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Muhammad Rashid* Int. Journal of Engineering Research and Application www.ijera.com
ISSN : 2248-9622, Vol. 6, Issue 9,(Part-5) September.2016, pp.54-57
www.ijera.com 54 | P a g e
Cyclic Response of Reinforced Concrete Moment Resisting Beams
Repaired with Epoxy Injection
Muhammad Rashid*
*(Department of Civil Engineering, University of Engineering & Technology Peshawar, KPK, Pakistan)
ABSTRACT
This paper presents the results of a quasi-static cyclic test carried out on a reinforced concrete special moment resisting beam
to study the efficiency of traditional repair techniques in restoring the strength and stiffness capacity of damaged RC beams.
The beam was tested in a cantilever mode and was subjected to a standard loading protocol with increasing amplitude of
displacement cycles. The final damage state of the beam consisted of severe cracking and spalling of the cover concrete. The
cracks were repaired with low-viscosity injection epoxy and the spalled concrete was repaired with early-strength grout. The
repaired specimen was subjected to the same loading protocol as the original specimen to study the efficiency of the repair
technique employed. It was observed that epoxy injection is not effective in restoring the strength and stiffness of beams with
bar slip of longitudinal bars at the support end.
Keywords - Bar slip, epoxy injection, reinforced concrete, reparability, strength, stiffness,
I. INTRODUCTION
Modern seismic design codes [1-3] design
buildings with the objective to avoid collapse and save
human lives. Structures are designed for seismic forces
that are considerably smaller than the design-level forces,
and therefore they are prone to damage during large
earthquakes [4]. Reinforced concrete special moment
resisting frames are designed according to the principles of
capacity design; which states that damage should be
concentrated at fixed locations in beams, often called
plastic hinges. The plastic hinges are located at the ends of
beams and should be proportioned and detailed to respond
primarily in flexure mode rather than brittle modes of
response such as shear. This philosophy forms the basis of
almost all the modern seismic design codes [1-3].
However, the subject of reparability of damaged
reinforced concrete structures, after being subjected to an
earthquake, has been addressed rarely. The performance
of reinforced concrete moment resisting frames, designed
to modern codes, in the recent earthquake of Christchurch
(2011) was satisfactory but raised the issue of reparability
of reinforced concrete structural components [5-6]. A
large number of damaged reinforced concrete frames had
to be demolished due to the lack of sufficient experimental
evidence to justify the use of traditional repair techniques
in restoring the capacity of damaged reinforced concrete
structural elements.
This paper addresses the issue of reparability of reinforced
concrete structural elements through an experimental
program. Since there has been a rampant increase in the
construction of reinforced concrete frames around the
world (especially
Pakistan), therefore, it is considered necessary to bring the
issue of reparability of reinforced concrete beams to the
knowledge of concerned authorities and structural design
engineers. To achieve this task, it was necessary to
conduct an experimental program to study the efficiency
of repair techniques and highlight the associated problems
with different repair techniques. Quasi-static cyclic testing
is conducted on a special moment resisting beam to study
the efficiency of epoxy injection and grout patching in the
restoring the strength and stiffness of a damaged beam.
Epoxy injection was chosen to be studied due to its ease of
application as in a real structure the repair process is
complicated by the presence of floor slab and infill walls.
II. LITERATURE REVIEW
Popov et al. (1975) tested three full-scale short
cantilever reinforced concrete beams and one half-scaled
interior beam-column joint representative of third floor
framing of a 20 story RC moment resisting frame. Two
repair schemes were investigated i.e. repair with a rapidly
setting epoxy resin and concrete depending on the damage
state of the beam. It was observed that the performance of
beams repaired using epoxy resin was satisfactory but
exhibited some loss of stiffness due to bond. Additionally,
replacing severely damaged concrete using fresh concrete
was found to be a satisfactory solution.
Corazao and Durrani (1989) carried out a
detailed experimental investigation on repair of reinforced
concrete sub-assemblages subjected to quasi-static cyclic
loading. A total of eleven sub-assemblages were tested,
which consisted of five exterior beam-column connections
and six two bay frames. Different repair techniques were
studied depending on the type and extent of damage. It
was found that epoxy injection is suitable for repairing
cracks in beams and slabs and its effectiveness in beam-
column joints depends on the quality of work. In case of
severe damage, such as damage to core concrete, the
strength can be effectively restored by replacing the
damaged concrete. Reinforcement jacketing and addition
of external rolled steel elements were found to be reliable
ways of restoring strength and stiffness.
III. EXPERIMENTAL WORK
The cross sectional dimensions of the beam are
12in. x 18 in. with a length of 96 in. The beam had 3-#8
bars in the top and bottom layer giving a longitudinal
reinforcement ratio of 1.26%. The transverse
reinforcement was provided according to the confinement
requirements of ACI-318 for beams.
RESEARCH ARTICLE OPEN ACCESS
Muhammad Rashid* Int. Journal of Engineering Research and Application www.ijera.com
ISSN : 2248-9622, Vol. 6, Issue 9,(Part-5) September.2016, pp.54-57
www.ijera.com 55 | P a g e
Figure 1: Specimen Reinforcement Details
III.1 Materials
III.1.1 Steel
The longitudinal and stirrup reinforcement
consisted of ASTM-A615 grade-60 bars. Steel coupons
were tested in tension for the #8 and #3 bars to test their
yield strengths. The details of tests are given in the Table
1.
Table 1: Reinforcement Steel Tensile Test Results
S. No Nominal
Dia
Yield
Strength
(Psi)
Ultimate
Strength
(Psi)
1 1.000 66140 91846
2 1.000 69837 95056
3 1.000 64612 89985
7 0.375 77939 107313
8 0.375 67006 92291
9 0.375 71171 99639
III.1.2 Concrete
Normal weight concrete with a specified
strength of 3000 psi was used for all the beams. The
concrete mix design ratio used was 1:2.13:3.61 with a
water-to-cement ratio of 0.57. Standard cylinders of 12 in.
height and 6 in. diameter were tested under compression
loading to validate the mix design. The results of
compression tests on the cylinders are given below in
Table 2.
Table 2: Concrete Compression Test Results
Specimen
ID
Age of
Concrete
(days)
Concrete Compressive
Strength, fc’ (psi)
28-1 28 3282.22
28-2 28 3204.25
28-3 28 3492.72
IV. SPECIMEN CONSTRUCTION AND
SETUP
The specimen was cast using plywood formwork
and was cured for a total of fourteen days. The beams
cantilevered out of an anchorage block which was
anchored to the strong floor of the laboratory using bolts
Fig. 2. The lateral load was applied at some distance from
the free end of the beam using a manual-controlled
hydraulic actuator. The actuator was attached to the beam
using a hinge assembly to allow the rotation of the
actuator Fig. 2.
Figure 2: Specimen Construction & Setup
V. LOADING HISTORY
The loading protocol used consisted of a series
of increasing displacement cycles with three cycles per
each displacement increment. The control point for the
displacement amplitude was the point of application of
load by the actuator.
Muhammad Rashid* Int. Journal of Engineering Research and Application www.ijera.com
ISSN : 2248-9622, Vol. 6, Issue 9,(Part-5) September.2016, pp.54-57
www.ijera.com 56 | P a g e
Figure 3: Loading Protocol for Testing
VI. TEST RESULTS
6.1 Damage Description and Hysteretic Response
The specimen was loaded with an initial
displacement of 0.375 in. Full depth flexural crack formed
at the northern face of the beam at a distance of 18 in.
from the face of the block, whereas a flexural crack at a
distance of about 16 in. formed on the southern face.
Cracking was not observed on the eastern and western
faces at this displacement demand. At displacement
amplitude of 0.75 in., no new cracks formed on any face
of the beam. With further increase in displacement
demand to 1.5 in., new flexural cracks formed at 8 in.,
13in. 26 in. and 34 in. from the support on the southern
face. A flexure crack formed at northern face at a distance
of 27 in., whereas slight diagonal cracking occurred on the
western face. A wide distribution of cracks took place
during the displacement cycles of 2.5 in., with cracks on
the northern and southern faces as high as 54 in. Full depth
inclined cracks were observed on the eastern and western
faces of the beam which increased in number at
displacement demand of 3.5in. Minimal new cracks were
observed further till the conclusion of test at 5.5 in.
Figure 4: Specimen Damage Patterns
Spalling of the concrete cover started on the
northern and southern faces at a displacement of 4.5 in.,
which escalated at final the displacement cycles of 5.5 in
exposing the reinforcing bars on the southern face. The
specimen could not be displaced further because the
maximum stroke of the hydraulic jack was 6 in. The
hysteretic response was marked by a strong pinching due
to the slip of longitudinal bars. No strength drop was
observed in the hysteretic response due to the fact that the
specimen was not tested till failure as shown in Fig. 5.
VII. REPAIR OF DAMAGES
The main objective of conducting this test was
to study the reparability of reinforced concrete beams
damaged by seismic loading. Since the specimen did not
sustain damage beyond spalling of cover concrete,
therefore, the repair techniques chosen were epoxy
injection into cracks and patching of spalled concrete. The
epoxy used was a low viscosity injection epoxy. The
patching of spalled concrete was done using non-shrink
and early-strength grout.
Figure 5: Hysteretic Response
Figure 6: Epoxy Injection and Patching of Spalled
Concrete
Muhammad Rashid* Int. Journal of Engineering Research and Application www.ijera.com
ISSN : 2248-9622, Vol. 6, Issue 9,(Part-5) September.2016, pp.54-57
www.ijera.com 57 | P a g e
VIII. DAMAGE DESCRIPTION AND
HYSTERETIC RESPONSE
The response of the repaired specimen was
unsatisfactory. The beam showed a considerable drop in
the strength and a severe pinched hysteretic response due
to loss of stiffness Fig. 7.
Figure 7: Comparison of Original& Repaired Response of
Specimen
The reason behind this performance is the fixed
end rotation at the interface between the beam and the
anchorage block. The interface opening was injected with
epoxy but based on the results it can be said that the
merely filling the interface opening with epoxy will not
restore the original stiffness of the beams which will
render the beam unable to achieve its original strength.
The efficiency of the epoxy injection in treating the cracks
could not be studied due to the fact that the beams did not
sustain the original loads which caused those cracks.
IX. CONCLUSIONS
i. The damage of the test specimen consisted of
cracking, spalling and fixed-end rotation due to slip
and inelastic extension of longitudinal bars. The
cracks of the plastic hinge region and the interface
crack (due to fixed-end rotation) were both injected
with low viscosity epoxy to restore the capacity of the
beam. It was, however, observed that the strength and
stiffness of the beam were not regained because
epoxy did not restore the bond between concrete and
steel.
ii. Therefore, it is concluded that the repair of reinforced
concrete beams, with fixed-end rotation, will be
ineffective by mere filling of interface crack with
epoxy. The significant loss of strength and stiffness
due to fixed-end rotation also renders the repair of the
rest of the damaged beam useless.
X. RECOMMENDATIONS
i. The effectiveness of other repair techniques in
restoring strength and stiffness of beams should be
studied experimentally. In this regard, special
attention should be paid to the ease of application of a
repair technique as the use of reinforcement
jacketing, fibre reinforced polymer sheets or steel
plates are complicated by the presence of floor slab
and infill walls.
REFERENCES
[1] ACI. 318. Building Code Requirements for
Structural Concrete, American Concrete
Institute, (2002).
[2] NZS 3101:2006 Concrete structures standard,
Standards New Zealand, Wellington, NZ.
[3] Eurocode 8: Design of structures for earthquake
resistance.
[4] Park, B., “Some controversial aspects of the
seismic design of reinforced concrete building
structures”Bulletin of the New Zealand Society
for Earthquake Eng., Vol. 36. No. 3, 165-188.,
(2003).
[5] Kam, W. Y., Pampanin, S., Dhakal, R. P.,
Gavin, H., and Roeder, C. W., “Seismic
performance of reinforced concrete buildings in
the September 2010 Darfield (Canterbury)
earthquakes” Bulletin of New Zealand Society
of Earthquake Eng., Vol. 43. No. 4, 340-350.,
(2010b).
[6] Kam, W. Y., Pampanin, S., and Elwood, K.,
“Seismic performance of reinforced concrete
buildings in the 22 February 2011 Christchurch
(Lyttelton) earthquake” Bulletin of the New
Zealand Society for Earthquake Eng., Vol. 43.
No. 4, 239-278., (2011).
[7] Popov,P. E., and Bertero, V. V.,“Repaired RC
members under cyclic loading” Earthquake
engineering and structural dynamics., Vol.4. No.
2, 129-144., (1975).
[8] Corazao M., and Durrani A. J., “Repair and
Strengthening of Beam-to-Column Connections
Subjected to Earthquake Loading” Technical
Report, NCEER-89-0013, State University of
New York, Buffalo, (1989).
[9] Hamburger, R. O., and Moehle, J.P., “State of
Performance Based-Engineering in the United
State” Proceedings of the Second US-Japan
Workshop on Performance-Based Design
Methodology for Reinforced Concrete Building
Structures” Sapporo, Japan, (2000).
[10] Lehman, E. D., Gookin, E. S., Nacamuli, M. A.,
Moehle, P. J., “Repair of Earthquake-Damaged
Bridge Columns” ACI Structural Journal., Vol.
98. No. 2: 233-242., (2001).

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Cyclic Response of Reinforced Concrete Moment Resisting Beams Repaired with Epoxy Injection

  • 1. Muhammad Rashid* Int. Journal of Engineering Research and Application www.ijera.com ISSN : 2248-9622, Vol. 6, Issue 9,(Part-5) September.2016, pp.54-57 www.ijera.com 54 | P a g e Cyclic Response of Reinforced Concrete Moment Resisting Beams Repaired with Epoxy Injection Muhammad Rashid* *(Department of Civil Engineering, University of Engineering & Technology Peshawar, KPK, Pakistan) ABSTRACT This paper presents the results of a quasi-static cyclic test carried out on a reinforced concrete special moment resisting beam to study the efficiency of traditional repair techniques in restoring the strength and stiffness capacity of damaged RC beams. The beam was tested in a cantilever mode and was subjected to a standard loading protocol with increasing amplitude of displacement cycles. The final damage state of the beam consisted of severe cracking and spalling of the cover concrete. The cracks were repaired with low-viscosity injection epoxy and the spalled concrete was repaired with early-strength grout. The repaired specimen was subjected to the same loading protocol as the original specimen to study the efficiency of the repair technique employed. It was observed that epoxy injection is not effective in restoring the strength and stiffness of beams with bar slip of longitudinal bars at the support end. Keywords - Bar slip, epoxy injection, reinforced concrete, reparability, strength, stiffness, I. INTRODUCTION Modern seismic design codes [1-3] design buildings with the objective to avoid collapse and save human lives. Structures are designed for seismic forces that are considerably smaller than the design-level forces, and therefore they are prone to damage during large earthquakes [4]. Reinforced concrete special moment resisting frames are designed according to the principles of capacity design; which states that damage should be concentrated at fixed locations in beams, often called plastic hinges. The plastic hinges are located at the ends of beams and should be proportioned and detailed to respond primarily in flexure mode rather than brittle modes of response such as shear. This philosophy forms the basis of almost all the modern seismic design codes [1-3]. However, the subject of reparability of damaged reinforced concrete structures, after being subjected to an earthquake, has been addressed rarely. The performance of reinforced concrete moment resisting frames, designed to modern codes, in the recent earthquake of Christchurch (2011) was satisfactory but raised the issue of reparability of reinforced concrete structural components [5-6]. A large number of damaged reinforced concrete frames had to be demolished due to the lack of sufficient experimental evidence to justify the use of traditional repair techniques in restoring the capacity of damaged reinforced concrete structural elements. This paper addresses the issue of reparability of reinforced concrete structural elements through an experimental program. Since there has been a rampant increase in the construction of reinforced concrete frames around the world (especially Pakistan), therefore, it is considered necessary to bring the issue of reparability of reinforced concrete beams to the knowledge of concerned authorities and structural design engineers. To achieve this task, it was necessary to conduct an experimental program to study the efficiency of repair techniques and highlight the associated problems with different repair techniques. Quasi-static cyclic testing is conducted on a special moment resisting beam to study the efficiency of epoxy injection and grout patching in the restoring the strength and stiffness of a damaged beam. Epoxy injection was chosen to be studied due to its ease of application as in a real structure the repair process is complicated by the presence of floor slab and infill walls. II. LITERATURE REVIEW Popov et al. (1975) tested three full-scale short cantilever reinforced concrete beams and one half-scaled interior beam-column joint representative of third floor framing of a 20 story RC moment resisting frame. Two repair schemes were investigated i.e. repair with a rapidly setting epoxy resin and concrete depending on the damage state of the beam. It was observed that the performance of beams repaired using epoxy resin was satisfactory but exhibited some loss of stiffness due to bond. Additionally, replacing severely damaged concrete using fresh concrete was found to be a satisfactory solution. Corazao and Durrani (1989) carried out a detailed experimental investigation on repair of reinforced concrete sub-assemblages subjected to quasi-static cyclic loading. A total of eleven sub-assemblages were tested, which consisted of five exterior beam-column connections and six two bay frames. Different repair techniques were studied depending on the type and extent of damage. It was found that epoxy injection is suitable for repairing cracks in beams and slabs and its effectiveness in beam- column joints depends on the quality of work. In case of severe damage, such as damage to core concrete, the strength can be effectively restored by replacing the damaged concrete. Reinforcement jacketing and addition of external rolled steel elements were found to be reliable ways of restoring strength and stiffness. III. EXPERIMENTAL WORK The cross sectional dimensions of the beam are 12in. x 18 in. with a length of 96 in. The beam had 3-#8 bars in the top and bottom layer giving a longitudinal reinforcement ratio of 1.26%. The transverse reinforcement was provided according to the confinement requirements of ACI-318 for beams. RESEARCH ARTICLE OPEN ACCESS
  • 2. Muhammad Rashid* Int. Journal of Engineering Research and Application www.ijera.com ISSN : 2248-9622, Vol. 6, Issue 9,(Part-5) September.2016, pp.54-57 www.ijera.com 55 | P a g e Figure 1: Specimen Reinforcement Details III.1 Materials III.1.1 Steel The longitudinal and stirrup reinforcement consisted of ASTM-A615 grade-60 bars. Steel coupons were tested in tension for the #8 and #3 bars to test their yield strengths. The details of tests are given in the Table 1. Table 1: Reinforcement Steel Tensile Test Results S. No Nominal Dia Yield Strength (Psi) Ultimate Strength (Psi) 1 1.000 66140 91846 2 1.000 69837 95056 3 1.000 64612 89985 7 0.375 77939 107313 8 0.375 67006 92291 9 0.375 71171 99639 III.1.2 Concrete Normal weight concrete with a specified strength of 3000 psi was used for all the beams. The concrete mix design ratio used was 1:2.13:3.61 with a water-to-cement ratio of 0.57. Standard cylinders of 12 in. height and 6 in. diameter were tested under compression loading to validate the mix design. The results of compression tests on the cylinders are given below in Table 2. Table 2: Concrete Compression Test Results Specimen ID Age of Concrete (days) Concrete Compressive Strength, fc’ (psi) 28-1 28 3282.22 28-2 28 3204.25 28-3 28 3492.72 IV. SPECIMEN CONSTRUCTION AND SETUP The specimen was cast using plywood formwork and was cured for a total of fourteen days. The beams cantilevered out of an anchorage block which was anchored to the strong floor of the laboratory using bolts Fig. 2. The lateral load was applied at some distance from the free end of the beam using a manual-controlled hydraulic actuator. The actuator was attached to the beam using a hinge assembly to allow the rotation of the actuator Fig. 2. Figure 2: Specimen Construction & Setup V. LOADING HISTORY The loading protocol used consisted of a series of increasing displacement cycles with three cycles per each displacement increment. The control point for the displacement amplitude was the point of application of load by the actuator.
  • 3. Muhammad Rashid* Int. Journal of Engineering Research and Application www.ijera.com ISSN : 2248-9622, Vol. 6, Issue 9,(Part-5) September.2016, pp.54-57 www.ijera.com 56 | P a g e Figure 3: Loading Protocol for Testing VI. TEST RESULTS 6.1 Damage Description and Hysteretic Response The specimen was loaded with an initial displacement of 0.375 in. Full depth flexural crack formed at the northern face of the beam at a distance of 18 in. from the face of the block, whereas a flexural crack at a distance of about 16 in. formed on the southern face. Cracking was not observed on the eastern and western faces at this displacement demand. At displacement amplitude of 0.75 in., no new cracks formed on any face of the beam. With further increase in displacement demand to 1.5 in., new flexural cracks formed at 8 in., 13in. 26 in. and 34 in. from the support on the southern face. A flexure crack formed at northern face at a distance of 27 in., whereas slight diagonal cracking occurred on the western face. A wide distribution of cracks took place during the displacement cycles of 2.5 in., with cracks on the northern and southern faces as high as 54 in. Full depth inclined cracks were observed on the eastern and western faces of the beam which increased in number at displacement demand of 3.5in. Minimal new cracks were observed further till the conclusion of test at 5.5 in. Figure 4: Specimen Damage Patterns Spalling of the concrete cover started on the northern and southern faces at a displacement of 4.5 in., which escalated at final the displacement cycles of 5.5 in exposing the reinforcing bars on the southern face. The specimen could not be displaced further because the maximum stroke of the hydraulic jack was 6 in. The hysteretic response was marked by a strong pinching due to the slip of longitudinal bars. No strength drop was observed in the hysteretic response due to the fact that the specimen was not tested till failure as shown in Fig. 5. VII. REPAIR OF DAMAGES The main objective of conducting this test was to study the reparability of reinforced concrete beams damaged by seismic loading. Since the specimen did not sustain damage beyond spalling of cover concrete, therefore, the repair techniques chosen were epoxy injection into cracks and patching of spalled concrete. The epoxy used was a low viscosity injection epoxy. The patching of spalled concrete was done using non-shrink and early-strength grout. Figure 5: Hysteretic Response Figure 6: Epoxy Injection and Patching of Spalled Concrete
  • 4. Muhammad Rashid* Int. Journal of Engineering Research and Application www.ijera.com ISSN : 2248-9622, Vol. 6, Issue 9,(Part-5) September.2016, pp.54-57 www.ijera.com 57 | P a g e VIII. DAMAGE DESCRIPTION AND HYSTERETIC RESPONSE The response of the repaired specimen was unsatisfactory. The beam showed a considerable drop in the strength and a severe pinched hysteretic response due to loss of stiffness Fig. 7. Figure 7: Comparison of Original& Repaired Response of Specimen The reason behind this performance is the fixed end rotation at the interface between the beam and the anchorage block. The interface opening was injected with epoxy but based on the results it can be said that the merely filling the interface opening with epoxy will not restore the original stiffness of the beams which will render the beam unable to achieve its original strength. The efficiency of the epoxy injection in treating the cracks could not be studied due to the fact that the beams did not sustain the original loads which caused those cracks. IX. CONCLUSIONS i. The damage of the test specimen consisted of cracking, spalling and fixed-end rotation due to slip and inelastic extension of longitudinal bars. The cracks of the plastic hinge region and the interface crack (due to fixed-end rotation) were both injected with low viscosity epoxy to restore the capacity of the beam. It was, however, observed that the strength and stiffness of the beam were not regained because epoxy did not restore the bond between concrete and steel. ii. Therefore, it is concluded that the repair of reinforced concrete beams, with fixed-end rotation, will be ineffective by mere filling of interface crack with epoxy. The significant loss of strength and stiffness due to fixed-end rotation also renders the repair of the rest of the damaged beam useless. X. RECOMMENDATIONS i. The effectiveness of other repair techniques in restoring strength and stiffness of beams should be studied experimentally. In this regard, special attention should be paid to the ease of application of a repair technique as the use of reinforcement jacketing, fibre reinforced polymer sheets or steel plates are complicated by the presence of floor slab and infill walls. REFERENCES [1] ACI. 318. Building Code Requirements for Structural Concrete, American Concrete Institute, (2002). [2] NZS 3101:2006 Concrete structures standard, Standards New Zealand, Wellington, NZ. [3] Eurocode 8: Design of structures for earthquake resistance. [4] Park, B., “Some controversial aspects of the seismic design of reinforced concrete building structures”Bulletin of the New Zealand Society for Earthquake Eng., Vol. 36. No. 3, 165-188., (2003). [5] Kam, W. Y., Pampanin, S., Dhakal, R. P., Gavin, H., and Roeder, C. W., “Seismic performance of reinforced concrete buildings in the September 2010 Darfield (Canterbury) earthquakes” Bulletin of New Zealand Society of Earthquake Eng., Vol. 43. No. 4, 340-350., (2010b). [6] Kam, W. Y., Pampanin, S., and Elwood, K., “Seismic performance of reinforced concrete buildings in the 22 February 2011 Christchurch (Lyttelton) earthquake” Bulletin of the New Zealand Society for Earthquake Eng., Vol. 43. No. 4, 239-278., (2011). [7] Popov,P. E., and Bertero, V. V.,“Repaired RC members under cyclic loading” Earthquake engineering and structural dynamics., Vol.4. No. 2, 129-144., (1975). [8] Corazao M., and Durrani A. J., “Repair and Strengthening of Beam-to-Column Connections Subjected to Earthquake Loading” Technical Report, NCEER-89-0013, State University of New York, Buffalo, (1989). [9] Hamburger, R. O., and Moehle, J.P., “State of Performance Based-Engineering in the United State” Proceedings of the Second US-Japan Workshop on Performance-Based Design Methodology for Reinforced Concrete Building Structures” Sapporo, Japan, (2000). [10] Lehman, E. D., Gookin, E. S., Nacamuli, M. A., Moehle, P. J., “Repair of Earthquake-Damaged Bridge Columns” ACI Structural Journal., Vol. 98. No. 2: 233-242., (2001).