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The Institution of Engineers,
Malaysia
Universiti
Teknologi MARAUniversiti Malaya
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Ultimate Strength and Deformation of Concrete Members
Strengthened by Jacketing with Various Materials
UEDA Tamon
Hokkaido University
Abstract
This paper presents the generic model to predict ultimate strength and deformation of
concrete members with and without jacketing by various materials. The generic
model consists of flexural strength and deformation model and shear strength and
deformation model, which interact each other. The model can predict the post-peak
behavior including fracture of strengthening material. The model clearly indicates the
advantage of material with large fracture strain and no yielding as shear reinforcement.
1. Introduction
Jacketing is the most popular method for strengthening of existing concrete structures,
especially for seismic strengthening. Jacketing does not require much additional space, so
that the functions of existing structures would not be disturbed after being strengthened.
When appropriate material is chosen for jacketing, disturbance during execution can be
minimized.
Jacketing is a type of strengthening, in which strengthening material is externally bonded to
existing structures, however debonding, as an ultimate state, is not a main issue like other
external bonding methods. The important parameter then is the stiffness of jacketing material
at the ultimate state; either peak load or ultimate deformation. In the case of steel jacketing
and concrete jacketing with steel reinforcement, the post-yielding stiffness at the ultimate state
needs to be known. For FRP sheet jacketing, the tension fracture of FRP sheet often causes
the ultimate state because the stiffness of FRP sheet suddenly drops after its fracture.
Therefore, it is necessary to predict the strainof jacketing material at the ultimate state.
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In this paper the generic model to predict load-deformation relationship including post-peak
region is introduced. This model consists of shear and flexure strength model as well as shear
and flexure deformation model. The shear strength model is developed with the concept of
potential shear strength, which is a function of stiffness of shear and tension reinforcement,
including jacketing material, and concrete strength. The shear deformation model is derived
from the truss mechanism. The flexure model is a fiber model with consideration of
confinement effect of shear reinforcement on concrete. The feature of the generic model is
also found in consideration of interaction between shear and flexure model, such as reduction
in neutral axis depth by shear cracking and increase in flexure deformation due to tension shift
induced by truss mechanism. The model can predict the experimental data of cases with
concrete, steel and FRP jacketing.
The paper also emphasizes on advantages of fiber materials for FRP sheet, whose fracturing
strain is large, and which is a natural fiber as green technology. The generic model can
predict the ultimate points of jacketing with large-fracturing strain FRP and natural fiber
reinforced polymers.
2. Generic Model for Load-Deformation Relationship (Jirawattanasomkul, et al 2013)
2.1 Flexural strength and deformation model
To calculate the flexural strength, a section analysis is performed by dividing the section area
into a number of discrete strips, and it is assumed that plane sections remain planes at any
loading level. In this analysis, the increments in strain for the compression at the top fiber are
fixed, and the strain across the depth of the cross-section is assumed to be proportional to the
distance from the neutral axis, as shown in Figure 1.
In the flexural strength model, the enhancement of the flexural strength is a consequence of the
confined concrete stress-strain relationship. Figure 2 shows the concept of the confinement
effect. For a given flexural cross section, Eq. (1) and Eq. (2) give the force and moment
equilibrium conditions, respectively. The corresponding shear force, Vmu, is obtained using Eq.
(3).
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Figure 1 Section analysis
Figure 2 Confinement effects by reinforcement
1 1
n mP A Aci ci sj sj
i j
(1)
1 1
n mM A d A dci ci i sj sj j
i j
(2)
/V M amu (3)
where ciand sjis stress in ithconcrete layer andj
thlongitudinal reinforcement, respectively, di
and dj is distance from top fiber to the centroid of ith concrete layer and j
th steel layer,
respectively, Aci andAsjis area of i
th
concrete layer andj
th
longitudinal reinforcement, Pis axialforce (N), M is moment at the considered cross section (N-mm), ais shear span (mm), and i, j
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= 1,2,3nor m.
As expressed in Figure 1, the strain compatibility equations of the ith concrete and the j
th
longitudinal reinforcement are given by the following equations:
di
ci ct cc ct h
(4)
h dj
sj ct cc ct h
(5)
From the section analysis, the secant modulus of material (Ese, Eje, Ewe, Ece), the effective
strength of concrete (f'ce), strain at the extreme fiber (cc) and neutral axis depth (x) can be
obtained. These values are applied in the shear strength model. However, the neutral axis
depth used in the flexural strength model is not the same as that used in the shear strength
model (Figure 4) because of the shear crack opening. In fact the neutral axis depth is
calculated by Eq. (12), meaning that the assumption of the plane-sections-remains-plane cannot
be applied.
Flexural deformation is calculated by doubly integrating strain obtained by the section analysis.
The tension shift, which is explained by the truss mechanism (see Figure 3 and the section of
Shear strength and deformation model) and causes increase in strain of tension
reinforcement, increases flexural deformation.
Figure 3 Tension shift
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2.2
Shear strength and deformation model
The main limitation of the section analysis is that the effect of the shear strength behavior,
shear crack opening and reduction of the neutral axis depth, on the flexural strength is not taken
into account. The post-peak region of the load-deformation response is dominated by the
shear strength behavior. To account for this, a truss mechanism approach proposed by Sato, et
al (1994, 1996, 1997) is combined with the section analysis to predict the shear strength more
precisely.
Figure 4 illustrates the concept of the shear strength model based on the truss mechanism.
Previous experimental observations by Sato, et al (1994, 1996, 1997) showed that the shear
strength of RC columns depends significantly on the secant stiffness of the flexural and shear
reinforcements. As explained previously, the secant stiffness is obtained from the stress-strain
relationships of materials, which satisfy the compatibility and equilibrium conditions in the
flexural strength model. The shear strength capacity continuously decreases after the yielding
of the shear reinforcement, because the shear reinforcement contribution shows no further
increase. In the generic model, the shear strength model is developed after modifying the
original model by Sato, et al (1994, 1996, 1997).
Figure 4 Shear strength model by Sato, et al (1997)
The total shear strength can be expressed as a sum of the contribution of the concrete (Vc) and
the shear reinforcement (Vs+j), as shown in Eq. (6). This shear reinforcement consists of
contribution from steel shear reinforcement and jacket.
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stress. Their formula (Sato, et al 1997) indicated that the concrete compression depth (xe) is
related to the initial neutral axis depth obtained from the section analysis (xi). Anggawidjaja, et al
(2009) modified formula proposed by Sato et al. by including the influence of fiber
reinforcement on the neutral axis depth as shown in the following equation:
0.4
0.70.420.08
1000
0.12
11 1.25
1 3.2
s se
w we f fe
a Ed
e n
E Ei cc
x ee
x f
(12)
Shear deformation becomes significant after shear cracking and is obtained by the truss
mechanism approach as shown in Figure 5 (Ueda, et al 2004). The original shear deformation
model is expanded for post-yielding range of tension and shear reinforcement. The angle of
diagonal compression strut, varies as the shear deformation evolves and its expression is
obtained based on the experimental results.
Figure 5 Truss analogy for shear deformation
2.3
Verification
Steel jacketing is a more common retrofit technique than concrete jacketing. Aboutaha, et al
(1999) proved that steel jacketing shows several advantages: a smaller increase in the
cross-sectional dimensions, ease and speed of construction, lower cost of structural intervention
and interruption of use, and a smaller increase in additional stiffness to the retrofitted column.
Figure 6 demonstrates the load-deformation responses from the experiment carried out by
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3. Advantages with Large Fracture Strain Materials
The sudden breakage of FRP as reinforcement is a drawback. It indicates that the greater
fracturing strain of material is preferable to achieve better member strength. For members
subjected to high seismic effects, plastic deformation becomes quite high in so called plastic
hinge zone, meaning that material would be subjected to quite high strain. High fracturing
strain can be achieved by only material with high fracturing strain but not material with low
fracturing strain.
According to the generic model proposedby the authors group (Jirawattanasomkul et al 2013),
shear strength of reinforced concrete members depend on stiffness of both tension and shear
reinforcement. The higher the stiffness of tension and shear reinforcement is, the higher the
concrete contribution is. The higher the stiffness of shear reinforcement is, the higher the
shear reinforcement contribution is. The post-peak behavior of concrete members can be
explained as the decrease in potential shear strength (or remaining shear strength) with the
decrease in stiffness of tension and shear reinforcement (see Figure 7). Generally the less
amount of shear reinforcement gives earlier reduction in shear reinforcement stiffness, thus the
post-peak region comes earlier.
(c) Specimen SP3 (d) Specimen SP4
Figure 7 Load-deformation relations (Anggawiddjaja et al 2006)
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Figure 9 Enhancement of shear strength and ultimate deformation by PET jacketing
Figure 10 PET jacket without fracture in hinge zone
4. Concluding Remarks
The generic model for prediction of ultimate strength and deformation of concrete members is
presented. This model has the following features:
(1) It consists of flexural strength and deformation models and shear strength and deformation
models, which interact each other.
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(2) It can predict the post-peak behavior as the reduction in potential shear strength. The
reduction in the shear strength is caused by reduction in stiffness of tension and shear
reinforcement.
(3) It can be applied to any strengthening materials and predict the fracture of reinforcement at
the ultimate state.
(4) It clearly indicates the advantage of strengthening materials with large fracture strain and
no yielding as shear reinforcement (jacket).
5. Acknowledgment
The author is grateful to all the members of the study team on generic model, especially Dr
SATO Yasuhiko, Dr DAI Jian-Guo, Dr ZHANG Da-Wei, Dr Tidarut
JIRAWATTANASOMKUL, Mr Dhannyanto ANGGAWIDJAJA, Mr SENDA Mineo and Mr
NAKAI Hiroshi.
6. References
Aboutaha, R S, Engelhardt, M D, Jirsa, J O and Kreger, M E. Rehabilitation of shear critical
concrete columns by use of rectangular steel jackets. ACI Structural Journal. 96(1), 1999:
68-78.
Anggawidjaja, D., Ueda, T., Dai, J., and Nakai, H. (2006). Deformation capacity of RC piers
wrapped by new fiber-reinforced polymer with large fracture strain. Cement and Concrete
Composites, 28(10), 2006: 914-927.
Anggawidjaja, D., and Ueda, T. PET, high fracturing strain fiber, for concrete structure
retrofitting: shear force and deformation enhancement: experiments, analysis and model. VDM
Verlag Dr. Mller, Germany; 2009: 1-64.
Jirawattanasomkul, T, Zhang, D W, and Ueda, T. Prediction of the post-peak behavior of
reinforced concrete columns with and without FRP-jacketing. Engineering Structures, 56,
2013: 1511-1526.
Sato Y, Ueda T, Kakuta Y. Shear resisting model of reinforced and prestressed concrete beams
based on finite element analysis.Bulletin of the Faculty of Engineering, Hokkaido University.
No 171. 1994:1-17.
Sato Y, Ueda T, Kakuta Y. Shear strength of prestressed concrete beams with FRP tendon.
Concrete Library of JSCE. 27, 1996: 189-208.
Sato Y, Ueda T, Kakuta Y. Shear strength of reinforced and prestressed concrete beams with
shear reinforcement. Concrete Library International of JSCE. 29, 1997: 233-47.
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8/10/2019 4. Ultimate Strength and Deformation of Concrete Members Strengthened by Jacketing With Various Materials
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Ueda, T, Sato, Y, Ito, T and Nishizono, K. Shear deformation of reinforced concrete beam.
Concrete Library International. JSCE. 43, 2004: 9-23.
Ueda, T. Structural performance of members strengthened by FRP jacketing with high
fracturing strain Proc. of the Second Asia-Pacific Conference on FRP in Structures (APFIS),
International Institute for FRP in Construction (IIFC), Seoul, Korea, 2009: 19-28.