVICES
The following data were
collected during the test: impact
force
and
horizontal
displacement at the end of the
column, deformation of the
joints, shear and bending
deformations of the beam,
Figure 3.12 Load routine
rotation of the beams and
columns, deformation of the concrete and reinforcement in the
critical zones of the beam, column, the development of the
cracks.
The devices used were LVDT, strain gauges, TDS 530 and data
recorders, hydraulic jack control devices.
3.6. BEHAVIOR OF SPECIMENS
Figure 3.17 Failure of NK1
Figure 3.20 Failure of NK2
In Cycle 19 (last), NK1 is
inelastic failure by plastic
hinges that appear at the ends of
the beams near the joint. The
joint deformation is evenly
distributed (Figure 3.17).
Figure 3.23 Failure of NK3
NK2 is brittle failure in the
17th cycle, the ends of the column and the beam is not deformed.
The perimeter of the core is crushed locally and the center is
intact (Figure 3.20).
11
NK3 was crushed in cycle 14th similar to NK2 (Figure 3.23).
Partial damage to the joint
nt of the focus at the corners. The
column and beam ends are deformed by bending and shear.
3.7. ANALYSIS RESULTS
3.7.1. Relationship between story shear - horizontal
displacement
The
hysteresis
show
the
relationship of V –story
story shear horizontal displacement
ement Δ of all
three samples are symmetric and
are pinching to different degrees
due to slip and yield of the beam
reinforcements,, especially in NK3
Figure 3.26: NK1
(Figure 3.26).
3.7.2. Story shear
Experiment results show that the maximum story shear Vtb,max
of NK1 appears at higher ductile levels, at later cycles and more
ductile than the NK2 and NK3 (Table 3.7).
Table 3.7 Parameters related to maximum story shear
Parameters
NK1
NK2
NK3
μΔ
4
3
3
Cycle
11 và 12
8 và 9
8 và 9
Vtb,max (kN)
+76,7; -64
+75,3; - 62,0
+69,0; --68,0
Δtb (mm)
69
54
81
Δtb/h (%)
2,3
1,8
2,7
3.7.3. The behavior of beams
Reinforcing steel of NK1 does
not lose bond,, does not slip, can
develop full plastic deformation, as
opposed to NK2 and NK3. This is
due to the NK1 with the
Figure 3.41 Relation θintermediate bar in column and the
μΔ at the section of 50mm
stirrup content 3.7 times greater
from column (brach +)
than that of NK2 and NK3. The
12
rotation angle θ of the beam end of the NK1 is also more stable
and linear than that of the NK2 and NK3 (Figure 3.41).
Deformation of beams of NK2 and NK3 is affected
ed by shear
distortion, low energy dissipation.
3.7.4. The behavior of columns
develop inelastic strain is better
than NK2 and NK3. Thus, the
rotation θ of the NK1 column end
is linear in contrast to the NK2
Figure 3.52 Relation θ-μΔ
and NK3.
at the section at the 100
3.7.5. Behavior of the joint
mm from surface of beam
Hình 3.56. γ - Δ/h
Hình 3.57.γ - μΔ
1. Shear deformation of the joint
The diagrams (3.56) and (3.57) show that the NK1 joint has the
smallest shear deformation γ and increases linearly, in contrast to
the NK2 and NK3. Deformation of the joint NK1 is ductile
ductile, the
remaining joints are brittle. The
stirrups in the joints has a
decisive influence on the
deformation characteristics of the
joint.
Figure 3.59: Vt - γ
2. Joint shear: joint shear Vt
indicates the shear strength of
concrete and reinforcement in the joints: Vt =Vjh = (As1 +As 2 )f s - Vc
(3.14)
NK1 shear strengthis more than NK2 và NK3 (Figure 3.59)
13
3.7.6. Analyzes the cause of failure of joints
Differences in the design and detail in the joints, columns and
beams led to various failures on the specimens (see Figures 3.17,
3.20 and 3.23).
a) NK1 is capable of launching the truss mechanism (Chapter
1) while the NK2 and NK3 do not have this capability.
b) As the load cycles increase in the non-elastic region, the
NK1 joint zone is compressed and bended lesser by the beams
and columns being flexed and the NK2 and NK3 joint zone
compressed locally by the beams and columns. Large rotational
displacement when longitudinal reinforcement loses bond and
weakened confined concrete is not capable of transmitting
diagonal compression force deep into the core as in NK1.
c) The cause of the large concrete splits along the column
reinforcement on the two sides of the joint zone of the NK2 (Fig.
3.20) is due to the expansion of the crack at the beam edge when
the reinforcement is yielded and loses bond, due to the local edge
of the panel joint is crushed and by the longitudinal
reinforcements of column are buckling (lack of stirrup). NK3 is
splitted less (Figure 3.23) due to the reinforcement of the column
are bigger .
In NK1, the beams are yielded before the column and finally
in the joint, following the principle of weak beam-strong column
design. In NK2 and NK3, the risk of damaging the beams,
columns and joints is equal.
3.7.7 Shear resistance of BC joint
The calculation of limit stress τjh of the NK1 in accordance
with TCVN 9386: 2012 gives a value (7.49 MPa) greater than
the value in ACI 318M-2011 (6.73 MPa) and NZS 3101 (2006)
(6.3 MPa). The stirrup ratio in NK1 joint zone is 2.5 times
greater than the ACI 318M-2011 minimum value, while NK2
and NK3 are 1.5 times smaller. While the maximum shear stress
τjh of all three samples (3.1 MPa, 2.93 MPa and 3.01 MPa) was
less than half the limit value τjh defined by the three criteria
above, but the behavior of NK2 and NK3 is completely
14
unacceptable. As a result, for joints in Vietnam, the content of
stirrup in the joint zone is more important than the shear stress
limit. It is therefore necessary to consider additional conditions
to ensure the rigidity and durability of TCVN 9396: 2012.
3.7.8 Secant stiffness of the specimens
The stiffness of all the specimens is degraded during loading.
The degradation of NK1 is the lowest, NK2 is the fastest, while
NK3 has smallest stiffness.
3.7.9 Energy dissipated of the specimens
The energy dissipated is represented by the area of the forcedisplacement hysteresis at each cycle. NK1 and NK2 have the
same amount of accumulated energy dissipated at the first 14
load cycles, while the NK3 was the largest.
3.7.10 Equivalent viscous damping factor
The equivalent viscous damping factor ξ is defined by the
dissipated energy balance in each cycle in the nonlinear system
with the equivalent linear system. After yielding, the ξ factor of
NK1 is much larger than that of NK2 and NK3. At the same
time, the energy dissipation of the NK1 was more stable than the
other specimens. The relationship ξ - μΔ of the NK2 and NK3
shows that ξ is strongly reduced at the high ductile level.
3.8. COMMENTS ON EXPERIMENTAL RESULTS
1. Under earthquakes, NK1 designed according to TCVN
9386: 2012 is inelastic failure, while NK2 and NK3 are brittle
failure.
2. The reinforced concrete frame systems are designed
according to SP 14.13330.2011 and according to TCVN 5574:
2012 are not suitable to develop inelatic failure mechanism.
3. For ductile class medium frames (DCM), the stirrup in the
joint zone is very important to ensure confined effect rather than
the shear stress limit as specified in the modern design standards.
4. Under earthquakes, the joints will be deformed, even when
designed in accordance with the modern standards. Therefore, it
is necessary to consider the shear deformation of joints.
15
CHAPTER 4. MODELING OF BC JOINTS
UNDER EARTHQUAKES
4.1 DEFORMATION OF JOINTS AND ITS EFFECTS TO THE
OVERALL BEHAVIOR OF FRAMES
Deformation of joint affects the behavior of the frame.
Therefore, it is necessary to model the shear deformation and
bond slip of reinforcement under earthquakes for nonlinear
analysis.
4.2 MODELLING OF BC JOINT
4.2.1.The contribution of
deformation of joint to the
lateral displacement of the
frame
Figure 4.2 shows the effect
of the shear deformationj
the
horizontal
Figure 4.2. The contribution (γj)on
displacement of the istory (Δi)
of the shear deformation
at the exterior and interior
joints. The shear deformation γj is
for the column with the relative
shear displacement Δci= γjhb and
the displacement of beam end:
Δbj= γjLb.
4.2.2. Modeling of shear
deformation
In view of the effect of the
shear deformation on the
behavior of the frame, using the
Figure 4.3. Modeling of
model in which the shear springs
shear deformation
in the column ends and the
bending springs in the beam ends.
In the physical view, for the
Hình 4.5
spring of shear, the relation of the
shear force Vjh and the displacement of the column end Δcj = γjhb,
for the rotate spring is the relation of the bending moment Mb and
the shear deformationγj.
16
4.2.3. Determine the characteristics of the springs
According to the results of theoretical studies in Chapter 1,
according to (1.1) the column shear force at the interiorjoint:
Vc=(Csb1+Cb1+Tsb2) – Vjh = A - Vjh (4.2a) , also in the exteriorjoint:
Vc=Tsb2-Vjh (4.2b). From (1.5), determine the horizontal shear force
Vjh from the values τjh. Thus, to determine the Vc and
corresponding to it, Vjh must perform a computational process
according to the diagram in Figure 4.5. The calculated result will
be relations Vc - Δcj and Mb - γj if know the relation τjh - γj of the
joint.
4.2.4. Establishing the
ideal relationship τjh–γ
a) Interior joint:
From the results of
experiments in Figure
Figure 4.6 Relationship: shear
3.59,
establish
the
deformation γj and a) Vjh; b) τjh
relationship τjh-γj (Figure
form NK1
4.6b) and idealized in the
form of a four-segment line
(Figure 4.7). Point B has
coordinates τjh,y=2,8MPa and
γj,y=0,0004rad
at
beam
reinforcement yielded, the point
Figure 4.7.τjh-γj
C has coordinates τjh,u=3,1MPa và
γj,u=0,0025rad. According to
ASCE
41-13,
assuming
residual durability τjh,D=0,2τjh,y,
The shear deformations at
points D and E are: γj,D=0,02rad
và γj,E=0,025 rad (Figure 4.7).
b) Exterior joint
Based
on
Biddah's
experiments on the exterior
Figure 4.8. J2 of Biddah
joint (Figure 4.8), establishing
the ideal τjh - γj relationship is also done in the same way as the
17
interiorjoint.
As shown in Figure 4.9b, point B has coordinates
τjh,y=1,8MPa; γj,y=0,0008rad, the
he point C has coordinates
τjh,u=2,0MPa và γj,u=0,003rad. Points D and E are similar Figure
4.7
4.2.5. Establish the relation Vc - Δc và Mb- γj of joint
4.2.5.1. RelationshipMb - A and Mb - Tsb
To establish relations VcΔc and Mb-γj follow
ollow the
diagrams in Figure 4.5
4.5, need
to determine the relations
relationship
Mb–A and Mb-Tsb, in which
A=Cbs1+Cb1+Tsb2. With the
Figure 4.9 Relation γj and
assumptions used, relation
a)Vjh; b) τjh of J2
Mb-A of NK1 và
Mb-Tsb of J2 are
given in Figures 4.10
and 4.11.
Figure 4.10
Figure 4.11
Figure 4.12. Vc – Δc and Mb - γj
4.2.5.2 Relation Vc –
Δc and Mb - γj
On the basis of the
results made, relation
Vc–Δc và Mb--γj for
shear and
nd bending
springs
used
in
nonlinear analysis, see
Figure 4.12.
4.3 MODELLING OF BOND SLIP
Figure 4.13:Mb–θsl
Based on theoretical and empirical
studies in Chapter 2, the bond slip
model of the reinforcement in the joint
indicates the rotational displacement
due to bond slipθsl and the bending
moment Mb as shown in Figure 4.13.
18
The values θy,sl and θu,sl are defined respectively in expressions
(2.5) and (2.8) in Chapter 2.
4.4CALIBRATION, MODEL EVALUATION OF JOINTS.
4.4.1 Interior joint NK1
Calibration is performed for the rigid joint case and flexible
joint (in terms of sheardeformation and slip) (Figure 4.14)..
Figure 4.14. Diagram of
plastic hinge for the case:
a) Rigid; b) flexible joint.
With the results of the
experiment,,
the
relationshipsVc-Δcj, Mb-γjandMb-θslare shown in Figures 4.15 and
4.16.Nonlinear analysis of specimenNK1 by push-over method
with SAP2000
Figure 4.15
Figure 4.16
for the capability curves as
shown in Figure 4.18. In
the case of flexible join
joints,
the
results
of
the
experiment are perfectly
consistent with the results
of the analysis. The
Figure 4.18.V-Δ of NK1
proposed
computational
models accurately reflect the actual behavior of the joints.
4.4.2 Exterior joint J2.
The calibration of the
proposed models is simi
similar to
that of the NK1. Figure 4.22
shows the curves obtained
from the analysis. Compared
Figure 4.22. V-Δ of J2
with the experimental results,
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