Modeling and Analysis of Retrofitted Exterior RC Beam Column Joint

Tanta University - Faculty of Engineering
Structural Engineering Department
Structure Project
4th
Year 2nd
Term 2016-2017
Prepared by
1-Abdelrahman Mustafa Al-Hashash .
2-Amr Mohamed El-Sharkawy .
3-Magid El-Saeed Salama .
4-Salah Mohamed Allam .
Under supervision
Prof.Dr / Mohammed Sakr

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ABSTRACT-1
A beam-column joint is a very critical zone in reinforced concrete framed
structure where the elements intersect in all three directions. Joints ensure
continuity of a structure and transfer forces that are present at the ends of
the members. In reinforced concrete structures.
During the past four decades, significant amount of research has been
conducted to investigate the behavior of RC beam-column joints. These
joints are studied due to its critical influence on the overall behavior of
RC moment-resisting frames subjected to seismic loads .
However, there is a lack of data and test results still exists on such
connections when they are totally reinforced with FRP reinforcement.
Nevertheless, none of the available FRP codes or guidelines provides any
recommendations on the seismic design of the moment-resisting frames
reinforced with FRP.
In this study, behavior of exterior R.C beam-column joint was
investigated according to FEMA 356 with a macro model using SAP
2000 using nonlinear pushover analysis procedure. The analysis included
2D model using one dimensional elements. Moreover, the 2D model was
extended to investigate the behavior of CFRP retrofitted exterior beam-
column joint. Group of modeling have 5 specimens with different area of

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CFRP. The study results showed that the failure in this case occurs in the
beam when the joint and 25% from column are rehabilitated with CFRP.
For the purpose of analysis of large scale structures, behavior of framed
ten multi-storey structure was investigated according to FEMA 356 with
a macro model using SAP 2000 using the nonlinear pushover analysis
procedure in order to withstand seismic lateral force applied on building.
Moreover, the 3D model was extended to investigate the behavior of
CFRP retrofitted frame building.

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TABLE OF CONTENTS
ABSTRACT .............. ………………………………………………21.
TABLE OF CONTENTS ....................................................................................................... 4
INTRODUCTION ............................... .............................................. 62.
2.1 BEAM COLUMN JOINT .......................................................................................... 7
2.2 EARTHQUAKE BEHAVIOUR OF JOINTS........................................................... 8
2.3 Aims of research………………………………………………….…………10
2.4 outline of the study…………………………………………………………..11
LITERATURE REVIEW ............... .................................................. 123.
3.1 GENERAL ................................................................................................................ 12
3.2 BACKGROUND........................................................................................................ 13
3.3 MECHANICS OF EXTERIOR AND CORNER UNCONFINED JOINTS SHEAR
STRENGTH TRANSFER MECHANISMS ........................................................... 14
3.4 SHEAR MECHANISM MODEL..............................................................................16
3.5 CONCRETE STRUT MECHANISM ...................................................................... 16
3.6 TRUSS MECHANISM............................................................................................. 16
BOND DISTRIBUTION ........................................................................................... 173.7
3.8 SOFTENED STRUT-AND-TIE MODEL ................................... ............................ 18
3.9 FINITE ELEMENT MODELLING.......................................................................... 19
3.10 Main parameters that affect the behaviour of exterior beam-column joints subjected
to earthquake loading........................................................................................... .. 19
-3.10 .1- INFLUENCE OF FLEXURAL STRENGTH RATIO AND JOINT SHEAR
STRESS ………………………………………………………………...……..19
3.10. 2- EFFECT OF TRANSVERSE BEAMS AND SLABS………………………20
3. 10.3-EFFECT OF LOADING RATE ...................................................................... 21
23..........................................................3.10 . 4- EFFECT OF DETAILING SCHEME

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3.11 FRP BARS AS REINFORCEMENT FOR CONCRETE STRUCTURE ……….25
25......................................3.12 CHARACTERISTICS OF FRP REINFORCEMENT
3.13 Main results of the researches use (FRP)………….…………………….….….. 27
3.14 Failure mechanism of the joint .................................................................... 30
4-Non Linear Analysis of Exterior RC beam column joint…………………………41
4.1 GENERAL ...................................................................................................................
4.2 OBJECTIVE ................................................................................................................ 41
4.3 MODELING AND ANALYSIS OF AN EXTERIOR JOINT……………….………42
4.4 INPUT DATA ............................................................................................................. 43
4.5 RESULTS .................................................................................................................... 46
4.6 CONCLUSION ........................................................................................................... 54
CASE STUDY ...................................................................................................... 555.
5.1 OBJECTIVE ................................................................................................................ 55
5.2 GENERAL ................................................................................................................... 55
5.3 INPUT DATA ............................................................................................................. 56
5.4 RESULTS ................................................................................................................... 59
5.5 Seismic force ............................................................................................................... 61
5.6 Retrofitting joint of frame and 10% of beam ………………………………………62
5.7 Retrofitting joint of frame and 20% of beam ………………………..…..……………63
5.8 Retrofitting joint of frame and 25% of beam …………………………………...…..…64
5.9 REPAIR AND STRENGTHENING TECHNIQUES FOR BEAM-COLUMN JOINTS…......65
5.10 Retrofitting cost estimation ....................................................................................71
726-CONCLUSION……………………………………………………………………..…….
7-REFERENCE…………………….……………………………………………..…74

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2-INTRODUCTION
A beam-column joint is a very critical zone in reinforced concrete framed
structure where the elements intersect in all three directions. Joints ensure
continuity of a structure and transfer forces that are present at the ends of
the members. In reinforced concrete structures, failure in a beam often
occurs at the beam-column joint making the joint one of the most critical
sections of the structure. Sudden change in geometry and complexity of
stress distribution at joint are the reasons for their critical behavior.
In early days, the design of joints in reinforced concrete structures was
generally limited to satisfying anchorage requirements. In succeeding
years, the behavior of joints was found to be dependent on a number of
factors related with their geometry; amount and detailing of reinforcement,
concrete strength and loading pattern. The requirements Criteria for the
desirable performance of joints can be summed up as: (Park. R & Paulay.T, 1975).
(i)The strength of the joint should not be less than the maximum demand
corresponding to development of the structural plastic hinge mechanism for
the frame. This will eliminate the need for repair in a relatively inaccessible
region and for energy dissipation by joint mechanisms, which, as will be
seen subsequently, undergo serious stiffness and strength degradation when
subjected to cyclic actions in thein elastic range.
(ii) The capacity of the column should not be jeopardized by possible

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strength degradation within the joint. The joint should also be considered as
an integral part of the column.
(iii)The joint reinforcement necessary to ensure satisfactory performance
should not cause undue construction difficulties.
BEAM COLUMN JOINT2.1
The functional requirement of a joint, which is the zone of intersection of
beams and columns, is to enable the adjoining members to develop and
sustain their ultimate capacity. The joints should have adequate strength
and stiffness to resist the internal forces induced by the framing members.
The joint is defined as the portion of the column within the depth of the
deepest beam that frames into the column. In a moment resisting frame,
three types of joints can be identified viz. interior joint, exterior joint and
corner joint.
When four beams frame into the vertical faces of a column, the joint is
called as an interior joint, When one beam frames into a vertical face of the
column and two other beams frame from perpendicular directions into the
joint, then the joint is called as an exterior joint, When a beam each frames
into two adjacent vertical faces of a column then the joint is called as a
corner joint.

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Interior Exterior Corner
Roof Interior Roof Exterior Roof
Corner
Beam-Column Joints are Special as their constituent materials have
limited strengths, the joints have limited force carrying capacity.
When forces larger than these are applied during earthquakes, joints are
severely damaged, Repairing damaged joints is difficult, and so damage
must be avoided. Thus, beam-column joints must be designed to resist
earthquake effects.
2.2 EARTHQUAKE BEHAVIOUR OF JOINTS
Under earthquake shaking, the beams adjoining a joint are subjected to
moments in the same (clockwise or counter-clockwise) direction , Under
these moments, the top bars in the beam-column joint are pulled in one

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direction and the bottom ones in the opposite direction , If the column is
not wide enough or if the strength of concrete in the joint is low, there is
insufficient grip of concrete on the steel bars In such circumstances, the
bar slips inside the joint region, and beams lose their capacity to carry
load. Further, under the action of the above pull-push forces at top and
bottom ends one diagonal length of the joint elongates and the other
compresses . If the column cross-sectional size is insufficient, the
concrete in the joint develops diagonal cracks .
Diagonal cracking , crushing of concrete can be prevented in Joints.
Mostly, for this large column size is the most effective.
Another way is providing steel ties also known as stirrups.

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researchAims of2.3
The primary tasks of the current study are to:
1. Construct macro models using the pushover analysis procedure for a
exterior beam-column joint able to predict the overall behavior, capacity
and the modes of failure.
2. Studying the behavior of a CFRP retrofitted exterior beam-column
joint constructing a macro model using the pushover analysis procedure
in order to predict its overall behavior, capacity and the modes of failure.
3. construct a model of ten-multi-story structure using the pushover
analysis procedure able predict its overall behavior. Safety of
construction members against earthquake and its mode of failure
4. studying the need of using retrofitting withstand the equivalent static
force calculated by response spectrum analysis for the building by
retrofitting only the first story then, retrofitting two stories and so on, and
predict the overall behavior for each case until the capacity of building
reach the safe zone against the earthquake.

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Outline of the study2.4
The present chapter, chapter 1, describes the problem which will be
studied and identify the general framework and structure of the current
study
Chapter 2 presents literature review that includes basic background
information in the context of beam-column joint, its failure mechanisms,
types of retrofitting.
Chapter 3 present a comparison between five models have different
volume of CFRP with same material properties, constructed by macro
model using the pushover analysis procedure in order to predict the
overall behavior, in addition to showing the effect of using CFRP
retrofitted.
Chapter 4 present a model of ten multi story buildings, constructed by
macro model using the pushover analysis procedure in order to predict
the overall behavior, Safety of construction members against earthquake
and its mode of failure, also evaluating the previous cases by the
performance curves resulted from pushover analysis.

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LITERATURE REVIEW-3
GENERAL3.1
During the past four decades, significant amount of research has been
conducted to investigate the behaviour of steel-reinforced beam-column
joints. These joints are studied due to its critical influence on the overall
behaviour of RC moment-resisting frames subjected to seismic loads.
Hanson and Connor (1967) [9] had conducted the first experiment on
exterior beam column joints reinforced with steel. Since then, many
researchers have been involved in studying the behaviour of the beam-
column connections through analytical models and experimental tests.
These researchers were able to provide knowledge on how beam column
joints work and what are the main parameters that affect their
performance , However, there is a lack of data and test results still exists
on such connections when they are totally reinforced with FRP
reinforcement. Nevertheless, none of the available FRP codes or
guidelines provides any recommendations on the seismic design of the
moment-resisting frames reinforced with FRP.

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BACKGROUND3.2
The performance of beam-column joints has long been recognized as a
significant factor that affects the overall behavior of reinforced concrete
(RC) framed structures subjected to large lateral loads.
The first design guidelines for reinforced concrete beam-column joints
were published in 1976 in the U.S. [2.1] and in 1982 in New Zealand
[2.2]. Buildings constructed before 1976 may have significant
deficiencies in the joint regions. Especially since the 1985 Mexico
earthquake, a considerable amount of research has been devoted to
identifying the critical details of nonseismically designed buildings as
well as to developing methods of strengthening. Through their reviews of
detailing manuals and design codes from the past five decades and their
consultation with practicing engineers .
Committee 352 [2.4] reads: “These joints need to be studied in detail to
establish their adequacy and to develop evaluation guidelines for building
rehabilitation. Methods for improving performance of older joints need to
be studied. Scarce information is available on connection repair and
strengthening"

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UNCONFINEDMECHANICS OF EXTERIOR AND CORNER3.3
JOINTS SHEAR STRENGTH TRANSFER MECHANISMS
Under seismic excitation, beam-column joints are subjected to shear
forces whose magnitudes typically are substantially higher than those
within the adjacent framing beams and columns, (Park and Paulay [12]. If
the demand exceeds the capacity, the joint may become the weak link that
limits strength and deformation capacity of the structure
Figure 2.12 displays the forces acting at the boundary of an exterior
beam-column joint subjected to earthquake-type loading, along with its
crack pattern and force transmission mechanisms. In exterior joints
without transverse reinforcement, the forces are initially transmitted by
bond bearing through secondary struts generated between beam and
column reinforcement. Those struts are represented by the minor diagonal
cracks in Fig. 2.12. After diagonal cracking in the joint core, the beam
and column forces are transferred across the joint core primarily by a
diagonal compression strut, (Park and Paulay [12] ). At the exterior face
of the joint, the strut is anchored in a node formed by the inside of the
standard hook of the beam longitudinal reinforcement, which establishes
the requirement that the hook be bent into the joint core as indicated in
the figure. If the beam reinforcement are bent away from joint, a common
practice in older construction, the required diagonal compression strut
will not be stabilized by a node within, potentially leading to premature
joint failure. .

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In a joint with bent-in beam reinforcement and transverse hoops, the two
shear-resisting mechanisms are the truss mechanism and the strut
mechanism shown in Fig. 2.13, where the joint hoops act as tension
members for the truss mechanism. The truss mechanism is initially
engaged along the straight segments of beam and column reinforcement
due to the bearing of reinforcement ribs or in other words through bond
strength. If bond strength is secured between beam’s and column’s
reinforcement and concrete until reaching shear capacity of the joint, both
strut and truss mechanisms could contribute to the strength. If bond
strength deteriorates early, a very common case in joints due to the
limited joint depth that does not allow full development length of beam
reinforcement at their straight segment within the joint, the truss
mechanism contribution to shear strength is nullified, giving the full shear
resistance to the strut mechanism. Since joint hoops are necessary to
develop such truss mechanism, only secondary struts can be developed
prior to bond strength deterioration in their absence.
Secondary struts have a “temporary role” in shear resistance until
delivering the beam reinforcement tension force to be pivoted at the main
diagonal joint strut. One argument to support this observation is the case
when the straight segment of beam reinforcement within the joint has
sufficient length to develop the full tension force to concrete through
bond stress; this is likely if beam reinforcement size is relatively small. In
this case, the main strut mechanism is “not needed”; hence, the joint

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could survive to high shear stresses with straight unhooked
reinforcement. This contradicts past experimental results. Thus, the
opinion of relying solely on the main strut mechanism, Fig. 2.14, to
provide joint shear strength is adopted throughout this manuscript.
The diagonal strut within the joint exists in a region of transverse tension.
Consequently, the effective compressive strength of the strut is less than
the concrete compression strength as measured in uniaxial compression.
Extensive diagonal cracking that leads to joint shear failure can result
from high principal tension stresses associated with developing the
capacity of the beam and columns connected to the joint. Cyclic loading
in cracked concrete leads to repeated opening and closing of cracks, as
well as movements parallel to open cracks. Grinding and progressive
splitting due to uneven concrete bearing may lead to further disintegration
of core concrete and subsequent loss of strength.
The key aspect in ensuring the safety and survival of the building during
strong shaking , is to maintain joint shear strength until developing full
plastic capacity of beams and columns. This can be done through
designing the joint strength to be greater than the plastic capacity of any
member it connects. In addition, it is necessary to maintain bond strength
by proper detailing to ensure integrity and full anchorage in the joints.
Special care has to be given to the bond of top beam reinforcement which
is much more affected by concrete bleeding and segregation.

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SHEAR MECHANISM MODEL3.4
Paulay et al. (1978) [10] were the first researchers to analytically
investigate the behaviour of steel-reinforced beam-column joints. They
believed that the concrete shear resisting mechanisms in a joint core are
significantly different from those encountered in flexural members (ACI-
ASCE 352-76 1976). Considering the seismic actions in equilibrium
acting on an interior joint, as shown in Figure 2.1-a, the locations and
magnitudes of the resulting internal forces developed in the beams and
columns can be determined accurately, as shown in Figure 2.1-b. The
maximum horizontal shear force in the joint core can be expressed from

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CONCRETE STRUT MECHANISM3.5
Defining the bond forces transmitted from the beam reinforcement within
the compression zone as the internal concrete compression forces
together with the column and beam shears and the force are forming a
system in equilibrium. The principal component of this mechanism is a
diagonal concrete strut with magnitude at an angle β
The horizontal component of the diagonal compression force can be
Defined , in terms of the forces at the lower right hand corner of the joint
shown in Figure 2.1-b and Figure 2.2-a, as
(a) Concrete strut mechanism (b) Steel truss mechanism
TRUSS MECHANISM3.6
The bond forces induced within the joint core due to all the remaining
longitudinal steel forces will introduce shear stresses. Theses shear
stresses in turn will result in diagonal tension stresses on the joint core,
which in most cases, are larger than the cracking tensile capacity of the
joint core. Figure 2.2-b shows a truss mechanism that can be developed

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from the combination of the horizontal joint reinforcement, the vertical
column bars and the diagonal concrete compression field between the
developed cracks. Defining the capacity of the diagonal compression
fields by , the horizontal shear resistance of the developed truss
mechanism can be calculated as:
Where is the compression force developed in the beam steel
reinforcement on one side of the joint and is the corresponding tension
force in the beam steel reinforcement on the other side of the joint .
BOND DISTRIBUTION3.7
It is recognized that the bond stress distribution on the beam
reinforcement inside the joint area plays very important role in the joint
performance. Hence, rational assumption for the bond transfer
distribution within the joint is needed. The authors assumed three
configurations for the probable bond stress distributions within the joint
core depending on the state of stresses of the beam reinforcement
stresses, as shown in Figure 2.3
The most important part is what shown in Figure 2.3-c where some bond
transfer is destroyed after a number of inelastic reversal cycles. Thus, the
effective anchorage length of a beam bar is reduced, and a bond stress
concentration is occurred near the center of the joint. Accordingly, after

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yield penetration, the concrete strut deteriorates ( ) and the major part of
the joint shear force will be resisted by the truss mechanism
.
TIE MODEL-AND-SOFTENED STRUT3.8
Hwang and Lee (1999) [15] had developed a new model for predicting
the shear strength of the exterior beam-column joints under seismic
loading; softened strut-and-tie model (SST), based on the same concept
that was followed by Paulay et al. (1978) [10]. However, instead of
having two mechanisms that are responsible to resist the joint shear
forces, as mentioned before, the proposed strut-and-tie model consists of
three mechanisms; the diagonal, horizontal and vertical mechanisms, as
shown in Figure 2.4

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The purpose of this model is to detect the contribution of both the
horizontal joint reinforcement and the vertical column reinforcement,
separately, in resisting the shear forces acting on the joint
FINITE ELEMENT MODELLING3.9
The finite element method is a powerful tool for the numerical solution of
a wide range of engineering problems including solving for deformation
and stress analysis of building and bridge structures. With the
development in computer technology and CAD systems, complex
problems can now be modelled easily and hence several alternative
configurations can be tested on a computer. Several FE software
packages are now commercially available to facilitate the process of
constructing and solving a model such as ANSYS, ABAQUS and
DIANA
iour of exteriorMain parameters that affect the behav3.10
column joints subjected to earthquake loading-beam
INFLUENCE OF FLEXURAL STRENGTH RATIO AND JOINT-13.10.
SHEAR STRESS
Ehsani and Wight, (1985-a) [25] displayed the experimental results of six
exterior reinforced concrete beam-column joints subjected to reversible
cyclic loading. Studied parameters at this research were the flexural
strength ratio, the percentage of transverse reinforcement used within the
joint and the shear stress in the joint as a function of where fc' is strength
of concrete inside the joint. Test results were compared with the draft
recommendations of the ASCE-ACI committee 352 available at that time
(ACI-ASCE 352 1985). The beam was in the range of 1060 to 1525 mm
long, 260 or 300 mm wide and 480 mm deep, while the column measures
2210 mm long with a 300 or 340 mm square section. Reversal lateral

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quasi-static cyclic loads were applied directly at the beam tip simulating
seismic loading. The specimens were tested where the column was
positioned in the horizontal direction while the beam was in the vertical
direction, It was observed that the flexural strength ratio affects the
location of the plastic hinges. For specimens with flexural strength ratio
slightly greater than 1.0, the plastic hinge formed in the beam but spread
into the joint and most of the damage was concentrated in the joint. This
resulted in significant deterioration of bar anchorage and led to the
pullout of the beam longitudinal steel and slippage of the column
longitudinal bars, which reduced the load-carrying capacity and stiffness
of the specimen as well. While, for specimens with flexural strength ratio
considerably greater than 1.0, the cracks were distributed more in to the
beam and away from the joint. It was concluded that:
 The flexural strength ratio should not be less than 1.4 to avoid
formation of hinges at joints, larger flexural strength ratios improve
the behaviour of the connections,
 The maximum shear stress in joints should not exceed 1.0 MPa to
reduce excessive joint damage, column bar slippage, and beam bar
pullout,
 Specimens that had minor slippage and bar pullout showed a very
good overall behaviour in the later cycles,
 When the first two recommendations are met, additional transverse
reinforcement doesn't enhance the behaviour of the specimens
3.10.2-EFFECT OF TRANSVERSE BEAMS AND SLABS
Ehsani and Wight (1985-b) [25] continued studying the behaviour of
exterior beam-column joints taking into account the effect of transverse
beams and slabs. The investigated variables were the flexural strength

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ratio, the percentage of transverse reinforcement used within the joint,
and shear stress in the joint as a function of . Six exterior beam column
joints were constructed and tested. Tested specimens were designed to
have flexural strength ratios of 1.1, 1.5, and 2.0 assuming the flexural
contribution of only the first two longitudinal slab reinforcement bars
adjacent to the main beam. The design shear stress varied between 0.83
and 1.16 . Beams and columns had the same dimensions and loading
history described previously by Ehsani and Wight, (1985-a) [25] . The
slabs attached to the beams measured 1015 mm in width and 100 mm in
depth. Tests showed that all the slab longitudinal reinforcement yielded
including the first two longitudinal reinforcement bars. Consequently, the
original design flexural strength ratios were recalculated and then reduced
to be 0.88, 1.16, and 1.58, respectively.
In specimens where the flexural strength ratios were less than 1.0, plastic
hinges were formed in the upper column near the slab and crushing of
concrete appeared in the column. The plastic hinge was formed in the
joint for the specimen with a flexural strength ratio slightly larger than
1.0 and relatively high joint shear stresses. For specimens that had the
same flexural strength ratio but lower joint shear stresses, the flexural
cracks extended into the beam for a distance of approximately twice the
depth of the beam from the face of the column. The behaviour of the test
specimens in this study was compared to their counterparts without slabs
or transverse beams from a previous study, Ehsani and Wight (1985-a)
[25]. For the specimens with transverse beams and slab, the hysteresis
diagrams demonstrated unequal pinching during the positive and negative
half cycles of loading. This was primarily due to the presence of flexural
cracks at the bottom of the main beam near the column, which remained
opened through the test.

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Furthermore, transverse beams provided additional confinement for the
joint, and the overall behaviour was beneficial and the confinement of the
joint in specimens with transverse beams and slabs improved
significantly over similar specimens without transverse beams and slab.
The Conclusions were that;
• A flexural strength ratio of a value not less than 1.20 is recommended
toensure flexural hinges in the beams and the behaviour was improved by
the presence of transverse beams which, were not directly loaded.
• Increasing joint transverse reinforcement did not improve the
behaviour of the joints with transverse slabs and beams as it did for the
specimens that had no transverse beams and slabs.
• The presence of transverse beams helped eliminate the beam bar
pullout, however, slippage of column longitudinal reinforcement was
observed in specimens with and without transverse beams and slabs.
3.10.3- EFFECT OF LOADING RATE
Chung and Shah (1989) [1] investigated the effect of cyclic loading rate,
shear span-to-depth ratio, and stirrup spacing on the bond performance of
exterior steel reinforced beam column joints. The test results included
mode of failure, energy dissipation, stiffness degradation, and bond stress
distributions along the bar. Twelve anchorage-bond specimens were
constructed and tested to study the effect of cyclic loading rate on a bar
embedded in reinforced concrete. Each specimen represented a horizontal
cantilever beam attached to a reinforced concrete block. The concrete
block was subjected to axial load in the vertical direction. Then the
outcomes of these tests were verified by testing three identical beam-
column joints. The first one was tested under monotonic loading to
determine the yield displacement of the beam; the second one was tested

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under cyclic loading at a frequency of 0.0025 Hz (slow-rate), while the
third specimen was tested at a frequency of 1.0 Hz (fast-rate). It was
observed that the maximum load-carrying capacity was quiet higher for
the fast-rate specimen. However, damage resulted by the cyclic loading
seemed to be higher for the faster rate of loading. This was observed by
the measurements of stiffness and natural frequency obtained from the
free vibration test conducted after each loading stage. It was concluded
that:
• Specimens that were subjected to faster rates of loading failed as a
result of early fracture of steel bars. This was induced by stress
concentration caused by improved bond strength at faster rates.
• For higher rates of loading, fewer and wider cracks were observed at
column face. In contrast, more widely-distributed cracks were observed
in the beam at the slower rates of loading, and
• Specimens with stirrup spacing of d/2 (where d is the beam depth) were
significantly influenced by the loading rate. A brittle mode of failure was
observed at fast rate of loading compared to a ductile mode of failure for
slow rate loading specimens. On the contrary, specimens with stirrup
spacing of dIA were not influenced by the loading rate.
3.10.4 EFFECT OF DETAILING SCHEME
Hakuto et al. (2000) [2] studied the influence of reinforcement detailing
on seismic behaviour of exterior and interior beam-column joints. For the
exterior beam-column joints, specimens had shear reinforcement less than
that required by the ACI 318-95 (1995) and NZS 3101:1995 (1995) in
both beam and joint. Two identical prototypes were tested, the
longitudinal beam bars at one of the specimens were anchored by bending
the hooks out of the joint core while in the other specimen the

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longitudinal bars were anchored as specified by the ACI 318-95. The
beam measured 1525 mm long, 300 mm wide and 500 mm deep, while
the column measured 2900 mm long with a 460 mm square section.
Reversal lateral quasi-static cyclic loads are applied directly at the
column top end simulating seismic loading. The column was positioned
in the vertical direction while the beam was in the horizontal direction
This study considers that the bearing stresses at the bend act as a node in
a strut-and-tie model where the diagonal compression strut acting against
the beam reinforcement as shown in Figure 2.1(a). On the other hand, the
detail shown in Figure 2.1(b) does not provide an effective node point at
the top of the diagonal strut to achieve a stable strut and tie model. When
an adequate amount of confinement is provided in the column above the
joint core, the missing strut node is introduced to resist the horizontal
component offeree from the compression strut as shown in Figure 2.1
During testing the specimen with the anchorage out of the joint core, it
was observed that the beam hook was not effective in carrying the
diagonal compression strut, which pushed against the longitudinal
column steel leading to wide splitting cracks along the column. It was
concluded that the performance is improved significantly when the hooks
of the beam bars are bent into the joint core

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3.11 FRP BARS AS REINFORCEMENT FOR CONCRETE
STRUCTURES
In the past two decades FRPs have proven to be a promising alternative
material for reinforcement of concrete structures. FRP materials have non-
corrodible and nonmagnetic nature. Therefore, they can be used in
reinforced-concrete structures to eliminate the corrosion problem
associated with the conventional reinforcing steel. The following section
provides a brief overview of FRP materials and some of their important
properties and characteristics related to their use as reinforcement in
concrete.
3.12 CHARACTERISTICS OF FRP REINFORCEMENT
Originally, FRP materials were used successfully in aerospace, marine
and automotive sectors. Their positive properties and the significant
reduction in their materials and manufacturing costs helped the
widespread of the FRP materials in civil engineering applications. FRP's
are increasingly being used in civil infrastructure in several forms such as;
reinforcing bars and tendons in new structures, wraps and laminates for
strengthening of existing structures, composite bridge decks, and
composite structural sections. To stay within the scope of this research,
the following section will only focus on the FRP materials in the form of
internal reinforcing bars.
FRP reinforcement is composed of high strength continuous fibres
embedded in a polymer matrix in addition to some fillers and additives.
Fibres are in very small diameters and are responsible to provide
mechanical strength and stiffness to the composite, while the polymer
matrix, (resin), has comparatively poor mechanical properties. Fibres are

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oriented in the longitudinal direction of the bars which is the direction of
the primary loads.
Aramid, Carbon, and Glass fibres are the most commonly used types of
fibres (Mallick 1988). Aramid fibres are classified as highly oriented
organic fibres derived from polyamide incorporating aromatic ring
structure. Aramid fibres also offer good mechanical properties at a low
density with the added advantage of toughness or impact resistance. They
are characterized as having reasonably high tensile strength (1310 MPa)
and poor compressive strength (290 MPa) if compared to other fibres. The
tensile strength of aramid fibres is higher than that of glass fibres. Aramid
composites have poor compressive strength. It has a medium
unidirectional tensile modulus of 83 GPa which is approximately fifty
percent higher than that of glass, and a very low density (1380 Kg/m3) if
compared to glass and carbon. These fibres increase the impact resistance
for composites and provide products with higher tensile strengths. Aramid
fibres are insulators of both electricity and heat. They are resistant to
organic solvents, fuels, and lubricants. Dry aramid fibres are tough and
have been used as cables or ropes, and frequently used in ballistic
applications .
Glass fibres are classified as fibre drawn from an inorganic product of
fusion that has cooled without crystallizing. Glass fibres are available in 4
types, E-glass for high electrical insulating properties, S-glass for high
strength, ECR glass for improved acid resistance and acid resistance (AR
glass). The average tensile strength of glass fibres ranges between
approximately 1.00 and 2.00 GPa (1.75 GPa for S-glass type and 1.1 GPa
for E-glass type). The compressive strength of both S & E types is
approximately 490 MPa. The tensile strength of glass fibres is reduced in
the presence of water or under sustained loads (creep). The tensile

-29-
strength degradation is also increased as the surface flaws grow under
cyclic and fatigue loads. The tensile modulus of glass fibres ranges
between 70 to 90 GPa. Glass fibres are sensitive to abrasion and corrosion
due to alkaline solutions, and are considered generally a good impact
resistant fibre. Specific gravity of glass fibres are approximately 2500
kg/m .
3.13 Main results of the researchs use (FRP) can be summarized as follows:
1-Using steel fibre reinforced concrete (SFRC) within beam-column
joints can significantly enhance the shear resistance capacity of joints. The
increased tensile strength and the bridging action of SFRC can confine
tension cracking to the joint diagonals and thus reduce the requirements
for closely spaced joint ties and preserving the integrity of the joint
concrete core. Furthermore, the inclusion of a proper steel fibre
reinforcement dosage within a beam– column joint may prevent shear
failure occurring in the joint core, altering the failure mode from joint
shear hinge to flexural failure of the beam or column. Moreover, using
SFRC in the seismically designed joint region can improve the seismic
performance due to the higher load levels, larger displacements and more
damage tolerance.
2 .Using 1% (by volume) steel fibre reinforcement can significantly
reduce the lateral reinforcement in the beam plastic hinge region. The
performance can be at least as satisfactory as that of a conventional
seismically detailed unit with similar joint shear reinforcement and
appropriate seismic details in the beam plastic hinge region. It can be
anticipated that the construction difficulties associated with reinforcement
congestion may be partially solved by employing SFRC in the critical
regions of the construction (i.e. joint and plastic hinges). 174

-30-
3-The presence of steel reinforcement alone cannot prevent the buckling
of the column longitudinal bars, even in the joint region. Therefore, a
minimal quantity of additional confinement, in the form of stirrups, shall
still be provided in the joints region
4- Steel fibre reinforcement combined with full designed lateral
reinforcement provides a very efficient seismic performance in flexural
members. Owing the advantages of SFRC, such as the improved energy
dissipation capacity and extended stress-strain characteristics, a high level
of moment can still be retained after high intensity cycle loading.
5- A simplified analytical procedure based on the hierarchy of strength
and joints strength degradation models has been proposed to evaluate the
sequence of events and assess the required fibre shear contribution. For
analysing and predicting the failure model of a joint, therefore, a simple
hybrid failure mechanism, which can demonstrate the failure mechanism
due to combination of plastic hinges in beam and column elements and
shear hinges in joint regions, is also introduced. The nominal shear stress
j v is typically used by adopting principle stresses to develop proper joint
strength degradation models of SFRC joints. The joint strength
degradation curves (principal tensile stress vs. joint shear deformation)
have been calibrated on the experimental data Based on the developed
formula, the shear stress j v contributed by steel fibres, concrete and
stirrups can be clear known. Then, M_N performance based domain
visualization has been used to evaluate the hierarchy of strength and
sequence of events of beam-column joint subassemblies. Joint shear
coefficient f K contributed by steel fibres has been also compared with

-31-
previous experimental test available in literature to obtain a reliable value
for design purpose.( By Liu, Cong January, 2006)
- Based on the studied dimensions of the beam–column joint and the
considered defects along with the proposed CFRP strengthening
configuration subjected to incrementally monotonic static loading, the
following conclusions can be drawn :
1-Using either CFRP fabric sheets or plates as strengthening material
showed its efficiency in enhancing the failure characteristics of the
defected beam–column joints if only the proper configuration was chosen
2- The diagonal overlaying sheets was observed to be the better
configuration to strengthen the defect of the absence of joint stirrups.
While, the L-shaped fabric sheet showed its adequacy to strengthen the
defect of insufficient bond length for the beam main steel Comparison
among all specimens concerning ultimate capacity, initial stiffness and
ductility.
3-The orientation of the CFRP plates has a great effect on the
performance of the strengthened joint. Comparing the responses of both
specimens JIII1 and JIII3 which had the same volume of the CFRP plate
assure that evidence. Specimen JIII1 has NSM plates while JIII3 has an
overlaying plate.
4-Generally, using CFRP as a strengthening material led to increased
ultimate capacity and decreased ductility compared to those of un-
strengthened joints.
5-End anchorage sheets manifested its advantage especially in case of
member under flexure. The visual observation of the failure of specimen
JII1 showed that the joint can sustain additional loading if the anchorage
U-shaped remained unpeeled off the beam soffit.

-32-
(E-mail address: hamdyafefy@hotmail.com (H.M. Afefy))
-The SFRHPC joints undergo large displacements without developing
wider cracks when compared to the HPC joints. This indicates that steel
fibres impart high ductility to the SFRHPC joints, which is one of the
essential properties for the beam-column joints
• Addition of fibres to the beam-column joints decreased the rate of
stiffness degradation appreciably when compared to the joints without
fibres. Hence, the technique of inclusion of steel fibres in beam column
joints appears to be a useful solution in the case of joints subjected to
repeated or cyclic loading.
• During testing it has been noted that addition of fibres could improve
the dimensional stability and integrity of the joints.
• Also, it is possible to reduce the congestion of steel reinforcement in the
beam-column joints by replacing part of ties in the columns by steel
fibres.
• Load carrying capacity of the joints also increased with the increasing
fibre content
(N. Ganesan, P.V. Indira and Ruby Abraham Calicut-673601)

-33-
3.14 Failure mechanism of the joint
In seismic design philosophy, the beam-column joint is designed based
on strong column-weak beam criteria, the plastic hinges are expected to
be formed on the beams near the face of the column and develop flexural
over strength beyond the design strength. The high internal forces
developed at plastic hinges cause critical bond conditions in the
longitudinal reinforcing bars passing through the joint and also impose
high shear demand in the joint core. The joint behavior exhibits a
complex interaction between bond and shear (Shiohara, H., 2001). The
bond performance of the bars anchored in a joint affects the shear
resisting mechanism to a significant extent.
1-Failure due to insufficient of bond length
The moment from the adjoining members cause tension or compression
forces in the longitudinal reinforcements passing through
the joint. During plastic hinge formation, these forces produce
large tensile forces that are transferred through bond. When
longitudinal beam bars near the column face are stressed
beyond yield stress, splitting cracks are
initiated along the joint face which is
referred to as ‗yield penetration‘.
Longitudinal bar is to be provided with
adequate development length at the joint, taking yield
penetration into consideration.
Therefore, the size of the beams and columns framing into the joint
depends on the bond requirement of the bar.
(Uma. S. R and Sudhir K . Jain, 2006).

-34-
2-Joint shear -Failure
The large shear forces may be introduced into beam-column joints
irrespective of whether plastic hinges develop at column faces or at some
other section of beams. These shear forces may cause a failure in the joint
core due to the breakdown of shear or bond mechanisms or both.The
joint region is subjected to horizontal and vertical shear forces whose
magnitude is typically many times higher than in the adjacent beams and
columns .If not designed for, joint shear fail ure can result. The reversal
in moment across the joint also means that the beam reinforcement is
required to be in compression on one side of the joint and at tensile yield
on the other side of the joint. The high bond stresses required to sustain
this fo rce gradient across the joint may cause bond failure and
corresponding degradation of moment capacity accompanied by
excessive drift. .
To gauge the relative severity of joint shear forces, it is convenient to
express this in terms of shear stresses. As different mechanisms are
involved. in the shear transfer after the onset of diagonal cracking, no
physical meaning should be attached to shear stress. It should be
considered only as a useful index of the severity of joint shear forces

-35-
The limitations
– Cylindrical compressive strength of concrete: 22 MPa ≤ 𝑓𝑐
,
≤ 92 Mpa.
– Angle of inclination ℎof the joint strut ST1: 40 deg ≤ ℎ ≤ 68 deg.
– Overall area of tensile principal reinforcement in the beam: 531 mm2
≤ 𝐴 𝑠𝑏 ≤ 2790 mm2.
– Overall area of compressive principal reinforcement in the beam: 396
mm2 ≤ 𝐴 𝑠𝑏
’
≤ 2790 mm2.
– Overall area of horizontal joint hoop reinforcement must be less than
1356 mm2.
– Overall area of vertical intermediate column bars must be less than
1257 mm2.
– Yield strength of beam tensile reinforcement must be less than 1069
Mpa.
– Yield strength of joint hoop reinforcement must be less than 480 Mpa.
– Yield strength of column bars must be less than 580 Mpa.
𝟎. 𝟕𝟏 ∗ (
𝛈 𝒇 𝒄
,
𝒃 𝒋 𝒂 𝒄 𝐜𝐨𝐬 𝒉
(
𝟐𝑯𝑳
𝟐𝑯𝑳−(𝟐𝑳+𝒉 𝒄)𝒋 𝒅𝒃
∗(𝟏−
𝑳 𝒉 ∗ √ 𝒇 𝒄
’
𝝓 𝒃∗
𝑽 𝒃𝒋∗𝑳
𝑨 𝒔𝒃∗ 𝒋 𝒅𝒃
) )≤𝟏.𝟎
+ 𝟎. 𝟕𝟗 𝑨 𝒉 𝒇 𝒚𝒉 +
𝟎. 𝟓𝟐
𝑨 𝒗 𝒇 𝒚𝒗
𝐭𝐚𝐧 𝒉
) =
𝑽 𝒃𝒋∗ 𝑳
𝒋 𝒅𝒃
(𝟏 −
(𝑳+
𝒉 𝒄
𝟐
) 𝒋 𝒅𝒃
𝑯∗𝑳
) (Galal Elsamak 2017 )
η = [0.74 ∗ (
𝑓𝑐
,
105
)
3
− 1.28 ∗ (
𝑓𝑐
,
105
)
2
+ 0.22 ∗ (
𝑓𝑐
,
105
) + 0.87 ]
𝑓𝑐
,
: The cylindrical compressive strength of concrete
𝑏𝑗 = 𝑡ℎ𝑒 𝑙𝑒𝑎𝑠𝑡 𝑜𝑓 {
𝑏 𝑏
𝑏𝑐
bb ∶ The width of beam cross section
𝑏 𝐶 ∶ 𝑇ℎ𝑒 width of column cross section

-36-
𝑎 𝑐 = (0.25 + 0.85 ∗
𝑁
𝐴 𝑔 𝑓𝑐
’
)ℎ 𝑐
N : The axial force in the column
Ag : The gross area of the column section.
ℎ 𝑐 : The depth of column in the beam direction
ℎ = 𝑡𝑎𝑛−1
(
(𝑑 − 𝑑
) 𝑏
(𝑑 − 𝑑) 𝑐
)
(𝑑 − 𝑑
) 𝑏 ∶ The distance between top and bottom beam longitudinal bars
(𝑑 − 𝑑
) 𝑐 ∶ The distance between left and right column longitudinal bars
H : The height between upper and lower column inflection points
L : The length from beam inflection point to column face
𝑗 𝑑𝑏 = ℎ 𝑏 −
𝑥 𝑏
3
− 𝐵𝑒𝑎𝑚 𝑐𝑜𝑣𝑒𝑟
𝑏 𝑏 𝑥 𝑏
2
2
+ (𝐴 𝑠𝑏 + 𝐴 𝑠𝑏
’
) n 𝑥 𝑏 − (𝐴 𝑠𝑏 𝑑 𝑏 + 𝐴 𝑠𝑏
’
∗ 𝐵𝑒𝑎𝑚 𝑐𝑜𝑣𝑒𝑟) ∗ 𝑛 − 𝐴 𝑠𝑏
’
∗
𝐵𝑒𝑎𝑚 𝑐𝑜𝑣𝑒𝑟 = 0
n =
𝐸𝑠
𝐸 𝑐
=
2∗105
4700 √ 𝑓𝑐
’
𝑗 𝑑𝑏 : The internal moment arm of the beam
ℎ 𝑏 : The beam depth
𝑥 𝑏 : The depth of the compression zone in the beam cross section
𝐴 𝑠𝑏 : The area of the beam longitudinal tensile reinforcement
𝐴 𝑠𝑏
’
∶ The area of the beam longitudinal compressive reinforcement
n : The modular ratio
𝐸𝑠 ∶ The steel elastic modulus of the beam reinforcement
𝐸𝑐 ∶ The concrete elastic modulus

-37-
𝑑 𝑏 : The effective depth of the beam cross section
𝐿ℎ = ℎ 𝑐 − 𝑎 𝑐
𝜙 𝑏 ∶ 𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟 𝑜𝑓 𝑏𝑒𝑎𝑚 𝑟𝑒𝑖𝑛𝑓𝑜𝑟𝑐𝑒𝑚𝑒𝑛𝑡 𝑖𝑛 𝑡𝑒𝑛𝑠𝑖𝑜𝑛
𝑉𝑏 : The beam vertical load
𝐴ℎ = 𝑚 𝐴ℎ𝑖
𝐴ℎ𝑖 =
𝑛𝑜. 𝜋 𝜙2
4
m : The number of horizontal stirrups reinforcement layers
no. : the number of stirrup legs
𝜙 ∶ 𝑡ℎ𝑒 𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟 𝑜𝑓 𝑠𝑡𝑖𝑟𝑟𝑢𝑝
𝐴ℎ𝑖 = 𝑎𝑟𝑒𝑎 𝑜𝑓 𝑎𝑙𝑙 𝑏𝑟𝑎𝑛𝑐ℎ𝑒𝑠 𝑜𝑓 𝑡ℎ𝑒 𝑜𝑛𝑒 𝑠𝑡𝑖𝑟𝑟𝑢𝑝
𝑓𝑦ℎ : stirrup yielding strength
𝐴 𝑣 = 𝜌 𝐴 𝑣𝑗
𝜌 : The number of intermediate vertical bars within the joint core
𝐴 𝑣𝑗 : 𝑇ℎ𝑒 area of the intermediate vertical bar within the joint core
𝑓𝑦𝑣 ∶ yielding strength of vertical reinforcement in the central region of
the column
α =
2𝐻𝐿
2𝐻𝐿−(2𝐿+ℎ 𝑐)𝑗 𝑑𝑏
∗ (1 −
𝐿ℎ ∗ √ 𝑓𝑐
’
𝜙 𝑏∗ 𝑓 𝑏
) ≤ 1.0
𝑓𝑏 ∶ 𝑠𝑡𝑟𝑒𝑠𝑠 𝑖𝑛 𝑡ℎ𝑒 𝑡𝑒𝑛𝑠𝑖𝑙𝑒 𝑠𝑡𝑒𝑒𝑙 𝑜𝑓 𝑡ℎ𝑒 𝑏𝑒𝑎𝑚
𝑉𝑛 = 0.71 ∗ (
η 𝑓𝑐
,
𝑏𝑗 𝑎 𝑐 cosℎ
α
+ 0.79 𝐴ℎ 𝑓𝑦ℎ + 0.52
𝐴 𝑣 𝑓𝑦𝑣
tanℎ
)
𝑉𝑗ℎ = 𝐴 𝑠𝑏 ∗ 𝑓𝑏 (1 −
(𝐿 +
ℎ 𝑐
2 ) 𝑗 𝑑𝑏
𝐻 ∗ 𝐿
)
If 𝑉𝑗ℎ > 𝑉𝑛 Joint shear failure occur.

-38-
3- Flexural -Failure of beam
Flexural cracking in the beam portion during early load stages is
followed by propagation of a diagonal crack in the connection zone.
Further loading leads to the joint failure, either by plastic hinge formation
in the beam at the face of the column or by extensive cracking in the
connection zone, depending upon the relative influence of reinforcement
percentage, detailing and column load.
Beam plastic hinge failure
0.67 𝑓𝑐𝑢 𝑎𝑏 + 𝐴 𝑠
’
𝑓𝑠
’
= 𝐴 𝑠 𝑓𝑦
Where 𝑓𝑠
’
= 0.003𝐸𝑠
1.25𝑎−𝑑’
1.25𝑎
≤ 𝑓𝑦
’
∗ 0.003𝐸𝑠
1.25𝑎 − 𝑑’
1.25𝑎
Get a = √
Check 𝜀 𝑠 = 0.003
𝑑−1.25𝑎
1.25𝑎
≥
𝑓𝑦
𝐸
Tension failure occur
𝑀 𝑢 = 0.67 𝑓𝑐𝑢 𝑎𝑏 (𝑑 −
𝑎
2
) + 𝐴 𝑠
’
𝑓𝑠
’
(𝑑 − 𝑑’
) − 0.67 𝑓𝑐𝑢 𝐴 𝑠
’
(𝑑 − 𝑑’
)
Where 𝑀 𝑢 = 𝑽 𝒃 ∗ 𝑳
Get 𝑽 𝒃𝒃 = √

-39-
4- Flexural -Failure of column
Column plastic hinge failure
𝑃𝑢 = 0.67 𝑓𝑐𝑢 𝑎𝑏 + 𝐴 𝑠
’
𝑓𝑠
’
− 0.67 𝑓𝑐𝑢 𝐴 𝑠
’
− 𝐴 𝑠 𝑓𝑦
Where 𝑓𝑠
’
= 0.003𝐸𝑠
1.25𝑎−𝑑’
1.25𝑎
≤ 𝑓𝑦
𝑃𝑢 = 0.67 𝑓𝑐𝑢 𝑎𝑏 + 𝐴 𝑠
’
∗ 0.003𝐸𝑠
1.25𝑎 − 𝑑’
1.25𝑎
− 0.67 𝑓𝑐𝑢 𝐴 𝑠
’
− 𝐴 𝑠 𝑓𝑦
Get a = √
Check 𝜀 𝑠 = 0.003
𝑑−1.25𝑎
1.25𝑎
≥
𝑓𝑦
𝐸
Tension failure occur
𝑀 𝑢 = 0.67 𝑓𝑐𝑢 𝑎𝑏 (
𝑡
2
−
𝑎
2
) + 𝐴 𝑠
’
𝑓𝑠
’
(
𝑡
2
− 𝑑’
) − 0.67 𝑓𝑐𝑢 𝐴 𝑠
’
(
𝑡
2
− 𝑑’
)
+ 𝐴 𝑠 𝑓𝑦 (𝑑 −
𝑡
2
)
Where 𝑀 𝑢 = 0.5 𝑽 𝒃 ∗ 𝑳
Get 𝑽 𝒃𝒄 = √
5- shear -Failure of beam
A shear and flexural stresses acts simultaneously in a complex
combination within the joint region.
Design of a joint is often
governed by shear forces which are
transferred through the joint, along with the ability
of the j oint to remain intact under reversed cyclic loading.
𝑄
𝑏. 𝑑
− .24√𝑓cu =
𝑛. 𝐴𝑠. 𝑓𝑦
𝑏. 𝑠

-40-
6- shear -Failure of column
The moments and shear forces generated in the beams and columns of a
building frame introduce internal stress resultants at the faces of joint
core .The stress resultants cause both horizontal and vertical shear forces
in the joint cores. Finally, internal diagonal tensile and compressive
stresses would occur due to the development of joint core shear. If the
diagonal stress is large enough , it would lead to diagonal cracking (in
tension) or crushing (in compression) of the core concrete. Unless
adequate shear resistance is provided in the joint core failure of the joint
core may eventually occur along the corner to corner diagonal plane
𝑄
𝑏. 𝑑
− .24√𝑓cu =
𝑏. 𝑠
Where :
n: number of stirrups branches
As :
𝜋𝐷2
4
S; spacing between stirrups

-41-
4- Non Linear Analysis of Exterior RC beam column joint
4.1 GENERAL
The local response of beam–column joints is not considered for the
seismic analysis of multistory reinforced concrete (RC) frame structures,
where these critical regions are typically assumed as rigid. Studies that
incorporate the local effect of the joints in the seismic analysis of
multistory RC frame structures are limited. Identifying the main
disadvantages of the analytical models that have been proposed so far, a
behavioral model is developed for the simulation of the local inelastic
response of exterior RC beam–column joints in multistory RC frame
structure.
As existing theoretical and experimental study of the joints are not
perfect, especially the Seismic performance, it is difficult to make a
comprehensive evaluation of the performance of the joints

-42-
4.2 OBJECTIVE
The main objective is to make modeling of a specimen of an exterior RC
beam column joint using SAP2000 program according to FEMA356 to
get the capacity of joint, max displacement and its mode of failure due to
cyclic load P.
G AND ANALYSIS OF AN EXTERIOR JOINTMODELIN4.3
Concrete dimensions, Reinforcement details of specimen

-43-
4.4 INPUT DATA
1- Material properties
 Fcu= 25 MPa
 Fyl =360 MPa
 Fys=240 MPa
2- Section properties
 Beam section (250*400) mm
Sections
 column section (250*250) mm
3- Hinges properties
 Joint shear failure
 Beam shear failure
 Column shear failure
 Beam flexural failure
 Column flexural failure
Hinges

-44-
o Joint shear failure
𝟎. 𝟕𝟏 ∗ (
𝛈 𝒇 𝒄
,
(
𝟐𝑯𝑳
∗(𝟏−
𝑳 𝒉 ∗ √ 𝒇 𝒄
’
𝝓 𝒃∗
) )≤𝟏.𝟎
+ 𝟎. 𝟕𝟗 𝑨 𝒉 𝒇 𝒚𝒉 +
𝟎. 𝟓𝟐
) =
𝒋 𝒅𝒃
(𝟏 −
(𝑳+
𝒉 𝒄
𝟐
) 𝒋 𝒅𝒃
𝑯∗𝑳
)
= 0.87η = [0.74 ∗ (
𝑓𝑐
,
105
)
3
− 1.28 ∗ (
𝑓𝑐
,
105
)
2
+ 0.22 ∗ (
𝑓𝑐
,
105
) + 0.87 ]
𝑏 𝑏
𝑏 𝑐
(Galal Elsamak 2017 )
𝑏𝑗 = 250 𝑚𝑚 𝐜𝐨𝐬 𝒉 = 0.7
𝑏 𝐶 ∶ 𝑇ℎ𝑒 width of column cross section=250 mm
bb ∶ The width of beam cross section=250 mm
hc=250mm
𝑎 𝑐 = (0.25 + 0.85 ∗
𝑁
𝐴 𝑔 𝑓𝑐
’ )ℎ 𝑐 =96.5
N : The axial force in the column=200 KN
Ag : The gross area of the column section=2502
=62500 mm2
𝑓𝑐
,
: The cylindrical compressive strength of concrete=20MPa
𝑥 𝑏
3
− 𝐵𝑒𝑎𝑚 𝑐𝑜𝑣𝑒𝑟 =375--
216
3
= 149.28

-45-
𝐴ℎ𝑖 =
𝑛𝑜.𝜋 𝜙2
4
=
2∗2∗.𝜋 82
4
= 201.6
𝑓𝑦ℎ : stirrup yielding strength=240 MPa
ϕ∶the diameter of stirrup =8 mm
𝐴 𝑣 = 𝜌 𝐴 𝑣𝑗 =4*118 =450
f_(yv ) ∶ yielding strength of vertical reinforcement in the central region
of the column =360 Mpa
𝟎. 𝟕𝟏 ∗ (
𝟎.𝟖𝟕∗𝟐𝟎∗𝟐𝟓𝟎∗𝟗𝟔.𝟔∗ 𝐜𝐨𝐬𝟒𝟓
(
𝟐∗𝟐𝟓𝟎∗𝟗𝟎𝟏
𝟐∗𝟐𝟓𝟎∗.𝟎𝟏−(𝟐.∗𝟎𝟏+𝟐𝟓𝟎)𝟏𝟒𝟗.𝟐𝟖
∗(𝟏−
𝟏𝟓𝟑.𝟓∗ √𝟐𝟎
𝟒𝟓∗
𝑽 𝒃𝒋∗.𝟎𝟏
𝑨 𝒔𝒃∗ 𝟏𝟒𝟗.𝟐𝟖
) )
+ 𝟎. 𝟕𝟗 ∗
𝟐𝟎𝟏. 𝟔 ∗ 𝟐𝟒𝟎 + 𝟎. 𝟓𝟐
𝟒𝟓𝟐∗𝟑𝟔𝟎
𝐭𝐚𝐧𝟒𝟓
) =
𝑽 𝒃𝒋∗ .𝟎𝟏
𝟏𝟒𝟗.𝟐𝟖
(𝟏 −
(.𝟎𝟏+
𝟐𝟓𝟎
𝟐
) 𝟏𝟒𝟗.𝟐𝟖
𝟐𝟓𝟎∗.𝟎𝟏
)
𝑽 𝒃𝒋 = 151236.25 𝑁

-46-
200 KN
P
o Beam shear failure
𝑄
𝑏. 𝑑
− 0.24√𝑓cu =
𝑏. 𝑠
𝑄
250 ∗ 375
− 0.24√25 =
2 ∗ 50.3 ∗ 240
250 ∗ 200
Beam shear capacity
QU=157770 N = 157.7 KN
o column shear failure
𝑄
𝑏. 𝑑
− 0.24√𝑓cu =
𝑏. 𝑠
𝑄
250 ∗ 225
− 0.24√25 =
2 ∗ 50.3 ∗ 240
250 ∗ 200
Column shear capacity
QU=94662 N = 94.6 KN
o Beam flexural failure
Beam capacity from tables in ASCE 41-13 using SAP2000
MU = 75600000 N.mm
o Column flexural failure
Column-capacity
from tables in ASCE 41-13 using SAP2000
MU = 16388202 N.mm
4- Loads
 Gravity load = 200KN
 Cyclic load P =??
Loads
2
3

-47-
4.5 RESULTS
Table: Joint Displacements,
JointOutput CaseCase TypeStep TypeSternumU3
mm
2cyclicNonStaticStep0.-0.206998
Table: Joint Reactions,
0
2
4
6
8
10
12
14
16
18
20
0 5 10 15 20 25 30 35 40 45 50 55 60
Displacement (mm)
basereaction(KN)
JointOutput CaseCase TypeStep TypeStep NumF3
N
3cyclicNonStaticStep0.200000.
3cyclicNonStaticStep1.208573.99

-48-
 Failure of connection occurred in column at load: P=18.6 KN.
Step 1
P=0
D=0.2 mm
Step 2
P=8.57 KN
D=2.57 mm
Step 3
P=16.97KN
D=4.9 mm
Step 4
P=17.67 KN
D=24.9 mm
Step 5
P=18.37 KN
D=44.9 mm
Step 5
P=18.6 KN
D=53.8 mm

-49-
By making retrofitting to column, the plastic hinge in column is
controlled
Table: Joint Displacements,
JointOutputCaseCaseTyp
e
StepTypeU3
mm
2CYCLICLOADNonStatic1-0.20699756
Table: Joint Reactions,
JointOutputCaseCaseTypeStepTypeF3
N
3CYCLICLOADNonStatic3235928.6417
0
5
10
15
20
25
30
35
40
0 1 2 3 4 5 6 7 8 9 10 11 12
Displacement (mm)
basereaction(KN)

-50-
 Failure of connection occurred in joint at load: P=35.9 KN
Step 1
P=0
D=0.2 mm
Step 2
P=24.8 KN
D=7.14 mm
Step 3
P=35.9 KN
D=10.47 mm

-51-
By making retrofitting to joint and 20% of column height, the plastic
hinge in joint is controlled.
Making retrofitting to joint and 40% of column height
Step 3
P=20.5 KN
D=6.02mm
Step 5
P=23.2 KN
D=45.7mm
Step 3
P=27.6 KN
D=7.8 mm
Step 5
P=30.4 KN
D=38.5mm
920mm
1440mm

-52-
By making retrofitting to joint and 50% of column height , the plastic
hinge in joint is controlled
0
5
10
15
20
25
30
35
40
45
0 10 20 30 40 50 60 70 80 90
Displacement (mm)
basereaction(KN)
Step 1
P=17.6 KN
D=5.22 mm
Step 2
P=35.7KN
D=10.15
mm
1700mm

-53-
 Failure of connection occurred in beam at load: P=39.6 KN
 The outputs were reviewed with experimental specimens have the
same dimensions.
Step 5
P=39.6 KN
D=82.08mm
Step 4
P=39.3KN
D=80.99
mm
Step 3
P=38.7KN
D=60.99mm

-54-
0
5
10
15
20
25
30
35
40
45
0 10 20 30 40 50 60 70 80 90
Displacement (mm)
basereaction(KN)
Without retrofitting
20% Column
40% Column
50% Column
CONCLUSION
case 1 case 2 case 3 case 4 case 5
Retrofitting without
2600 mm
column
920 mm
joint + 20%column
1440 mm
joint + 40%column
1700 mm
joint + 50%column
Capacity
(KN)
18.6 35.9 23.2 30.4 39.6
Failure column joint column column beam
Max
displacement
(mm)
53.8 10.47 45.7 38.5 82.8
The result showed that :
1-the failure occur in beam by retrofitting the joint and 25% from column
2-when failure occur in beam ,frame ductility and energy dissipation
increase .

-55-
5- CASE STUDY
5.1 OBJECTIVE
The main objective of the present chapter is to explanation the behavior
and capacity of the frame under the study. Also survey influence use
(CFRB) in repairing the external beam column joint under seismic load.
5.2 GENERAL
residential building (30m*6m) consists of 10 floor . there are 2 frames
to resist earthquakes forces with column cross section 300*700 mm and
beam cross section 300*700 mm
fcu=25MPa
fy=360MPa

-56-
5.3 INPUT DATA
o Joint shear failure
𝟎. 𝟕𝟏 ∗ (
𝛈 𝒇 𝒄
,
(
𝟐𝑯𝑳
∗(𝟏−
𝑳 𝒉 ∗ √ 𝒇 𝒄
’
𝝓 𝒃∗
) )≤𝟏.𝟎
+
𝟎. 𝟕𝟗 𝑨 𝒉 𝒇 𝒚𝒉 + 𝟎. 𝟓𝟐
) =
𝒋 𝒅𝒃
(𝟏 −
(𝑳+
𝒉 𝒄
𝟐
) 𝒋 𝒅𝒃
𝑯∗𝑳
)
= 0.87η = [0.74 ∗ (
𝑓𝑐
,
105
)
3
− 1.28 ∗ (
𝑓𝑐
,
105
)
2
+ 0.22 ∗ (
𝑓𝑐
,
105
) + 0.87 ]
𝑏 𝑏
𝑏 𝑐
(Galal Elsamak 2017 )
𝑏𝑗 = 300 𝑚𝑚 𝐜𝐨𝐬 𝒉 = 0.7
𝑏 𝐶 ∶ 𝑇ℎ𝑒 width of column cross section=250 mm
bb ∶ The width of beam cross section=250 mm
hc=700mm
𝑎 𝑐 = (0.25 + 0.85 ∗
𝑁
𝐴 𝑔 𝑓𝑐
’ )ℎ 𝑐 =175.35
N : The axial force in the column
Ag : The gross area of the column section=300*700 mm2
𝑓𝑐
,
: The cylindrical compressive strength of concrete=20MPa
𝑥 𝑏
3
− 𝐵𝑒𝑎𝑚 𝑐𝑜𝑣𝑒𝑟 = 175

-57-
𝐴ℎ𝑖 =
𝑛𝑜.𝜋 𝜙2
4
=
0∗2∗.𝜋 82
4
=0
𝑓𝑦ℎ : stirrup yielding strength=240 MPa
ϕ∶the diameter of stirrup =8 mm
𝐴 𝑣 = 𝜌 𝐴 𝑣𝑗 =8*118 =1680
f_(yv ) ∶ yielding strength of vertical reinforcement in the central region
of the column =360 Mpa
𝟎. 𝟕𝟏 ∗ (
𝟎.𝟖𝟕∗𝟐𝟎∗𝟑𝟎𝟎∗𝟏𝟕𝟓.𝟑𝟓∗ 𝐜𝐨𝐬𝟒𝟓
(
𝟐∗𝟑𝟎𝟎∗.𝟎𝟏
𝟐∗𝟕𝟎𝟎∗.𝟎𝟏−(𝟐.∗𝟎𝟏+𝟕𝟎𝟎)𝟏𝟕𝟓
∗(𝟏−
𝟏𝟓𝟑.𝟓∗ √𝟐𝟎
𝟒𝟓∗
𝑽 𝒃𝒋∗.𝟎𝟏
𝑨 𝒔𝒃∗ 𝟏𝟕𝟓
) )
+ 𝟎. 𝟕𝟗 ∗ 𝟎 ∗
𝟐𝟒𝟎 + 𝟎. 𝟓𝟐
𝟏𝟔𝟎𝟖∗𝟑𝟔𝟎
𝐭𝐚𝐧𝟒𝟓
) =
𝑽 𝒃𝒋∗ .𝟎𝟏
𝟏𝟕𝟓
(𝟏 −
(.𝟎𝟏+
𝟕𝟎𝟎
𝟐
) 𝟏𝟕𝟓
𝟕𝟎𝟎∗.𝟎𝟏
)
𝑽 𝒃𝒋 = 302574.2 𝑁

-58-
o Beam shear failure
𝑄
𝑏. 𝑑
− 0.24√𝑓cu =
𝑏. 𝑠
𝑄
300 ∗ 650
− 0.24√25 =
2 ∗ 50.3 ∗ 240
300 ∗ 200
Beam shear capacity
QU=157770 N = 327.6KN
o column shear failure
𝑄
𝑏. 𝑑
− 0.24√𝑓cu =
𝑏. 𝑠
𝑄
300 ∗ 650
− 0.24√25 =
5 ∗ 50.3 ∗ 240
300 ∗ 200
Column shear capacity
QU=94662 N = 469.4 KN
o Beam flexural failure
Beam capacity from tables in ASCE 41-13 using SAP2000
MU = 188100. KN.mm
o Column flexural failure
Column-capacity from tables in ASCE 41-13 using SAP2000
MU = 268300. kN.mm

-59-
5.4 RESULTS
Step 0
gravity load
mm))
(KN)
Step 1
P=73.3 KN
D=50 mm

-60-
Step 2
P=103.2KN
D=65.7 mm
the first plastic
hinge formed in
joint
Step 3
P=162 KN
D=115.9 mm
the plastic hinge
formed in beam
Step 4
P=176.5 KN
D=130 mm
the plastic hinge
formed in beam

-61-
5.5 Seismic force
Fb=ZICSKW
Z=0.2 I=1
C=
1
15√ 𝑇
T=
.09𝐻
√𝑏
=0.69 C=0.08
S=1.5 W=2063 ton
Fb = 619 KN
Force /frame = 309.5 KN
Step 9
P=248.8 KN
D=397.6 mm
the plastic hinge
formed in column
Step12
P=256.8 KN
D=510.6 mm
Max load
failure at joint

-62-
5.6 Retrofitting joint of frame and 10% of beam at floor 1 , 2 ,3
At Step 3
P=135.3KN
D=92.1mm
the first plastic hinge formed in beam
(KN)
mm))
At Step 6
P=268.2KN
D=417.7mm
At Step 10
P=275.8KN
D=486.6mm
max load , failure at beam
530 mm

-63-
At Step 3
P=136.2KN
D=92.1mm
(KN)
mm))
At Step 7
P=293.6KN
D=442.5mm
At Step 15
P=298.7KN
D=485.4mm
1060 mm

-64-
At Step 3
P=137.8KN
D=92.1mm
(KN)
mm))
At Step 7
P=312.3KN
D=482. 5mm
At Step 8
P=317.6KN
D=484.9mm
1325 mm

-65-
0
50
100
150
200
250
300
350
0 50 100 150 200 250 300 350 400 450 500 550 600
Displacement (mm)
basereaction(KN)
Without retrofitting
10% beam
20% beam
25% beam
case 1 case 2 case 3 case 4
Retrofitting without
joint +
530mm beam
joint +
1060mm beam
joint +
1325mm beam
Capacity
(KN)
256.8 275.8 298.7 317.6
Failure joint beam beam beam
Max
displacement
(mm)
547.2 486.6 485.4 484.9

-66-
evaluating the previous cases by the performance curves resulted
from pushover analysis .
.
The performance based analysis is based on quantifying the deformation
of the members and the building as a whole, under the lateral forces of an
earthquake of a certain level of seismic hazard. Traditional Approach-
Force based Design has no measure of the deformation capability of
members or of building.
The deformation or strains are better quantities to assess damage than
stress or forces. Since the deformation are expected to go beyond the
elastic values.
The performance based analysis gives the analyst more choice of
‘performance’ of the building as compared to the limit states of collapse
and serviceability in a design based on limit state method.
Advantages of Performance Based Seismic Design
Systematic methodology for assessing the performance capability of a
building
Design individual buildings with a higher level of confidence
Design individual buildings to achieve higher performance and lower
potential losses.
Performance-based seismic design offers society the potential to be both
more efficient and effective in the investment of financial resources to
avoid future earthquake losses
Before retrofitting After retrofitting

-67-
5.9 REPAIR AND STRENGTHENING TECHNIQUES FOR BEAM-
COLUMN JOINTS
The goal is to protect human life, ensuring that the structure will
not collapse upon its occupants or passersby, and that the structure
can be safely exited. Under severe seismic conditions the structure
may be a total economic write-off, requiring tear -down and
replacement
1- Concrete jackets
Purpose for jacketing:
•To increase concrete confinement.
•To increase shear strength.
•To increase flexural strength.
Beam jacketing
Ultimate capacity bending moment of beam section
before retrofitting =188100. KN.mm
3Ø16
3Ø16

-68-
’
𝑓𝑠
’
0.67 ∗ 25 ∗ 𝑎 ∗ 300 + 7 ∗ 201 ∗ .003 ∗ 0.003𝐸𝑠
1.25𝑎 − 50’
1.25𝑎
= 6 ∗ 201 ∗ 360
a=127.1 mm
𝑀 𝑢 = 0.67 𝑓𝑐𝑢 𝑎𝑏 (𝑑 −
𝑎
2
) + 𝐴 𝑠
’
𝑓𝑠
’
(𝑑 − 𝑑
’
) − 0.67 𝑓𝑐𝑢 𝐴 𝑠
’
(𝑑 − 𝑑
’
)
𝑀 𝑢 = 0.67 ∗ 25 ∗ 127.1 ∗ 300 (650 −
127
2
) + 7 ∗ 201 ∗ .003
∗ 0.003𝐸𝑠
1.25 ∗ 127 − 50
1.25 ∗ 127
(650 − 50) − 0.67 ∗ 25 ∗ 7
∗ 201 (650 − 50)
𝑀 𝑢 = 287985.3 𝐾𝑁. 𝑚𝑚
Additional RFT required for repair
Beam jacketing

-69-
2-Fiber-reinforced polymeric composites (CFRP )
FRP composite materials have experienced a continuous increase of use
in structural strengthening and repair applications around the world in
the last years .
Installation technique
•The joint is wrapped with two U-shaped composite layers.
•The first layer was bi-directional sheet and the second was
unidirectional sheet. .
•The ends of the sheets are anchored using steel plates and tie rods
driven through the joint. .
•Four unidirectional glass fiber sheets were applied to the beam bottom
face for a horizontal distance of 1325 mm and extended along the inner
column face vertically for a distance of 100 mm, as shown in Fig

-70-
The design objective is to achieve the same flexural capacity of the
adequately anchored section. In this design procedure, three assumptions
are made :
1-strain compatibility between the different materials is assumed
2-the ultimate concrete strain in compression is taken as 0.003
3-the contribution of the existing steel bars is ignored
The tensile force developed in the fiber sheets can be estimated as
𝑇𝑓𝑟𝑝 = 𝐸𝑐𝑓𝑟𝑝 𝜀 𝑐𝑓𝑟𝑝 𝐴 𝑐𝑓𝑟𝑝
𝜺 𝒇𝒓𝒑 = 𝜺𝒄
𝒕 − 𝒄
𝒄
’
𝑓𝑠
’
= 𝐸 𝑐𝑓𝑟𝑝 𝜀 𝑐𝑓𝑟𝑝 𝐴 𝑐𝑓𝑟𝑝
0.67 ∗ 25 ∗ 𝑎 ∗ 300 + 4 ∗ 201 ∗ .003 ∗ 0.003𝐸𝑠
1.25𝑎 − 50’
1.25𝑎
= 𝐸 𝑐𝑓𝑟𝑝
∗ 003
700 − 1.25 ∗ 𝑎
1.25 ∗ 𝑎
∗ 300 ∗ 3
Get a=
𝑀 𝑢 = 0.67 𝑓𝑐𝑢 𝑎𝑏 (𝑑 −
𝑎
2
) + 𝐸𝑐𝑓𝑟𝑝 𝜀 𝑐𝑓𝑟𝑝 𝐴 𝑐𝑓𝑟𝑝(𝑑 − 𝑑’
)
− 𝐴 𝑠
’
𝑓𝑠
’
(𝑑 − 𝑑’
)

-71-
𝑀 𝑢 = 0.67 ∗ 25 ∗ 𝑎 ∗ 300 (650 −
𝑎
2
) + 𝐸 𝑐𝑓𝑟𝑝 ∗ 003
700 − 1.25 ∗ 𝑎
1.25 ∗ 𝑎
∗ 300 ∗ 3 ∗ (650 − 50
’
) − 4 ∗ 201
∗ 0.003𝐸𝑠
1.25𝑎 − 50’
1.25𝑎
(650 − 50)
Mu =387365 KN
Advantage of using (CFRP):
1. Resistance to tension 10 tenfold steel
2. Ease in using because lightweight
3. Take low period in construction
5.10 Retrofitting cost estimation
a- Cost of using (concrete jacket)
Use 3Ø16 upper and 3Ø16 lower
Cost of steel = 3500 p
Cost of concrete = 1500 p
Time period = 30 days
Cost of steeplejacks = (4*200)*15+(6*200)*15= 30000 p
For site overhead, risks = 30000*2= 60000
Total cost = 5000+60000 = 65000 p
b - Cost of using (CFRP)
((1.325+.7)*2+.4)*.7+(.25+1.325)*2)=3.115+.5525=3.5 m2
3.5*6=21 m2
Cost of material= 21*600=12600 p
Time period = 4 days
Cost of steeplejacks = (6*200)*2=2400 p
Total cost = 12600+2400 = 15000 p

-72-
15000
65000
4 day
30 day
0
10000
20000
30000
40000
50000
60000
70000
cfrp concrete jaketing
pound
total cost (pound)
time of repair (day)
6- CONCLUSION
Based on the studied dimensions of the beam–column joint and the
considered defects along with the proposed CFRP strengthening
conﬁguration subjected to cyclic loading, the following conclusions can
be drawn
1. Web-bonded CFRP-retrofitting technique can be used to relocate
the beam plastic hinging zone away from the column face in RC
ordinary moment resisting frames.
cfrp concrete jaketing
material cost (pound) 12600 5000
labors cost (pound) 2400 60000
total cost (pound) 15000 65000
time of repair (day) 4 30

-73-
2. Use of over-designed FRP-retrofitting increases the strength of the
beam end so that the beam sections adjacent to the column face remain
essentially elastic.
3. Use of (CFRP) transverse wrap is recommended in order to confine
the retrofitted areas and reduce the shear deformation.
4. Generally, using (CFRP) as a strengthening material led to
increased ultimate capacity and ductility compared to those of un-
strengthened joints
5. The result showed that increasing capacity for the frame by
retrofitted using (CFRP)
6. Use (CFRP) in repairing better than concrete jacketing as it take
short time and lower total cost .

-74-
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-75-
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