Effect ofthe distance between points load on the behavior of

Chemistry and Materials Research www.iiste.org
ISSN 2224- 3224 (Print) ISSN 2225- 0956 (Online)
Vol.6 No.8, 2014
Effect of the Distance between Points Load on the Behavior of
Strengthened Reinforced Concrete Beams
Lec.AamerNajim Abbas1*Asst.Lec.NuraJasim Muhammed1**Asst.Lec.shaimaa Tariq Sakin1***
1. Al_Mustansiriya University ,College of Engineering ,Civil Department
*Amir_najim@yahoo.com**nura_jacob@yahoo.com***shtsakin@yahoo.com
6
Abstract
The general behavior of the reinforced concrete beams depends on many variables, including what is the
quality of the concrete and strength and including those on reinforcement type and quantity of reinforcement in
the beam. But there is an important variable which nature of loads application on the beam and type of load is it
point or distributed. Sometimes the distance between points load is variable such as vehicle wheel load because
each vehicle as different distance between wheels.
In this research, the effect of changing the distance between the points load were studied and compared with
model carrying a single point load at mid span, as well as studying the effect of the use of carbon fiber with a
length equal to the distance between the points load.
Theoretical results consists of eight models were compared in this study with the results of the previous
experimental results. The study contains a discussion of the general behavior of the beam in addition to the study
of the failure carrying load, cracking load, ductility and the relationship between the stages of load application
and the deflection of concrete beams with and without carbon fiber sheets.
Key words: Ansys, strengthening, ductility, carbon fiber.
1. Introduction
Concrete structural components require the understanding into the responses of these components to a variety of
loadings application.
A simply-supported reinforced concrete beam may fail primarily- either in flexure or in shear. Failure in flexure
will occur if the ultimate flexural moment capacity is exceeded at any section of the beam before the conditions
for shear failure have been satisfied at any section. Failure in shear will occur when the limiting shear-moment
capacity is reached at some section of the beam at which inclined cracks have developed sufficiently to reduce
the available compressive area.
Whether a given beam will fail in flexure or in shear will depend on the relative magnitudes of the ultimate
flexural moment (Mf), the limiting shear-moment (Ms) and the critical shear(V) at various locations along the
span and on the actual values of moment and shear at these locations. The relationship between mode of failure
and properties of the beam cross-section and loading arrangement is illustrated most simply by considering the
hypothetical behavior of a simply-supported beam as illustrated in Fig.(1).
The beam shown in Figure (l) is simply-supported at its end span is assumed to carry two concentrated loads
arranged symmetrically about mid span. Only half of the span is shown in the Figure, The distance from the
support to the load is called the "shear-span" and is designated by the symbol (a). For the particular type of
loading shown, the maximum moment and the maximum shear both occur at the location of the load and their
ratio is M/V = a.

Vol.6 No.8, 2014
Figure (1) Effect of moment-shear ratioon failure mode
7
2. Carbon Fiber
Carbon fiber is defined as a fiber containing at least 92 wt % carbon, while the fiber containing at least 99 wt %
carbon is usually called a graphite fiber. Carbon fibers generally have excellent tensile properties, low densities,
high thermal and chemical stabilities in the absence of oxidizing agents, good thermal and electrical
conductivities, and excellent creep resistance. They have been extensively used in composites in the form of
woven textiles, prepregs, continuous fibers/rovings, and chopped fibers. The composite parts can be produced
through filament winding, tape winding, pultrusion, compression molding, vacuum bagging, liquid molding, and
injection molding.
In terms of final mechanical properties, carbon fibers can be roughly classified into ultra-high modulus (>500
GPa), high modulus (>300 GPa), intermediate modulus (>200 GPa), low modulus (100 GPa), and high strength
(>4 GPa)(1).
Ehsan Ahmed et al(2). studied the flexural behavior of reinforced concrete beams strengthened with carbon fiber
through an experimental and theoretical study includes six models, one without carbon fiber and the others with
different number of layers of carbon fiber. They concluded that there is an increase in member stiffness in
addition to improvement in yield and ultimate load. Another group of researchers (tom Norris et al.)(3) used in
their research different ways to paste carbon fiber to concrete beams to see what is the proper way to use carbon
fiber for strengthening the concrete beams, All ways showed that there is a clear improvement in carrying
capacity of beams in addition to the improvement in ductility and yield load.
3. Test Program
The experimental work program conducted by Mohammad Z.Y(4) was selected to validate the simulations
presented in this paper. In his study, two experimental programs were carried out to investigate the behavior of
reinforced concrete (RC) beams strengthened with CFRP fabrics between points load using a wet layup method.
The aim of the research was to study the failure characteristics, deflection behavior and general performance. A
total of six reinforced concrete beams were tested under two points bending with different distances between
points of loading. In this test program, The variables of the beams were the distance between points load, CFRP
bond length (equal to the distance between points load). To simulate the behavior under service, the beam named
as (B) was selected. The geometrical properties and reinforcement details are illustrated in Table(1) and Figure
(2).
Table (1) Experimental Work Variables
Beam No. Distance Between Point Load Length of Carbon Fiber
B1 0 0
B2 20 20
B3 40 40
B4 60 60

Vol.6 No.8, 2014
In this study, the main flexural and shear steel reinforcements in the finite element models were assumed to be
an isotropic linear elastic material until the yield point. The ultimate and yield stresses are summarized in Table
(2). The Poisson’s ratio of steel was taken as 0.3.Concrete properties are selected as (fc'=52.88, fr =4.75 and the
Poisson’s ratio of steel was taken as 0.2).
The dimensions of beams was selected (100x150)mm with 2ɸ4mm at the top ,2ɸ10 at the bottom and
ɸ4@150mm shear reinforcement along the beam.
Table (2) Steel Properties
8
Bar type Modulus of elasticity
(kN/m2)
Yield strength (fy)
(MPa)
Ultimate strength (fu)
(MPa)
Main Reinforcement 200000 484 719
Shear Reinforcement 200000 383 620
Figure (2) Reinforced Concrete Beam With Loading
4. Finite Element Analysis
ANSYS computer program has been used for the finite element modeling. Four beams that have been studied
were of a simply supported beamslengthof1.5mand an area100X150mm and loaded with two symmetrically
placed concentrated vertical loads with Variable distances between point load, see Figure (3) below and Table
(3). Table (3) shows the distances between the points load and length of carbon fiber sheets for each model.
Model includes linear relationship to the properties concrete, a linear bond-slip relation and bilinear steel
properties. The method of load application was applied incrementally each 2 kN. See Plate below which
represents position of load application and position of supports. In ANSYS program symmetry properties were
applied for the purpose of representation models.
Figure (3) FEM Discretization for a Half of the Beam
1
X
Y
Z
APR 12 2013
09:53:16
ELEMENTS
U
F

Vol.6 No.8, 2014
Table (3) Distance Between Points Load
Model Number Description Distance Between
9
Point Load (mm)
Length of Carbon
Fiber Sheet
B1 Without carbon fiber
one point load
One point load -------
B2 With carbon fiber
two point load
200 200
two point load
400 400
two point load
600 600
B1W Without carbon fiber
one point load
One point load -------
two point load
200 200
two point load
400 400
two point load
600 600
5. Material Modeling
SOLID65 isotropic element is used to represent the concrete material, since it has a capability of both cracking in
tension and crushing in compression. SOLID65 element is defined by 8 nodes with three degrees of freedom at
each node; translations in the nodal x, y, and z directions, see Figure below.
LINK8 element (It is a uniaxial tension-compression member) is used to represent the reinforcing steel (main
and stirrups steel material). LINK8 element is defined by two nodes with three degree of freedom at each node;
translations in the nodal x, y, and z directions, see Figure below.
SHELL41 element is used to represent the carbon fiber sheets. SHELL41 element is defined by four nodes with
three degree of freedom at each node.it is a 3-D element having membrane (in-plane) stiffness but no bending
(out of plane) stiffness. See Figure below.
Figure (4) Solid 65 Figure (5) Link 8 Figure (6) Shell41

Vol.6 No.8, 2014
5.1 Real Constants
The real constants for this model are shown in Table below
Table (4) Real Constant
10
Real constant
set
Element type Constant
1
SOLID65
concrete
Real constant for
Rebar 1
Real constant for
Rebar2
Real constant for
Rebar 3
Material number 0 0 0
Volume ratio 0 0 0
Orientation angle 0 0 0
2 LINK8
Reinforce-ment
Steel Bar Diameter (f 10 mm )
Cross-sectional area
78.54
(mm2)
Initial strain (mm/mm) 0
3 LINK8
Reinforce-ment
Steel Bar Diameter (f 4 mm )
Cross-sectional area
12.566
(mm2)
Initial strain (mm/mm) 0
3 SHELL41
CFRP
CFRP type Fabric
Shell thickness at node I
(mm)
0.1
Shell thickness at node J
(mm)
0.1
Shell thickness at node
K (mm)
0.1
Shell thickness at node L
(mm)
0.1
Element x- axis rotation 0
Elastic foundation
stiffness
0
Added mass/unit area 0

Vol.6 No.8, 2014
5.2 Material Properties
The material properties for this model are shown in Table below:
Table (5) Materials Properties
11
Material model
number
Element type Material properties
1
SOLID65
Linear Isotropic
EX 34178
PRXY 0.2
Multilinear Isotropic
Strain Stress
Point 1 0.000464 15.864
Point 2 0.001 30.94
Point 3 0.00158 42.83
Point 4 0.0018 45.96
Point 5 0.00 3 52.88
Concrete
ShrCf-Op 0.2
ShrCf-CI 0.3
UnTensSt 3.64
UnCompSt -1
BiCompSt 0
HydroPrs 0
BiCompSt 0
UnTensSt 0
TenCrFac 0
Material model
number
Element type Material properties
2 LINK8
Linear Isotropic
EX 200000
PRXY 0.3
Bilinear Isotropic
Yield Stress 484
Tang Mod. 0
3 LINK8
Bilinear Isotropic
Yield Stress 383
Tang Mod. 0
Linear Isotropic
EX 200000
PRXY 0.3
4 SHELL41
Linear Orthotropic
Ex 234000
Ey 1
Ez 1
PRXY 0.3
PRYZ 0
PRXZ 0
Gxy, Gyz, Gxz 1
6. Theoretical Results
6.1 Failure Load
After the data was analyzed and carefully considered, it can be said that the collected data of the failure load
obtained from the theoretical solution for all beams is approximately equal experimental load and all the beams
failed by flexure. The final loads for the ANSYS finite element method are the last applied load step before the
solution diverges due to numerous cracks and large deflections.
Through an extensive comparison between the unsupported specimens with carbon fiber and other supported
specimens, it can be concluded that the specimens with carbon fiber have failure load more than other specimens
without carbon fiber. This can be explained that the carbon fibers connecting both sides of the crack together and

Vol.6 No.8, 2014
delay extension more during the concrete section (increase in tensile cracking strength of concrete due to
confinement).
Also, the increasing Length of the carbon causes an increase in the amount of carrying capacity to bending
stresses, because the increase in length means cover as much as possible the bending area and are controlled
more cracks generated during download stages.
The moment generated in the mid length of the beam is the result of multiplying the reaction by the distance
between the reaction and applied force (couple). When the distance between the two points load increased this
leads to decrease of the distance between the applied force and the reaction, this leads naturally to a decrease in
couple as a result of decrease in the distance between them, for the above reasons we can say that the increasing
in the distance between the loading points provides to some extent an increase in carrying capacity for
specimens.
6.2 Behavior at First Cracking
The analysis of reinforced concrete beams in the linear region depends mainly on the appearance of cracks in
that region where maximum bending stresses are concentrated. As was expected through a comparison between
the different beams (different distances between the points of loading), the greater distance between points load
delayed appearance of first cracks in the beams the reason for that is as stated previously that the increase in
distance between point loads means decrease the applied moment on beam for same value of load if compared
with the other models with less distance.
A comparison of values obtained from the FE model and experimental can be seen in Table (6). The results in
Table (6) indicate that the FE analysis of the beam prior to cracking is acceptable.
The first cracks for the beams without carbon fiber (B1W, B2W, B3W and B4W) were observed at (27.27%,
25%, 26.6% and 26.3%) of the ultimate load respectively where for carbon fiber reinforced beam the first crack
load was found to be between (13.63% to 15% ) the ultimate load. There is a 11.5% to 12.8% increase in
ultimate load for carbon fiber reinforced concrete beams when compared with beams without carbon fiber
reinforcement. Thus the experimental results show that there is increase in the ultimate load and the first crack
load for the fiber reinforced concrete beams.
Table (7) Cracking and Ultimate Load Deflection
Model Load at First Cracking (kN) Centerline Deflection
12
(mm)
Ultimate load
(kN)
Pcr/pultimate
%
Exper. Theo. Exper. Theo. Exper. Theo. Exper. Theo.
B1 6.5 6 0.5 0.33 36 38 18 15.8
B1W 6 0.332 22 27.27
B2 7 6 0.255 0.3175 44 44 15.9 13.63
B2W 6 0.321 24 25
B3 9 8 0.54 0.386 54 58 16.6 13.79
B3W 8 0.392 30 26.6
B4 10.5 10 0.52 0.414 70 68 15 14.7
B4W 10 0.42 38 26.3

Vol.6 No.8, 2014
Figure (7)Comparison Between Theoretical Cracking, Yielding and Ultimate load.
6.3 Load-Deflection Relationship
The theoretical results for all specimens are displayed and compared with experimental results. Figures below
contain a load-deflection curves predicted by ANSYS and the test results for all specimens Examined by
Mohammad Z.Y.. The results of ANSYS converge with the non-strengthened specimens more than other
strengthened specimens with carbon fiber because of not taking the slip between the concrete and the carbon
fiber into account in the theoretical study.
In general, the beams strengthened with carbon fiber were stiffer and more ductile than the control specimens
with a higher ultimate load see Figure (7). In every stage of loading application, the deflections are reduced
significantly thereby increasing the stiffness for the strengthened beams.
13
Figure (8) Experimental and Theoretical Load
Deflection Curve for Beam (B1)

Vol.6 No.8, 2014
14
Figure (12) Theoretical Load Deflection Curve for
Beam (B1) and (B1W)
Figure (13) Theoretical Load Deflection Curve for Beam
(B2) and (B2W)
Figure (14) Theoretical Load Deflection Curve for
Beam (B3) and (B3W)
Figure (15) Theoretical Load Deflection Curve for Beam
(B4) and (B4W)
6.4 Ductility
Ratio of curvature at crushing of concrete to that at yielding of steel gives the numerical value of ductility,
known as ductility index.
It can be seen that for a given dimension and strength, the load versus displacement curves for both specimens
with carbon fiber and other specimens without carbon fiber appear similar. In addition, as can be seen in Table
(8) the deflection at yielding and ultimate strength for beams without carbon fiber appear lower than those of
beams with carbon fiber. It has been known that the deflection ductility, μΔ, in terms of ultimate deflection to
yielding displacement, is highly correlated to the length of the carbon fiber sheet. As can be seen in Table (8),

Vol.6 No.8, 2014
the ductility of both types of concrete beams exhibit a extrusive length effect, i.e., ductility increase with the
increase of carbon fiber sheets, namely, a strengthened beam performs more ductile.
The effect of increasing the distance between the points load seemed clear as when you increase this distance
increases the ductility due to decrease moments that cause for ultimate deflection in the beam at failure.
Table (8) Ductility of tested beams
Beam No. Deflection at Yield
(mm)
Deflection at Failure
(mm)
Ductility Index
B1 4.16 12.5045 3
B2 4.64 13.4386 2.896
B3 5.09 18.357 3.606
B4 4.97 18.3 3.682
B1W 3.1 5.22 1.683
B2W 3.6 4.01 1.113
B3W 4.3 15.822 3.679
B4W 4.7 4.917 1.046
7 .Conclusions
Based on the results obtained from theoretical analysis and comparison with the experimental work, the
following conclusions are drawn:
1. At any given load level, the deflections are reduced significantly thereby increasing the stiffness for the
15
strengthened beams.
2. All the beams strengthened with carbon fiber experience flexural failures. None of the beams exhibit
brittle failure.
3. The failure load of specimens with carbon fiber more than other specimens without carbon fiber.
4. The bending stresses are reduced when length of the carbon was increased.
5. The increasing in the distance between the loading points provides an increase in carrying capacity for
specimens.
6. In this study, the appearance of the first crack mainly depends on the distance between the points load,
higher distance between the mount points load lead to the delay in appearance of the cracks.
7. Through the adoption of the distance between the point load as a variable show that increasing the
distance between the points load result a decreasing in moment in the mid span of the beam, this means
an increase in carrying capacity for specimens.
8. Through a comparison theoretical results with the experimental, showing that there is a convergence
between the two results.
9. It is very clear the development in ductility as a result of increasing the length of carbon fiber sheets and
increase the distance between the points load.
References
1. Xiaosong Huang, " Fabrication and Properties of Carbon Fibers ",www.mdpi.com.
2. Ehsan, A., Habibur, R. and Norsuzailina, M. S., " Flexural performance of CFRP strengthened RC
beams with different degrees of strengthening schemes", International Journal of the Physical Sciences,
Malaysia, Vol. 6(9), 4 May, 2011, pp. 2229-2238.
3. Tom, N., Hamid, S., Mohammad, R., " Shear and Flexural Strengthening of Reinforced Concrete
Beams with Carbon Fiber Sheets", Journal of Structural Engineering, Vol.123, No.7, July,
1997,PP.903-911.
4. Mohammad, Z., " Reinforced Concrete Beams Strengthening by Carbon Fiber Reinforced Polymer
Against Two Points Load Divergence", Journal of Engineering and Development" Vol.16, No.2, June,
2012 ,PP.266-280.

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