International Journal of Civil Engineering and Technology (IJCIET)
Volume 10, Issue 03, March 2019, pp. 336–348, Article ID: IJCIET_10_03_035
Available online at http://www.iaeme.com/ijmet/issues.asp?JType=IJCIET&VType=10&IType=3
ISSN Print: 0976-6308 and ISSN Online: 0976-6316
© IAEME Publication
Scopus Indexed
NUMERICAL INVESTIGATION ON THE
PUNCHING BEHAVIOR OF RC FLAT SLABS
STRENGTHENING BY TRM AND FRP
Majid H. Abdulhussein, Dr. Muhammad J. Kadhim
Department of Civil Engineering, Babylon University, College of Engineering, Babylon, Iraq
ABSTRACT
In this paper, the effectiveness of textile-reinforced mortar (TRM) and fiberreinforced polymer (FRP), as a means of improving the punching behavior of
reinforced concrete flat slabs were numerically investigated. Finite element (FE)
model using ABAQUS computer program was developed to analyze eight half-scaled
slabs, in terms of load-carrying capacity, ductility, stiffness, and crack patterns. These
eight specimens were divided into two groups (G1 and G2) with four specimens for
each of them. Specimens of G1 was similar to that of G2 in all details but differ in the
eccentricity of the applied load. Specimens of G1 were tested with concentric load,
while these of G2 were tested with 150 mm eccentricity. For each group, one specimen
was built as control (unstrengthened), one was strengthened by FRP-sheet, and the
other two was strengthened by TRM-jacket with two different mesh opening (10 and
20 mm). The results obtained from FE analysis showed that the efficiency of TRM in
increasing the punching shear capacity of strengthened slabs was less than that of
FRP. In addition, the slabs strengthened by TRM showed stiffer behavior than that
strengthened by FRP, but lesser ductile. TRM effectiveness was sensitive to the mesh
size of the textile. When the mesh size decreased, stiffness was increased and ductility
was decreased.
Key words: flat slab, punching sheer, stiffness, ductility, TRM, FRP.
Cite this Article: Majid H. Abdulhussein, Dr. Muhammad J. Kadhim, Numerical
Investigation on the Punching Behavior of RC Flat Slabs Strengthening by TRM and
FRP, International Journal of Civil Engineering and Technology 10(3), 2019, pp.
336–348.
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1. INTRODUCTION
The flat plate is a two-way framing systems composed of uniform slabs supported directly by
columns without drop panels or capitals. This type of system has many applications in the
construction industry due to many advantages that it offers, which include the simplified
formwork, fast construction, reduction of story heights and architectural flexibility. Park and
Gamble (2000) [1] indicated that for each ten stores in a structure, an additional store may be
added automatically for the same overall height in the flat plate systems, as compared to the
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Numerical Investigation on the Punching Behavior of RC Flat Slabs Strengthening by TRM and FRP
other systems having the same height. Despite of these benefits, there are many drawbacks
with using of this system. The important one is punching shear failure at the slab columnconnection that is caused by shear transferring and the supporting column moments. In nature,
punching shear failure is brittle and maybe leads to building progressive collapse. In general,
two types of punching can be distinguished: symmetrical punching and non-symmetrical. It
can be said that the punching is symmetrical if the geometry, the load, the bearing conditions,
and the composition of the structural element (concrete and reinforcement) can be considered
symmetrical with respect to the two axes of symmetry. If one of these conditions is missing, it
will be possible to enter the term of non-symmetrical punching. In this case, it is still possible
to distinguish between two different types: non-symmetrical punching without eccentricity
and non-symmetrical punching with eccentricity. The difference between these two types is
that, in case of eccentric punching, the conditions of non-symmetry lead to generate a bending
moment transfers from the slab to the column, and that what called by the unbalanced
moment [2]. The phenomenon of transmission of the moment between the slab and the
column is one of the main problems of the study of eccentric punching.
Existing reinforced concrete (RC) slabs have usually been designed without shear
reinforcement. Previous design codes have made possible to assume that the shear capacity of
regular reinforced concrete was sufficient. Punching strength in slabs can become insufficient
due to several reasons such as changes of building usage and loading, need of installing new
services that requires openings in the slabs, and in the relevant updated design codes [3]. Over
the past decade, a number of research has dealt with various strengthening techniques for RC
flat slabs in order to increase the punching shear capacity. These include enlarging the
supporting area by adding concrete capitals or steel collars at the connection zone [4], [5],
introducing post-installed shear reinforcement around columns [6], using of post-installed
prestressed members [7], and more recently applying FRP sheets to the tension face [8], [9].
Some of these methods provides an enough additional strength to the slabs; however, they are
elaborate, difficult to install, expensive and aesthetically not pleasing. Strengthening slabs
with FRPs is simple, does not require excessive labor or equipment, and does not change the
appearance of the slab. However, the FRP strengthening technique has a few disadvantages
mainly associated with the use of epoxy resins, namely high cost, poor performance in high
temperatures, inability to apply on wet surfaces, as discussed by Triantafillou et al. (2018)
[10].
One possible solution to the above problems would be the replacement of organic with
inorganic binders, e.g. cement-based mortars, leading to the replacement of FRP with textilereinforced mortar (TRM) [11]. A TRM is a composite comprises high-strength fibers made of
carbon, basalt or glass in form of textiles embedded into inorganic materials such as cementbased mortars. The textiles typically consist of fiber rovings woven or stitched at least in two
orthogonal directions, thus creating an open-mesh geometry. TRM is a relatively low cost
strengthening material, friendly for manual workers and compatible to concrete or masonry
substrates material, whereas can be applied on wet surfaces or at low temperatures. The same
material can also be found in the literature as FRCM. Significant research effort has been put
in the last decade to use TRM system as strengthening materials for reinforced concrete (RC)
members [12]–[14]. Few research studies have been reported in the technical literature on
using TRM to strengthen a flat slab against punching shear failure [15], [16]. To the author
knowledge, the effect of applying TRM jackets on the punching shear behavior of the RC flat
slabs subjected to combined action of shear force and unbalanced moment were not
investigated in the literature. In this paper, a nonlinear finite element analysis using ABAQUS
program (2016) was conducted to investigate the effect of using TRM composite system on
the punching behavior of flat slabs in terms of load carrying capacity, stiffness, ductility, and
crack patterns thereby compared that with the effect of using CFRP system. The parameter
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investigated in the numerical analysis are the eccentricity of the load (zero and 150 mm), type
of external strengthening (CFRP and TRM), and mesh opening of the carbon fiber textile (10
and 20 mm).
2. CONSTRUCTION AND VERIFICATION OF FINITE ELEMENT
MODEL
2.1. Experimental specimens and investigated parameters
Three slab specimens test by Abdulhussein (2018) [17] were selected to simulate the finite
element model. The slab’s dimensions of 1200 × 1200 × 100 mm represent models on the
scale of 1/2 with respect to a real multi-story building, taking into consideration the
supporting clearness, Fig. 1. The tested specimen represented the zone of negative moments
enclosed by the lines of contra-flexure around an interior column. In addition, a 150 × 150
mm central column stub was extended from the compression faces of the slab and a
rectangular bracket was connected to the top of the column in order to simulate the
unbalanced moment. The perimeter of the slab was simply-supported on 25 mm diameter
steel rods fixed on the upper rectangular steel base of a rigid steel frame. All test specimens,
which have same dimensions, were reinforced with a flexural reinforcement ratio 2.24% in
one orthogonal gathered set on the tension side. one of the three slabs (S1-e75-CFRP) was
strengthened by adding a (1000×1000 mm) unidirectional carbon fiber sheet (CFRP) to the
tension face of the slab as explain in Fig. 2 a. whereas the other two slabs S3-e75-TRM1 and
S4-e75-TRM2 were strengthened by using textile-reinforced mortar (TRM) with two different
mesh openings 10 and 20 mm, respectively, as shown in Fig. 2 b, c. All the three slabs were
tested under an eccentricity equal to half-length of the column side (75 mm).
A comparison between the simulation and the testing results was made and Based on the
validity of the numerical model, the numerical investigation was extended to analyzed the
three specimens under concentric and high-eccentric loading (i.e., under an eccentricity equal
to zero and to the column dimension, 150 mm). The analyzed specimens were also divided
into two groups, namely G1 and G2 based on eccentricity amount 0 and 150 mm,
respectively. Each group compares three strengthened specimens and one control specimen
(unstrengthened) as presented in Table 1.
(b) Section A-A
(a) Top view
Figure 1 Geometry of specimen and typecal reinforement(dimension in mm).
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Numerical Investigation on the Punching Behavior of RC Flat Slabs Strengthening by TRM and FRP
(a) Specimen (S1-e75-CFRP)
(b) Specimen (S3-e75-TRM1)
(c) specimen (S4-e75-TRM2)
Figure 2 Details and configrations of CFRP and TRM strengthening systems (dimensions in mm).
Table 1 Details of invesitgated specimens.
Eccentricity
Specimen
Strengthening systems
Descriptiona
mm
S2-e00-XX
Control specimen (unstrengthened)
S1-e00-CFRP
CFRP-sheet + epoxy risen.
G1
0
b
S3-e00-TRM1
Carbon fiber textile + two layers of cement mortar.
c
S4-e00-TRM2
Carbon fiber textile + two layers of cement mortar.
S5-e150-XX
Control specimen (unstrengthened)
S1-e150-CFRP
CFRP-sheet + epoxy risen.
G2
S3-e150-TRM1
150
Carbon fiber textile + two layers of cement mortar.
S4-e150-TRM2
Carbon fiber textile + two layers of cement mortar.
a) Specimen description composed of three parts: the first represent slab number, the second is a number stands
for the load eccentricity, and the third is a character symbolizes for the strengthening type, characters “XX”
was used when there were no strengthening provided. b and c) the numbers 1 and 2 referred to the mesh size of
the textile, which equal to 10 mm and 20 mm, respectively.
Group
No.
2.2. Finite element modeling
In this paper, a three-dimensional nonlinear finite element analysis has been carried out to
simulate the punching behavior of RC flat slabs by using a powerful nonlinear finite element
package ABAQUS/Standard 2016.The geometry, applied load, and boundary condition were
simulated to be similar to that in experimental work. The modeling including element types,
mesh details, and interactions will be presented in this section.
2.2.1. Mesh details
Selection of mesh size is an important step in finite element modeling. Before the analysis is
started, an adequate pre-analysis of different mesh densities to determine the best density that
giving the required accuracy according to the level of analysis complexity. Therefore, a
convergence analysis was made on the FE model to get the appropriate mesh size. It can be
observed that the change in the results can be ignored when the mesh size decreased from 30
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to 20 mm and the FE results become more accurate with experimental ones, therefore, 25 mm
mesh size was selected for the analysis.
2.2.2. Material modeling, element types, and contraction
In general, five parts were involved in the modeling of the specimens. These five parts were
concrete slab, concrete column, flexural reinforcement of the slabs, reinforcing bars of the
column, and bearing plate. These parts were drawn separately and then assembled and merged
to form the modeling specimens. Fig. 3 explains the assembly of these five parts.
Flexural
Concrete
column
Column
Bearing plate
reinforcemen
reinforcemen
Concrete
slab
Figure 3 The assembled parts of FE model.
Concrete material
ABAQUS offers different constitutive models to analyze concrete structures. In this paper, the
concrete damaged plasticity (CDP) is chosen for the punching shear simulations. The concrete
damaged plasticity model is based on the scalar isotropic damage assumption considering the
stiffness degradation in both compression and tension [18], [19]. Tensile cracking and
compressive crushing of concrete are assumed as two main failure mechanisms in this model.
The nonlinear behavior of the concrete material is represented by an equivalent uniaxial
stress-strain response. Concrete in tension can be characterized by stress-crack displacement
response instead of a stress-strain relationship due to its brittle behavior, Fig.4 a. In this study,
bilinear stiffening response is used and calculated according to Genikomsou (2016) [18].
While the uniaxial stress-strain response of concrete in compression is elastic until the initial
yield is reached, Fig.4 b. To define the stress-strain curve of concrete, the model of Collins
and Mitchell (1997) [20] were used after converting the nominal strain to inelastic strain.
The concrete of the slab and the column was meshed into solid brick elements to achieve
suitable stress distribution in the 3D Finite element analysis. There are several forms of solid
brick elements available in ABAQUS. In this study, Linear Hexahedral elements with reduced
integration (C3D8R) have been selected.
Steel materials
The required input parameters for material definition of steel materials, includes density,
elastic and plastic behavior. Elastic behavior of steel material is defined by specifying
Young’s modulus (Es) and Poisson’s ratio () of which typical values are 200 GPa and 0.3,
respectively. Plastic behavior is defined in a tabular form, included yield stress and
corresponding plastic strain. According to Hibbit et al. (2011) [21], true stress and logarithmic
strain should be defined, so input values of stress in each point for an isotropic material are
calculated according to that. yielding strength of the flexural reinforced is listed in Table 2.
In this simulation, the steel reinforcement for the slab and column was divided into Linear
Truss element (T3D2). While the bearing plate was divided into Linear Hexahedral elements
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Numerical Investigation on the Punching Behavior of RC Flat Slabs Strengthening by TRM and FRP
with reduced integration (C3D8R). Steel reinforcement was linked by embedded region
constrain to the surrounding concrete.
TRM-jacket
TRM was represented by a linear truss element (T3D2), for the textile, embedded into a solid
brick element for mortar (i.e. Linear Hexahedral elements with reduced integration (C3D8R)
have been selected to simulate the mortar matrix). To model the textile, an equivalent
diameter for the textile was calculated and a circular profile was assumed. A perfect bond was
assumed not only between the textile and the surrounding mortar but also between TRM
composite system and concrete substrate. The properties of the textile and the mortar, based
on the manufacturer’s product data sheet, were presented in Table 2. The constitutive model
used to simulate mortar was adopted from Awani (2015) [22].
CFRP-sheet
A unidirectional CFRP lamina can usually be treated as an orthotropic material whose
mechanical properties in the fiber direction are different from those in the other two
orthogonal directions. That is, the elastic modulus, shear modulus and Poisson’s ratios are
different in different directions. the FRP lamina is modeled as plane stress element, and the
mechanical properties of the FRP lamina can be obtained from the two constituents (i.e.,
fibers and epoxy) and their volume fractions based on the mechanics of materials approach
[23] are calculated and listed in Table 3.
A bilinear cohesive model available in ABAQUS is a best select for modelling the
interface behavior between CFRP lamina and concrete surface, as shown in Fig. 4 b. The
cohesive model defines surfaces of separation and prescribes their interaction by describing a
proportional displacement at each contact point. The definition of the model is characterized
by the parameters, initial stiffness, shear strength, fracture energy and curve shape of the bond
slip model. These parameters as a function of the adhesive and concrete properties are
determined according to Obaidat (2011) [24].
.
(a) Bilinear cohesive model [24]
(a) Bilinear tension softening [18]
Figure 4 Bilnear tension softening and cohesive model used in this study.
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Table 2 Properties of Materials used in this study
Parameter
Concrete
Average compressive strength (MPa)
Average modulus of rapture (MPa)
Mortar*
Compressive strength (MPa)
Tensile strength (MPa)
Property
Parameter
Carbon fiber textile*
42.38
Tensile strength of fibers (GPa)
7.38
Elastic modulus of fibers (GPa)
Equivalent dry fiber thickness (mm)
70
Width per one textile (mm)
6.0
Fracture strain (%)
Steel
Yield strength of flexural reinforcement (MPa)
* As provided by manufacture.
Property
4.9
230
0.4
4.0
2.0
461
Table 3 Properties of CFRP laminate used in this study.
Composite
CFRP
Longitudinal
Young’s
modulus
E1
(MPa)
77,560
Transverse
Young’s
modulus
E2
(MPa)
6,600
Major
Poisson's
Ratio
V12
--0.267
Tensile
strength
Shear
modulus
G12
Thickness of
lamina
(MPa)
3,500
(MPa)
2,540
(mm)
1
3. RESULTS AND DISCUSSION
As previously mentioned, three half-scale specimens were used for calibrating a 3D nonlinear
finite element model. These specimens were strengthened with two different system (CFRP
and TRM) and tested experimentally under an eccentricity equal to half of the column side
(75 mm). A comparison between the simulation and the testing results showed good validity
of the numerical analysis where the punching load of the analyzed models are more than the
experimental values by a difference less than 2.91%. Fig. 5 depict the experimental and
numerical curve for the three slabs. Based on that, the constructed FE model used to conduct a
numerical study on the punching behavior of these strengthened specimens with concentric
and high-eccentric load (i.e. with 0 and 150 mm eccentricity). The concentrically loaded
specimens named as G1 and eccentrically loaded specimens named as G2, as explained in
Table 1. In addition, one unstrengthened specimen was built as control for each group. The
output data that have been extracted from the analysis are the load-carrying capacity and
central deflection, which are directly obtained from the ABAQUS simulation. The summary
of the results are given in Table 4.
Table 4 Numerical results.
Group No.
G1
G2
Specimens
Symbol
S1-e00-CFRP
S3-e00-TRM1
S4-e00-TRM2
S2-e00-XX
S1-e150-CFRP
S3-e150-TRM1
S4-e150-TRM2
S5-e150-XX
Ultimate
Load
Ultimate
Deflection
KN
362.14
335.24
306.56
259.29
216.45
206.63
186.88
155.84
mm
12.82
8.11
8.49
10.08
11.92
5.62
5.78
8.72
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Energy
Absorption
Index
--3.85
2.95
2.71
3.27
3.15
1.84
1.52
2.84
Uncracked
Stiffness
Cracked
Stiffness
Loss in
Stiffness
KN/mm
62.33
89.88
67.52
45.74
35.02
47.39
41.07
31.13
KN/mm
36.37
66.59
52.97
28.03
21.86
36.90
32.00
20.23
%
58
74
78
61
62
78
78
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Numerical Investigation on the Punching Behavior of RC Flat Slabs Strengthening by TRM and FRP
S1-e75-CFRP
250
Experimental
Numerical
200
200
150
150
100
100
50
50
0
0
2
4
6
8
10
12
0
14 0
250
Experimental
Numerical
Punching Load (KN)
Punching Load (KN)
250
S4-e75-TRM2
S3-e75-TRM1
Experimental
Numerical
200
150
100
50
0
2
Central Deflection (mm)
4
6
8
10
Central Deflection (mm)
12
0
2
4
6
8
10
12
Central Deflection (mm)
Figure 5 Comparison between the experimental and numerical load-deflection curves.
3.1. Load-deflection curves
Concentrically loaded specimens
Evaluate the efficiency of using CFRP and TRM strengthening techniques on punching shear
behavior under concentric loading. In comparison with the control specimen (S2-e00-XX), the
analytical results showed that strengthening of slabs by installing CFRP-sheet on the tension
face of the slab reduced the deflection at the failure load of control specimen by 24.70%.
Whereas the load carrying capacity and the ultimate deflection increased by 39.67% and
27.18%, respectively. The slab strengthening with TRM1 showed a reduction in the ultimate
deflection and deflection at the failure load of control specimen by 19.54 and 58.83%,
respectively. However, the ultimate punching capacity improved by 29.29% in compare with
the control specimen. Appling TRM2 as an external strengthening system decreased the
ultimate deflection and deflection at the failure load of control specimen by 15.77 and
47.32%, respectively. Whereas the ultimate punching strength improved by 18.28% in
compare to the control slab. Fig. 6 shows the variety of the load-deflection curves for the
three specimens and the reference one.
From the above mention, the efficiency of using TRM strengthening system in increasing
the punching shear capacity of strengthened slabs was less than that of CFRP system.
However, TRM efficiency was sensitive to the mesh size of the carbon fiber textile. It was
found that using of carbon fiber textile with mesh size 20 and 10 mm increased the punching
capacity by 18.28 and 29.29%, respectively as compared with control specimen.
Eccentrically loaded specimens
Examining the efficiency of using CFRP and TRM strengthening techniques on punching
shear behavior of flat slabs under high-eccentric loading (i.e. under eccentricity equal to the
column side, 150 mm). It was noted from the analytical results that adding CFRP-sheet on the
tension face of the slab increased the load carrying capacity and the ultimate deflection by
about 38.90% and 36.70%, respectively, as compared with the control specimen (S5-e150XX). On the other hand, installing TRM-jackets on the tension face of the slabs was slightly
affected by the mesh size of the textile. It was observed that using textile with 10 and 20 mm
mesh size resulted in increasing the punching capacity of the specimens by around 38.90 and
32.60%, respectively, and decreasing the ultimate central deflection by about 35.55 and
33.72%, respectively. Fig. 6 presents the load-deflection curves for eccentrically loaded
specimens.
3.2. Stiffness of analyzed slabs
In general, the stiffness can be expressed as the slope of the load-displacement relationship.
Marzouk and Hussein (1991) [25] stated that "For most slabs failing in punching shear, the
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350
350
300
300
Punching Load (KN)
Punching Load (KN)
load deflection curves can be represented by two straight lines with different slopes". initial
stiffness (Uncracked stiffness, Ki) described by the slope of the Load-displacement curve
reaching up to the first change in the slope (first cracking load), while secant stiffness
(cracking stiffness, Ks) defined by the slope of the load-displacement curve extending up to
the first yielding of the flexural reinforcement [26], see Fig 7a. Table 5 elucidates the results
of the initial and secant stiffness. In addition, the percentage of reduction in the stiffness after
cracks initiated also calculated and summarized in this Table.
It can be concluded that using CFRP and TRM as external flexural reinforcement
increased the initial and secant stiffness. Compared to the control specimens, the maximum
increase in the uncracked and cracking stiffness was about 96.49 and 137.56%, respectively,
for concentrically loaded specimens, and about 52.24 and 82.41%, respectively, for
eccentrically loaded specimens. Specimens strengthening with TRM jacket showed a better
improvement in stiffness and that was sensitive to the mesh size of the textile (i.e. stiffness
increased, when the mesh size decreased). The effects of applying external strengthening on
initial and secant stiffness are explained in Fig. 8.
It was observed from Fig.8 that increasing the stiffness in by applying external
strengthening was highly affected by eccentricity amount. For concentrically loaded
specimens, the average increase in the initial and secant stiffness was around 60.13 and
85.42%, respectively. While for eccentrically loaded specimens (i.e., in case of eccentricity
150 mm), the average increase in the initial and secant stiffness in was around 32.23 and
49.56%, respectively. It was shown that the best improvement in the stiffness was by applying
TRM of 10 mm mesh size on the tension face of the slab.
250
200
150
Control:
S2-e00-XX
Specimens of G1:
S1-e00-CFRP
S4-e00-TRM2
S3-e00-TRM1
100
50
250
200
150
Control:
S5-e150-XX
Specimens of G2:
S4-e150-TRM2
S1-e150-CFRP
S3-e150-TRM1
100
50
0
0
0
2
4
6
8
10
12
14
16
0
Central Deflection (mm)
2
4
6
8
10
12
14
16
Central Deflection (mm)
Figure 6 load-deflection curves (left: concentric, right: eccentric)
(a) Evaluation of initial and secant
(b) Evaluation of energy absorption
Figure 7 Determination of stiffness and energy absorption index.
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+96.49%
110
100
40
+12.51%
31.13
50
45.74
60
+31.94%
70
+52.24%
+47.63%
+36.27%
80
S4-e150-TRM2
S3-e150-TRM1
S1-e150-CFRP
S5-e150-XX
S4-e00-TRM2
10
S3-e00-TRM1
20
S1-e00-CFRP
30
S2-e00-XX
Initial Stiffness (KN/mm)
90
+137.56%
0
80
+82.41%
S4-e150-TRM2
S3-e150-TRM1
S1-e150-CFRP
20.23
S5-e150-XX
S4-e00-TRM2
10
S3-e00-TRM1
20
S1-e00-CFRP
30
28.02
40
+8.07%
+29.74%
50
+58.20%
+88.97%
60
S2-e00-XX
Secant Stiffness (KN/mm)
70
0
eccentricity = 150 mm
eccentricity = 0
Eccentricity Effect
Figure 8 Effect of eccentricity and external strengthening on the initial and secant stiffness.
3.3. Ductility of analyzed slabs
Abdulraheem and Mohammed (2018) [27] stated that calculating the energy absorption index
(EAI) provides a better approach for determining the ductility of RC members. Energy
absorption index (EAI) defined by Husain et al. (2017) [26] as the ratio of the total area under
load-deflection curve to that under the ascending portion only as explained in Fig 7 b.
According to that, the effect of concentric and high-eccentric loading on the ductility of
externally strengthened specimens was determined by calculating and comparing the energy
absorption index of them with the control specimens. Table 4 summarizes the results of the
energy absorption index of the analyzed specimens.
Fig. 9 Show the effect of applying external strengthening on the energy absorption index
with different cases of eccentricity, (i.e., zero and 150 mm eccentricities). It can be clarified
from the results that using CFRP-strengthening technique increased the ductility of the tested
specimen and that was also affected by the eccentricity as shown in Fig 9. In the other hand,
TRM-strengthened slabs showed a different behavior in terms of ductility than CFRPstrengthened slabs. Using TRM-strengthening techniques showed a reduction in the ductility
of the specimens and that was sensitive to the mesh size of the textile used. It was also noted
that increased the eccentricity of the load decreased the calculated ductility.
3.4. Crack patterns
The cracks in Finite Element Analysis spreads within the slab near the column. It starts
tangentially close to the column and so extends radially as the load increases. At the failure
load, the punching cone is obvious due to the sudden cracks opening. Concrete damaged
plasticity model considers that the cracking initiates when the maximum principal plastic
strain (PE) is positive [18]. The direction of the cracks is taken into account to be
perpendicular to the maximum principal plastic strains (PE) and so, the orientation of the
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Majid H. Abdulhussein, Dr. Muhammad J. Kadhim
cracks are visualized through the maximum principal plastic strains [28]. The tensile principal
stresses can be utilized in Finite Element Analysis in order to indicate crack patterns but the
maximum principal plastic strains provide a higher illustration of the cracks [18]. For that
reason, the strains will be used for viewing the crack patterns for all tested slabs.
Fig. 10 showed the crack patterns (on the tension face of the slabs) of the all analyzed
specimens. It can be seen from Fig. 10 that the crack propagation of specimens strengthened
by CFRP were within the direction of the fiber distribution. While the crack patterns for slabs
strengthened by TRM-jackets were similar to that of control ones, but these cracks were
spread in different directions towards the edges. In addition, presence of eccentricity of
applied load resulted in excessive damage to the half tension surface of the slab (right portion
of the photograph shown in Fig. 10 as compared with the other half). Whereas the crack
patterns of specimen tested under concentric load was approximately symmetric about the two
axes.
-35.21%
+46.46%
S3-e150-TRM1
S4-e150-TRM2
2.84
+11.07%
-9.79%
3.27
3
S1-e150-CFRP
S5-e150-XX
S4-e00-TRM2
S3-e00-TRM1
1
S1-e00-CFRP
2
S2-e00-XX
Energy apsorbtion index
4
-17.21%
+17.69%
5
0
eccentricity = 150 mm
eccentricity = 0
Eccentricity Effect
Figure 9 Effect of eccentricity and external strengthening on energy absorption index.
S2
S5-
S1-
S3-
S1-
S3-
S4-
S4-
Figure 10 Crack patterns of analyzed specimens.
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Numerical Investigation on the Punching Behavior of RC Flat Slabs Strengthening by TRM and FRP
4. CONCLUSIONS
Based on the results obtained in this paper using numerical analysis for the RC fat slabs
strengthened by CFRP and TRM and tested with two different eccentricities (0 and 150 mm),
the conclusions can be drawn as the following:

For concentrically loaded specimens, using CFRP increases the punching load and the central
deflection of the slabs by about 39.67 and 27.18%, respectively. While using TRM with 10
and 20 mm mesh opening increases the punching load by around 29.29 and 18.28%,
respectively, but decreases the central deflection by 58.83 and 47.32, respectively as
Compared with control specimens.

For eccentrically loaded specimens, using CFRP increases the punching load and the central
deflection of the slabs by about 38.9 and 36.7%, respectively. While using TRM with 10 and
20 mm mesh opening increases the punching capacity by around 38.90 and 32.60%,
respectively, and decreases the central deflection by about 35.55 and 33.72%, respectively, as
compared with control specimens.

It was observed that increasing the stiffness by applying external strengthening was highly
affected by eccentricity amount. For concentrically loaded specimens, the average increase in
the initial and secant stiffness was around 60.13 and 85.42%, respectively. While for
eccentrically loaded, the average increase in the initial and secant stiffness was around 32.23
and 49.56%, respectively.

It was shown that the best improvement in the stiffness was by applying TRM and that was
sensitive to the mesh opening of the textile (i.e. stiffness increased, when the mesh size
decreased).
Using CFRP increases the ductility of the specimens. In the other hand, Using TRM
shows a reduction in the ductility of the specimens and that was sensitive to the mesh size of
the textile used. It was also noted that increased the eccentricity of the load decreased the
calculated ductility
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