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Finite Element Modeling of High Strength Reinforced Concrete Slabs

Article  in  International Journal of Structural Engineering · September 2014

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 International Journal of Structural Analysis & Design – IJSAD
Volume 1 : Issue 3 [ISSN : 2372-4102]
Publication Date : 30 September,2014

Finite Element Modeling of

High Strength Reinforced Concrete Slabs
[Mohamed Kandil, Khalid Heiza, and Moneir Soliman]

Abstract—The analysis of Reinforced Concrete (RC) structures

The study was beneficial in determining the length of the
by using finite element techniques takes great attentions through cantilever and the maximum dimensions of the opening
the last two decades. A lot of finite element packages like ANSYS, relative to the RC slab dimensions. Many researchers found
ABAQUS, COSMOS, Dyna-3D, and NASTRAN have been that experimental results were very close to the results
modified to be used in the analysis of different elements of RC obtained for finite element model using ANSYS [7-11].
structures. In this paper ANSYS finite element software was used

Research Significance
to analyze the structural behavior of high strength RC slabs. The
analysis of RC slabs was considered in three dimensions finite II.
element analysis, where effects of material and geometric
nonlinearities were taken into consideration to increase the Execute a theoretical 3D model in order to investigate the
accuracy of the results. Flexural capacity of RC slabs was behavior of high strength reinforced concrete slabs supported
measured experimentally and calculated analytically using on four columns under the variation of Reinforcement ratios
ANSYS. Comparisons between experimental and analytical for group (A) and having different central opening size for
results were performed. Comparisons between typical cracks group (B). Finally check the validity and the accuracy of the
patterns and modes of failure were comparable.
finite element modeling used in this study to predict the
Keywords— Flexural capacity, High strength concrete, behavior of the high strength reinforced concrete slabs.
Material nonlineaities, Reinforcement ratio, Silica fume,
Deflection, Finite element, ANSYS.
Methodology of Finite Element
III.

I. Introduction Analysis Using ANSYS

The beginnings of the finite element method surfaced in the The FEM is a computer aided mathematical technique for
early 1940s but it was not became a concept until the 1960s. obtaining approximate numerical solutions to the abstract
Nowadays, the finite element method is the most accepted equations of calculation that predict the response of
technique for numerical analysis in structural mechanics (or in mechanical structural or physical systems subjected to external
civil engineering structures). The finite element method is influences. The finite element method is an approximate
essentially a means to finding an approximate solution to technique, and as such, results computed using the finite
partial differential equations. ANSYS is a complete FEA element method must be critically evaluated before relied
software package used by engineers worldwide in virtually all upon in a design application. The number of elements used in
fields of engineering, like structural, electrical, mechanical and a model can greatly affect the accuracy of the solution. In
electromagnetic. Saifullah et al., and Nguyen et al. [1-2] used general, as the number of elements, or the fineness of the
ANSYS analysis to make comparisons between experimental mesh, is increased, the accuracy of the model increases as
and analytical investigations of flexural behavior of reinforced
well.
concrete elements. Salah Kh [3] used 2-D finite element
analysis to describe the structural behavior of reinforced
concrete beams. Since the comparison of obtained results A. Reinforced Concrete Elements
indicated that main reinforcement, strengths of concrete, stress An eight-node solid element (Solid65) was used to model the
yielding of steel may affect the ductility of RC beams [3]. concrete. The solid element has eight nodes with three degrees
Heiza et al. [4] used 2-D and 3-D finite element analysis for of freedom at each node – translations in the nodal x, y, and z
high strength concrete flat slabs. Masti et al. [6] studied the
directions. The element is capable of plastic deformation,
nonlinear behavior of high strength concrete flexural beams,
cracking in three orthogonal directions, and crushing. The
using 2-D and 3-D ANSYS. The comparison of load-
deflection, load-concrete strain and energy observed diagrams geometry and node locations for this element type are shown
of tested beams and numerical results made by ANSYS in Figure (1) [8 and 12]. Requires input data for reinforced
modeling are in a good agreement [5]. Tayel et al. [6] made a concrete were as follows [13 and 14]: Elastic modulus (Ec) =
comparison between analytical and experimental behavior of 35474 MPa, ultimate uniaxial compressive strength (Fcu) = 65
cantilever RC concrete slabs with opening. MPa, ultimate uniaxial tensile strength (fr) = 4.4 MPa,
Poisson’s ratio (ν) = 0.2, and shear transfer coefficient (βt) =
Mohamed Kandil, Khalid Heiza, and Moneir Soliman
Civil Engineering Department / Faculty of Engineering of Shebin El-kom / 0.2.
Menoufia University
Egypt.

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 International Journal of Structural Analysis & Design – IJSAD
Volume 1 : Issue 3 [ISSN : 2372-4102]
Publication Date : 30 September,2014

B. Steel Reinforcement Elements Results of Finite Element

V.
Three techniques were used to model steel reinforcement in
finite element models for reinforced concrete. See figure (2),
Analysis using ANSYS
where the discrete model, the embedded model, and the
smeared model are illustrated. The reinforcement in the A. Load-Deflection Behavior for RC
discrete model was shown in Figure (2-a) shows the bar or slabs using ANSYS
beam elements (Link 8) that are connected to concrete mesh
nodes. Therefore, the concrete and the reinforcement mesh  Group (A):
share the same nodes and concrete occupies, the same regions Figure (9) shows the comparison between load - deflection
curves of RC slabs HSR1, HSR2, HSR3, HSR4, and HSR5 at
occupied by the reinforcement [12-14]. Requires input data for
point (1) by ANSYS. It is clear that at the same RC slab
steel reinforcement were as follows [13 and 14]: Elastic
loading conditions, compressive strength the reinforcement
modulus (Es) = 210000 MPa, yield stress (fy) = 240 MPa, and ratio has a clear effect on the flexural capacity of RC plates.
poisson’s ratio (ν) = 0.3. As the reinforcement ratio increase the deflection decrease.
For RC slab HSR1; the initial cracking load was (14 kN) and
IV. Experimental Work the ultimate load was (28 kN), the maximum deflection
recorded at point (1) was 5.93 mm. For RC slab HSR2; the
A. Details of Test Slabs: initial cracking load was (15 kN) and the ultimate load (29.6
kN), the maximum deflection recorded at point (1) was 4.07
Group (A): High Strength RC Slabs with mm. For RC slab HSR3; the initial cracking load was (17.5
Different Steel Reinforcement Ratios: kN) and the ultimate load was (30.4 kN), the maximum
Heiza et al [4] had tested five high strength RC square deflection recorded at point (1) was 4.97 mm. For RC slab
slabs with dimensions 1200 mm × 1200 mm × 70 mm with HSR4; the initial cracking load was (18 kN) and the ultimate
different steel reinforcement ratios were considered in this load was (35.7 kN), the maximum deflection recorded at point
investigation as follows: (1) was 5.50 mm. For RC slab HSR5; the initial cracking load
a) Slab (HSR1) has a steel reinforcement ratio (μ) of 0.43 %. was (18 kN) and the ultimate load (35.7 kN), the maximum
deflection recorded at point (1) was 4.70 mm. Figures (10)
b) Slab (HSR2) has a steel reinforcement ratio (μ) of 0.57 %. illustrate the contour lines in 3D for RC slab HSR1 at ultimate
c) Slab (HSR3) has a steel reinforcement ratio (μ) of 0.72 %. loads using ANSYS.

d) Slab (HSR4) has a steel reinforcement ratio (μ) of 0.87 %.  Group (B):

e) Slab (HSR5) has a steel reinforcement ratio (μ) of 1.08 %. Figure (11) shows the comparison between load -
deflection curves of RC slabs HSO1, HSO2, HSO3, HSO4,
All RC slabs had the same compressive strength and HSO5 at points (1) by ANSYS. For RC slab HSO1; the
Fcu=65N/mm2. Figure (3) and (4) shows dimensions of a initial cracking load was (22 kN) and the ultimate load (41
typical test RC slabs and it reinforcement details and also kN), the maximum deflection recorded at point (1) was 4.76
arrangement of dial gauges. Figure (5) shows the 3D finite mm. For RC slab HSO2; the initial cracking load was (21 kN)
element meshes for reinforced concrete slabs. and the ultimate load (41 kN), the maximum deflection
recorded at point (1) was 4.81 mm. For RC slab HSO3; the
Group (B): High Strength RC slabs with
initial cracking load was (19 kN) and the ultimate load (39.73
different central opening size:
kN), the maximum deflection recorded at point (1) was 5.06
To investigate the effect of central square open size on the mm. For RC slab HSO4; the initial cracking load was (18.5
behavior of the high strength reinforced concrete slabs. Heiza kN) and the ultimate load (37.5 kN), the maximum deflection
et al [4] had tested five high strength concrete square slabs recorded at point (1) was 4.71 mm. For RC slab HSO5; the
with dimensions 1200 mm × 1200 mm × 70 mm having initial cracking load was (18 kN) and the ultimate load (36.15
different central opening sizes were considered as follows: kN), the maximum deflection recorded at point (1) was 5.99
a) Slab (HSO1) has no central opening. mm. Figures (12) illustrate the contour lines in 3D for RC slab
HSO5 at ultimate loads using ANSYS.
b) Slab (HSO2) has a central square opening size of 100 mm.

Comparison for load deflection

c) Slab (HSO3) has a central square opening size of 200 mm.
VI.
d) Slab (HSO4) has a central square opening size of 300 mm.
e) Slab (HSO5) has a central square opening size of 400 mm.
between ANSYS and Experimental
These slabs had the same compressive strength and the
results
same steel reinforcement ratio (Fcu=65N/mm2 and μ=0.57%).  Group (A):
Figure (6) and (7) shows dimensions of a typical test RC slabs Figure (13) shows comparison of load deflection diagram
and its reinforcement details and also arrangement of dial between ANSYS and experimental work at point 1 at the
gauges. Figure (8) shows the 3D finite element meshes for center of the slab. For RC slab HSR1; it is noticed that the
reinforced concrete slabs. difference between experimental results and ANSYS results

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 International Journal of Structural Analysis & Design – IJSAD
Volume 1 : Issue 3 [ISSN : 2372-4102]
Publication Date : 30 September,2014
were 0.0%, 0.0%, and 2.7% for initial cracking load, ultimate
load, and maximum deflection respectively. For RC slab
A. Figures and Tables
HSR2; it is noticed that the difference between experimental
results and ANSYS results were 6.2%, 7.5%, and 42.8% for TABLE I. MIX PROPORTIONS OF CONCRETE USED [4]
initial cracking load, ultimate load, and maximum deflection Mix proportions (kN / m3 )

W/(C+S)%

C.A. / F.A.
Specimen

A/(C+S)%
C28 Mpa
Mix for

(S/C)%
respectively. For RC slab HSR3; it is noticed that the
difference between experimental results and ANSYS results A mix S.f Dolomite Sand W C
were 9.3%, 5.0%, and 10.2% for initial cracking load, ultimate All
load, and maximum deflection respectively. For RC slab slabs
0.12 0.68 11.74 5.87 1.4 4.5 65 2.39 15 27 2
HSR4; it is noticed that the difference between experimental C: Cement, W: Water, F.A.: Fine aggregate sand, C.A.: Course aggregates
results and ANSYS results were 12.5%, 5.0%, and 13.1% for
initial cracking load, ultimate load, and maximum deflection
respectively. For RC slab HSR5; it is noticed that the
difference between experimental results and ANSYS results
were 10%, 5.3%, and 6.3% for initial cracking load, ultimate
load, and maximum deflection respectively.
 Group (B):
Figure (14) shows comparison of load deflection diagram Figure 1. Solid 65 – 3-D reinforced concrete solid element used for concrete
between ANSYS and experimental work at point (1) at a
distance 30 cm from the plate edge for RC slab HSO1; it was
noticed that the difference between experimental results and
ANSYS results were 0.0%, 2.4%, and 6.7% for initial cracking
load, ultimate load, and maximum deflection respectively. For
RC slab HSO2; it was noticed that the difference between
experimental results and ANSYS results were 5%, 2.4%, and
7.7% for initial cracking load, ultimate load, and maximum
deflection respectively. For RC slab HSO3; it was noticed that
the difference between experimental results and ANSYS
results were 5.5%, 0.01%, and 11.4% for initial cracking load,
ultimate load, and maximum deflection respectively. For RC
slab HSO4; it was noticed that the difference between
experimental results and ANSYS results were 2.8%, 6.2%, and
32.5% for initial cracking load, ultimate load, and maximum
deflection respectively. For RC slab HSO5; it was noticed that
the difference between experimental results and ANSYS
results were 2.7%, 9.6%, and 12.4% for initial cracking load, analysis [8 and 12]
ultimate load, and maximum deflection respectively.
Figure 2. Models for reinforcement in reinforced concrete; (a) Discrete; (b)
Embedded; (c) Smeared [12]

Figure 3. Shows dimensions of typical test RC slabs and arrangement of dial

gauges of group (A)

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 International Journal of Structural Analysis & Design – IJSAD
Volume 1 : Issue 3 [ISSN : 2372-4102]
Publication Date : 30 September,2014

Figure 4. Shows Reinforcement of typical test RC slabs of group (A)

Figure 9. Comparison between Load - Deflection Curves of all RC Slabs of

group (A) at Point (1) by ANSYS.

Figure 5. 3D finite element meshes for RC slabs of group (A).

Figure 10. Deflection Contour lines for RC slab HSR1 in m using ANSYS

Figure 6. Shows dimensions of typical test RC slabs and arrangement of dial

gauges of group (B)

Figure 11. Comparison between Load - Deflection Curves of all RC Slabs of

group (B) at Point (1) by ANSYS.

Figure 7. Shows Reinforcement of typical test RC slabs of group (B)

Figure 12. Deflection Contour lines for RC slab HSO5 in m using ANSYS
Figure 8. 3D finite element meshes for RC slabs of group (B).

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 International Journal of Structural Analysis & Design – IJSAD
Volume 1 : Issue 3 [ISSN : 2372-4102]
Publication Date : 30 September,2014
e) As steel reinforcement ratio (μ) increases, plate stiffness,
and flexural capacity increase with decrease in the
deflection values.

References
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[3] Salah, Kh., "2D FE description of reinforced concrete beams
behavior" Journal of Engineering and Applied Sciences. No. 3(1)
Figure 13. Comparison between expermintal and analytical values from pp 7-15. 2008.
ANSYS for Load - Deflection Curves of RC Slabs of group (A) at Point (1). [4] Heiza Kh. M., N. Meleka, Tayel M. and Farah N. "Behavior of high
strength reinforced concrete flat slabs using nonlinear finite
element analysis" Engineering Research Journal. Vol. 28, No. 1, pp
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[5] Masti, K., Maghsoudi, A. A and Rahgozaz, R. "Nonlinear models
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[6] Tayel, A. M., Soliman, H. M. and Ragi, S. A. "Expermintal behavior
of cantilever reinforced concrete plates with opening" ERJ. Vol. 26
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[7] Luca, S. Constantinnides, G. Franz, J. U., and Toutlemonde "The
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[8] Curpreet stigh. " Finite Element analysis of reinforced concrete
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[9] Heiza M. Kh. " Finite Element analysis of reinforced continuous
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[10] Heiza M. Kh., N. N. Meleka, N. Y. Elwkad. " Behavior and
Analysis of Self-Consolidated Reinforced Concrete Deep Beams
Strengthened in Shear", ISRN Civil Engineering, vol. Article ID
Figure 14. Comparison between expermintal and analytical values from 202171. 2012.
ANSYS for Load -Deflection Curves of all RC Slabs of group (B) at Point (1). [11] Heiza M. Kh. "New Finite Element Approach for Reinforced
Concrete Beams", Magazine of Concrete Research, Vol. 65, No. 2.
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Conclusions [12] Saeed moaveni. "Finite element analysis theory and applications
with ansys" CRC Press,Fifth Edition, 2010.
From the experimental and theoretical investigation carried [13] Khaled M. Heiza, Mounir H. Soliman and Mohamed Kandel,
out in this study it can be concluded that: "Finite Element Modelling of Strengthened RC Plates Using
ANSYS", CIC June 2014, Oslo, Norway.
a) The nonlinear three dimensional finite element model [14] Kandil A. M., “Finite Element Modeling of Reinforced Concrete
used in this study predict with acceptable accuracy the Structures Strengthened with FRP System” M.Sc. Civil Engineering
structural behavior of the high strength RC slabs. Department, Faculty of Engineering, Minufiya University, Egypt. 2012.

b) RC Slabs recorded approximately the same deflection

values in the linear part before cracking and after the
linear part, the higher reinforcement ratio the lower
deflection values.
c) There is a quite agreement and harmony between all Using Finite Element Modeling enables us
experimental and theoretical results by using ANSYS, to predict the results of experimental work
especially till the initial cracking loads.
before starting, which lead to minimize
d) Load – deflection curves of all RC plates at different the cost of laboratory work
locations were linear till first cracking load. After
cracking, deflections increased rapidly as the load
increased.

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