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International Journal of Civil & Environmental Engineering IJCEE-IJENS Vol: 11 No: 01 63
1110301-2727 IJCEE-IJENS © February 2011 IJENS I J E N S
Nonlinear Analysis of RC Beam for Different
Shear Reinforcement Patterns by Finite
Element Analysis I. Saifullah
1*, M.A. Hossain
2, S.M.K.Uddin
3, M.R.A. Khan
4 and M.A. Amin
5
1,2,3 Department of Civil Engineering, Khulna University of Engineering & Technolog y (KUET), Khulna-9203,
Bangladesh, email: [email protected]* 4,5
Undergraduate student, Department of Civil Engineering, Khulna University of Engineering & Technology
(KUET), Khulna-9203, Bangladesh.
Abstract-- Several methods have been utilized to study the
response of concrete structural components. Experimental
based testing has been widely used as a means to analyze individual elements and the effects of concrete strength under
loading. The use of finite element analysis to study these
components has also been used. This paper focuses on the
behavior of reinforced concrete beam for different pattern of
shear reinforcement to evaluate the effective shear reinforcement pattern and also compare the variation in
behavior of reinforced concrete beam for with and without
shear reinforcement with a simulation. To carry out the
analysis, six 3D beams without and with different patterns of shear reinforcement is built using comprehensive computer
software ANSYS 10 © 2005 SAS IP, Inc package. The static
non linear analysis is done to find out ultimate capacity,
formation of first crack and its distance from support,
initiation of diagonal crack and its distance from support. Load deflection response was also closely observed and
compared with the result from theoretical calculation. From
close observation of analyses results it was found that all types
of web reinforcements were almost same effective for static
loading condition.
Index Term-- ANSYS, shear reinforcement, finite element
analysis, diagonal crack.
I. INTRODUCTION
Concrete structural components exist in buildings and bridges
in different forms. Understanding the response of these
components during loading is crucial to the development of an
overall efficient and safe structure. Different methods have
been utilized to study the response of structural components.
Experimental based testing has been widely used as a means
to analyze individual elements and the effects of concrete
strength under loading. While this is a method that produces
real life response, it is extremely time consuming, and the use
of materials can be quite costly. The use of finite element
analysis to study these components has also been used.
Unfortunately, early attempts to accomplish this were also
very time consuming and in feasible using existing software
and hardware.
When a simple beam is loaded, bending moments and shear
forces develop along the beam. To carry the loads safely, the
beam must be designed for both type of forces. Flexural
design is considered first to establish the dimensions of the
beam section and the main reinforcement needed. The beam
is then designed for shear. If shear reinforcement is not
provided, shear failure may occur. Shear failure is
characterized by small deflections and lack of ductility,
giving little or no warning before failure [1]. On the other
hand, flexural failure is characterized by a gradual increase
in deflection and cracking, thus giving warning before total
failure. This is due to ACI Code limitation on flexure
reinforcement. The Design for shear must ensure that shear
failure does not occur before flexural failure [1]. The use of
FEA has been the preferred method to study the behavior of
concrete (for economic reasons). With the advent of
sophisticated numerical tools for analysis like the finite
element method (FEM), it has become possible to model the
complex behavior of reinforced concrete beams [2].
In recent years, however, the use of finite element analysis has
increased due to progressing knowledge and capabilities of
computer software and hardware. It has now become the
choice method to analyze concrete structural components.
The use of computer software to, model these elements are
much faster, and extremely cost-effective. To fully understand
the capabilities of finite element computer software, one must
look back to experimental data and simple analysis. Data
obtained from a finite element analysis package is not useful
unless the necessary steps are taken to understand what is
happening within the model that is created using the software.
Also, executing the necessary checks along the way is key to
make sure that what is being output by the computer software
is valid. By understanding the use of finite element packages,
more efficient and better
analyses can be made to fully understand the response of
individual structural components and their contribution to a
structure as a whole. This paper focuses on the behavior of
reinforced concrete beam for different pattern of shear
reinforcement to evaluate the effective shear reinforcement
pattern and also compare the variation in behavior of
reinforced concrete beam for with and without shear
reinforcement with a simulation.
II. SCOPE
This study is focuses on the numerical simulation technique
of 3D approach of beams of without and with shear
reinforcement of different patterns and also a simulation
and compared with another group experimental and
analytical data. This 3D approach is extensible with making
variation on loading and support condition and is a basis for
the evaluation of the topics of interest for future study
International Journal of Civil & Environmental Engineering IJCEE-IJENS Vol: 11 No: 01 64
1110301-2727 IJCEE-IJENS © February 2011 IJENS I J E N S
includes providing the principles and guidelines to aid in the
optimization in a easier manner. The paper may also
provide low laborious procedure for modeling of versatile
RCC like structure.
III. EXPERIMENTAL STUDY
A. CRACKS IN CONCRETE MODEL
Concrete crack plots were created at different load levels to
examine the different types of cracking that occurred within
the concrete as shown in Fig. 1. The different types of
concrete failure that can occur are flexural cracks,
compression failure (crushing), and diagonal tension cracks.
Flexural cracks (Fig. 1a) form vertically up the beam.
Compression failures (Fig. 1b) are shown as circles.
Diagonal tension cracks (Fig. 1c) form diagonally up the
beam towards the loading that is applied. Crack develops in
concrete element when the concrete element stress exceeds
modulus of rupture of concrete (tensile strength of concrete).
Crash develops in concrete element when the concrete element
stress exceeds compressive crashing strength of concrete. This
study indicates that the use of a finite element program to
model experimental data is viable and the results that are
obtained can indeed model reinforced concrete beam behavior
reasonably well.
Fig. 1. Typical Cracking Signs in Finite Element Models: a) Flexural Cracks,
b) Compressive Cracks, c) Diagonal Tensile Cracks (Kachlakev, et al. 2001)
B. FAILURE CRITERIA FOR CONCRETE
The model is capable of predicting failure for concrete
materials. Both cracking and crushing failure modes are
accounted for. The two input strength parameters i.e., ultimate
uniaxial tensile and compressive strengths are needed to define
a failure surface for the concrete. Consequently, a criterion for
failure of the concrete due to a multiaxial stress state can be
calculated (William and Warnke 1975). A three-dimensional
failure surface for concrete is shown in Fig. 2.
Fig. 2. 3-D failure surface for concrete (William and Warnke 1975)
C. Finite Element Modeling of Steel Reinforcement
Tavarez (2001) discusses three techniques that exist to
model steel reinforcement in finite element models for
reinforced concrete is shown in fig. 3: the discrete model,
the embedded model, and the smeared model.
Fig. 3. Models for Reinforcement in Reinforced Concrete (Tavarez 2001):
(a) discrete; (b) embedded; and (c) smeared
D. ANSYS FINITE ELEMENT MODEL
T ABLE I
ELEMENT T YPES FOR WORKING MODEL
Material Type ANSYS Element
Concrete Solid65
Steel Plates and
Supports Solid45
Steel Reinforcement Link8
International Journal of Civil & Environmental Engineering IJCEE-IJENS Vol: 11 No: 01 65
1110301-2727 IJCEE-IJENS © February 2011 IJENS I J E N S
E. REAL CONSTANTS
The real constants for this model are shown in Table II. Note
that individual elements contain different real constants. No
real constant set exists for the Solid65 element.
T ABLE II
REAL CONSTANT FOR MODEL
F. MATERIAL PROPERTIES
Parameters needed to define the material models can be
found in Table III.
T ABLE III MATERIAL MODELS FOR THE CALIBRATION MODEL
Mate
rial
Mo
del
Nu
mb
er
Ele
men
t
Ty
pe
Material Properties
1
So
lid
65
Linear Isotropic
EX 3604974.865
PRXY 0.25
Multilinear Isotropic
Strain
(in/in)
Stress
(psi)
Point 1 0.00049931 1800
Point 2 0.00065 2158.06
Point 3 0.00080 2552.24
Point 4 0.001 2996.43
Point 5 0.0012 3347.11
Point 6 0.0014 3609.99
Point 7 0.0016 3794.94
Point 8 0.0018 3913.71
Point 9 0.002 3978.22
Point 10 0.0022 3999.57
Point 11 0.002219 4000
Point 12 0.003 4000
Concrete
ShrCf-Op 0.3
ShrCf-Cl 1
UnTensSt 474.34
UnCompSt -1
BiCompSt 0
HydroPs 0
BiCompSt 0
UnTensSt 0
TenCrFac 0
2
So
lid
45
Linear Isotropic
EX
29,000,000
psi
PRXY 0.3
3
Lin
k8
Linear Isotropic
EX
29,000,000
psi
PRXY 0.3
Bilinear Isotropic
Yield Stress 60,000 psi
Tangent
Modulus 2,900 psi
The Solid65 element requires linear isotropic and multi-
linear isotropic material properties to properly model
concrete. The multi-linear isotropic material uses the von
Real
Co
nst
ant
set
Ele
men
t
Ty
pe
Constants
1
So
lid
65
Real
Co
nst
an
ts
for
Reb
ar
1
Real
Co
nst
an
ts
for
Reb
ar
2
Real
Co
nst
an
ts
for
Reb
ar
3
Mate
rial
Nu
mb
er
0 0 0
Vo
lum
e
Rati
o
0 0 0
Ori
en
tati
on
An
gle
0 0 0
Ori
en
tati
on
An
gle
0 0 0
2
So
lid
45
Cro
ss-
secti
on
al
Are
a,
(in
2)
1.0
Init
ial
Str
ain
(in
./in
.)
0
3
Lin
k8
Cro
ss-
secti
on
al
Are
a (
in2 )
0.11
Init
ial
Str
ain
(in
./in
.)
0
International Journal of Civil & Environmental Engineering IJCEE-IJENS Vol: 11 No: 01 66
1110301-2727 IJCEE-IJENS © February 2011 IJENS I J E N S
Mises failure criterion along with the Willam and Warnke
(1975) model to define the failure of the concrete. EX is the
modulus of elasticity of the concrete (Ec), and PRXY is the
Poisson‟s ratio (µ). The modulus of elasticity was based on
the equation,
Ec = 57000√f’c (1)
with a value of f’c equal to 4,000 psi. Poisson‟s ratio was
assumed to be 0.25. The compressive uniaxial stress -strain
relationship for the concrete model was obtained using the
following equations to compute the multi-linear isotropic
stress-strain curve for the concrete (MacGregor 1992)
(2)
(3)
(4)
Where;
f = stress at any strain ε, psi
ε = strain at stress f
= strain at the ultimate compressive strength, f’c
The multi-linear isotropic stress-strain implemented requires
the first point if the curve to be defined by the user. It might
satisfy Hook‟s Law;
(5)
The multi-linear curve is used to help with convergence of
the nonlinear solution algorithm.
Fig. 4. Uniaxial Stress-Strain Curve
Fig. 4 shows the stress-strain relationship used for this study
and is based on work done by Kachlakev,et al. (2001).
MacGregor Nonlinear model curve Point 1, defined as ' 0.45
fc’ is calculated in the linear range (Equation 4). Other
points are calculated from Equation 2 with ε0 obtained from
Equation 3.Last point is defined at f‟c and ε0=0.003 in./in.
indicating traditional crushing strain for unconfined
concrete.
Fig. 5. Idealized Stress-Strain Curve of Reinforcing Steel
G. MODELING
Fig. 6. Typical Beam Dimensions
Fig. 7. Quarter Beam for Model
International Journal of Civil & Environmental Engineering IJCEE-IJENS Vol: 11 No: 01 67
1110301-2727 IJCEE-IJENS © February 2011 IJENS I J E N S
Fig. 8. Different types of shear reinforcements
Fig. 9. Reinforcement Detailing for Beam Model
Fig. 10. Mesh of the Concrete, Steel Plate and Steel Support
Link8 elements were used to create the flexural and shear
reinforcement. Only half of the stirrup is modeled because of the
symmetry of the beam. Fig. 10 illustrates that the rebar shares the
same nodes at the points that it intersects the shear stirrups. The
element type number, material number, and real constant set
number for the calibration model were set for each mesh as shown
in Table IV.
Fig. 11. Reinforcement Configuration and Meshing for Type 1
T ABLE IV MESH ATTRIBUTES FOR THE MODEL
Mo
del
Part
s
Ele
men
t
Ty
pe
Mate
rial
Nu
mb
er
Real
Co
nst
ant
Set
Concrete Beam 1 1 1
Steel Plate 2 2 N/A
Steel Support 2 2 N/A
Longitudinal
Reinforcement 3 3 2
Shear
Reinforcement 3 3 3
Fig. 12. Reinforcement Configuration and Meshing for without shear
reinforcement
Fig. 13. Reinforcement Configuration and Meshing for Type 2
International Journal of Civil & Environmental Engineering IJCEE-IJENS Vol: 11 No: 01 68
1110301-2727 IJCEE-IJENS © February 2011 IJENS I J E N S
Fig. 14. Reinforcement Configuration and Meshing for Type 3
Fig. 15. Reinforcement Configuration and Meshing for Type 4
Fig. 16. Different Patterns of Shear Reinforcement in ANSYS
III. ANALYTICAL STUDY
For this purpose it is eventual to compare the develop model
with an existing one. And here this simulation was made by
using the data given by „Anthony J. Wolanoski B.S.‟ in his
thesis paper [2]. Where, he used following specification-
1. Beam size – The width and height of beam
were 10 in. and 18 in respectively
2. Clear span length – 15 ft
3. Area of steel – 0.93 in.2
4. Yield Stress of Steel, fy = 60,000 psi
5. 28-days Compressive Strength of Concrete,
f’c = 4800 psi
The detail of Wolanoski‟s beam and also the beam for
simulation is given below:
Fig. 17. Reinforcement Detailing of Wolanoski‟s Beam
Fig. 18. Load-Deflection curve comparison of ANSYS and Backouse
(1997) [2]
The graph of present analysis of Wolanoski‟s thesis is given
bellow:
Fig. 19. Load-Deflection Curve after simulation
The comparison of Wolanoski‟s analysis and present
analysis are given in table.
International Journal of Civil & Environmental Engineering IJCEE-IJENS Vol: 11 No: 01 69
1110301-2727 IJCEE-IJENS © February 2011 IJENS I J E N S
T ABLE V COMPARISON BETWEEN ANTHONY J.WOLANOSKI ANALYSIS AND
PRESENT STUDY BY ANSYS
A.
CRA
CK
DEV
ELO
PED
IN
THE
CON
CRE
TE
BEA
MS
At
first
the
crack
is
forme
d in
the concrete beams because of flexural stress. For the
increasing of loads the diagonal tension crack is initiated
after the formation of 1st
crack. The crack increase with the
increase of loads and the steel stress reach to its yielding
stress. The failure of concrete beams also observes by the
formation of crack which is shown in fig.s 20, 21, 22, 23
and 24.
(a) 1
st Crack of the Concrete Model (load 9686 lb)
(b) Initiation of Diagonal Tension crack (load 20423 lb)
(c) Yielding of Reinforcement (load 57533 lb)
(d) Failure of the Concrete beam (load 61615 lb)
Fig. 20 (a),(b),(c)&(d). Represents Cracks Formation in Beam of present study for Without Shear Reinforcement in different stages during the
application of load
(a
) 1st
Crack of the Concrete Model (load 9658 lb)
(b) Initiation of Diagonal Tension crack (load 23048 lb)
Mo
del
Ex
trem
e
Ten
sio
n F
iber
Str
ess
(p
si)
Rein
forc
em
en
t
Ste
el
Str
ess
(p
si)
Cen
terl
ine
Defl
ecti
on
(in
)
Lo
ad
at
Fir
st
cra
ck
ing
(lb
)
Fro
m t
hesi
s p
ap
er
of
An
tho
ny
J. W
ola
no
ski
B.S
. [2
] Man
ual
calc
ula
tio
n
53
0
30
24
0.0
52
9
51
18
AN
SY
S
53
6
28
40
0.0
53
4
52
16
Pre
sen
t
stu
dy
Sim
ula
ted
AN
SY
S
52
5
28
43
.8
0.0
53
4
52
12
International Journal of Civil & Environmental Engineering IJCEE-IJENS Vol: 11 No: 01 70
1110301-2727 IJCEE-IJENS © February 2011 IJENS I J E N S
(c) Yielding of Reinforcement (load 57898 lb)
(d) Failure of the Concrete beam (load 62020 lb)
Fig. 21. (a),(b),(c)&(d) represents Cracks Formation in Beam of present study for Shear Reinforcement Type 1 in different stages during the
application of load
(a) 1
st Crack of the Concrete Model (load 9646 lb)
(b) Initiation of Diagonal Tension crack (load 19949 lb)
(c) Yielding of Reinforcement (load 57450 lb)
(d) Failure of the Concrete beam (load 61852 lb)
Fig. 22. (a),(b),(c)&(d) represents Cracks Formation in Beam of present
study for Shear Reinforcement Type 2 in different stages during the application of load
(a) 1
st Crack of the Concrete Model (load 9657 lb)
(b) Initiation of Diagonal Tension crack (load 17453 lb)
International Journal of Civil & Environmental Engineering IJCEE-IJENS Vol: 11 No: 01 71
1110301-2727 IJCEE-IJENS © February 2011 IJENS I J E N S
(c) Yielding of Reinforcement (load 57576 lb)
(d) Failure of the Concrete beam (load 61880 lb)
Fig. 23. (a),(b)(c)&(d) represents Cracks Formation in Beam of present
study for Shear Reinforcement Type 3 in different stages during the
application of load
(a) 1
st Crack of the Concrete Model (load 9658 lb)
(b) Initiation of Diagonal Tension crack (load 20313 lb)
(c)
Yielding of Reinforcement (load 57451 lb)
(d) Failure of the Concrete beam (load 61964 lbs) Fig. 24. (a),(b),(c)&(d) represents Cracks Formation in Beam of present
study for Shear Reinforcement Type 4 in different stages during the
application of load
B. LOAD-DEFLECTION CURVE
Fig. 25. Combined Load-Deflection Curve for Different patterns of shear
Reinforcement
Load-Deflection Curve is linear with a sharp slope up to
9,000-10,000 lb. Within this load first cracking occur. The
graph changes its nature after first cracking i.e. its slope is
changed continuously. This is due to change in crack depth
with the load increment. The location of initiation of the
diagonal tension cracking of concrete in curves is in
between the 1st
cracking loads and steel yielding loads. This
crack is observed from concrete cracks and crushing plots
which is within 17400 lb to 23050 lb. The cracks & curves
were observed and the data from cracks & curves were
listed as tabular form in results.
International Journal of Civil & Environmental Engineering IJCEE-IJENS Vol: 11 No: 01 72
1110301-2727 IJCEE-IJENS © February 2011 IJENS I J E N S
IV. RESULTS AND DISCUSSIONS T ABLE VI
CRACK FORMATION AND DISTANCE OF CRACK FROM SUPPORT AND
DEFLECTION AT FAILURE LOADS ON THE BASIS OF ANALYSIS
Type
1st
crack
Init
iati
on
of
dia
go
nal
ten
sio
n c
rack
Lo
ad
at
Fail
ure
(lb
)
Defl
ecti
on
at
Fail
ure
(in
.)
Lo
ad
(l
b)
Dis
tan
ce f
rom
sup
po
rt (
in.)
Lo
ad
s (
lb)
Dis
tan
ce fr
om
sup
po
rt (
in.)
Wit
ho
ut
shear
rein
forc
em
en
t
96
86
78
20
42
3
51
61
61
6
2.3
1
Ty
pe 1
96
58
75
23
04
8
33
62
02
0
4.0
34
0
Ty
pe 2
96
46
82
.5
19
94
9
42
61
85
2
3.3
88
5
Ty
pe 3
96
57
75
.75
17
45
3
37
.5
61
88
0
3.6
87
9
Ty
pe 4
96
58
75
20
31
3
36
61
96
4
3.4
60
8
T ABLE VII COMPARISON BETWEEN THEORETICAL CALCULATION AND ANSYS
T ABLE VIII
FORMATION OF 1ST CRACK AND RESPECTIVE DEFLECTION & STEEL
STRESS IN FINITE ELEMENT ANALYSIS
Mo
del
Rein
forc
ing
(main
bar)
Ste
el
Str
ess
(psi
)
Cen
terl
ine
Defl
ecti
on
(in
.)
Lo
ad
at
Fir
st
Cra
ck
(fl
ex
ure
cra
ck
)
(lb
)
*M
an
ual
Calc
ula
tio
n
AN
SY
S
* M
an
ual
Calc
ula
tio
n
AN
SY
S
*H
Man
ual
Calc
ula
tio
n
AN
SY
S
Wit
ho
ut
Sh
ear
Rein
forc
em
en
t
27
72
.34
27
88
.0
0.0
53
94
0.0
54
78
6
94
45
.5
96
86
Ty
pe 1
27
88
.4
0.0
54
7
96
58
Ty
pe 2
27
88
.5
0.0
54
75
1
96
46
Ty
pe 3
27
88
.6
0.0
54
75
0
96
57
Ty
pe 4
27
88
.5
0.0
54
74
8
96
58
Model
Lo
ad
at
Fir
st
Cra
ck
(lb
)
Cen
terl
ine
Defl
ecti
on
(in
.)
Rein
forc
ing
Ste
el
Str
ess
(p
si)
Without Shear
Reinforcement 9686 0.056181 2859.0
Type 1 9658 0.064117 3870.0
Type 2 9646 0.057770 3077.0
Type 3 9657 0.058253 3138.3
Type 4 9658 0.062322 3651.1
International Journal of Civil & Environmental Engineering IJCEE-IJENS Vol: 11 No: 01 73
1110301-2727 IJCEE-IJENS © February 2011 IJENS I J E N S
T ABLE IX FLEXURAL STEEL STRESS ON THE BASIS OF ANALYSIS
Mo
del
Ste
el
Str
ess
at
yie
ldin
g o
f st
eel
(psi
)
Defl
ecti
on
at
yie
ldin
g o
f st
eel
(in
.)
Lo
ad
s o
n b
eam
at
yie
ldin
g o
f
steel
(lb
)
Ste
el
Str
ess
at
fail
ure
(p
si)
Lo
ad
s o
n b
eam
at
fail
ure
(lb
)
*T
heo
reti
cal
calc
ula
tio
n
60
00
0
-
57
70
3
- -
Wit
ho
ut
shear
rein
forc
em
en
t
60
00
9
0.8
58
35
0
57
53
3
60
10
8
62
02
0
Ty
pe 1
60
01
0
0.9
17
14
57
89
8
60
14
3
62
02
0
Ty
pe 2
60
00
4
0.8
29
57
8
57
45
0
60
16
3
61
85
2
Ty
pe 3
60
01
0
0.8
84
73
6
57
57
6
60
11
4
61
88
0
Ty
pe 4
60
00
4
0.8
55
752
57
45
1
60
12
8
61
96
4
A. COMPARISON
From another thesis group [7] performing on “Experimental
and Analytical Investigation of Flexural Behavior of
Reinforced Concrete Beam” got the results as follows:
T ABLE X
1ST CRACK FORMATION DISTANCE FROM SUPPORT (WITHOUT SHEAR
REINFORCEMENT) [7]
From present analysis: T ABLE XI
1ST CRACK FORMATION DISTANCE FROM SUPPORT FOR THIS ANALYSIS
B. COMMENTS ON RESULTS
Initiation of diagonal tension crack occurs in Type
1 at larger loads in compare to others.
For the beam without shear reinforcement diagonal
tension crack initiates at larger distance from
support with compared to others.
The ultimate load carrying capacity is larger for
Type 1 with respect to other types and also
showing large deflection for its better ductile
property.
Theoretical calculation and ANSYS analysis give
almost same results for steel stressing at 1st
crack.
At steel yielding the steel stress is almost same to
the theoretical value. These data was collected
from ANSYS output after analysis.
Steel stress at failure is maximizing for Type 2
shear reinforcement. These data was collected from
ANSYS output after analysis.
Compare with another group, the behavior of 1st
crack formation, is found satisfactory level.
From combined load deflection curve, the 1st
cracking point and the steel yielding point for with
and without different patterns of shear
reinforcement are almost same.
V. CONCLUSION
The project emanated with an aim to find out the ultimate
load carrying capacity of beams of without and with
different patterns of shear reinforcements and also find out
the different behaviors of beams for different stages of
loading. The project is expected to generate reasonable
solutions of focused problem defined under some parametric
condition. Initially some parameters are chosen for these
beams by analysis with finite element method. The ultimate
load carrying capacity is then determined by without
considering and considering different patterns of shear
reinforcement with a constant flexural reinforcement. After
completing the analysis curves are drawn for without and
with different patterns of shear reinforcement, to find out
various parameters (1st
crack formation in beams, initiation
1st
Crack Formation Distance from
Support
Without shear
reinforcement 0.413L
Type 1 0.396L
Type 2 0.437L
Type 3 0.401L
Type 4 0.396L
1st
Crack Formation Distance from Support
Lab Test 0.421L
ANSYS 0.414L
International Journal of Civil & Environmental Engineering IJCEE-IJENS Vol: 11 No: 01 74
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of diagonal cracks, failure load etc.) for finding effective
shear reinforcement pattern for beam to this loading
condition. Also a simulation and comparison to another
group is done to the satisfactory use of finite element
modeling in structural components. The following
conclusion can be stated based on the evaluation of the
analyses:
ANSYS 3D concrete element is very good
concerning the flexural and shear crack
development but poor concerning the crushing
state. However this deficiency could be eas ily
removed by employing a certain multi-linear
plasticity options available in ANSYS.
From close observation of analyses results it can be
concluded that all types of web reinforcements are
almost same effective for static loading condition.
VI. REFERENCES [1] Nilson, Arthur H.; Darwin, David; Dolan Charles W., 2006
“Design Of Concrete Structures”, McGraw-Hill, 13th
Edition. [2] Wolanski, Anthony J., B.S., 2004, “Flexure Behavior of
Reinforced and Prestressed Concrete Beams Using Finite
Element Analysis”, Faculty of Graduate School, Marquette University, Milwaukee, Wisconsin, May.
[3] SAS (2005) ANSYS 10 Finite Element Analysis System, SAS IP, Inc.
[4] Hossain, M. Nadim, 1998, “ Structural Concrete; Theory & Design”, Addison-Wesley Publishing Company.
[5] Nakasone, Y., Yoshimoto, S., Stolarski, T . A., 2006, “ENGINEERING ANALYSIS WITH ANSYS SOFTWARE”,
ELSEVIER, 1st Published.
[6] Kachlakev, D.; Miller, T.; Yim, S., May, 2001, “Finite Element Modeling of Reinforced Concrete Structures Strengthened With FRP Laminates”, California Polytechnic State University, San
Lius Obispo, CA and Oregon State University, Corvallis, OR for Oregon Department of Transportation, May.
[7] Nasir-Uz-Zaman, M, Sohel Rana, M, 2009 “Experimental And
Analytical Investigation of Flexural Behavior of Reinforced Concrete Beam”, Undergraduate Thesis Report, Department of Civil Engineering, Khulna University of Engineering and Technology, Khulna, April.
[8] Willam,K. J. and Warnke, E. P. (1975), “Constitutive models for the triaxial behavior of concrete”, Proceedings of the International Assoc. for Bridge and Structural Engineering , vol 19, pp. 1- 30.
[9] Murdock, L. J., Brook, K. M. and Dewar, J. D., “Concrete: Materials and Practice”, 6th Edition, Edward Arnold, London, 1991
[10] American Concrete Institute, “Material and General Properties
of Concrete”, ACI Manual of Concrete Practice, part 1, 1996 [11] Tavarez, F.A., (2001), “Simulation of Behavior of Composite
Grid Reinforced Concrete Beams Using Explicit Finite Element
Methods,” Master‟s Thesis, University of Wisconsin-Madison, Madison, Wisconsin.