Effect of skew angle on uplift and deflection of rcc skew slab

IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308
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Volume: 04 Issue: 05 | May-2015, Available @ http://www.ijret.org 105
EFFECT OF SKEW ANGLE ON UPLIFT AND DEFLECTION OF RCC
SKEW SLAB
Deepak C1
, Sabeena MV2
1
MTech Student, Department of Civil Engineering, AWH Engineering College, Kerala, India
2
Professor and Head, Department of Civil Engineering, AWH Engineering College, Kerala, India
Abstract
The study deals with the finite element modeling of simply supported skew slab with varying skew angles using ANSYS software.
The behavior of the simply supported skew slab under point load applied at the centre depends on the ratio of short diagonal to its
span. Skew slabs with ratio of short diagonal to span less than unity show lifting of acute corners whereas slabs with ratio of
short diagonal to span greater than unity do not. Skew slab specimen with ratio of short diagonal to span less than unity is
considered here for studying the effect of skew angle on the behavior of skew slab. The dimensions of skew slab were taken from
available experimental data. In this paper skew angles varying from 0º to 30º were taken for the study. After the nonlinear finite
element analysis of all skew slabs it is revealed that when skew angle increases the uplift at both the acute corners also increases.
The result also suggests that the load carrying capacity increases with increase in skew angle.
Keywords: Reinforced concrete, Finite element analysis, Skew slab, Uplift
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1. INTRODUCTION
Reinforced concrete skew slabs are widely used in bridge
construction when the roads cross the streams and canals at
angles other than 90 degrees. They are also used in floor
system of reinforced concrete building as well as load
bearing brick buildings where the floors and roofs are
skewed for architectural reasons or space limitations. Skew
slab bridges may be required to maintain the geometry of
the road or keep the road straight at crossing or for any other
reason.
To model the complex behavior of reinforced concrete
analytically in its nonlinear zone is difficult. This has led
engineers in the past to rely heavily on empirical formulas
which were derived from numerous experiments for the
design of reinforced concrete structures. The Finite Element
Method (FEM) is an analytical tool which is able to model
RCC structure and is able to calculate the nonlinear behavior
of the structural members. For structural design and
assessment of reinforced concrete members, the nonlinear
finite element analysis has become an important tool. The
method can be used to study the behavior of reinforced and
pre-stressed concrete structures including both force and
stress redistribution.
In the present work finite element modeling of RCC skew
slab has been done in ANSYS. The behavior of the simply
supported skew slab under point load applied at the centre
depends on the ratio of short diagonal to its span. Skew
slabs with ratio of short diagonal to span less than unity
show lifting of acute corners whereas slabs with ratio of
short diagonal to span greater than unity do not. This is
because the reactions act at the obtuse corner only when the
ratio of short diagonal to its span less than unity and it is
well within supports when ratio of short diagonal to span is
greater than unity [6]. So skew slabs with ratio of short
diagonal to span less than unity is used here for studying the
effect of skew angle on the uplift and deflection of skew
slabs.
2. GENERAL DESCRIPTION OF STRUCTURES
Here, the modeling of skew slabs is based on experimental
data obtained from the study on Flexural behavior of
reinforced concrete skew slabs by Sharma B.R. [6]. In this
study two skew slab specimens were considered. Specimen
1 having ratio of short diagonal to span less than unity and
Specimen 2 having ratio of short diagonal to span greater
than unity. The dimensions of Specimen 1 are used in this
study. Skew slab Specimen 1 has been modeled with skew
angle of 16.49º, the support length and span is kept as 1200
mm and 2470 mm respectively with M25 grade concrete.
Thickness of slab has been kept as 70 mm. Length of short
diagonal of the slab is 2420 mm which is less than span
2470 mm. Fig -1 shows the dimensions of specimen 1. Slab
has been reinforced with main reinforcement of 8 mm
diameter for steel bars @ 100 mm c/c at the bottom face of
the slab at right angles to the supports and distribution
reinforcement of also 8 mm diameter tor steel bars @ 125
mm c/c laid over main reinforcement, parallel to the
supports [6].

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Fig -1: Dimensions of Experimental Test Specimen 1 [6]
In addition to 16.49º skew angle, 0º, 20º and 30º are also
considered here for studying the effect of skew angle on the
uplift and deflection of skew slab.
3. FINITE ELEMENT MODELLING
ANSYS, commercially available Finite Element (FE)
software, of version 12.1 was used for the analysis of skew
slabs. Concrete generally exhibits large number of micro
cracks, especially, at the interface between coarse
aggregates and mortar, even before it is subjected to any
load. The presence of these micro cracks has a great effect
on the mechanical behavior of concrete, since their
propagation during loading contributes to the nonlinear
behavior at low stress levels and causes volume expansion
near failure. Some micro cracks may develop during loading
because of the difference in stiffness between aggregates
and mortar. Since the aggregate-mortar interface has a
significantly lower tensile strength than mortar, it constitutes
the weakest link in the composite system. This is the
primary reason for the low tensile strength of concrete. The
response of a structure under load depends largely on the
stress-strain relation of the constituent materials and the
magnitude of stress. The stress-strain relation in
compression is of primary interest because mostly for
compression members are cast using concrete. The actual
behavior of concrete should be simulated using the chosen
element type. For the present type of model solid65 and
Link 8 elements were chosen. The Solid65 element was
used to model the concrete. The solid element has eight
nodes with three degrees of freedom at each node-
translation in the nodal x, y and z directions. The element is
capable of plastic deformation, cracking in three orthogonal
directions, and crushing. The geometry and node location
for this element type are shown in Fig -2.
Fig -2: Solid65 element
A Link 8 was used to model the steel reinforcement. Two
nodes are required for this element. Each node has three
degrees of freedom at each node-translation in three nodal x,
y and z directions as shown in Fig -3. The element is also
capable of plastic deformation.
Fig -3: Link 8 element
3.1 Nonlinear Analysis
In nonlinear analysis, the total load applied to a finite
element model is divided into a series of load increments
called load steps. At the completion of each incremental
solution, the stiffness matrix of the model is adjusted to
reflect nonlinear changes in structural stiffness before
proceeding to the next load increment.
The usefulness of the finite element method for nonlinear
analysis very much depends on various numerical
parameters which influence the solution. Different methods
are available in ANSYS for solving non-linear equations
such as, linear method, Full Newton-Raphson Method,
Modified Newton-Raphson method etc. Among these the
Full Newton-Raphson Method and Modified Newton-
Raphson Method are more commonly used methods. In our
present study, Full Newton-Raphson method is used for
solving the simultaneous equations. It is an iterative process
of solving the non-linear equations.

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Skew slabs having skew angle 0º, 16.49º, 20º and 30º are
modeled in ANSYS and are presented in Fig -4, Fig -5,
Fig -6 and Fig -7 respectively.
Fig -4: FE Model of Skew slab with 0º skew
Fig -5: FE Model of Skew slab with 16.49º skew
4. RESULTS AND DISCUSSIONS
In FE Model skew slab specimens loads have been applied
at the centre of the slabs as done in case of experiment. The
load on the structure has been gradually increased in the
steps till failure. When the FE non linear analysis is
completed, the results can be obtained from the Post
processing part of ANSYS. The load-deflection and uplifts
values at every step have been recorded.
4.1 Validation of FE Results
Experimental results [6] available for skew slab with skew
angle 16.49º are compared here with obtained FE results
corresponding to skew slab with 16.49º skew angle.
The load v/s deflection and load v/s uplift graphs comparing
the experimental and finite element analysis results are
presented in Chart -1 and Chart -2 respectively.
From Chart -1 and Chart -2, the FE model and Experimental
results shows almost same results. The ultimate load and
corresponding deflection for FE model are 27.6kN and
29.983mm respectively whereas the ultimate load and
corresponding deflection came from experimental result was
25kN and 29.3mm respectively. When analyze these data,
the FE results shows, the load is increased by 2.6kN and
deflection is increased by 0.683mm. Maximum uplift
obtained from experimental data was 1.65mm whereas that
for FE model was 1.324mm. Experimental data suggested
that both LHS and RHS acute corners have same uplift but
FE Model result suggested that up to ultimate load both
acute corners have same uplift and after that they shows
slight difference from each other. But from Chart -2 it is
clear that, there is no noticeable change between LHS and
RHS uplift values. So it can be concluded that FE model
result shows good agreement with the experimental result.
4.2 Load v/s Deflection Comparison
From Chart -3, it is observed that when skew angle increases
from 0º to 30º the load carrying capacity of slab also
increases. The ultimate load for 0º, 16.49º, 20º and 30º is
19.9kN, 27.6kN, 28.4kN and 34.5kN respectively.

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Skew angle 0º indicates that the slab is rectangular in shape.
It can be seen from the Chart -3 that the structure behaved
linearly elastic up to the value of load 19.9kN. The
deflection corresponding to 19.9kN is 29.004mm. After
29.004mm deflection started increasing without any
significant decrement in load. The 40mm deflection is
reached with the load value of about 17.2kN.
Considering graph corresponding to 16.49º in Chart -3, it
can be seen that the structure behaved linearly elastic up to
the value of load 27.6kN. The deflection corresponding to
27.6kN is 29.983mm. After 29.983mm deflection, load
started decreasing with increase in deflection. The 40mm
deflection is reached with the load value of about 24.2kN.
For skew angle 20º, it can be seen that the structure behaved
29.011mm deflection, load started decreasing with increase
in deflection. The 40mm deflection is reached with the load
value of about 25.2kN.
Chart -1: Load v/s Deflection Comparison Graph of Skew slab with 16.49º skew
Chart -2: Load v/s Uplift Comparison Graph of Skew slab with 16.49º skew
0
5
10
15
20
25
30
0 10 20 30 40 50
Load(kN)
Deflection (mm)
Load Deflection Comparison Graph of Skew slab
with 16.49º Skew angle
Finite Element
result
Experimental
result
0
5
10
15
20
25
30
0 0.5 1 1.5 2
Load(kN)
Uplift (mm)
Load v/s Uplift Comparison Graph of Skew slab
with 16.49º Skew angle
FE Model Uplift at
LHS acute corner
FE Model uplift at
RHS acute corner
Experimental result

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Chart -3: Load v/s Deflection Comparison Graph of Different Skew angle
For skew angle 30º, it can be seen that the structure behaved
30.045mm deflection, load started decreasing with increase
in deflection. The 40mm deflection is reached with the load
value of about 31.4kN.
4.3 Load v/s Uplift Comparison
The graph representing load v/s uplift at LHS and RHS
acute corners for skew angles 0º, 16.49º, 20º and 30º are
shown in Chart -4 and Chart -5 respectively.
For 0º skew angle, the maximum uplift occurred was
0.0131mm in both the corners. This obtained value is very
less compared to other skew angles. So the uplift at the
corners for a rectangular slab is negligible.
Chart -4: Load v/s Uplift (LHS) Comparison Graph of Different Skew angle
0
5
10
15
20
25
30
35
40
0 10 20 30 40 50
Load(kN)
Deflection (mm)
Load v/s Deflection Comparison Graph for
Different Skew Angle
Rectangular
16.49 Skew
20 Skew
30 Skew
0
5
10
15
20
25
30
35
40
0 0.5 1 1.5 2
Load(kN)
Uplift (mm)
Load v/s Uplift(LHS) Comparison Graph for
Different Skew Angle
Rectangular
16.49 Skew
20 Skew
30 Skew

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Chart -5: Load v/s Uplift (RHS) Comparison Graph of Different Skew angle
For 16.49º skew angle, up to the ultimate load i.e. 27.6kN,
uplift at both LHS and RHS acute corners were same. After
that they show slight difference from each other.
Up to the ultimate load i.e. 28.4kN, uplift at both LHS and
RHS acute corners were same for skew slab with 20º skew
angle. After that, uplift started increasing rapidly and both
corners started to exhibit slight difference in uplift values.
For 30º skew angle also, up to the ultimate load i.e. 34.5kN,
uplift at both LHS and RHS acute corners were same. After
that they show slight difference from each other.
Here, all the slabs excluding rectangular slabs exhibits slight
difference in uplift values after ultimate load. But this
variation in uplift at both LHS and RHS acute corners are
negligible.
from 0º to 30º the uplift at LHS acute corner also increases.
The maximum uplift for 0º, 16.49º, 20º and 30º is 0.011mm,
1.324mm, 1.331mm, and 1.435mm respectively.
from 0º to 30º the uplift at RHS acute corner also increases.
The maximum uplift for 0º, 16.49º, 20º and 30º is 0.011mm,
1.261mm, 1.279mm, and 1.396mm respectively.
5. CONCLUSION
The results of FE model of the skew slab with skew angle
16.49º have found to be same as that of the experimental
result. So it can be concluded that FE model results holds
good with the experimental results.
The maximum deflection for skew slabs decreases with the
increase in skew angle. This indicates that the load carrying
capacity of skew slab increases with increase in skew angle.
The uplift at acute corners of skew slab increases with
increase in skew angle.
REFERENCES
[1] Mirzabozorg and Khaloo (2003) “Load Distribution
Factors in Simply Supported Skew bridges.” Journal
of bridge engineering © ASCE, Vol. 8, Issue 4
[2] Huang, Shenton, and Chajes. s.l. (2004) “Load
Distribution for a Highly Skewed Bridge” Journal of
Bridge Engineering, Vol. 9, Issue 6
[3] James A.K. and Habib J.D. (2005), “Nonlinear FE
analysis of RC skewed slab bridges”, Journal of
structural engineering, Vol. 12, Issue 19, pp. 1338-
1345
[4] Menassa, Mabsout, Tarhini and Frederick. (2007),
“Influence of Skew Angle on Reinforced Concrete
Slab Bridge.”. : The Journal of Bridge Engineering,
Vol.12, Issue 2.
[5] Misra, Trilok Gupta and Anurag. (2009) “Effect on
support reactions of t-beam skew bridge decks.”
ARPN Journal of Engineering and Applied Sciences,
Vols. Vol. 2, Issue 1
[6] Sharma B.R. (2009), “Flexural Behaviour of
Reinforced Cement Concrete Skew Slabs” M.E.
Thesis, GNDEC, Panjab Technical University
[7] Dr. Ihsan A.S., Al-Shaarbaf, Munaf A.A., Al-
Rmahee. (2009), “Nonlinear Finite Element Analysis
of High Stregth Reinforced Concrete Slabs” Al-
Qadisiya Journal For Engineering Sciences, Vol. 2,
Issue 3
0
5
10
15
20
25
30
35
40
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
Load(kN)
Uplift (mm)
Load v/s Uplift(RHS) Comparison Graph for Different
Skew Angle
Rectangular
16.49 Skew
20 Skew
30 Skew

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[8] Das, D. , Sahoo, P. and Saha, K. (2010), “A
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Kar. (2012), “Study on Effect of Skew Angle in Skew
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[11] Sindhu B.V, Ashwin K.N, Dattatreya J.K. and S.V
Dinesh. (2013), “Effect Of Skew Angle On Static
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[12] Arindam Dhar, Mithil Mazumder, Mandakini
Chowdhury and Somnath Karmakar. (2013), “Effect
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[14] Abozaid L.A. Ahmed Hassan, Abouelezz A.Y. and
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1493

Effect of skew angle on uplift and deflection of rcc skew slab

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Effect of skew angle on uplift and deflection of rcc skew slab