Page 1 of 9
European Journal of Business &
Social Sciences
Available at https://ejbss.org/
ISSN: 2235-767X
Volume 07 Issue 05
May 2019
Available online: https://ejbss.org/ P a g e | 1082
Deflection of Curved Deck Slab Subjected to
Uniformly Distributed Load
Amit Kumar Raj1
, Kundan Kulbhushan2
1Dept. of Civil Engineering, Maharishi University of Information Technology, Lucknow, UP
(INDIA)
amitrajcivil@gmail.com
2Assistant Professor of Maharishi University of Information Technology, Lucknow, UP
(INDIA)
kundankulbhushan@gmail.com
Abstract: When the deck slab is curved there is
problem stability and torsion is of paramount
importance. And first designing of curved deck was
done then the physical model was casted .The
suitable support frame arrangement was made to
keep specimens stable. Loading taken was SCALED
IRC CLASS AA TRACKED VEHICLE LOADING
and Uniformly Distributed Loading. The specimen
was tested for deflections in laboratory, and a
similarity was tried to make between crack pattern
and values obtained of Maximum Stress. Then the
results are compared with Finite Element Computer
Programmed of deflection. And Longitudinal
Bending Moment and torsion moments were also
compared with A.A.Witecki method of calculating
moments. There was also a check performed for
stability with the help of computer programmed. The
objective is to study the deflection of curved deck
slab subjected to uniformly distributed load and
concentrated loads. This study was done with the
help of Experimental work and Finite Element
Analysis computer programmed. A comparative
analysis to torsion moment was done with the done
with the Witecki expression for torsion moment and
with Finite element Analysis. The stability analysis
was done with the help of computer programmed
1. Introduction
As a result of complicated geometrics, limited rights
of way, and traffic mitigation, horizontally curved
bridges are becoming the norm of highway
interchanges and urban expressways. This type of
superstructure has gained popularity since the early
1960s because it addresses the needs of
transportation engineering. Bridge superstructure
with horizontal curvature generally has higher cost
than comparable structures on straight alignment due
to increased design fabrication and construction
costs. In most instances, however, the extra cost is
nominal and offset by the associated functional
improvement. In the past, curved bridges had deck
formed to follow the roadway curvature, but were
supported a straight beams and girders with changing
direction to accommodate the deck alignment. Since
the early 1960s, curved spans and framing systems
have become standard features of highway
interchanges and urban expressways. A curved deck
may still be placed on a series of straight beams or
girders if the curvature is not very steep and the
maximum slab overhang resulting from this
arrangement is compatible with the practical slab
thickness. Roadway curvature with small radius is
common in access ramps and elevated roadways
where the plan alignment is restricted by site
conditions. In such cases clearance requirement and
structural optimization may indicate a curved
framing system that limits the cross-sectional
variation and may also be economically competitive
.The appearance of a curved framing system is more
pleasing compared to straight girders placed on
chord configuration.
2. Literature Review
Issam E. Harik (1983) gave the analytical solution
to orthotropic sector. A solution for the bending of
polar orthotropic pie and ring-sector plates was
presented for three cases of boundary conditions
along the straight edges. The classical method of
separation of variables was employed and the basic
function in the angular direction satisfied the
boundary conditions of the radial edges.
Satisfaction of the governing differential
equation of the plate was achieved by the derivation
Page 2 of 9
European Journal of Business &
Social Sciences
Available at https://ejbss.org/
ISSN: 2235-767X
Volume 07 Issue 05
May 2019
Available online: https://ejbss.org/ P a g e | 1083
of appropriate radial functions. The deflection
expression was generated. Isotropic and Orthotropic
sector plates of various end conditions had been
analyzed and compared with other methods wherever
comparisons were possible. In his work three cases
of radial edge conditions had been analyzed by an
analytical solution for the flexural behavior of
transversely loaded orthotropic sector plates.
Moon Ho Park and Issam E. Harik (1986)
presented the design of horizontally curved two-way
slab panels was formulated as an optimization
problem. The curved slab panels are rigidly
supported on all four sides and are subjected to
uniformly distributed loads. Each slab panel is
subdivided, in both the radial and angular direction,
into two half-edge strips and a middle strip. An
analytical solution was first presented for the
bending problem of uniformly loaded isotropic
curved (sector) plates with 12 possible combinations
of clamped (continuous) and simply supported
(discontinuous) edges. The solution, which
constituted the theoretical basis of the proposed
method, is based on the classical theory of sector
plates. The design moments for the radial and
angular directions are distributed to the
corresponding strips.
R.Shreedhar and Rashmi Kharde (2013) carried
out comparative study of grillage method and finite
element method of RCC bridge deck in this they
used STAAD PRO and found out that, In general for
practical slab bridge deck, result for finite element
gives lesser value in terms of bending moment
compared with grillage model. Therefore it can be
concluded that analysis by using finite element
method gives more economical design when
compared with the grillage analysis. But the benefit
for grillage analysis is that it is easy to use and
comprehend.
3. Experimental Analysis of Curved Deck
Slab
3.1.CURVED DECK SPECIMEN
SPECIFICATION
In order to facilitate analytical solution three curved
deck slab specimens were casted which were curved
at 90 degree of outer curved span of 2m arc length
and .90m width and radius 1.27m.The depth of deck
was 80mm. with reinforcements 6mm@
115mmc/c.The two girders curved were placed to the
bottom of curved deck at .30m spacing of sizes
150mm×200mm which were designed for torsional
moments. Straight beams were provided along radial
direction at 0degree, 45 degree and at90 degrees of
sizes 150mm×200mm.Concrete used were of
strength M40.
3.2 MAKING OF MODEL
3.2.1 MATERIAL
Cement, sand, course aggregate and steel of good
quality is required for casting the test slab specimen.
Material has been used after testing in the laboratory.
Details of the material used are given below.
a) CEMENT
Fresh ACC cement of grade 43 (Portland pozzolana
fly ash based confirming to IS: 1489) has been used
for casting cubes and slab specimen.
b) FINE AGGREGATE
The crusher sand used for casting of test specimen
was clean, course and free from organic matter. The
sand was washed to remove any dust.
c) COARSE AGGREGATE
The crushed and graded hard stone coarse aggregate
used in the project was clean and free from organic
matter. The maximum size of coarse aggregate was
10mm.
d) STEEL
Steel use was of strength Fe-500 of size 6mm for
deck slab and 10 mm used in curved girders and
straight beams
e) WATER
Potable tap water as per IS: 456 (2000) has been used
for concrete mixing and curing of test specimens.
3.2.2 CASTING OF SPECIMEN
A) Making of moued:-Themould of suitable size
was made with the help of bricks and was made into
proper shape with the proper plastering. A suitable
mix of motor was used in its plastering. And it was
cured properly to get the desired strength.
B) Making of reinforcement mesh:-Steel Bars were
properly cut of required sizes with the help of steel
cutter and were bended to desired shape .And
stirrups of desired shape were also made. The
reinforcement mesh was of made into the shape with
the help of binding wires which were tied properly.
Page 3 of 9
European Journal of Business &
Social Sciences
Available at https://ejbss.org/
ISSN: 2235-767X
Volume 07 Issue 05
May 2019
Available online: https://ejbss.org/ P a g e | 1084
Fig 1: Reinforcement mesh
3.3. INSTRUMENTATION
Dial gauges reading to0.01mm were placed at all
junctions of the longitudinal and the transverse
stiffeners to measure the vertical deflections. Dial
gauges were placed at the following position given in
figure.
Fig 2: Positions of dial gauges
The model under test was placed on rigid steel
supports which were restrained against vertical
deflections as shown in figure.
3.4 LOADING ARRANGEMENTS
It was tested by two types of loadings conditions:-
1. Uniformly Distributed loading:-In this three
reading were taken of deflections at 5 points. For
UDL testing cubes were used total 53 cubes
were put in three layers .After putting the cube
in one layer the readings of deflections were
taken from 6 points then subsequently 2nd layer
and 3rd layer.
The average weight of cube was 8.24 kg.
Load due to 1st layer =0.003707N/mm2
Load due to 2nd layer=0.007414N/mm2
Load due to 3rd layer=.011121N/mm2
Fig 3: Curved Deck on testing frame with loading
arrangement
2. Concentrated Loading: Scaled IRC CLASS AA
TRACKED LOADING:-
Fig 4: IRC CLASS AA LOADING
Specification for this loading:-
1. The nose to tail spacing between two successive
vehicles shall not be less than 90m.
2. For multi-lane bridges and culverts, one train of
Class AA tracked or wheeled vehicles whichever
creates severer conditions shall be considered for
every two traffic lane width. No other live load shall
be considered on any part of said 2-lane width
carriageway of the bridge when the above mentioned
train of vehicle is crossing the bridge.
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