1. Engineering Structures 24 (2002) 1397–1407
www.elsevier.com/locate/engstruct
Seismic rehabilitation of beam–column joint using GFRP sheets
T. El-Amoury, A. Ghobarah ∗
Department of Civil Engineering, McMaster University, Hamilton, Ontario, Canada, L8S 4L7
Received 13 July 2001; received in revised form 24 September 2001; accepted 24 May 2002
Abstract
Techniques for upgrading reinforced concrete beam–column joints are proposed. The test specimens represent a typical joint that
was built in accordance to pre-1970s’ codes. The objective of the rehabilitation is to upgrade the shear strength of these joints and
reduce the potential for bond-slip of the bottom bars of the beam. Glass fibre-reinforced polymer (GFRP) sheets are wrapped around
the joint to prevent the joint shear failure. GFRP sheets are attached to the bottom beam face to replace the inadequately anchored
steel bars. Three beam–column joints are tested; namely, a control specimen and two rehabilitated specimens. The specimens are
tested under quasi-static load to failure. The control specimen showed combined brittle joint shear and bond failure modes while
the rehabilitated specimens showed a more ductile failure mode. A simple design methodology for the rehabilitation scheme is
proposed.  2002 Elsevier Science Ltd. All rights reserved.
Keywords: Beam-column joints; Seismic rehabilitation; Joint shear strength; Bond-slip; Ductility; GFRP composites; Design
1. Introduction
Recent earthquakes in urban areas such as the 1994
Northridge, the 1995 Hanshin-Awaji (Kobe) and the
1999 Kocaeli (Turkey) have repeatedly demonstrated the
vulnerability of existing structures to seismic defor-mation
demands. These structures were designed and
detailed for gravity loads and lateral forces that are lower
than those specified by the current codes. Post-earth-quake
examination of these structures showed that one
of the weakest links in the lateral load-resisting system
is the beam–column joint. Fig. 1 shows the exterior joint
failure in a reinforced concrete building after the 1999
Kocaeli earthquake. Exterior beam–column joints are
more vulnerable than interior joints, which are partially
confined by beams attached to four sides of the joint
and contribute to the core confinement. There are some
differences between the shear response of interior and
exterior joints when subjected to earthquake ground
motion due to joint confinement by beams. However, the
bond-slip mode of failure of exterior and interior joints
is similar.
∗ Corresponding author. Tel.: +1-905-525-9140x124913; fax: +1-
905-529-9688.
E-mail address: ghobara@mcmaster.ca (A. Ghobarah).
When built according to earlier code provisions,
beam–column joints in reinforced concrete moment-resisting
0141-0296/02/$ - see front matter  2002 Elsevier Science Ltd. All rights reserved.
PII: S0141-0296(02)00081-0
frames have inadequate or no transverse shear
reinforcement, and the bottom reinforcement of the beam
is anchored only 150 mm from the column face, with
inadequate development length when the bars are in ten-sion.
This was done under the assumption that the beam
positive moment reinforcement at the column face is
always in compression. Because of these deficiencies,
the joint may experience shear or bond-slip failure
modes. These brittle types of failure will significantly
reduce the overall ductility of the structure.
The objective of beam–column joint rehabilitation is
to strengthen the shear and bond-slip resistance in order
to eliminate these types of brittle failure and ensure
instead that ductile flexural hinging in the beam will take
place. Recent studies on the effect of shear and bond-slip
rehabilitation on the behaviour of reinforced con-crete
frame have shown significant improvements in the
overall frame ductility [1,2]. It is important to develop
effective and economic rehabilitation techniques for
upgrading the vulnerable beam–column joints in exist-ing
structures.
Rehabilitation of existing structures has received
much attention during the past two decades. The objec-tive
is to upgrade the joint shear strength before it is
subjected to an earthquake. An interior beam-column

2. 1398 T. El-Amoury, A. Ghobarah / Engineering Structures 24 (2002) 1397–1407
Fig. 1. Exterior joint failure during the 1999 Kocaeli (Turkey) earthquake.
joint was rehabilitated and tested [3]. Steel plates were
anchored to the beam bottom face at each side of the
joint and connected together using threaded steel rods
driven through the column. The idea is to replace the
inadequately anchored steel bars with equivalent steel
plates. Steel-plate jacketing was used to enhance the
joint shear strength. Test results showed that joint jacket-ing
was ineffective in improving the joint shear strength
due to slippage of the steel plates. The specimen reached
a drift of 4% without significant deterioration in strength.
Flat steel plates were used to confine the joint in an
attempt to prevent the spalling of concrete and to main-tain
the concrete integrity [4,5]. Steel channels were
attached to the beam bottom face to prevent slip of the
bars. This scheme was found to be efficient in preventing
the bars’ slippage, increasing the joint shear strength and
reducing the rate of strength deterioration.
Ghobarah et al. [6] used corrugated steel-sheet jacket-ing
for joint confinement, leaving a gap between the con-crete
and the jacket to be filled with grout. The shear
strength of the rehabilitated joints was increased and the
failure mode became flexural hinging in the beam.
Carbon fibre-reinforced polymer (CFRP) materials
were used to strengthen an external beam–column joint
in shear [7]. The retrofitted specimen was wrapped with
multiple layers of CFRP sheets. The joint shear capacity
was increased by 25% and the specimens reached 5%
drift.
Ghobarah and Said [8] investigated the rehabilitation
of beam–column joints using glass fibre-reinforced poly-mers
(GFRP). One joint was tested as control specimen
and two were tested after rehabilitation. The proposed
rehabilitation scheme was to wrap the joint with U-shaped
GFRP sheets. The ends of the composite sheets
were tied together using two steel plates and four steel
tie rods through the joint. The behaviour of the rehabili-tated
specimen was significantly improved. The brittle
shear failure of the beam–column joint was eliminated
and instead ductile flexural hinging of the beam
occurred. The joints tested in this research programme
were designed with deficient shear strength but with
adequate positive reinforcement anchoring in the joint.
In other words, bond-slip failure was not included in the
rehabilitation scheme.
Limited testing was conducted on beam–column joints
rehabilitated using composite rods to strengthen the col-umn
flexural strength and fibre wrap to strengthen the
joint shear [9]. Joint rehabilitation using fibre-reinforced
polymers (FRP) has the advantages of simplicity of
application and less need for skilled labour. The econ-omic
advantages of FRP rehabilitation were evaluated
by Ehlen and Marshall [10].
So far, most of the research conducted on beam–
column joints has mainly been concerned with upgrading
joint shear strength using steel plates, sheets and sections
and FRP. However, the rehabilitation of bond-slip in
reinforced concrete beam–column joints has not received
much attention.
The objective of the present research programme is to
develop new rehabilitation systems for strengthening the
shear resistance of beam–column joints and for upgrad-ing
resistance to bond-slip of the positive reinforcement
anchored in the joint.
2. Experimental programme
2.1. Test specimens
Three reinforced concrete beam–column joints were
tested: T0, TR1 and TR2. The specimens represent an
exterior joint in a typical concrete frame that has been
built before 1970 [11]. Exterior joints are selected
because they are more vulnerable and are normally

3. T. El-Amoury, A. Ghobarah / Engineering Structures 24 (2002) 1397–1407 1399
expected to fail first. If the rehabilitation system is suc-cessful,
it can be easily adapted to interior joints as well.
The beam–column joints are designed assuming that
points of contra-flexure occur at the mid-height of col-umns
and the mid-span of beams. The top longitudinal
reinforcements in the beam are bent down into the col-umn,
whereas the bottom reinforcement was anchored
150 mm from the column face. No transverse reinforce-ment
was installed in the joint region. The beam was
reinforced using 4#20 as top and bottom longitudinal
bars and #10 as transverse steel. The column was
reinforced with 6#20 plus 2#15 as longitudinal bars and
#10 ties spaced 200 mm. The dimensions and reinforce-ment
details of all of the specimens are identical, as
shown in Fig. 2.
After testing the control specimen, T0, the cracked
concrete was removed from the joint region and the
adjacent parts of the columns and beam. The specimen
was laid inside the wooden forms again and new con-crete
was poured to replace the removed materials. The
specimen was then rehabilitated and tested again as
specimen TR1. However, specimen T2 is an original
specimen that was retrofitted then tested. The concrete
compressive strength on the test day was 30.6, 43.5 and
39.5 MPa for the control specimen T0, the repair con-crete
of specimen TR1 and for specimen TR2, respect-ively.
The yield strength of the steel bars #10, #15 and
#20 was 450, 408 and 425 MPa, respectively.
Bi-directional GFRP material were used in the joint
rehabilitation. The bi-directional material is woven in the
±45° directions. The properties of the fibre sheets used
in the current testing programme, as supplied by the
manufacturer, are given in Table 1.
2.2. Test set-up and instrumentation
The specimens were tested in the column vertical pos-ition,
hinged at the top and bottom column ends and sub-jected
to a cyclic load applied at the beam tip as shown
in Fig. 3. The beam-tip displacement and the column
lateral displacement were measured using poten-tiometers.
Two diagonal linear voltage differential trans-formers
(LVDTs) were attached to the joint to measure
the joint shear deformation. The displacement of the col-umn
above and below the joint was measured using two
additional LVDTs attached to the top and bottom of the
beam, as shown in Fig. 3. Twelve strain gauges were
installed on the reinforcement steel bars to measure the
strains at different loading levels, as shown in Fig. 4.
For the retrofitted specimens, 10 strain gauges were
installed on the fibre sheets, two strain gauges were
installed on the tie rods driven through the joint.
A reversed quasi-static cyclic load was applied at the
beam tip using a hydraulic actuator of ±250 mm stroke.
The applied load was measured using a load cell. The
loading routine consisted of two phases as shown in Fig.
5. The first phase was load control, where the specimen
was subjected to an increasing load up to the first yield
of the steel bars. This phase of loading was used to deter-mine
the displacement of the beam tip when first yield
Fig. 2. Specimen dimensions and reinforcement details.

4. 1400 T. El-Amoury, A. Ghobarah / Engineering Structures 24 (2002) 1397–1407
Table 1
Properties of the composite materials
GFRP Tensile strength in 0° direction (MPa) Elongation at break (%) Tensile modulus (GPa) Thickness (mm)
Bi-directional (±45°) 279 1.5 19 0.864
Unidirectional 1700 2 71 0.353
Fig. 3. Test set-up.
of the steel occurs, y. After the beam steel bars reached
the yield strain, the second loading phase was initiated
which was displacement control. Multiples of the dis-placement
corresponding to the bars’ first yield, y, were
used to load the specimen. A constant axial load of 600
kN was applied to the column, using another hydraulic
jack provided with a load cell to measure the applied
load. This load represents the gravity load that acts on
the column, and was approximately equal to 0.2Agfc,
where Ag is the gross cross-sectional area and fc is the
compressive strength of concrete.
2.3. Rehabilitation schemes
The proposed rehabilitation schemes consist of two
systems. The first system is for upgrading the shear
strength of the joint. The joint was wrapped with two
U-shaped composite layers. The first layer was bi-direc-tional
sheet and the second was unidirectional sheet. The
ends of the sheets were anchored using steel plates and
tie rods driven through the joint. This system was similar
to previously tested systems [8] but differed in material
design and details. The second system was for upgrading
the steel bars’ bond-slip. This system is new and was
Fig. 4. Location of strain gauges on the reinforcement steel bars.
Fig. 5. Loading routine.
being tested for the first time. In specimen TR1, four
unidirectional glass fibre sheets were applied to the beam
bottom face for a horizontal distance of 1000 mm and
extended along the inner column face vertically for a
distance of 500 mm, as shown in Fig. 6a. In specimen

5. T. El-Amoury, A. Ghobarah / Engineering Structures 24 (2002) 1397–1407 1401
Fig. 6. Retrofitting schemes: (a) specimen TR1, (b) specimen TR2.
TR2, eight unidirectional glass fibre sheets were applied
to the bottom beam face and provided with two U-shaped
3 mm thick steel plates to enhance the bond
between the GFRP and the concrete, as shown in Fig.
6b. Using the described configuration, the resultant of
the tensile forces developed in the composite sheets may
cause debonding of the sheets from the concrete surface
at the beam–column corner. To overcome this potential
problem, a steel angle was installed at the lower beam–
column corner as shown in Fig. 6a. To install the angle
in place, the beam bottom bars were exposed for a dis-tance
of 150 mm from the column face and the heads
of A375 steel bolts of diameter 20 mm were welded to
the beam bars in two rows. For specimen TR1, four 28
mm diameter and 170 mm depth holes were drilled in
the column in two rows. The steel angle was fixed in
place using washers and nuts to the bolts welded to the
beam reinforcement and using Hilti HVA 5/8×6-5/8
adhesive anchors to the column. For specimen TR2, four
25 mm diameter external threaded rods with
500 mm × 200 mm × 25 mm steel plate were used to tie
the angle to the column as shown in Fig. 6b.
3. Experimental results
In this section, the behaviour of the control and
rehabilitated specimens is described and the effective-ness
of the rehabilitation schemes is evaluated.
3.1. Specimen T0
In the first loading cycle, the specimen was loaded up
to 3.0 kN up and down to test the instrumentations. The
first beam crack was observed during the second cycle
at the column face at load of 7.7 kN up. In the fourth
cycle, a load of 30.0 kN was applied up and down to the
specimen; new flexural and flexural–shear cracks formed
along the beam length. In the sixth cycle, vertical cracks
formed in the joint region at beam-tip load of 35.5 kN
due to bond-slip of the beam bottom bars. During the
eighth cycle, diagonal shear cracks developed in the joint
region, and the specimen reached a load of 60.0 kN at
a beam-tip displacement of 20 mm. Repeating the same
cycle, the beam reached the same displacement but at
lower load level and the beam bars started to slip out of
the joint with an associated reduction in the developed
strain in the bars. The beam-tip displacement of 20 mm
was used as a reference value for the displacement-con-trolled
loading phase. In the following cycles the beam
tip was displaced up and down by multiples of this value.
The reason for selecting this arbitrary displacement as
reference displacement in the test is that yield of the
reinforcement steel is not expected to occur. When the
specimen was pushed up, the bond-slip cracks opened
and the lateral load-carrying capacity deteriorated sig-nificantly;
however, when it was pulled down, the diag-onal
shear cracks opened. This caused disintegration of
the concrete, deterioration of the bond condition of the
beam top bars and degradation of the lateral load-carry-ing
capacity. The specimen reached a maximum load of

6. 1402 T. El-Amoury, A. Ghobarah / Engineering Structures 24 (2002) 1397–1407
60.0 kN up and 86.0 kN down, which is much less than
the expected theoretical load at first steel yield of
approximately 110.0 kN. The test was halted at displace-ment
of 50 mm as the load-carrying capacity was greatly
reduced. In effect, when pushing up on the beam, bond-slip
failure of the beam bottom reinforcement occurred
and when pulling down, joint shear failure occurred. The
final failure pattern is shown in Fig. 7. A reduction in
the column axial load up to 10% of the original load
was recorded in the last cycles due to joint shear failure.
Examining the hysteretic behaviour of the specimen
showed considerable pinching, severe strength deterio-ration
and stiffness degradation, as shown in Fig. 8.
Bond slip was found to be a more brittle type of failure
when compared with shear failure, as it occurred earlier
and is associated with a higher rate of strength deterio-ration.
In the figure, beam-tip displacement of 20 mm
corresponds to 1.0 % storey drift.
3.2. Specimen TR1
Specimen TR1 was subjected to the same loading
sequence as specimen T0. The first crack occurred dur-
Fig. 7. Failure pattern of specimen T0.
Fig. 8. Beam-tip load–displacement of specimen T0.
ing the second cycle at load of 14.0 kN. The specimen
was loaded at increments of 20.0 kN until reaching the
first yield of the steel reinforcement. Before yielding, the
behaviour of the specimen was almost elastic with no
residual deformation observed. Examining the strain
values showed that the fibre sheets attached to the beam
face were carrying most of the developed tensile forces,
indicating that the glass fibre fabric was working effec-tively.
During the sixth cycle, vertical cracks appeared
in the lower column under the joint region, due to the
tensile forces developed in the adhesive anchors. These
cracks caused a sudden drop in the beam-tip load from
58.0 kN to 53.0 kN. During the test, FRP debonding was
regularly checked by fingertip tapping on the composite
sheets. During the eighth cycle, the wrapped laminates
around the joint started to debond between the free edges
and the steel plates. In the 10th cycle, the beam top steel
bars reached the yield strain at beam displacement of 25
mm and beam-tip load of 110.0 kN. This displacement
was designated the yield displacement y, and the dis-placement-
controlled loading phase was initiated. Dur-ing
the 12th cycle, the specimen was displaced to 37.5
mm up and down (1.5y). The fibre sheet attached to
the bottom beam face reached a strain of 0.0045 when
the specimen was pushed up. As the beam tip was pulled
down, the fibre sheets buckled and started to debond
from the beam face. In the following cycles, as the ten-sion
in the fibres is lost due to debonding, the existing
steel bars started to carry the developed tension force.
The tension force in the bars was transferred to the col-umn
by bonding, the welded bolts and the steel angle.
The specimen showed increased load-carrying capacity
as it was pulled down. During the 16th cycle, at displace-ment
of 75 mm up and down (3.0y), the weld around
the bolt heads fractured, the beam bars slipped out of
the joint and sudden a drop in the beam load was
observed. During the next cycle, the specimen experi-enced
a loss of load-carrying capacity when pushed up,
whereas it continued to carry the same load level when
it was pulled down, indicating no shear failure in the
joint region. The final failure condition is shown in Fig.

7. T. El-Amoury, A. Ghobarah / Engineering Structures 24 (2002) 1397–1407 1403
Fig. 9. Failure pattern of specimen TR1.
9. The composite sheets were completely debonded from
the beam and column faces. Examining the hysteretic
loops of the specimen showed that the behaviour
remained almost elastic up to the first steel yield, as
shown in Fig. 10. Severe pinching and stiffness degra-dation
occurred in the last two cycles following the frac-ture
of the weld.
3.3. Specimen TR2
Specimen TR2 was subjected to the same loading rou-tine
as the previous specimens. The first crack occurred
during the second cycle at load of 20.0 kN while it was
being pulled down. During the following cycle, the first
yield of the beam top bars occurred at beam displace-ment
of 26.5 mm and beam-tip load of 114.5 kN. This
displacement was designated the yield displacement y,
and the displacement-controlled loading phase was
initiated. Vertical cracks appeared in the lower column
under the joint region at a beam-tip load of 75 kN. Dur-ing
the sixth cycle, the wrapped laminates around the
joint started to debond at the free edges. In the ninth
cycle, the fibre attached to the column face started to
Fig. 10. Beam-tip load–displacement of specimen TR1.
delaminate behind the steel angle. The forces developed
in the composite sheets were transferred to the column
by the steel angle and the tie rods. This caused a
reduction in the beam-tip load when the specimen was
being pushed up accompanied with large deformations
to the angle. In the 11th cycle, while the specimen was
being pulled down, it reached its ultimate load of 131.0
kN and displacement of 79.5 mm (3y). This high load
caused new cracks in the column part above the joint
and initiated joint shear failure. Degradation of the load-carrying
capacity was observed in the following cycles.
During the 16th cycle, the specimen displaced to 132.5
mm (5y) was still able to carry load of 74.0 kN up and
89.0 kN down, which are more than half of the yield
load.
The two U-shaped steel plates proved to be effective
in preventing fibre debonding from the concrete face to
the end of the test. The strain in the GFRP reached
approximately 0.005 in both tension and compression.
In the 17th cycle, the specimen was displaced to 159
mm (6y); however, the load-carrying capacity deterio-rated
to 52.0 kN. The test was halted after the 19th cycle
where the specimen reached displacement of 185 mm
(7y) and the load-carrying capacity deteriorated to 32.0
kN. The specimen showed shear cracking in the joint
region under the GFRP, as shown in Fig. 11. The load–
displacement cycles are shown in Fig. 12.
Although the final failure mode of specimen TR2 was
due to joint shear high load-carrying capacity, the overall
joint performance is much more ductile compared with
the control specimen T0. During the test, it was con-firmed
that the large plastic deformation of the steel
angle provided significant ductility to the joint behav-iour.
4. Discussion
In this section, the hysteretic behaviour, energy dissi-pation,
stiffness degradation, joint strength and ductility
levels of the tested specimens are discussed.
The envelopes of the hysteretic loops of the tested
specimens are shown in Fig. 13. Specimen TR1 showed
almost 100% increase in the load-carrying capacity com-pared
with specimen T0. Specimen TR2 reached a higher
load level and maintained the load-carrying capacity at
displacement levels much higher than those of the other
two specimens. The pinching effect is severe in speci-men
T0 as compared with the rehabilitated specimens.
The top steel in the beam of specimen T0 did not reach
its yield stress. On the other hand, in the rehabilitated
specimens, the yield of the top beam reinforcement was
exceeded. This indicates the effectiveness of the shear
rehabilitation scheme in strengthening the joint shear
capacity and maintaining the joint concrete integrity
by confinement.

8. 1404 T. El-Amoury, A. Ghobarah / Engineering Structures 24 (2002) 1397–1407
Fig. 11. Failure pattern of specimen TR2.
Fig. 12. Beam-tip load–displacement of specimen TR2.
The area enclosed by a hysteretic loop at a given cycle
represents the energy dissipated by the specimen during
this cycle. The capability of a structure to dissipate
energy has a strong influence on its response to an earth-quake
loading. The total energy dissipated by a structure
consists of (1) energy dissipated by the steel reinforce-ment;
(2) energy dissipated by friction along existing
cracks in concrete; and (3) energy dissipated during the
formation of new cracks. Fig. 14 shows the cumulative
energy dissipated by the three beam–column joints. It is
observed that the rehabilitated specimen TR1 had the
ability to dissipate three times the energy dissipated by
Fig. 13. Hysteretic loop envelopes of the test specimens.
Fig. 14. Cumulative energy dissipated by the tested specimens.
the specimen T0, while specimen TR2 dissipated almost
six times the energy dissipated by the control speci-men
T0.
The beam–column joint stiffness was approximated as
the slope of the peak-to-peak line in each loop. Test
results indicated that stiffness degradation was due to
various factors such as non-linear deformations, flexural
and shear cracking, distortion of the joint panel, slippage
of reinforcement, and loss of cover. The control speci-men
T0 showed high initial stiffness compared with
specimen TR1 because of the pre-cracking of the
rehabilitated specimen TR1 before repair. Specimen
TR2, which was tested for the first time after rehabili-tation,
showed also high initial stiffness. Comparing the
peak-to-peak stiffness of the tested joints shows that the
stiffness degradation of the control joint T0 was higher
than that of the rehabilitated specimens TR1 and TR2,
as shown in Fig. 15.
While the control specimen did not reach the steel
yield due to bond-slip and shear failure, the rehabilitated
specimens TR1 and TR2 reached higher ductility levels
than the control specimen T0.
5. Design of GFRP sheets
The design approach is based on providing fibre
reinforcement to replace the missing joint shear

9. T. El-Amoury, A. Ghobarah / Engineering Structures 24 (2002) 1397–1407 1405
Fig. 15. Degradation of stiffness with storey drift.
reinforcement or the inadequately anchored steel
reinforcement.
5.1. Flexural strengthening sheets
The fibre is used to replace the inadequately anchored
bottom steel bars of the beam. In the design process,
fibre sheets are provided to develop the same design
flexural moment of the reinforced concrete beam section.
This moment limit is imposed on the flexural strengthen-ing
system to avoid creating a beam that is stronger than
the column.
5.1.1. The beam flexural moment
The moment capacity of the beam section is determ-ined
according to the provisions of CSA A23.3-94 [12].
To account for overstrength in steel, the tensile force in
the steel is calculated using the actual yield strength,
which equals the nominal yield strength increased by
25%,
Ts 1.25fyAs, (1)
where
Ts is the tension force in the bottom steel bars
As is the area of the tension steel bars.
fy is the nominal yield strength of the steel
The concrete compression block depth “a” can be calcu-lated
using the force equilibrium expression:
Ts Cc Cs a1fcab AsEses, (2)
where
Cc is the concrete compression force
Cs is the steel compression force
a1 is the equivalent compression block reduction factor
[12], a1 0.85–0.0015 for fc 0.67
fc is the concrete compression strength
b is the beam width
As is the area of the compression steel
Es is the modulus of elasticity of the steel
es is the strain in the compression steel.
The resisting positive moment of the section at the face
of the column, Mr, is:
Mr Cc(da/2) Cs(dd), (3)
where
d is the effective beam depth
d is the concrete cover above the top steel.
In the particular case of joint T0, Eq. (1) gives the ten-sion
force in the steel bars to be Ts 600 kN, and Eq.
(2) gives the depth of the concrete block to be a
61.0 mm. The resisting moment capacity given by Eq.
(3) is Mr 187.32 kN m.
5.1.2. Required number of GFRP layers
The design objective is to achieve the same flexural
capacity of the adequately anchored section. In this
design procedure, three assumptions are made:
strain compatibility between the different materials
is assumed;
the ultimate concrete strain in compression is taken
as 0.0035; and
the contribution of the existing steel bars is ignored.
The tensile force developed in the fibre sheets can be
estimated as
Tfrp efrpEfrpAfrp, (4)
where efrp is the strain developed in the GFRP sheets,
which should be less than the ultimate strain, and could
be derived from the geometry, as shown in Fig. 16; Efrp
is the modulus of elasticity of the GFRP and Afrp is the
area of the GFRP sheets.
The depth of the concrete compression block “a” can
be calculated from the moment equilibrium equation:
Mr a1fcab(ta/2) AsesEs(td). (5)
The strain in the fibre can be written as:
efrp ec
tc
c
, (6)
where ec is the compression strain in concrete and c is
the location of the neutral axis. From the equilibrium
of forces:
Tfrp Cc Cs (7)
Tfrp efrpEfrpnfrptfrpb. (8)
Using the same resisting moment capacity of joint T0,
Mr 187.32 kN m, Eq. (5) gives the depth of the con-crete
block to be a 55.95 mm. Eqs. (6) to (8) give the

10. 1406 T. El-Amoury, A. Ghobarah / Engineering Structures 24 (2002) 1397–1407
Fig. 16. Calculation of the required number of GFRP sheets.
strain in the fibre efrp 0.0189 with the number of
GFRP layers, nfrp, as 4.35.
In specimen TR1, the number of GFRP layers, nfrp, is
taken as 4, while in specimen TR2 the nfrp is taken as 8.
5.2. Joint shear strengthening
The developed joint shear force is calculated as
[12,13]:
Vj 1.25AsfyVcol, (9)
where
Vj is the developed joint shear force
Vcol is the shear force in the column.
The total shear resistance consists of the concrete
resistance, the resistance of the ties and the resistance
provided by the composite sheets:
Vj Vc Vs Vfrp. (10)
The concrete shear resistance can be estimated using
ACI 352 [14] provision to be:
Vc 0.3fc(1 0.3fcol)bjdj, (11)
where
fcol is the axial stress applied to the column
bj is the joint width
dj is the joint effective width.
As there are no ties provided in the joint, Vs is taken to
be zero.
The fibre contribution, Vfrp, is estimated to be:
Vfrp AfrpefrpEfrp. (12)
For the rehabilitated specimen TR2, the column shear
force is obtained by dividing the nominal moment
capacity by the shear arm, which is equal to 2850 mm:
Vcol 187.32/ 2.85 65.73 kN.
Eq. (9) gives the total joint shear as Vj 534.27 kN. Eq.
(11) gives Vc 276.06 kN. From Eq. (10), the required
shear resistance contributed by the fibre is Vfrp
258.21 kN.
The shear strength provided using one bi-directional
and one unidirectional layers can be estimated from Eq.
(12), by assuming that both sheets will reach the same
strain level of 1.0%, which is equal to 2/3 of the smallest
maximum strains of the two composite sheet types. This
gives the provided shear resistance by the FRP, Vr
290.35 kN, which is greater than the required fibre
resistance Vfrp.
6. Conclusions
Based on the experimental results, the following con-clusions
can be made.
The control specimen with no shear reinforcement in
the joint and with inadequate anchorage for the beam
bottom steel bars showed a brittle joint shear failure
accompanied by slippage of the beam bottom bars.
The bond conditions of the beam top bars were affec-ted
by the disintegration of the concrete in the control
joint, leading to a significant reduction in the load-carrying
capacity and the ductility of the joint. Using
GFRP jacketing maintained the concrete integrity by
confinement and significantly improved the ductility
and the load-carrying capacity of the rehabilitated
joint.
Comparison between the control and the rehabilitated
specimens emphasized the effectiveness of the
rehabilitation schemes. The joint rehabilitation elim-inated
the brittle joint shear failure, improved the
bond conditions of the beam top reinforcement,
delayed the slippage of the bottom steel bars,
increased the energy dissipated by the specimen and
reduced the stiffness degradation of the joint.
In specimen TR1, the fibre debonded from the con-crete
surface when it reached a strain of 0.004, which
is approximately 25% of the proposed strain by the
design methodology. However, specimen TR1

11. T. El-Amoury, A. Ghobarah / Engineering Structures 24 (2002) 1397–1407 1407
reached the proposed strength due to the contribution
of the existing steel bars, which was ignored in the
design.
In specimen TR2, use of U-shaped steel plates to
restrain the GFRP eliminated debonding of the GFRP
from the concrete surface. The FRP reached a strain
that is approximately 1/3 of its ultimate strain in both
tension and compression without failure. The rehabili-tated
joint achieved 52% higher load-carrying
capacity and dissipated six times the energy dissipated
by the control specimen.
Acknowledgements
The authors are grateful to Fyfe Co. and R.J. Watson,
Inc. for providing the GFRP material used in the tests,
and to ISIS Canada for supporting the research pro-gramme.
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