This paper presents numerical modelling of slabs, linear modelling and analyzing of two way slab in a finite element based programming software ATENA and comparing with SAP for accuracy, The difference in result came to 14.3% hence, tolerable. Considering this, further nonlinear modelling and analysis is done in ATENA for one way and two way rectangular slabs, which includes both material and geometric modelling.Flexural load is applied for analysis of one way and two way slab. The displacement contour and crack pattern of slabs is presented which shows the appropriate behavior of slabs.

1. International Journal For Research & Development in Technology
Volume: 2, Issue: 4, Oct -2014 ISSN (Online):- 2349-3585
5 Copyright 2014- IJRDT www.ijrdt.org
Numerical Modeling and Analysis of slabs
N.R.Gowthami 1
, Dr.K.Ramanjaneyulu2
,B.Ajitha3
1
P G Student, JNTUACEA , Anantapuramu, India
2
Chief Scientist, CSIR-SERC, Chennai, India
3
Associate professor, JNTUACEA , Anantapuramu, India
Abstract--This paper presents numerical modelling of slabs,
linear modelling and analyzing of two way slab in a finite
element based programming software ATENA and
comparing with SAP for accuracy, The difference in result
came to 14.3% hence, tolerable. Considering this, further
nonlinear modelling and analysis is done in ATENA for one
way and two way rectangular slabs, which includes both
material and geometric modelling.Flexural load is applied
for analysis of one way and two way slab. The displacement
contour and crack pattern of slabs is presented which shows
the appropriate behavior of slabs.
Key words: Slabs,Modeling,ATENA
I. INTRODUCTION
Generally as per IS 456-2007, ratio of longer span to shorter
span is greater than two is classified as One way slab and less
than two is considered as Two way slab. The behavior of one
way slab, bending only in one direction, whereas for two way
slab the bending occurs in bi-directional. To resemble this
exact behavior by applying the appropriate boundary
condition, material modelling and geometric modelling.
Numerical modelling and analysis is done in ATENA a
computer code which is based on finite element methods. The
concept of finite element modeling involves discretizing the
element into number of finite elements and applying the same
boundary conditions to all the elements which is supposed to
resemble the practical condition. Flexural analysis is done for
One way slab - two line load is applied at equidistance and for
Two way slab - four point load is applied at equidistance
i.e.,( at L/3 span).
II. LINEAR MODELING AND COMPARISON
WITH SAP AND ATENA
In order to found the accuracy of results in ATENA,
comparing with SAP. A linear modeling of two way slab is
done in both the software. Taking the dimensions of the slab
as 3mX1m a solid concrete slab without reinforcement. In
ATENA Concrete and steel plate for application of load is
considered as linear elastic isotropic. Whereas in SAP linear
analysis is done. After analyzing in both SAP and ATENA by
applying flexural load of 0.5KN on each of four plates, the
resultant displacement is 0.56m and 0.48m respectively. The
difference in results is 14.3%, hence tolerable. The two way
behavior and displacement contour of slab in ATENA and
SAP as shown in fig.1.compressive strength of concrete is
taken as 20N/mm2
.The boundary conditions as used in section.
Fig.1.a. Two way behavior and displacement contour of slab
in SAP
Fig.1.b.Two way behavior and displacement contour of slab in ATENA
III. NON LINEAR MODELING AND ANALYSIS
OF SLABS
A. Geometric modeling of slabs
One way slab of, dimension 1mX2m with a clear cover of
15mm, the reinforcement of 8mm diameter 4nos along the
longer span and distribution steel of 6mm diameter at
325mm.Two way slab of 1.5mX2m dimension with a clear
cover of 15mm, the reinforcement of 8mm diameter at
150mmc/c along both spans. Overall depth of slab is
120mm.Concrete is taken as 8 noded 3 dimensional

2. International Journal For Research & Development in Technology
Paper Title:- Numerical Modeling and Analysis of Slabs (Vol.2, Issue-4) ISSN(O):- 2349-3585
6 Copyright 2014- IJRDT www.ijrdt.org
isoparametric brick element and reinforced bar as the two
noded bar element. Three degree of freedom at each node is
taken in to account.
B. Material modeling
Concrete is modelled as CC3DNonLinCementitious concrete
i.e., linearly elastic and perfectly plastic in compression.
Compressive strength of concrete is 20Mpa and the non
linear behaviour of concrete in the bi axial state is described
by means of effective stress and the equivalent uniaxial strain.
Tensile strength of concrete ft,from EUROCODE-2 is
Considering shrinkage effect dividing the tensile strength by a
factor 1.7.There fore ft =1.3Mpa;
Modulus of elasticity of concrete Ec. From EUROCODE-2 is
Considering practical conditions dividing by the factor
1.24,There fore Ec=2.32X104
Mpa
Poison’s ratio of concreteµ=0.2
Fracture energy Gf of concrete from The CEB-FIP model code
( )
There fore Gf = 5.36X10-5
MN/m and
Poisson’s ratio of steel µ=0.3.
Aggregate interlock was used. The steel plates used at loading
points are assumed as linearly elastic and isotropic. The
reinforcement bars are modelled as bilinear discrete elements.
Yield strength of the steel is taken to be 415Mpa.Analysis and
Iterations are done by modified Newton Raphson’s method.
Connection between concrete and reinforced bar is considered
as perfect. The formulae are considered according to
Eurocode 2: “Design of Concrete Structures”, EN
1992-1-1.
C. Finite element mesh
Mesh size is taken as 75mm.For slab it is taken as brick type
mesh and for loading plate it is taken as tetrahedron mesh
type.0.5KN load is applied on each plate for both one way and
two way slabs.The variation of mesh type is as shown in fig.2.
Fig.2.Variation of finite element mesh type
D. Boundary conditions
In the case of one way slab, to obtain simply supported and
one way slab behavior, the slab is supported along short span
i.e., x(along the width) and z(along the depth) are restrained as
shown in Fig.3.a and the flexural load of two point line load at
equidistant as shown in fig.3.b. The one way slab behavior is
obtained as shown in Fig3.c by the displacement contour and
initial crack pattern.
Fig.3.a.Boundary condition for one way slab
Fig.3.b.Flexural load application of one way slab
Fig.3.c.Displacement contour and crack pattern of
one way slab
To achieve simply supported condition and two way slab
behavior, the sides of the plate are restrained, along shorter
span – x axis (along the breadth) and z axis (along the depth)
direction as shown in Fig.3.a.Similarly along longer span,
degrees of freedom along – y axis(along the length) and z
axi(along the depth) are restrained and corresponding four
point load is applied as shown in fig.3.b. The two way slab
behavior is achieved as shown in Fig.3.c. by the displacement
contour and initial crack pattern.

3. International Journal For Research & Development in Technology
Paper Title:- Numerical Modeling and Analysis of Slabs (Vol.2, Issue-4) ISSN(O):- 2349-3585
7 Copyright 2014- IJRDT www.ijrdt.org
fig.4.b.flexural load application of two way slab
Fig.4.c.Displacement contour and crack pattern of two way slab
The corresponding load Vs deflection profile of one way and
two way slab is as shown in fig.5.a and fig.5.b. Which shows
the ultimate load of 28KN and 168KN respectively? It is
observed that two way slab is carrying higher load than that of
one way slab.
Fig.5.a.Load Vs deflection profile of one way slab.
Fig.5.b.Load Vs deflection profile of one way slab.
IV.CONCLUSIONS
a. In linear analysis the comparison of results of SAP
and ATENA and the difference in results is 14.3%
only.
b. Non linear analysis of simply supported one way and
two way slab is done and their behavior is achieved.
c. Flexural analysis is done and corresponding Load Vs
Deflection profile is plotted. It is observed that two
way slab is taking comparatively higher load of
168KN than one way slab.
V. FUTURE RESEARCH
Numerical modeling and flexural analysis of segmental
composite one way and two way slabs by using truss type,
lattice type and dual steel type shear connectors.
REFERENCES
1. IS456:2000 Part 1: Indian Standard Plain and
Reinforced Concrete.
2. ATENA Theory manual by Vladimír Červenka,
Libor Jendele and Jan Červenka, Cervenka Ltd.
3. Benayoune, A.A. Abdul Samad, D.N. Trikha, A.A.
Abang Ali, S.H.M. Ellinna, Flexural behaviour of
pre-cast concrete sandwich composite panel –
Experimental and theoretical investigations,
Construction and Building Materials 22 (2008) 580–
592
4. Damian Kachlakev, Thomas Miller and PE; Solomon
Yim, Finite element modeling of reinforced concrete
structures strengthened with frp laminates,Oregon
Department of Transportation Research Group200
Hawthorne SE, Suite B-240Salem, OR 97301-5192.
5. Eurocode 2: “Design of Concrete Structures”, EN
1992-1-1
6. CEB-FIP Model Code 1990, Comite Euro
International Du Beton.
0
10
20
30
0 5 10 15 20 25 30
LoadinKN
Deflection in mm
One way slab
0
50
100
150
200
0 5 10 15 20 25 30 35
LoadinKN
Deflection in mm
Two way slab