Study on Economics of Superstructure of Post-tensioned Highway Bridge in Co-relation with Span to Depth Ratio

International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
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Study on Economics of Superstructure of Post-tensioned Highway
Bridge in Co-relation with Span to Depth Ratio
Ashish Chandra1, L.P.Shrivastava2
1PG Student, 2Professor
1,2 Department Of Civil Engineering, M.M.College of Technology, NH-06, Raipur
Chhattisgarh Swami Vivekananda Technical University, Bhilai, Chhattisgarh, India
---------------------------------------------------------------------***---------------------------------------------------------------------
Abstract - Span-to-depth (Slenderness ratio) ratio is an
important bridge design parameter that affects structural
behavior, construction costs and aesthetics. A study of 86
constant-depth girders indicates that conventional ratios
have not changed significantly since 1958. These
conventional ratios are now questionable, because recently
developed high-strength concrete has enhanced mechanical
properties that allow for slenderer sections.
Based on material consumption, cost, and aesthetics
comparisons, the thesis determines optimal ratios of a 7-
span highway viaduct constructed with high-strength
concrete. Two bridge types are investigated: cast-in-situ on
false work box-girder and cast in situ solid slabs. Results
demonstrate that total construction cost is relatively
insensitive to span-to-depth ratio over the following ranges
of ratios: 10-35 and 30-45, for the two bridge types
respectively. This finding leads to greater freedom for
aesthetic expressions because, compared to conventional
values (i.e. 18-23 and 22-39), higher ranges of ratios can
now be selected without significant cost premiums.
Key Words: Highway Bridge, Slenderness ratio, span
to depth ratio, Box girder, Solid slab
1. INTRODUCTION
The bridge design is very complicated design and
in the designing of bridge deck the most important
parameter is span to depth ratio which is also called as
slenderness ratio. This ratio is generally used to fix the
superstructure depth and it is chosen during the
conceptual designing before any detailed calculation
performed. The selection of the ratio at an early stage of
the process of design gives the approximate dimension
which is necessary for the analysis of bridge girders and
cost efficiency and aesthetic merits of the design in
comparison with alternative design concept. Span to the
depth ratio is generally selected based on the field
experience and some values used in previously
constructed bridges with satisfactory performance. The
ratio can also be determined by optimizing the
combinations of ratios and superstructure depth to create
cost efficient and aesthetic structure but this requires an
iterative process therefore the optimization of the span to
depth ratio in every design concept, it is common to select
ratios from the given ranges of conventional values.
The selection of span to depth ratio is generally critical
in the design of bridge with girders because the cost of
materials and construction of the superstructure is
directly affected by span to the depth ratio. For example,
using high span to depth ratio reduces the volume of
concrete and increases the requirement of prestressing
force and simplifies the construction, because in a lighter
structure the cost of the bridge is highly dependent on the
proportion of the superstructure, so the selection of span
to depth ratio is very important for economy. Some proven
ranges of span to depth ratios over the past decades given
by different organization and Authors for different types
of bridges, like; cast in situ box girder, cast in situ slab, and
precast segmental box girder shown below in table 1.1,
Table 1.1 Recommended Ratios for Box-Girder
Organization/Author Year
Span to
depth
ratio
Leonhardt 1979 12 to 16
ACI-ASCE 1988 25 to 33
Menn 1990 17 to 22
AASHTO 1994 25
Cohn &Lounis 1994 12 to 20
AASHTO-PCI-ASBI 1997 25
Recommended ratios for Cast in Situ Slab
Organization/Author Year
Span to
depth ratio
Leonhardt 1979 18 to 36
ACI-ASCE 1988 24 to 40
Menn 1990 25
AASHTO 1994 37
Cohn &Lounis 1994 22 to 29
Hewson 2003 20
A table 1.1 and 1.2 shows there has been no more
changes in the recommended span-to-depth ratio since
1979 although the improvement in material strengths and
construction technologies.

2. Literature Review
Miss. P.R. Bhivgade (2001)[1] in her paper has studied a
simply supported Box Girder Bridge for two lane road
made up of prestressed concrete which is analysis for
moving loads as per Indian Road Congress (IRC:6)
specification, Prestressed Code (IS: 1343) and also as per
IRC: 18-2000 specifications. The analysis was done by
using SAP 2000 14 Bridge Wizard and prestressed with
parabolic tendons in which utilize full section. The various
slenderness ratios considered to get the proportioning
depth at which stresses criteria and deflection criteria get
within the permissible limits recommended by IS codes. It
is concluded that the basic principles for proportioning of
concrete box girder help designer to design the section.
For the torsion of superstructure box girder shows better
resistance. The various slenderness ratios are carried out
for Box Girder Bridges, deflection and stress criteria
satisfied well within recommended limits. As the depth of
the box girder increases, the prestressing force decreases
and the number of cables decrease.
Rajamoori Arun Kumar, B. Vamsi Krishna (2014)[7] in
their paper has studied the practical approach that on a
major bridge having 299 meters span, 36 no’s of PSC
Beams & 8 no’s of RCC Beams. The main code that follow
in this course is IS: 1343. The title is Code of Practice for
Pre-stressed Concrete published by the Bureau of Indian
Standards. Remembering that IS: 456 - 2000 which is the
Code of Practice for Structural Concrete. Some of the
provisions of IS: 456 are also applicable for Pre-stressed
Concrete.
The following conclusion were made –
1. Shear force and bending moment for PSC T-beam
girder are lesser than RCC T beam Girder Bridge
which allow designer to have less heavy section
for PSC T-Beam Girder than RCC T-Girder for 24
m span.
2. Moment of resistance of steel for both PSC and
RCC has been evaluated and conclusions drawn
that PSC T-Beam Girder has more capacity for 24
m and more than 24m of span.
3. PROBLEM IDENTIFIC ATION
The study of 86 used bridges has been done to presents
the variations of span-to-depth ratios. Specifically, the
study determines the range of ratios typically used for
construction and examines its variations over the past 49
years. Two types of bridge decks are to be analyzed. (i)
box-girder bridge deck (ii) solid slab bridge deck
3.1 Some Existing bridges and their span to depth
ratio in
3.1.1 Cast in situ Box-Girder Bridge
First 44 cast-in-situ box-girders with constant
depth throughout the length are investigated. Table 2-1
provides the basic information of each bridge. Additional
information, including the span of the bridges, dimension
of girders, detail of designer and references, is given in
Appendix A.1. Graph 3-1 shows the variation of span-to-
depth ratios with respect to the span lengths and
compares these ratios with the recommended values
described in chapter 1. Graph 3-2 shows the variation of
span to depth ratio with respect to the completion years.
Table no. 2.1 Summary of Cast in Situ Box Girder.
Bridge.
No. Bridge Name Year
Span to
depth
ratio
1 Grenz Bridge at Basel 2000 17.7
2 Sart Canal-Bridge 2002 12
3 WeyermannshausBridge 1987 18.9
4
Eastbound Walnut
Viaduct
1986 23
Graph 3-1 variation of span to depth ratio of box
Graph 3-1 demonstrates that all 44 cast-in-situ
box-girders have span lengths varies between 35.4m and
138 m and demonstrates span-to-depth ratios that ranges
varies from 11.4 to 29.5. The graph shows that 42 out of
44 bridges (95%) investigated have span lengths varies
from 35m to 75m which is the typical range for constant-
depth cast in situ box-girders as suggested by Hewson .
You can see in above the frequency plot on top of the
graph are bridge numbers that relate each data point to its
corresponding bridge in Table 3-1. The red line shows the
border of large concentration of bridges that have span-to-
depth ratios varies between 17.7 and 22.6. In fact, 34 out
of 44 bridges (75%) have ratios within the range of values
17.7
12
18.9
23
11.4
22.2
18.218.218.220 21.6
17.7 18.518.518.5
28.1
12.912.8
16
20.820.8
29.5
2020.9
14.7
20202020202020
15.1
21.3
18.1
22.5
19.3
22.6 21.2
0
10
20
30
40
1950 1960 1970 1980 1990 2000 2010
span
to depth
ratio
Year
span to depth ratio
span to…

suggested by Menn (17 to 22) and Hewson (20) which are
based on existing bridges with acceptable performance.
3.1.2 Cast-in-Situ Solid Slab
In addition to cast-in-situ box-girders, 28 cast-in-
situ constant-depth solid slab bridges are also
investigated.
Table 3.1 Summary of cast in situ solid slab
Bridge
No.
Location Year
Span to
Depth
Ratio
1 Khandeshwar Bridge 2000 20.3
2
Spadina Ave. Bridge
#16, Hwy 401
1967 22.2
3
Spadina Ave. Bridge
#18A, Hwy 401
1967 22.2
4
Spadina Ave. Bridge
#18B, Hwy 401
1967 22.2
4. Methodology & Analysis
4.1 Analysis Overview
The purpose of this analysis is to compute the
amount of prestressing force and the concrete strength
needed to satisfy design requirements for bridges with
varying span lengths and slenderness ratios. These
material consumption results are then used to compute
the cost of construction as a function of span-to-depth
ratio. By analyzing the variations in construction cost and
aesthetic impacts, the study determines the most
economical span to depth ratios for different bridge types
like box girder bridge, solid slab bridge etc . The two types
of post-tensioned bridge are considered ie cast-in-situ
box-girder, cast-in-situ solid slab.
4.2 DESIGN AND ANALYSIS
4.2.1 Analysis of Box Girder Bridge Deck
Analysis is performed on 22 cases with span
lengths (interior) of 35m, 50m, 60m, and 75 m and
slenderness ratios of 10, 15, 20, 25, 30, and 35. This set of
span lengths is chosen because cast-in-situ box-girders are
economical for spans up to about 100 m according to
Menn (1990) and bridges with longer spans need to be
haunched in order to reduce self weight. The end spans
are made 10 m shorter than interior spans to balance
moments along the entire bridge and to make simpler the
treatment of prestressing in the study.
.
Graph 4.1 Variation of concrete volume with span
by depth ratio for different span
Graph 4.2 Variation of span to depth ratio for different
span with depth
Graph 4.3 Variation of no. of strands with span by
depth ratio
0.00
200.00
400.00
600.00
800.00
1000.00
1200.00
1400.00
5 15 25 35 45
concrete
volume
in
cubic
meter
L/d
L=75m
L=60m
L=50m
L=35m
0
1
2
3
4
5
6
7
8
5 15 25 35 45
depth
L/d
L=75m
L=60m
L=50m
L=35m
0
5
10
15
20
25
30
35
40
45
0 10 20 30 40
no.
of
tendon
L/d
L=75
mL=60
m
L=50
m L=35
m

Graph 4.4 Variation of reinforcement with span by
depth ratio
Graph 4.5 Variation of concrete volume with span by
depth ratio for different span
Graph4.6 Variation of span to depth ratio for
different span with depth
Graph 4.7 Variation of no. of strands with span by
depth ratio
Graph 4.8 Variation of no. reinforcement with span
by depth ratio
5. COST ANALYSIS
This cost study investigates the changes in
superstructure and total cost of construction, which are
based on the previously described material consumption
results, when slenderness ratio varies. Comparison of
these costs reveals the optimal slenderness ratio for each
type of bridge. The study also demonstrates the cost
benefits of using the optimal ratios instead of conventional
ratios.
0
2000
4000
6000
8000
10000
12000
14000
16000
18000
20000
0 20 40
mass
of
rienforce
ment
L/d ratio
L=75m %82
L=60m,39%
L=50m 31%
L=35m 24%
L=75m,60m,50m and
35m for box girder
0
50
100
150
200
250
300
350
400
450
20 30 40 50
concrete
volume
in cubic
meter
L/d
L=35m
L=30m
L=25m
L=20m
0
0.2
0.4
0.6
0.8
1
1.2
20 30 40 50
depth in
(m)
L/d
L=35m
L=30m
L=25m
L=20m
0.0
10.0
20.0
30.0
40.0
50.0
60.0
70.0
80.0
90.0
100.0
20 30 40 50
prestress
tendon
L/d
L=35m
L=30m
L=25m
L=20m
0
1000
2000
3000
4000
5000
20 30 40 50
rienforce
ment
in
kg
L/d
L=35m
L=30m
L=25m
L=20m

Graph 5.1 variation of cost of concrete with different
span with different l/d ratios
Graph 5.1 summarizes cost of concrete of all the
analysis cases calculated. In general concrete cost
decreases with increasing span to depth ratio. For box
girder, however, cost increases drastically for the very
slender cases which require concrete strengths higher
than 60Mpa
Graph 5.2 Variation of Cost of Tendons
Graph 5.3 variation of cost of concrete with different
span with different l/d ratios
Graph 5.4 variation of cost of tendons
5.1 Comparison of Cost
This cost study has been done to know the
changes in superstructure and total construction costs,
which are based on the previously described material
consumption results, when span-to-depth ratio varies.
Comparison of these costs reveals the optimal slenderness
ratio for each bridge type. The cost study also
demonstrates the cost benefits of using the optimal ratios
instead of conventional ratios.
Graph 5.5 Comparison of Cost of Concrete
0
1000000
2000000
3000000
4000000
5000000
6000000
7000000
8000000
0 20 40
cost
of
concrete
in Rs
L/d
L=75m, 41.55%
L=60m,39%
L=50m 31%
L=35m 24%
L=75m,60m,50m and 35m fot
box girder
0
2000000
4000000
6000000
8000000
10000000
0 20 40
cost
of
tendons
in Rs
L/d ratio
L=75m %82
L=60m,39%
L=50m 31%
L=35m 24%
L=75m,60m,50m and
35m fot box girder
0
500000
1000000
1500000
2000000
2500000
10 20 30 40 50
cost
of
concrete
in Rs
L/d
L=35m 38%
L=30m 61%
L=35m 40%
L=20m 51%
L=35m,30m,25m and 20m forcast in
solid slab
0
1000000
2000000
3000000
4000000
5000000
6000000
7000000
8000000
9000000
20 30 40 50
cost
of
tendons
in Rs
L/d ratio
L=75m %82
L=60m,39%
L=50m 31%
L=35m 24%
L=30m,35m,40m and
45m fot solid slab
0
1000000
2000000
3000000
4000000
5000000
6000000
7000000
8000000
0 10 20 30 40 50
concrte
cost
per
cubic
meter
L/d ratio
L=75m, 41.55%
L=60m,39%
L=50m 31%
L=35m 24%
L=35m
38%L=30m
61%L=25m
40%L=20m
51%

Graph 5.6 Comparison of Prestressing Tendon Cost
Graph 5.7 Cost comparisons of stirrups and minimum
reinforcing steel
Graph 5.8 Cost distributions of reinforcement and
stirrups
5.2 Cost comparison of total Superstructure
(including cost of concrete placement)
Graph 5.9 Total concrete of superstructure cost
comparison
Graph 5.10 Total construction cost comparison
Table 5.1 Summary of cost study
Cat in situ box-
girder
Cast in situ
solid slab
Analysis range of ratios 10 - 35 30 – 50
Typical range of ratios 17.7 - 22.6 22 – 39
Conventional ratio 20.1 30.2
Cost-optimal ratio 25 40
Cost component
Concrete -5.1% (41.55%) -19% (22%)
Prestressing tendon +28% (285%) +53% (61%)
Reinforcement steel -1.3 %( 17%) -5.3 % (5.7%)
Total superstructure -0.6 %( 19%) -11% (11%)
Total construction cost -0.4 %( 11%) -5.8 %( 6.2%)
0
1000000
2000000
3000000
4000000
5000000
6000000
7000000
8000000
9000000
0 20 40 60L/d
L=75m,
285%L=60m,
223%L=50m
209%
L=35m
38%
L=25
m
38%
L=30m
61%
L=35m
162%
L=20
m
51%
0
200000
400000
600000
800000
1000000
1200000
0 10 20 30 40 50
L/d ratio
L=60m,
39%L=50m
31%L=35m
24%
L=35m
38%L=30m
61%L=25m
40%L=20m
51%
L=75m,
41.55%L=60m,
39%L=50m
31%L=35m
24%
L=35m
38%L=30m
61%L=25m
40%L=20m
51%
minimu
m
reinforc
ement
line
0%
20%
40%
60%
80%
100%
10 15 20 25 30 35 30 35 40 45
minimum
reinforc…L=75m L=35m
0
5000000
10000000
15000000
20000000
0 10 20 30 40 50L/d ratio
L=75m,
17%L=60m,17%
L=50m 17%%
L=35m 16
%
L=35m
12%
L=30m
12%L=25m
9.6%L=20m
3.6%
0
10000000
20000000
30000000
40000000
0 10 20 30 40 50
L/d ratio
L=75m,
12%L=60m,
11%L=50m
9.0%%L=35m 7.7
%
L=35m
6.1%
L=30m
6.2%L=25m
5.0%L=20m
1.9%

6.1 Conclusion
Girder-type bridges have commonly been
designed using conventional slenderness ratios which
have not changed significantly despite recent development
in material strengths and construction technologies. This
study determines the optimum slenderness ratios for two
types of girder bridges constructed with high-strength
concrete: cast-in-situ box-girder and solid slab, the ratios
are optimized based on material consumption and total
construction cost. The results of this thesis are
summarized as follows.
A study of 86 constant-depth girder bridges
reveals that the typical ranges of slenderness ratios are
17.7 to 22.6 for cast-in-place box-girder, 22 to 39 for cast-
in-situ solid slab, and 15.7 to 18.8 for precast segmental
box-girder. The study demonstrates that the ratios for
cast-in-situ box-girders have not varied significantly from
1958 to 2007. The study also indicates that cast-in-situ
solid slabs constructed after 1975 are mostly voided slabs
with slenderness ratios below 25 due to the more
stringent code requirements in recent years.
REFERENCES:
[1] ‘Miss Bhivgade. R.P.(2001)’ “Analysis and design
of prestressed concrete box girder bridge”
[2] ‘Prof. Joseph Ancy, Babu Elsa , Babu Karthika ,
Lakshmi G, Krishna R Meera, “Analysis And Design
Of Railway Over Bridge At Kumaranellur”,
International Journal of Civil and Structural
Engineering Research, ISSN 2348-7607
(Online)Vol. 2, Issue 2, pp: (124-127), Month:
October 2014 - March 2015
[3] ‘Mulesh K. Pathak (M. E. Casad)’ “Performance of
RCC Box type Superstructure in Curved bridges”
International Journal of Scientific & Engineering
Research, Volume 5, Issue 1, January-2014, ISSN
2229-5518
[4] IS: 1343, Indian Standard Code of Practice for
Prestressed concrete (2nd Revision), Bureau of
Indian Standards, New Delhi.
[5] IRC : 18-2000, Design Criteria for Prestressed
Concrete Road Bridges (Post tensioned concrete)
(2nd Revision), Indian Road Congress, New Delhi
2000, pp 1-61

Study on Economics of Superstructure of Post-tensioned Highway Bridge in Co-relation with Span to Depth Ratio

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